Advances in Physical Organic Chemistry Volume 44
Editor JOHN P. RICHARD Department of Chemistry University at Buffalo, SUNY Buffalo, NY, USA
Amsterdam – Boston – Heidelberg – London – New York – Oxford Paris – San Diego – San Francisco – Singapore – Sydney – Tokyo Academic Press is an imprint of Elsevier
Contributors to Volume 44 Claude F. Bernasconi Department of Chemistry and Biochemistry, University of California, Santa Cruz, CA 95064, USA W.W. Cleland Department of Biochemistry and Institute for Enzyme Research, University of Wisconsin-Madison, Madison WI 53726, USA Ronald Kluger Davenport Chemistry Laboratories, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada Scott O.C. Mundle Davenport Chemistry Laboratories, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada Rory More O’Ferrall School of Chemistry and Chemical Biology, University College Dublin, Belfield, Dublin 4, Ireland Charles L. Perrin Department of Chemistry & Biochemistry, University of California—San Diego, La Jolla, CA 92093-0358, USA Jakob Wirz Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland Hiroshi Yamataka Department of Chemistry, College of Science and Research Institute for Future Molecules, Rikkyo University, Tokyo, Japan
xi
The low-barrier hydrogen bond in enzymic catalysis W.W. CLELAND Department of Biochemistry and Institute for Enzyme Research, University of Wisconsin-Madison, Madison, WI 53726, USA 1 Introduction 1 2 Properties of hydrogen bonds 1 3 Role of low-barrier hydrogen bonds in enzymatic reactions 3 Enolization reactions 3 Facilitated tetrahedral intermediate formation 6 Facilitated proton ionization 10 Aspartic proteases 12 Miscellaneous enzymes 13 Acid–Base catalysis 14 4 Conclusion 15 References 15
1
Introduction
The term ‘‘low-barrier hydrogen bond’’ was introduced by me in 1992 to describe hydrogen bonds between groups of equal pK that showed low deuterium fractionation factors (as low as 0.3).1 It was not until an Enzyme Mechanisms conference in Key Largo, however, that a number of us finally realized how such bonds can help catalyze enzymic reactions and papers describing this appeared in 1993 and 1994.2–5 Since then such bonds have been shown to play a role in many enzymic reactions and a Google search under ‘‘low-barrier hydrogen bond’’ turns up over 5000 hits. In this review I shall describe the properties of low-barrier hydrogen bonds and then give a number of examples. I have not tried to cover the entire literature and apologize to those whose works are not mentioned.
2
Properties of hydrogen bonds
Hydrogen bonds come in a continuum of bond lengths and strengths. Those in water which hold it together as a liquid are 2.8 A˚ between oxygens and are weak (only a few kcal mol1). Since the pK of water as an acid is above 15 and its pK as a base is less than –1, the pK’s of the two 1 ADVANCES IN PHYSICAL ORGANIC CHEMISTRY VOLUME 44 ISSN: 0065-3160 DOI: 10.1016/S0065-3160(08)44001-7
Ó 2010 Elsevier Ltd. All rights reserved
2
W.W. CLELAND
oxygens in the hydrogen bond are drastically different and the hydrogen is covalently bound to one oxygen with a bond distance of 1 A˚ and weakly bonded electrostatically to the other oxygen. When the pK’s of the two groups are the same, as in a hydrogen bond between formic acid and formate ion, the bond is shorter (2.5–2.6 A˚) and the zero point energy level of the hydrogen is at or above the barrier (thus ‘‘low-barrier hydrogen bond,’’ Fig. 1).6–8 Neutron diffraction of crystals containing such bonds show a diffuse distribution centered between the two heavy atoms.9 In certain cases where the bond is especially short, there is no barrier as in the F–H–F or HO–H–OH ions which are only 2.3 A˚ long.10,11 Low-barrier hydrogen bonds are quite strong (as much as 27 kcal mol1 in the gas phase and perhaps 12 in aqueous solution7), but in a medium with a dielectric constant of 7 (similar to what occurs in an enzyme active site) the strength decreases by 1 kcal mol1 per pH unit mismatch in the pK’s of the groups involved.12 Thus there is a continuum between the very strong ones with matched pK’s and the weak ones with very different pK’s and the distances similarly differ as well. Low-barrier hydrogen bonds have considerable covalent character,6,13 which decreases as the bonds weaken and lengthen, so that the weak ones are only electrostatic in nature. As noted in 1992, low-barrier hydrogen bonds show low fractionation factors, with up to threefold discrimination against deuterium. They show downfield chemical shifts in proton nuclear magnetic resonance (NMR) of 18–20 ppm. At first it was thought that they only occur in the gas phase or organic solvents, but it is now clear that they can occur in solutions containing a high mole fraction of water, even at room temperature.14,15 What limits their determination in aqueous solution is rapid exchange with solvent protons. Hydrogen bonds can occur between two oxygens, two nitrogens, or one of each. We will show examples of O–O and O–N bonds in the discussion below.
(a)
O O
(b)
H H
O O
O
(c)
H
O
O
H
O
Fig. 1 Energy diagrams for hydrogen bonds between groups of equal pK. (a) Weak hydrogen bond; O–O distance 2.8 A˚. (b) Low-barrier hydrogen bond (2.55 A˚); the hydrogen diffusely distributed. (c) Single-well hydrogen bond (2.29 A˚). Horizontal lines are zero point energy levels for hydrogen (upper) and deuterium (lower).
THE LOW-BARRIER HYDROGEN BOND IN ENZYMIC CATALYSIS
3
3
Role of low-barrier hydrogen bonds in enzymatic reactions
ENOLIZATION REACTIONS
The first examples of enzymatic reactions where low-barrier hydrogen bonds played a role involved enolization of the substrate to change the pK of a key group in the reaction. Mandelate racemase enolizes R or S mandelate to convert the carboxyl group into an aci-carboxylate which can be protonated on opposite sides to give the R or S forms. In the ground state, one oxygen of the carboxyl group of mandelate is coordinated to Mg2þ and the other oxygen is hydrogen bonded to Glu317 which is protonated.16 The pK of a CTO group is low, so this is a weak hydrogen bond. In the aci-carboxylate intermediate, however, the pK of its oxygen will be similar to that of Glu317 and the hydrogen bond becomes a low-barrier one (Fig. 2). The energy liberated by formation of the strong hydrogen bond lowers the activation for formation of the intermediate. The 105 reduction in kcat for the E317Q mutant supports this model.17 A similar situation occurs with triose-P isomerase, where Glu165 abstracts a proton from either glyceraldehyde-3-P or dihydroxyacetone-P to give an enediolate intermediate. The carbonyl group of the substrate is hydrogen bonded to a neutral imidazole in the active site; this will be a weak hydrogen bond because of the huge mismatch in pK’s.18 The pK of both the imidazole and the enediol intermediate, however will be 11, and thus this hydrogen bond becomes a low-barrier one in the intermediate Fig. 3). An isoenergetic shift of the imidazole from one OH to the other shifts the strong hydrogen bond to the oxygen destined to become a carbonyl group when the intermediate is protonated by Glu165 to complete the reaction. Ketosteroid isomerase is another enzyme in which enolization of the substrate changes the pK of a key atom so that a low-barrier hydrogen bond forms and helps stabilize the intermediate. Asp38 is the general base that removes a proton from the substrate, and Tyr14 is hydrogen bonded to the carbonyl oxygen of the substrate. The pK’s of a ketone and of tyrosine are
Mg
Mg
HO
HO O
C H
O
C
C O
Lys166 (bases) His297
C
H Glu
O
H
Glu
H-base
Fig. 2 Mechanism of mandelate racemase.16,17 Lys166 and His297 are the two general bases and are on opposite sides of mandelate.
4
W.W. CLELAND H Glu– HC
H OH
C
OH
C
O
GluH C
O
HN
N
H
CH2OPO32–
CH2OPO32–
H
H
C
O
HN
N
C
O
C
OH
H
N
N
N
N
GluH Glu– HC
OH
CH2OPO32–
CH2OPO32–
Fig. 3 Mechanism of triose-P isomerase.4 Note the isoenergetic shift of the histidine between the two OH groups of the enediolate intermediate; a low-barrier hydrogen bond is present in both structures.
drastically different, but in the dienolate intermediate, the pK’s become more similar. An analog aromatic in the A ring and containing a phenolic hydroxyl in place of the ketone bound at least 1000-fold tighter to the D38N mutant than to wild-type isomerase.19 The neutral Asn38 mimics the protonated state of Asp38 after the formation of the intermediate dienolate. In the inhibitor complex proton NMR peaks were at 18.15 and 11.6, with the proton at 18.15 having a deuterium fractionation factor of 0.34 and the hydrogen bond having a strength of 7.1 kcal mol1 more than one between inhibitor and water. This increase in hydrogen bond strength corresponds to over 5 orders of magnitude rate acceleration and matches the decrease in rate of 4.7 orders of magnitude in the Y14F mutant. Subsequent work has shown that Asp99 is involved in the hydrogen bond network in this enzyme and the 18.15 ppm NMR peak is from a hydrogen bond between it and Tyr14.20 The 11.6 ppm peak comes from the hydrogen bond between the intermediate and Tyr14. Despite this complexity, it is still true that formation of a strong hydrogen bond in the presence of the intermediate decreases the activation energy of the reaction and thus provides catalysis. Aconitase contains a 4Fe–4S center with citrate or isocitrate binding with one of their carboxyl groups and the OH group coordinated to the Fe at one corner of the Fe–S cluster.21,22 A water molecule is also coordinated to this
THE LOW-BARRIER HYDROGEN BOND IN ENZYMIC CATALYSIS
5
Fe and is hydrogen bonded to a free carboxyl group. The general base for the elimination reaction is Ser642, which donated its proton to the Fe-bound hydroxide when the substrate bound. Proton removal by Ser642 produces an aci-carboxylate from the carboxyl next to the carbon from which the proton was removed, and the pK of the aci-carboxylate now is a close match to the pK of the Fe-bound water to which it is hydrogen bonded. This hydrogen bond thus becomes a low-barrier one, its formation providing part of the energy needed to form the aci-carboxylate (Fig. 4). His101 then protonates the Fe-coordinated OH of the substrate to allow it to be eliminated to give cis-aconitate. In the E-isocitrate X-ray structure the hydrogen bond between the Fe-bound water and the carboxyl of isocitrate is 2.7 A˚ long, while in a similar structure with the nitro analog of isocitrate bound as an aci-nitronate the distance is 2.5 A˚.21 Citrate synthase catalyzes the enolization of acetyl-CoA and attack of the enolate on oxaloacetate to form citryl-CoA, which is then hydrolyzed. Asp375 takes the proton from the methyl group of acetyl-CoA and neutral His274 hydrogen bonds to the carbonyl oxygen to stabilize the enolate.23 X-ray structures of carboxyl or amide analogs of acetyl-CoA showed 2.4–2.5 A˚ hydrogen bonds between the carboxyl or amide group of the inhibitor (replacing the methyl of acetyl-CoA) and Asp375.24 The Ki of the amide inhibitor was pH independent, while that of the carboxylate decreased as the pH decreased, showing that the protonated form was the inhibitor. The carboxyl inhibitor binds 4 orders of magnitude tighter than acetyl-CoA and thus the low-barrier hydrogen bond (chemical shift 20 ppm25) contributes at least this much to binding. During the catalytic reaction, the low-barrier hydrogen bond should be between His274 and the enolate oxygen, since their pK’s will be similar, and the energy from formation of the stronger hydrogen bond will help catalyze the enolization (Fig. 5). Vitamin K-dependent carboxylase uses vitamin K epoxidation to drive the carboxylation of glutamate groups in Gla domains. It is thought that reaction of oxygen with reduced vitamin K produces a strongly basic form of an
H
H
OH Fe
O
Fe
O
O HO C
O
C H
H His C
C CH2
H – – O Ser
O HO
O
C COO–
O
C
H H
H His C
OH Fe
O C CH2
H HO–Ser
O–
COO–
O
O
O HOH
His
C
C
C
C CH2
H
O
COO–
HO–Ser
Fig. 4 Mechanism of aconitase.4 The aci-carboxylate intermediate shares a low-barrier hydrogen bond with the Fe–OH group.
6
W.W. CLELAND COO–
O
HN
N
Arg
COO–
O
C
C SCoA
H
N
N
Arg O
C
CH3
O
C SCoA
His
CH2
His CH2
CH2
Asp–
COO–
AspH
COO–
COO–
O
HN
N
Arg
COO–
O
C
C SCoA
HN
N
Arg HO
C
CH2
HO
C SCoA
His
CH2
His CH2
Asp–
COO–
COO–
O
H
Arg
N
N
CH2
O
H
COO–
H
Asp
COO–
O
HN
C
C
N
Arg HO
C
CH2
HO
C SCoA
His
CH2
His CH2
O –
COO
H Asp
H
CH2 COO
H + HSCoA
O –
Asp
–
Fig. 5 Putative mechanism of citrate synthase.4 A low-barrier hydrogen bond helps to stabilize the enol and tetrahedral intermediates.
epoxide that removes a proton from a glutamate residue to give a carbanion intermediate that reacts with CO2. It was recently found that a H160A mutant carried out epoxidation readily, but carboxylation very poorly.26 It was postulated that His160 forms a hydrogen bond to one oxygen of the carboxyl group of glutamate. This will be a weak hydrogen bond before enolization, but proton removal will give an aci-carboxylate whose pK is a close match to that of neutral histidine. Thus the authors proposed that a low-barrier hydrogen bond between aci-carboxylate and His160 helped to stabilize the intermediate. As yet there is no structural evidence in support of this attractive hypothesis.
FACILITATED TETRAHEDRAL INTERMEDIATE FORMATION
A low-barrier hydrogen bond forms between Asp102 and His57 in the tetrahedral intermediate of the reaction catalyzed by chymotrypsin and similar serine proteases. In the free enzyme the pK of Asp102 and the neutral form of His57 are quite different, but when the Ser195 proton is transferred to His57 during formation of the tetrahedral intermediate, the pK’s of Asp102 and protonated His57 now become matched and the hydrogen bond between
THE LOW-BARRIER HYDROGEN BOND IN ENZYMIC CATALYSIS
7
them becomes a low-barrier one, thus providing the energy for formation of the unstable intermediate (Fig. 6).5 Transfer of the proton from His57 to the leaving amino group gives an acyl enzyme and dissipates the strength of the His57 O Ser195
:N
OH
N H
C
Asp102
C
Asp102
O
O C Peptidyl
NHR
O C Peptidyl Ser195
His57 O
NHR :N
OH
N H
O
O–
Peptidyl C
His57 O
NHR
y–
Ser195
O
HN
y+
N
H
C
Asp102
O
H2NR
O
Peptidyl
His57 O
C
C Ser195
O
:N
N H
Asp102
O
Fig. 6 Mechanism of chymotrypsin.5 A low-barrier hydrogen bond between Asp102 and His57 helps stabilize the tetrahedral intermediate.
8
W.W. CLELAND
low-barrier hydrogen bond. Clear evidence for this mechanism is provided by observation of tetrahedral adducts of trifluoromethyl ketone inhibitors with the enzyme. In these complexes the proton chemical shift of the proton in the Asp102–His57 hydrogen bond is 18–19 ppm and the fractionation factor is 0.3–0.4. The exchange rate of the proton with the solvent ranges from 282 s1 for N–AcF–CF3 with a Ki of 26 mM to 12.4 s1 for N–AcLF–CF3 with a Ki of 1.8 mM. The pK of His57 in these complexes is 10.7 or 12.1. The pK of 12.1 is 5 pH units higher than that in free enzyme, corresponding to 5 orders of magnitude rate acceleration.27,28 This situation was mimicked by observing complexes of N-alkylimidazoles with carboxylic acids in chloroform.29 As the pK of the acid increased, the chemical shift of the proton in the hydrogen bond moved downfield to 18 ppm and then moved back upfield. With 2,2-dichloropropionate the chemical shift of 18 ppm did not change with dilution, suggesting a strong hydrogen bond between the two molecules. The chemical shifts of complexes with more upfield protons moved further upfield on dilution, showing that they were weaker. Calorimetric measurements of complexes between 2,2-dichloropropionate and N-methyl or N-t-butylimidazole gave values of 12 or 15 kcal mol1 for the enthalpy of formation.30 The IR spectrum of a complex with 2,2-dichloropropionate showed two peaks for the CTO stretch at 1700 cm1 for the low-barrier hydrogen bond (2/3 of the complex) and 1647 cm1 for the edge-on ion pair where the carboxyl group is perpendicular to the ring of the imidazole and both oxygens are in contact with the positively charged nitrogens (1/3 of the complex). The NMR shift of 18 ppm is an average for the two species, which are in rapid equilibrium on the NMR timescale. An 0.78 A˚ structure of subtilisin resolved the proton between His64 and Asp32 of the catalytic triad.31 The distance of the hydrogen bond was 2.62 A˚ with the proton 1.2 A˚ from His64 and 1.5 A˚ from Asp32. The authors felt that this was not a low-barrier hydrogen bond because His64 was not protonated, but the short distance suggests that when His64 does become protonated during formation of the tetrahedral intermediate, it will become a low-barrier one. For the reaction catalyzed by cytidine deaminase, an analog of cytidine where the 3–4 bond is a single one and there is a hydroxy group at C4 (zebularine 3,4-hydrate) is a competitive inhibitor with a Ki of 1012 M.32 An X-ray structure of this inhibitor bound to the enzyme shows a 2.45 A˚ hydrogen bond between the OH group at C4 and the carboxylate of Glu104.33 The OH group is also coordinated to a Zn2þ ion and the other oxygen of Glu104 is hydrogen bonded to N3 (2.74 A˚). This structure corresponds to the putative tetrahedral intermediate formed by attack of the Zn-bound hydroxyl group on C4 of the pyrimidine ring, but with the amino group at C4 replaced with hydrogen (Fig. 7). It appears that the formation of a low-barrier hydrogen bond between the OH group and Glu104 may provide some of the energy
THE LOW-BARRIER HYDROGEN BOND IN ENZYMIC CATALYSIS
9
His102 Cys132
S Zn
S
C C
Glu104
2.49Å O H O H
C
Cys129
HN
O HN O
NH
N
Ala103
Ribose
Fig. 7 Structure of cytidine deaminase with zebularine 3,4-hydrate bound.33 The lowbarrier hydrogen bond between Glu104 and the Zn–OH would help stabilize the tetrahedral intermediate, which would have an NH2 in place of the H at C4 of the ring in this structure.
needed to form the tetrahedral intermediate. Transfer of the proton in this bond to the amino group then permits it to leave as ammonia to complete the reaction. However, the proton NMR spectrum of the bound inhibitor did not show any downfield peaks that could be assigned to a low-barrier hydrogen bond, so its importance in the reaction is uncertain. Thermolysin and carboxypeptidase use Zn2þ to polarize the carbonyl group of the amide substrate to permit attack by Zn-bound water. A glutamate residue (143 in thermolysin and 270 in carboxypeptidase) acts as a general base and is hydrogen bonded to the Zn-bound water. A proton is transferred to the leaving nitrogen, which permits the tetrahedral intermediate that is bidentately coordinated to Zn to decompose to the final products of the reaction (Fig. 8). The tetrahedral intermediate has been mimicked by several phosphonates with Ki values as low as 10 fM. X-ray structures show these inhibitors as bidentate ligands of Zn and the hydrogen bond between the catalytic glutamate and one Zn-coordinated oxygen of the phosphono group is 2.3–2.5 A˚ in the three structures of each of the two enzymes.34–37 These short
R–NH
Glu
H
R–NH
R C
H O
O Zn
Glu
H
R
R–NH
C
H
O
O Zn
Glu
H
R
R–NH
C
H O
O Zn
Glu
H
R C
H
O
O Zn
Fig. 8 Mechanism of thermolysin and carboxypeptidase based on X-ray structures of enzymes with bound phosphonate inhibitors.34–37
10
W.W. CLELAND 18.00 ppm 12.67 ppm (normal H-bond) (strong H-bond) His48
Asp99
CH2–(CH2)5–CH3 O
O–
H
N
N
H
Oδ–
P
Oδ– O
O H3C–(CH2)7 –S–CH2
C H
H2C
O
P
O
+
(CH2)2 –NH3
O–
Fig. 9 Structure of phospholipase A2 with bound phosphonate inhibitor mimicking the tetrahedral intermediate.38
distances suggest that this hydrogen bond in the tetrahedral intermediate is a low-barrier one, with the energy released by its formation helping to form the high-energy intermediate. Phospholipase A2 catalyzes the hydrolysis of phospholipids at the sn-2 bond, using a water molecule coordinated to Ca2þ. Enzymes from bovine pancreas and bee venom are similar in many respects and both contain an aspartate and histidine as catalytic groups. In the presence of phosphonate inhibitors that mimic a tetrahedral intermediate, a low-barrier hydrogen bond exists between the histidine and a phosphonate oxygen, while the hydrogen bond between the histidine and aspartate is a normal one (Fig. 9).38 The proton NMR chemical shifts for the protons in the low-barrier hydrogen bond is 18 ppm, while the other proton has a chemical shift of 13 ppm. The lowfield proton has a fractionation factor of 0.6 and the pK of the histidine is shifted from 5.7 in free enzyme to 9 in the presence of the inhibitor. This suggests a minimum of 4.5 kcal mol1 extra energy made available for catalysis by the low-barrier hydrogen (the actual value is probably higher, as the inhibitor dissociates when the histidine is deprotonated).
FACILITATED PROTON IONIZATION
In the liver alcohol dehydrogenase reaction the alcohol substrate is bound to a Zn2þ ion in the active site. The proton of the OH group is transferred via a hydrogen bond network involving Ser48 and the ribose 20 -OH of NAD to His51. Hydride transfer from the alkoxide intermediate then completes the reaction. In a structure with NAD and pentafluorobenzyl alcohol bound, the distance between the oxygens of the alcohol and Ser48 is 2.5 A˚.39 In D2O solvent isotope effects on single turnover reactions of benzyl alcohol with
THE LOW-BARRIER HYDROGEN BOND IN ENZYMIC CATALYSIS
11
E-NAD, the fractionation factor of the proton between the alcohol and Ser48 was 0.37 and that in the transition state was 0.73, partway to 1.0, the value expected for the weak hydrogen bond between Ser48 and the aldehyde product.40 It thus appears that in the alkoxide intermediate the hydrogen bond between the alcohol substrate and Ser48 is a low-barrier one, with the energy released by its formation driving the proton movement to His51, which would otherwise not be energetically favorable (Fig. 10). UDP-galactose 4-epimerase contains bound NAD and catalyzes the interconversion of UDP-glucose and UDP-galactose via a 40 -keto intermediate. Two residues, Ser132 and Tyr157 are in close proximity of the 40 -OH of the substrate, with Ser132 only 2.5 A˚ from the 40 -OH. It was postulated that Tyr147 is the general base for proton removal from the 40 -OH during hydride transfer to give the 40 -keto intermediate, but that a low-barrier hydrogen bond between Ser132 and the 40 -OH provided the energy to help drive the process.41 This situation is reminiscent of that with liver alcohol dehydrogenase discussed above. Yeast pyrophosphatase uses a water molecule bound between two Mg2þ ions as the nucleophile to attack bound Mg-pyrophosphate. Asp117 acts as a general base to deprotonate this bound water, whose pK is 5.85.42 It was suggested on the basis of X-ray structures and the similar pK’s that the hydrogen bond between Asp117 and the nucleophilic water was a low-barrier one.43 Coordination to both Mg2þ ions as well as formation of a low-barrier hydrogen bond should certainly be sufficient to lower the pK of the bound water to the observed value. Pyruvate decarboxylase binds thiamine diphosphate as its cofactor, and the pK of the pyrimidine ring of the cofactor is 5.0. N10 of the ring can form a hydrogen bond to Glu50 when the ring is in the 10 ,40 -imino tautomer and it has been suggested that a low-barrier hydrogen bond forms between N10 and Glu50 in order to enhance the proportion of imino tautomer, with the N40 NH group then removing the proton to give the active ylide form of the cofactor (Fig. 11).44
Zn O H
C
S48 H
Zn δ
O
H NAD
H
O
H
C
H
S48
Zn
O
O δ
NAD
H
C
R
R
R
ΦR = 0.37
ΦT = 0.73
ΦP = 1.0
S48 H
O NADH
Fig. 10 Changes in the hydrogen bond between Zn–OH and Ser48 during hydride transfer to NAD in the liver alcohol reaction.40 The values are deuterium fractionation factors.
12
W.W. CLELAND O Glu
C O
CH2 N N
N
NH2 H
S
OPP ThDP
O Glu
C O
H
CH2 N N
N
NH H
S
OPP 1′,4′-imino tautomer of ThDP
O Glu
C O
H
CH2 N N
NH2
N S
OPP ThDP ylide
Substrate
Fig. 11 Possible formation of a low-barrier hydrogen bond between Glu50 and bound thiamin-PP to enhance the proportion of ylide in the pyruvate decarboxylase reaction.44
ASPARTIC PROTEASES
Aspartic proteases have two aspartates hydrogen bonded to each other and sharing a water molecule between their other oxygens. This water then becomes the nucleophile for attack on the substrate. Ab initio calculations on human immunodeficiency virus (HIV)-1 protease found that the most stable form is one where there is a low-barrier hydrogen bond (2.5 0.1 A˚) between the aspartates and a net negative charge to the cluster (Fig. 12).45 Northrop then formulated a mechanism for the protease in which the lowbarrier hydrogen bond becomes a normal one as protons shift during attack on the substrate to form a tetrahedral intermediate.46 The central proton then
THE LOW-BARRIER HYDROGEN BOND IN ENZYMIC CATALYSIS
13
O H
H
O
O C
C Asp25
O
H
O
Asp25′
Fig. 12 Low-barrier hydrogen bond between aspartates of HIV protease to generate nucleophilic water.45 The overall cluster has a negative charge.
shifts back to the other aspartate as the leaving group is protonated and the tetrahedral intermediate falls apart. Product release, replacement with water, and deprotonation then reform the low-barrier hydrogen bond and the enzyme is cocked for the next catalytic cycle. In contrast to this proposal, X-ray and neutron diffraction studies of complexes of aspartic proteases with bound inhibitors have found hydrogen bonds other than that between the two aspartates to be short and likely low-barrier ones. The 1.03 A˚ structure of a complex with a phenylnorstatine inhibitor shows a 2.97 A˚ hydrogen bond between the aspartates with the proton visible midway between the two oxygens.47 By contrast, the hydrogen bonds from the other oxygens of the aspartates to a hydroxyl and ketone of the inhibitor are 2.61 and 2.55 A˚. A 1.65 A˚ structure with the products bound showed the hydrogen bond between the two aspartates to be 2.30 A˚ long, certainly a low-barrier hydrogen bond.48 In a neutron diffraction structure of endothiapepsin with an inhibitor thought to mimic the tetrahedral intermediate, hydrogen bonds from the aspartates to the hydroxyl of the inhibitor were 2.6 A˚, and a hydrogen bond was not seen between the aspartates.49 A neutron diffraction structure of endothiapepsin with an inhibitor with a gem-diol in the active site showed hydrogen bonds of 2.54 and 2.65 A˚ between the gem-diol oxygens and oxygens of the aspartates, while the other aspartate oxygens were 2.93 A˚ apart.50 A 1.6 A˚ X-ray structure of HIV-1 protease with bound products shows 2.4 and 2.45 A˚ hydrogen bonds from the aspartates to the carboxyl of one product, with the distance between the other oxygens of the aspartate being 2.95 A˚.51 It is clear from these structures that a number of possible hydrogen bond orientations are possible, depending on what is bound. Whether Northrop’s mechanism is correct in all of its details is not yet clear, but it appears that low-barrier hydrogen bonds do play a role in aspartic proteases.
MISCELLANEOUS ENZYMES
A low-field resonance at 19.1 ppm is seen in the proton NMR spectrum of 2-amino-3-ketobutryate-CoA ligase. The signal is present only when the cofactor pyridoxal-P is bound and it was assigned to the proton between the
14
W.W. CLELAND
pyridinium nitrogen and a putative aspartate.52 The pK of this signal was 6, which is consistent with a low-barrier hydrogen bond. Such a bond would in this case stabilize and help bind the cofactor in the proper position. A structure of the N-terminal half of hen ovotransferrin has a 2.3 A˚ distance between the terminal nitrogen atoms of Lys209 and Lys301 which are in separate domains.53 It was proposed that this was a low-barrier hydrogen bond holding the two domains together and that when the transferrin entered an acidic endosome, the protonation of this lysine pair would cause the lysines to move apart, thus allowing release of the bound Fe3þ. This lysine pair would thus be a pH-sensitive trigger for Fe3þ release. A recent neutron crystallography study of photoactive yellow protein discovered a low-barrier hydrogen bond between the phenolic oxygen of the 4-hydroxycinnamic acid chromophore and Glu46 in the ground state.54 The deuterium atom in the structure was 1.37 A˚ from the phenolic oxygen and 1.21 A˚ from the oxygen of Glu46. The role of the low-barrier hydrogen bond is postulated to be stabilization of the negative charge on the chromophore and Glu46 system. Upon photoactivation the chromophore is isomerized and the hydrogen bond is no longer a low-barrier one, with the proton transferred to Glu46. In H148D mutants of green fluorescent protein it appears that a low-barrier hydrogen bond is present between Asp148 and the phenolic oxygen of the chromophore (2.4 A˚ in a S65T/H148D mutant).55 Despite the change in hydrogen bonding in the active site, the Asp148 mutants permit fluorescence in S65T and E222Q mutants, which do not fluoresce if His148 is still present. A recent sub-A˚ngstrom X-ray structure of a phosphate-binding protein showed that there are 11 hydrogen bonds to the phosphate oxygens from OH or NH groups, and the proton on one oxygen of the phosphate dianion forms a 2.5 A˚ low-barrier hydrogen bond with an aspartate.56 Formation of this strong bond ensures that even at pH 4.5 the protein binds phosphate as the dianion.
ACID–BASE CATALYSIS
Low-barrier hydrogen bonds are likely to form during general acid and general base catalysis. In the lactate dehydrogenase reaction, for example, the hydroxyl group of lactate is weakly hydrogen bonded to His195 before catalysis and weakly hydrogen bonded to the carbonyl oxygen of pyruvate after reaction. As the hydride ion is transferred from lactate to NAD the pK of the oxygen on lactate changes from 14 in lactate to –5 in pyruvate. At the point where the pK of this oxygen is 6, the pK’s of it and His195 will be matched and the hydrogen bond will become a low-barrier one. As the pK’s diverge the bond will weaken and the proton will transfer to His195. The transition state for the reaction should be close to the point where the pK’s match and thus
THE LOW-BARRIER HYDROGEN BOND IN ENZYMIC CATALYSIS
15
the energy released by forming the low-barrier hydrogen bond will lower the activation barrier for the reaction. General acid–base catalysis provides as much as 5 orders of magnitude rate acceleration in enzymatic reactions, which is consistent with the energy provided by forming a low-barrier hydrogen bond in the transition state.57
4
Conclusion
It should be clear from this brief review that low-barrier hydrogen bonds play an important role in many enzymatic reactions, in many cases contributing the energy of their formation to provide catalysis. I have not reviewed the extensive computational literature on low-barrier hydrogen bonds, but an early review will provide more information.10 Other short reviews on their role in enzymatic reactions have been published.4,15,58,59 I have not included references to early critics of the role of low-barrier hydrogen bonds, as I think their criticisms have been shown to be invalid. References to those articles are available in the reviews noted above.
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.
Cleland WW. Biochemistry 1992;31:317–9. Gerlt JA, Gassman PG. J Am Chem Soc 1993;115:11552–68. Gerlt JA, Gassman PG. Biochemistry 1993;32:11943–52. Cleland WW, Kreevoy MM. Science 1994;264:1887–90. Frey PA, Whitt SA, Tobin JB. Science 1994;264:1927–30. Gilli P, Bertolasi V, Ferretti V, Gilli G. J Am Chem Soc 1994;116:909–15. Pan Y, McAllister MA. J Am Chem Soc 1998;120:166–9. Kumar GA, Pan Y, Smallwood CJ, McAllister MA. J Comput Chem 1998;19:1345–52. Steiner T, Saenger W. Acta Chrystallogr Sect B Struct Sci 1994;50:348–7. Hibbert F, Emsley J. Adv Phys Org Chem 1990;26:255–379. Abu-Dari K, Raymond KN, Freyberg DP. J Am Chem Soc 1979;101:3688–9. Shan S-ou, Loh S, Herschlag D. Science 1996;272:97–101. Schiott B, Iverson BB, Madsen GKH, Larsen FK, Bruice TC. Proc Natl Acad Sci USA 1998;95:12799–802. Frey PA, Cleland WW. Bioorg Chem 1998;26:175–92. Cleland WW. Arch Biochem Biophys 2000;382:1–5. Landro JA, Gerlt JA, Kozarich JW, Koo CW, Shah VJ, Kenyon GL, et al. Biochemistry 1994;33:635–43. Mitra B, Kallarakal AT, Kozarich JW, Gerlt JA, Clifton JR, Petsko GA, et al. Biochemistry 1995;34:2777–87. Lodi PJ, Knowles JR. Biochemistry 1991;30:6948–56. Zhao Q, Abeygunawardana C, Talalay P, Mildvan AS. Proc Natl Acad Sci USA 1996;93:8220–4. Zhao Q, Abeygunawardana C, Gittis AG, Mildvan AS. Biochemistry 1997;36:14616–26.
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21. 22. 23. 24.
Lauble H, Kennedy MC, Beinert H, Stout CD. Biochemistry 1992;31:2735–48. Werst MM, Kennedy MC, Beinert H, Hoffman BM. Biochemistry 1990;29:10526–32. Remington SJ. Curr Opin Struct Biol 1992;2:730–5. Usher KC, Remington SJ, Martin DP, Drueckammer DG. Biochemistry 1994;33:7753–9. Gu Z, Drueckhammer DG, Kurz L, Liu K, Martin DP, McDermott A. Biochemistry 1999;38:8022–31. Rishavy MA, Berkner KL. Biochemistry 2008;47:9836–46. Cassidy CS, Lin J, Frey PA. Biochemistry 1997;36:4576–84. Lin J, Westler WM, Cleland WW, Markley JL, Frey PA. Proc Natl Acad Sci USA 1998;95:14664–8. Tobin JB, Whitt SA, Cassidy CS, Frey PA. Biochemistry 1995;34:6919–24. Reinhardt LA, Sacksteder KA, Cleland WW. J Am Chem Soc 1998;120:13366–9. Kuhn P, Knapp M, Soltis SM, Ganshow G, Thoene M, Bott R. Biochemistry 1998;37:13446–52. Frick L, Yang C, Marquez VE, Wolfenden RV. Biochemistry 1989;28:9423–30. Xiang S, Short SA, Wolfenden R, Carter CW Jr., Biochemistry 1995;34:4516–23. Tronrud DE, Monzingo AF, Matthews BW. Eur J Biochem 1986;157:261–8. Holden HM, Tronrud DE, Monzingo AF, Weaver LH, Matthews BW. Biochemistry 1987;26:8542–53. Kim H, Lipscomb WN. Biochemistry 1990;29:5546–55. Kim H, Lipscomb WN. Biochemistry 1991;30:8171–80. Poi MJ, Tomaszewski JW, Yuan C, Dunlap CA, Andersen NH, Gelb MH, et al. J Mol Biol 2003;329:997–1009. Ramaswamy S, Park D-H, Plapp BV. Biochemistry 1999;38:13951–9. Sekhar VC, Plapp BV. Biochemistry 1990;29:4289–95. Thoden JB, Wohlers TM, Fridovich-Keil JL, Holden HM. Biochemistry 2000;39:5691–701. Belogurov GA, Fabrichniy IP, Pohjanjoki P, Kasho VN, Lehtihuhta E, Turkina MV, et al. Biochemistry 2000;39:13931–8. Heikinheimo P, Tuominen V, Ahonen A-K, Teplyakov A, Cooperman BS, Baykov AA, et al. Proc Natl Acad Sci USA 2001;98:3121–6. Tittmann K, Neef H, Golbik R, Hubner G, Kern D. Biochemistry 2005;44:8697–700. Piana S, Carloni P. Proteins: Struct Funct Genet 2000;39:26–36. Northrop DB. Acc Chem Res 2001;34:790–7. Brynda J, Rezacova P, Fabry M, Horejsi M, Stouracova R, Sedlacek J, et al. J Med Chem 2004;47:2030–6. Das A, Prashar V, Mahale S, Serre L, Ferrer J-L, Hosur MV. Proc Natl Acad Sci USA 2006;103:18464–9. Coates L, Erskine PT, Wood SP, Myles AA, Cooper JB. Biochemistry 2001;40:13149–57. Coates L, Tuan H-F, Tomanicek S, Kovalevsky A, Mustyakimov M, Erskine P, et al. J Am Chem Soc 2008;130:7235–7. Tyndall JDA, Pattenden LK, Reid RC, Hu S-H, Alewood D, Alewood PF, et al. Biochemistry 2008;47:3736–44. Tong H, Davis L. Biochemistry 1995;34:3362–7. Dewan JC, Mikami B, Hirose M, Sacchettini JC. Biochemistry 1993;32:11963–8. Yamaguchi S, Kamikubo H, Kurihara K, Duroki R, Nimura N, Shimizu N, et al. Proc Natl Acad Sci USA 2009;106:440–4. Stoner-Ma D, Jaye AA, Ronayne KL, Nappa J, Meech SR, Tonge PJ. J Am Chem Soc 2008;130:1227–35.
25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55.
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56. Liebschner D, Elias M, Moniot S, Fournier B, Scott K, Jelsch, C, et al. J Am Chem Soc 2009;131:7879–86. 57. Meloche HP, O’Connell EL. J Protein Chem 1983;2:399–410. 58. Gerlt JA, Kreevoy MM, Cleland WW, Frey PA. Chem Biol 1997;4:259–67. 59. Cleland WW, Frey PA, Gerlt JA. J Biol Chem 1998;273:25529–32.
Stabilities and Reactivities of Carbocations RORY MORE O’FERRALL School of Chemistry and Chemical Biology, University College Dublin, Belfield, Dublin 4, Ireland 1 Introduction 19 2 Stabilities of carbocations 21 Measures of stability 21 Equilibrium measurements of pKR 28 Kinetic methods for determining pKR 30 Arenonium ions 37 Alkyl cations 46 Vinyl cations 48 The methyl cation: a correlation between solution and the gas phase Oxygen-Substituted carbocations 51 Metal-Coordinated carbocations 64 Carbocations as protonated carbenes 68 Halide and azide ion equilibria 71 3 Reactivity of carbocations 76 Nucleophilic reactions with water 77 Reactions with water as a base 87 Reactions of nucleophiles other than water 90 Reactivity, selectivity, and transition state structure 105 Hard and soft nucleophiles 110 Summary and conclusions 112 Acknowledgments 114 References 114
1
49
Introduction
There have been a number of reviews of carbocation chemistry in the past 10 years,1–11 including a volume of essays marking the 100th anniversary of the subject.1 That volume illustrates the variety of structures and reactions that characterize carbocations. It is this variety which suggests scope for a further study, namely of the stability and reactivity of carbocations in (mainly) aqueous solution. Dedication to AJ Kresge is appropriate. He has pioneered the quantitative characterization of reactive intermediates in water as solvent. If he is best known for his work on enolic species, his steady referencing throughout this chapter reflects the breadth of his influence in physical organic chemistry.
19 ADVANCES IN PHYSICAL ORGANIC CHEMISTRY VOLUME 44 ISSN: 0065-3160 DOI: 10.1016/S0065-3160(08)44002-9
2010 Elsevier Ltd. All rights reserved
20
R. MORE O’FERRALL
Attempts to measure the stabilities of carbocations are not new. Hughes and Ingold established the essential features of solvolysis reactions in the 1930s.12 They identified the SN1 mechanism as involving the formation of a carbocation intermediate and recognized that the rate of solvolysis reflects the stability of that carbocation. For more than 80 years, rate constants of solvolyses have provided measures of stability (with allowance for variations in the stability of reactants).13 Only recently have the stabilities of more than mildly reactive carbocations, accessible by direct equilibrium measurements,14–16 been determined. Indeed the emergence of gas-phase ion chemistry and new techniques of mass spectrometry in the 1980s led to a wider knowledge of the stabilities of carbocations in the gas phase than in solution.2,17 The extension of equilibrium measurements to normally reactive carbocations in solution followed two experimental developments. One was the stoichiometric generation of cations by flash photolysis or radiolysis under conditions that their subsequent reactions could be monitored by rapid recording spectroscopic techniques.3,4,18–20 The second was the identification of nucleophiles reacting with carbocations under diffusion control, which could be used as clocks for competing reactions in analogy with similar measurements of the lifetimes of radicals.21,22 The combination of rate constants for reactions of carbocations determined by these methods with rate constants for their formation in the reverse solvolytic (or other) reactions furnished the desired equilibrium constants. Important contributors to these developments were McClelland and Richard, who have published reviews of their own and related studies.3–8 The present chapter will focus on recent work therefore and present earlier results mainly for comparison with new measurements. It will consider two further methods for deriving equilibrium constants: (a) from kinetic measurements where the reverse reaction of the carbocation is controlled by diffusion or relaxation of solvent molecules23–25 and (b) from a correlation of solution measurements with the more extensive measurements of stabilities of carbocations in the gas phase.26 It will also show that stabilities of highly reactive carbocations can be determined from measurements of protonation and hydration of carbon–carbon double bonds. The existence of equilibrium measurements today usually implies access to a rate constant for direct reaction of the carbocation with a nucleophile or base. The chapter will also consider reactivity and selectivity for these reactions. This area too has been well studied and reviewed,3–8 especially by Mayr’s group in Munich, who have made extensive recent contributions to the field.27–31 It should be admitted that the author’s own work25,26,32 will be a further focus for the chapter, which in part will be an ‘‘account of research,’’ and indeed an update of an earlier multiauthored review.9 The chapter begins, however, with a digression on the significance of different measures of the stabilities of carbocations. This is followed by a discussion of the use of a solvent free energy relationship to extrapolate equilibrium and kinetic measurements in concentrated solutions of strong acids to a purely aqueous medium. Some readers may
STABILITIES AND REACTIVITIES OF CARBOCATIONS
21
wish to omit these sections. However, throughout the first third of the chapter experimental results are presented in the context of methods used for measurements. The emphasis on methods is followed by discussions of oxygen substituent effects, coordination of metal ions, protonations of carbenes, and equilibria for the reactions of carbocations with halide or azide ions. The discussion of reactivity concludes the chapter.
2
Stabilities of carbocations
MEASURES OF STABILITY
The choice of equilibrium constant for measuring the stability of a carbocation depends partly on experimental accessibility and partly on the choice of solvent. A desire to relate measurements to the majority of existing equilibrium constants implies the use of water as solvent. Water has the advantage and disadvantage that it reacts with carbocations. It follows that the most widely used equilibrium constant is that for the hydration reaction shown in Equation (1), which is denoted KR (or pKR). A simple interpretation of KR is that it measures the ratio of concentrations of unionized alcohol to carbocation in an (ideal) solution of aqueous acid of concentration 1 M. Rþ þ 2H2 O ¼ ROH7 þ H3 Oþ KR ¼
ð1Þ
½R OH½H3 Oþ ½Rþ
Nucleophile affinities As pointed out by Mayr,28 Ritchie,15 and Hine33,34 KR also measures the relative affinities of Rþ and H3Oþ for the hydroxide ion. It can be regarded as providing a general affinity scale applicable to electrophiles other than carbocations.33,35 It can also be factored into independent affinities of Rþ and H3Oþ as shown in Equations (2) and (3). Such equilibrium constants have been denoted Kc by Hine.33 KR corresponds to the ratio of constants for reactions (2) and (3) and, in so far as Kc for H3Oþ is the inverse of Kw the autoprotolysis constant for water, KR = KcKw Rþþ HO ¼ ROH Kc ¼
½ROH ½Rþ ½HO
ð2Þ
22
H3 Oþ þ HO ¼ 2H2 O
R. MORE O’FERRALL
ð3Þ
A distinction between the reactions of Rþ and H3Oþ is that while Rþ reacts with hydroxide ion in an associative process, H3Oþ reacts by transfer of a proton. The difference corresponds to that between the product-forming step of an SN1 mechanism and an SN2 reaction. Many carbocations are capable of existing in solution independently of a nucleophile, but this is not true of highly reactive electrophiles such as Hþ (or, e.g., CHþ 3 ) reactions of which involve breaking as well as making a bond to a nucleophile. If we focus on Hþ rather than H3Oþ, affinities for nucleophiles (bases) must be expressed relative to a suitable reference. In principle, the familiar equilibrium constants Ka and Kb measure affinities relative to water and hydroxide ion, respectively [Equations (4) and (5)]. AH þ H2 O ¼ A þ H3 Oþ
ð4Þ
A þ H2 O ¼ AH þ HO
ð5Þ
In practice, it is perhaps unfortunate that the complementary character of the KR and Ka scales is somewhat obscured by the formulation of Ka as a measure of acidity, so that the appropriate measure of affinity (in this case basicity) is 1/ K a. For carbocations, an electrophilicity (Lewis acidity) scale can be based on ions other than the hydroxide ion as is shown in general for X in Equation (6), for which the equilibrium constant can be denoted K X R . Scales based on chloride ion, for example, have been used in the gas phase2,17,36 and are also appropriate for nonaqueous solvents. Rþ þ X ¼ RX
ð6Þ
A further popular scale in the gas phase is hydride ion affinity (HIA)2,37 for which X = H. To avoid dealing explicitly with H, this scale is conveniently referenced to a particular ion such as CHþ 3 as in Equation (7). Commonly HIAs are expressed as free energies rather than pK’s. Rþ þ CH4 ¼ R H þ CH3þ
ð7Þ
The hydride affinity scale is also applicable to aqueous solution. In analogy with KR we can take H3Oþ as reference as in Equation (8). Rþ þ H2 þ H2 O ¼ RH þ H3 Oþ
ð8Þ
STABILITIES AND REACTIVITIES OF CARBOCATIONS
23
The two scales are readily interconverted and a ratio of KR values K H R =K R is given by Equation (9). KH ½R H½H2 O R ¼ KR ½ROH½H2
ð9Þ
The right-hand side of this equation is evaluated in terms of free energies of formation in aqueous solution at 25C of R–H, R–OH, H2O, and H2.38 Free energies of formation, hydride ion affinities, and pKR: Is there an optimum measure of carbocation stability? The problem arises, which equilibrium constant offers the most effective measure of carbocation stability? A good discussion of this question has been provided by Mayr and Ofial,29 who point out that a rigorous comparison of stabilities is possible only for isomeric cations. Comparisons between nonisomeric cations depend on the equilibrium chosen for the measurements. They argue that the appropriate choice depends on the context and imply that it is not possible to identify a ‘‘best’’ measure of carbocation stability. While this is certainly true it is worthwhile pursuing further the likelihood that some equilibria provide better measures of stability than others, and to assess their effectiveness and limitations. For carbocations possessing a b-hydrogen atom, an alternative to nucleophilic affinities is provided by the pKa for dissociation of a proton to form an alkene. It is rather easy to recognize that a pKa is not always a good measure of carbocation stability. This is evident from an example chosen by Mayr and Ofial, namely, the cyclohexadienyl cation, for which the conjugate base is benzene [Equation (10)]. Thus, if we seek to compare stabilities of the cyclohexadienyl cation and t-butyl cation [Equation (11)] in terms of pKas, the difference will strongly reflect the different stabilities of the carbon–carbon double bonds of their conjugate bases. In this case comparing values of pKR provides a better measure of stability because a contribution from the difference between the corresponding alcohols is smaller. C6 H7 þ ¼ C6 H6 þHþ
ð10Þ
ðCH3 Þ3 Cþ ¼ ðCH3 Þ2 C¼CH2 þ Hþ
ð11Þ
Of course, to speak of the stability of a double bond implies further equilibria or reference structures with which the energy of the unsaturated molecule itself is compared. An obvious reference is the saturated hydrocarbon, with respect to which stability is measured, for example, by a heat of hydrogenation.
24
R. MORE O’FERRALL
Perhaps less obviously, the hydrocarbon also provides a reference for the carbocation. It is worthwhile examining the implications of such a reference, by considering briefly ‘‘thermodynamic’’ measurements of carbocation stabilities in terms of heats (enthalpies) or free energies of formation. Mayr and Ofial contrast our ability to measure the relative energies of tertiary and secondary butyl cations with the significant differences in relative stabilities of secondary butyl and isopropyl cations derived from different equilibrium measurements, namely, hydride, chloride, or hydroxide ion affinities. It is convenient to focus on this example and to assess the effectiveness of hydride affinities for comparing the stabilities of these three ions. Extensive measurements of heats of formation of carbocations in the gas phase exist and there have been more limited measurements in solution for nonhydroxylic solvents.39 For comparison with equilibrium measurements in water, however, the most appropriate measurement would appear to be free energies of formation in aqueous solution. It is fortunate therefore that a convenient compilation of values of DGf (aq) at 25C has been provided by Guthrie.38 This allows us for example to derive a value of DGf (aq) for a carbocation from a measurement of its pKR value, provided that the free energy of formation of the corresponding alcohol [R–OH in Equation (1)] is known. Heats or free energies of formation can be used to compare directly the energies of isomeric carbocations. Such a comparison is similar to the more familiar comparisons of energies of isomeric olefins, such as cis- and trans-butene. It depends on the energies of formation of isomeric molecules or ions being based on the same combination of elements. Energies of isomerization can also be measured directly, and Bittener, Arnett, and Saunders have measured the enthalpy of isomerization of secondary to tertiary butyl cations in CH2Cl2 as solvent.39 It is possible to compare direct measurements of relative stabilities of isomeric ions with comparisons of nonisomeric ions by use of a ‘‘group additivity’’ scheme. Group additivity schemes have been developed by Benson for heats of formation (and other thermodynamic properties) of organic molecules in the gas phase,40 and by Guthrie to represent free energies of formation in aqueous solution.38 In both cases, energies of unstrained hydrocarbons accurately correspond to a sum of contributions from primary, secondary, tertiary, and quaternary carbons CH3, CH2, CH, and C. Such a scheme can be extended to carbons bearing functional groups (X) by assigning contributions for CH2X, CHX, and CX. In principle, carbocations can be included, with the positively charged carbon considered as a functional group, with characteristic contributions for primary, secondary, and tertiary cation centers. For strict additivity, a group scheme implies that the influence of a functional group does not extend beyond the carbon atoms adjacent to the functionalized atom, that is, in our case the carbon bearing the positive charge.
STABILITIES AND REACTIVITIES OF CARBOCATIONS
25
This can be tested by drawing on extensive information on carbocation stabilities in the gas phase. Heats of formation of ethyl, isopropyl, sec-butyl and tbutyl cations2 are shown below. From these values it is evident that the t-butyl cation is more stable than the sec-butyl cation by 13 kcal mol1. This corresponds to the direct comparison of (isomeric) ion stabilities noted above by Arnett and Mayr.
DHf (g)
1
(kcal mol )
(CH3)3Cþ
CH3CH2CHþCH3
(CH3)2CHþ
CH3 CH2
170
183
193
215
It can also be seen that the heat of formation of the iso-butyl cation is 10 kcal mol1 less than that of the isopropyl cation. Based on this difference, we may assess the effectiveness of group additivity by comparing the changes in energy for inserting a methylene group into the isopropyl cation to give a sec-butyl cation with the same change in propane to give butane or in propanol to give sec-butyl alcohol. For an effective additivity scheme these changes should be the same because the methylene group is two carbons removed from the charge center of the cation. In practice, whereas converting the isopropyl cation to a sec-butyl cation reduces the heat of formation by 10 kcal mol1, the corresponding conversion for propane and isopropyl alcohol reduces it by 5.0 and 4.8 kcal mol1, respectively. While this implies that to a good approximation an OH functional group is well accommodated by the additivity scheme the carbocation center certainly is not. The situation in solution is quite different. The difficulty of stabilizing charge in the gas phase is well known and in solution smaller differences between structures are expected. There should also be less dependence on the size of the ion, which is a well-recognized feature of gas-phase ion stabilization, but does not appear to be significant in solution.41 Shown in Table 1 are free energies of formation of the same ions in aqueous solution at 25C. The measurements of pKa from which they are derived are described later in the chapter (p. 47). Suffice to say here that the relative values for isopropyl and secondary butyl cations are based on the inference from measurements of equal rate constants for protonation of propene and 1-butene42 that the pKas of the conjugate acids of these alkenes are the same. It can be seen that the differences in energies of formation between the cations are significantly less than in the gas phase. Thus the difference between the t-butyl and ethyl cations is reduced from 45 kcal mol1 to less than 20 kcal mol1. On the other hand, the difference between the t-butyl and sec-butyl cations shows a much smaller reduction, from 13 to 10.2 kcal mol1. Moreover, instead of the energy of the isopropyl cation being 10 kcal mol1 greater than the sec-butyl cation it is now 2.3 kcal mol1 less. In the gas phase the extra CH2
26
R. MORE O’FERRALL
provides important stabilization. In aqueous solution this is overridden by an unfavorable effect on solvation (recall that the standard state remains the gas phase).43 If as above we compare the value of this ‘‘group contribution’’ for CH2 with values based on increases in free energies of formation between propane and butane (2.0 kcal mol1) and isopropyl alcohol and sec-butanol (1.6 kcal mol1), it is apparent that there is a much better cancellation, and thus better prospect that energies of alkyl carbocations can be approximated by an additivity scheme in solution than in the gas phase. Calculated group contributions to free energies of formation for tertiary, secondary, and primary carbocations in aqueous soloution based on the above data are shown below and are compared with Guthrie’s values for hydrocarbons (which were also used for remote methyl groups in deriving the carbocation group contributions). As expected the cations have large positive values. Indeed the values are substantially larger than for alkyne carbons, which fall in the range 27–29 kcal mol1 and currently represent the largest carbon group contributions. CH2þ CHþ Cþ
57.9 50.7 45.7
CH3 CH2 CH C
3.93 2.16 6.43 10.40
The group contributions apply only to alkyl cations and are of limited practical value. However, apart from illustrating the application of group additivity contributions to energies of formation of carbocations, they offer a significant insight into comparisons of stability based on hydride ion affinities (HIAs) and pKR values. HIAs of the carbocations are listed in Table 1 as differences in values from the t-butyl cation (DHIA in free energies mol1). Returning to the comparison of isopropyl and sec-butyl cations it can be seen that the difference in their
Table 1 Free energies of formation, HIAs, and pKR values for alkyl cations in aqueous solution
DGf (aq) (kcal mol1) DHIAa 1.364pKRb 1.364DpKRc
(CH3)3Cþ
CH3CH2CHþCH3
(CH3)2CHþ
CH3 CH2
33.9 9.8 –22.4
45.6 9.7 –30.6 8.2
43.3 23.3 –30.1 7.7
54.0
HIAs relative to (CH3)3Cþ. pKR converted to free energy mol1. c Relative to (CH3)3Cþ. a
b
–40.8 18.4
STABILITIES AND REACTIVITIES OF CARBOCATIONS
27
HIAs is only 0.1 kcal mol1. This reflects almost complete cancellation of contributions from the extra CH2 group in the butyl structure between the cation and hydrocarbon. It indicates that HIAs provide a good approximation to differences in stability between a carbocation center and the corresponding group contribution from a hydrocarbon, independently of structural variations at carbon atoms not attached to the carbocation center. Moreover, a comparison between two secondary carbocations leads to almost complete cancellation of the contributions from the parent hydrocarbons and from alkyl groups of the carbocations too far removed from the charge center to influence stability. One is very close therefore to a comparison of stabilities comparable to that between isomeric cations. It should be noted that such ‘‘intrinsic’’ stabilities are not expressed in heats of formation of carbocations because they include uncanceled contributions from more remote portions of the structure. Also shown in Table 1 are differences in pKR. These are multiplied by 1.364 to give free energies for easier comparison with HIAs. They correspond to ‘‘intrinsic’’ differences between tertiary, secondary, and primary carbocation centers (CHþ, CH2þ, and CH3þ ) and the corresponding values for the carbon bound to an OH functional group (C–OH, CH–OH, and CH2–OH). In principle, carbocation stabilities may be expressed relative to any functional group, but clearly the convenience and prevalence of measurements of pKR give a special place to the OH group. However, note that the DpKR and DHIA values are not the same. This is because there is a stabilizing geminal interaction between the OH group and methyl groups attached to the a-carbon atom.44–46 These interactions are cumulative so their net contribution depends on the number of methyl groups. They also depend on the nature of the functional group if this differs from OH. As a consequence, stabilities of carbocations defined in terms of affinity for a nucleophile depend on the choice of nucleophile as emphasized by Mayr and Ofial. The magnitudes of the interactions are by no means negligible, particularly between oxygen and another electronegative atom (usually O or N). Nevertheless they are well understood and easily estimated, especially for the OH group,47 which provides the most convenient affinity (pKR) scale. As indicated above, pKR values are readily converted to an HIA scale, which provides a convenient reference for comparisons between scales as well as a better approximation to cation stabilities. However, note that even for HIAs, if cations differ significantly in substitution at their charge center, there may be uncanceled geminal interactions in the reactant hydrocarbon, for example, between methyl groups when comparing secondary and tertiary cations: this will be evident from inspection of the relevant group contributions. Of course, the ‘‘intrinsic’’ stabilities, and the evidence for localization of the influence of carbocation centers, apply only to aliphatic ions. Phenyl or vinyl substitutents lead to extended delocalization of a positive charge. More generally, however, cancellations of ‘‘group’’ contributions between reactants and
28
R. MORE O’FERRALL
products in measurements of pKR or HIAs are subsumed into analyses in terms of substituent effects. This extended discussion brings us then to the conventional conclusion that stabilities of carbocations considered in the context of comparisons of equilibrium constants, benefit from substantial cancellation of effects of noninteracting functional and substituent groups between pairs of reactants and products for structures far removed from those of simple alkyl cations.33,48
EQUILIBRIUM MEASUREMENTS OF pKR
Turning to experimental measurements, the majority of equilibrium constants measured for carbocation formation refer to ionization of alcohols or alkenes in acidic aqueous solution, and correspond to pKR or pKa. Considering the instability of most carbocations it is hardly surprising that only unusually stable ions such as the tropylium ion 149 or derivatives of the flavylium ion 250,51 are susceptible to pK measurements in the pH range. +
CH2 +
O
Me
Ph
+
Me
+
+ +
1
2
3
4.75
3.65
–1.70
4 Me
5 Me
–16.3
–11.9
6
~ –7.4
A wider range of structures can be accessed through measurements in strong acid solutions.52–55 Such solutions have the characteristic that pK values vary strongly with acid concentration. This is because H3Oþ has a uniquely high solvation energy and the depletion of water molecules at high acid concentrations leads to increasing protonation of a base (or ionization of an alcohol) if its conjugate acid (or carbocation) is less strongly solvated than H3Oþ. This is illustrated in Equation (12), in which the solvated proton is represented as H9 O 4þ . H9 O4þ þB ¼ BHþ þ 4H2 O
ð12Þ
What is required is a value of pK extrapolated to water pKH2 O . Fortunately, the dependences of the relevant equilibrium constants on the composition of the acidic medium are well described by free energy relationships. This means that an unknown pKa (or pKR) can be obtained from measurements in concentrated acidic solutions by plotting values against known pKas for the protonation of a reference base.52,53 In practice, medium acidity parameters, Xo ¼ pKa pKaH2 O , are conveniently defined for a family of structurally
STABILITIES AND REACTIVITIES OF CARBOCATIONS
29
related bases with a large enough range of basicities to span measurements from dilute to concentrated solutions of strong acids. Such a family is provided by primary anilines substituted with nitro and other electron-withdrawing groups. Historically, there has been an uncomfortable period of evolution of the free energy treatment of measurements of pK’s in strongly acidic media from their original formulation as acidity functions. In the context of acidity functions, a pKa was treated as fixed at its value in water, and ‘‘apparent’’ variations in equilibrium constants were assigned to changes in activity coefficient.56,57 It is now well established that plots of pKa against Xo are impressively linear and correspond to the relationship represented by Equation (13), in which m* is the slope of the plot and the pKa in water is the intercept. pKa ¼ m Xo þ pKaH2 O
ð13Þ
The value of m* reflects medium effects on the acid dissociation constant under study, as represented in Equation (14). BHþ þ H2 O ¼ B þ H3 Oþ
ð14Þ
Thus in the case that BHþ is H3Oþ, Equation (14) becomes an ‘‘identity’’ reaction, for which there is no medium effect, and m* = 0. On the other hand, if BHþ is a protonated aniline, m* = 1. These values provide fixed points on a scale of solvation energy changes associated with proton transfer between H3Oþ and the protonated base under study. Our interest in this chapter is in carbocations. In general, these are poorly solvated unless there is an OH or NH group bound to the charge center, and typically m* falls in the range 1.5–2.0. Their equilibria are accessible as pKas for protonation of carbon–carbon double bonds,58–60 or pKR values.61–64 Strictly speaking, free energy treatments of medium acidity apply to pKa rather than pKR. The relationship between these equilibria is shown for the hydration and protonation of styrene in the thermodynamic cycle of Scheme 1 and Equation (15). Thus pKR corresponds to pKa þ pKH2 O where pKH2 O is the equilibrium constant for the hydration reaction. If pKa increases with acidity +
CH CH3 + H2O pK R
pK a
pK H2O H+ + H2O +
CH=CH2
CHCH3 + H+ OH
Scheme 1
30
R. MORE O’FERRALL
in proportion to Xo, the dependence of pKR on Xo will be modified by that of pKH2 O . In practice, KH2 O is likely to increase with increasing acidity because of the premium placed on the availability of solvating water at high acid concentrations. If the variation is not too great, as suggested by data for p-methoxystyrene,65 plots of pKR against Xo should still be close to linear and extrapolate to satisfactory values of pKR in water. KH2 O ¼
KR ½ROH ¼ Ka ½alkene½H2 O
ð15Þ
In practice, extrapolations of pKR in water have usually used the older acidity function based method, for example, for trityl,61,62 benzhydryl,63 or cyclopropenyl (6) cations.66,67 These older data include studies of protonation of aromatic molecules, such as pKa = 1.70 for the azulenium ion 3,59 and Kresge’s extensive measurements of the protonation of hydroxy- and methoxy-substituted benzenes.68 Some of these data have been replotted as pKR or pKa against Xo with only minor changes in values.25,52 However, for more unstable carbocations such as 2,4,6-trimethylbenzyl, there is a long extrapolation from concentrated acid solutions to water and the discrepancy 2O ¼ 17:5,61 is greater; use of an acidity function in this case gives pKH R * compared with 16.3 (and m = 1.8) based on Xo. Indeed because of limitations to the acidity of concentrated solutions of perchloric or sulfuric acid pK’s of more weakly nucleophilic carbocations are not accessible from equilibrium measurements in these media. Care also needs to be taken with the interpretation of UV–visible spectra in concentrated acid solutions. Richard and Amyes have shown that H2 O ¼ 16:6 for the 9-methylfluorenyl cation involves an incorrect assignpK R ment of spectra and that a value based on azide clock measurements (see below) is 11.9.69 In addition to carbocations, extensive measurements of pKas of oxygen and nitrogen protonated bases have been undertaken, including pKas of protonated ketones.65,74 As described below, these lead indirectly to pKR values for a-hydroxycarbocations if the equilibrium constants for hydration of the ketones are known.
KINETIC METHODS FOR DETERMINING pKR
More recent measurements related to carbocation stabilities in strongly acidic media have involved rates of reaction rather than equilibria.52,54,72–75 Application of the Xo function to the correlation of reaction rates as well as equilibria mirrors the use of structure-based free energy relationships. Of interest is the access this gives to rate constants for (a) protonation of weakly basic alkenes and (b) acid-catalyzed ionization of alcohols to relatively unstable
STABILITIES AND REACTIVITIES OF CARBOCATIONS
31
carbocations.73–75 These are kinetic counterparts of equilibrium measurements of pKa and pKR, and allow rate constants of intrinsically slow reactions to be extrapolated to aqueous solution. They are particularly important for the determination of highly negative values of pKa or pKR through combination of the measured values with rate constants for the reverse reactions of the carbocations with water acting as a base or nucleophile. Plots of log k against Xo are consistently linear, facilitating extrapolation of rate constants as small as 1014.72 Combination with the maximum rate constant for reaction of a carbocation with aqueous solvent, which is controlled by the rotational constant for relaxation of water of 1011 s1,24,76 yields a pK of 25, significantly higher than the maximum (negative) value possible from equilibrium studies. The application of kinetic methods to determining pKa and pKR for carbocations, by combining rate constants for their formation from an alcohol or alkene with a rate constant for the reverse reaction of the carbocation with water, has provided the most important development in measurements of these equilibrium constants in recent years. The use of laser flash photolysis to generate carbocations under conditions that rates of their reactions can be monitored by rapid recording of their absorbance in the UV or visible region represents a milestone in studies of carbocations.20,77 Particularly important in this development has been a collaboration between Steenken and McClelland.19,78–84 Their work, and some of the varied photochemistry associated with it, which led to the generation not only of carbocations but of radicals, radical cations, and carbenes, has been reviewed by McClelland.3,4 Detection methods have included conductivity as well as UV–visible spectrophotometry, and the carbocations have been generated by radiolysis79,80 as well as photolysis. These studies ushered in the modern era of stability studies in carbocation chemistry which has extended over the past 20 years. Diffusion-controlled trapping of carbocations: benzylic cations A ‘‘modern era’’ of stability studies can be extended to more than 30 years by taking as its beginning the application of ‘‘clock’’ methods to the determination of rate constants for direct reactions of carbocations with water or other nucleophiles or bases. Young and Jencks used bisulfite ions to trap acetalderived alkoxycarbocations, and assigned equilibrium constants for reaction of the cations with methanol by measuring product ratios for trapping by bisulfite ion. It was assumed that reaction of the bisulfite was diffusion controlled with a rate constant 5109 M1 s1 and that the rate constants for reaction of water and methanol were the same.21 Subsequently, Jencks and Richard used trapping by azide ion to measure pKR values of a-phenethyl cations in 50:50 (v/v) trifluoroethanol (TFE)–H2O mixtures and presented strong arguments for the efficacy of azide ions as a diffusion trap.22 Their conclusions were endorsed by McClelland who measured directly rate constants for reaction of benzhydryl and trityl cations with azide ions and
32
R. MORE O’FERRALL
showed that limiting rate constants were close to 5109 M1 s1.81 Similar measurement were made for a-substituted and unsubstituted p-methoxybenzyl cations.82 It was concluded that the reaction of azide ions with carbocations is diffusion controlled provided that kH2 O , the rate constant for reaction of the carbocation with water, is >105 s1 or pKR is <–5 (cf Fig. 7 on p. 91). Other nucleophiles achieve a diffusion limit only with more reactive cations. Sulfur anions are exceptional in approaching azide ions in efficiency as nucleophilic traps. Flash photolytic generation of carbocations has been achieved through photosolvolysis reactions involving a number of leaving groups. The effectiveness of the leaving group is important in determining competition between formation of carbocations and radicals and does not always correlate with efficiency in thermal reactions. Thus 4-cyanophenoxy is a good leaving group partly because it has an absorption maximum close to the wavelength (248 nm) of the photolyzing laser.17 Carbocations may also be formed from protonation of excited states of double bonds, from photochemically generated carbenes or by fragmentation of radical cations.4 The flash photolytic and ‘‘azide-clock’’ methods are complementary. Trapping a carbocation with azide ion may be applicable where a photolytic method for generating the carbocation is not available. It is a simpler method which can be used by laboratories not equipped for photolysis measurements and depends only on the availability of high-performance liquid chromatography (HPLC) equipment. Even when a sample of azido product is not available for comparison with the chromatogram of trapped products its peak can be identified by (a) its retention time relative to the alcohol, (b) its growth at a rate equal to the disappearance of reactant or appearance of a known product, and (c) the dependence of its intensity on the concentration of azide ion used for trapping.22 Photolytic generation of carbocations and direct measurement of their rates of reaction has been implemented in a limited number of laboratories. This lends special importance to the wide-ranging and thorough investigations carried out by McClelland and Steenken, including an extended plot of logs of rate constants for reaction of azide ions against log kH2 O for trityl and benzhydryl cations.77 This plot is reproduced in a review article by Mayr and Ofial30 and the same data is shown as plots of log k against pKR in Fig. 7 below (p. 91). Carbocation-forming reactions Surprisingly, the kinetic measurements now available for the nucleophilic trapping of carbocations with water are not always matched by measurements of rate constants for formation of the carbocation from the corresponding alcohol required to evaluate the equilibrium constant KR. Although carbocations are reactive intermediates in the acid-catalyzed dehydration of alcohols to form alkenes,85,86 the equilibrium in this reaction usually favors the alcohol and the carbocation forming step is not rate-determining. Rate constants may
STABILITIES AND REACTIVITIES OF CARBOCATIONS
33
then have to be determined from racemization of a chiral alcohol73 or isotope exchange with 18O-labeled water.78 These methods are not always applicable or convenient. A more general method used by Richard and Jencks utilizes HPLC analysis of carbocation formation in alcohol–water mixtures.22 As shown in Scheme 2 for an a-aryl ethyl cation, formation of the ether product from reaction of the carbocation with the alcohol depends on the rate constant for carbocation formation kH and the partition ratio between product formation and the back reaction to form the alcohol kROH =kH2 O . This ratio may be determined from the ratio of products formed from reaction of the carbocation generated from a suitable solvolytic precursor such as an alkyl halide. Richard has used 50:50 TFE–H2O for measurements of kH by this method and has reported values of pKR determined in this solvent mixture. The solvent mixture has the slight disadvantage that other measurements refer to water and comparisons suggest that the values in water are more negative by amounts of up to 1 log unit depending on the structure of the cation.69,73,87 Richard used an initial rate method to derive kH, but kH can also be obtained by combining the rate constant for approach to equilibrium and the equilibrium ratio of alcohol to ether.88 Richard and Jencks combined the above method with use of the azide clock to determine values of pKR for a-phenethyl carbocations bearing electron-donating substituents in the benzene ring and for the cumyl cation for a wider range of substituents.22,89 They inferred values for the parent
kROH [ROH] kH[H+] ArCH(CH3)+ OH k H2O [H2O]
ArCH(CH3)
k obs
OR
ArCH(CH3)
OH
ArCH(CH3)
OR
kH[H+]
=
(1 + k H2O [H2O]/k ROH[ROH]) H2O
ArCH(CH3)
Cl
ArCH(CH3)+ + Cl – ROH
kH
2O
kROH
Scheme 2
ArCH(CH3)
=
[ArCH(CH3)
OH]/[ArCH(CH3)
[H2O]/[ROH]
OR]
34
R. MORE O’FERRALL CH+CH3
X
X=
pKR TFE H2O pKR H2O
(estimated53)
MeO
Me
H
–8.6
–12.6
–15.4
–8.9
–12.8
–15.7
Carbocation
Ph3C+
Ph2CH+
PhCH2+
PhC+Me2
pK R (H2O)
–6.93
(–12.5)
(–21)
(–12.5)
Scheme 3
a-phenethyl cation and derivatives with electron-withdrawing substituents from a Yukawa–Tsuno correlation of substituent effects.22 Representative measurements are shown in Scheme 3 for 50% TFE–H2O and for estimates of corresponding values in water.73 Shown for comparison are pKR values for trityl, benzhydryl, and benzyl carbocations. For the trityl cation pKR was measured by McClelland and Steenken by combining a rate constant kH2 O measured following flash photolytic generation of the carbocation and kH from acid-catalyzed 18O exchange.78 For the benzhydryl and benzyl cations, kH2 O was measured by Amyes and Richard inTFE–H2O mixtures using the azide clock.69 For the benzhydryl cation, kH was determined by the method summarized in Scheme 2 and gave pKR = –11.7 in TFE–H2O. This value is corrected by 0.8 log units below to give a value of 12.5 in H2O (shown in brackets to indicate that this implies an approximation). For the benzyl cation, no value of kH has been determined, but an upper limit of 21 for pKR was established by Amyes and Richard (also shown in brackets), and it has been suggested that this must be close to the correct value in water.26 These values have been discussed in some detail to indicate that care is required to take account of the differences in solvents for measurements. They illustrate, nevertheless that a good framework of stabilities of benzylrelated carbocations exists. Other (oxygen-substituted) benzylic cations for which pKR measurements have been reported are discussed below (p. 57–63). Cations structurally related to benzhydryl are anthracenyl (7)75,87 and fluorenyl (8).69 There has been some dispute as to whether or not the fivemembered ring of the fluorenyl cation is antiaromatic. Clearly the antiaromatic character is less than for the indenyl or cyclopentadienyl cations, but current opinion favors antiaromaticity also for the fluorenyl cation.90–92 This is supported by the large difference in pKR from the anthracenyl cation, (although an additional reason for this difference will be noted later in the chapter, p. 61). Again, the brackets indicate ‘‘correction’’ of a measurement from TFE–H2O to water.
STABILITIES AND REACTIVITIES OF CARBOCATIONS
+ 7 pK R
–6.0
35
+ 8 (–15.7)
Solvent relaxation, hydration equilibria, and the t-butyl cation Recognition that the rotational relaxation constant of water (1011 s1)24,76 provides a limit to values of kH2 O for reaction of sufficiently reactive carbocations offers an important means of establishing this rate constant. It has been invoked by Richard to evaluate equilibrium constants for protonation by water of highly unstable carbanions23,24 and for deriving a value of pKR for the t-butyl cation.93 Evidence that kH2 O has indeed reached its limiting value includes minimal trapping by azide ions and correlations of kH2 O with pKR which approach this limit for more stable cations (see below, p. 43). For the tbutyl cation, Richard has also pointed to formation of a relatively large amount of alkene compared with that from more stable cations. This is consistent with the rate constant reaching a limiting value for nucleophilic attack on the cation, but not for its reaction with water as a base (for which k = 8.0108 s1).86 The rate constant kH has been measured from the rate of 18 O exchange94 and combination with kH2 O ¼ 1011 s 1 yields pKR = –16.4. In so far as the limit of solvent relaxation can be expected to apply to cations less stable than t-butyl, the task of assigning stabilities in such cases might seem straightforward. However, a difficulty now arises with the measurement of kH. For secondary alkyl or simple benzylic carbocations lacking electron-donating substitutents, it is possible that kH will represent SN2 substitution by water rather than carbocation formation, especially as the alcohol precursors of these cations are less well protected from nucleophilic attack by steric hindrance than t-butyl alcohol. It can be argued that if secondary alkyl halides react by an SN1 mechanism the same should be true of a substrate with a leaving group as good as a protonated alcohol. However, despite extensive study,95 it remains unclear whether 18O exchange for 2-butanol, which has a half-life of 25 h in 0.55 M HClO4 at 100C,96 involves a carbocation intermediate. For such unstable carbocations, an alternative approach to pKR can be developed, by recognizing the relationship that exists between pKR and pKa implied in Equation (15) (p. 30). For carbocations with b-hydrogen atoms, loss of a proton normally yields an alkene. Then, as discussed by Richard, pKR and pKa form two arms of a thermodynamic cycle, of which the third is the equilibrium constant for hydration of the alkene, pKH2 O , as already indicated in Scheme 1. The relationship between these equilibrium constants is shown for the t-butyl cation in Scheme 4. In the scheme the equilibria are
36
R. MORE O’FERRALL (CH3)3C+ + H2O –16.4
–12.5
H2O + H+ + (CH3)2C = CH2
–3.9
(CH3)3C OH + H+
Scheme 4
conveniently represented by single arrows to indicate the direction of reaction and thus signs of the quantities in the implied relationship, pKR ¼ pKa þpKH2 O . For isobutene, the equilibrium constant for hydration has been measured as 9.1103, corresponding to pKH2 O ¼ 3:94.86 It follows that the pKa for the t-butyl cation is 12.5. In so far as values of pKH2 O for the hydration of alkenes are known or can be estimated,47 values of pKR can be derived by combining rate constants for protonation of alkenes with the reverse deprotonation reactions of the carbocations. The protonation reactions seem much less likely to be concerted with attack of water on the alkene than the corresponding substitutions. Indeed arguments have been presented that even protonation of ethylene in strongly acidic media involves the intermediacy of the ethyl carbocation.97,98 The situation for the reverse deprotonation reaction is indicated by the derivation of a rate constant 8.0108 s1 for deprotonation of the t-butyl cation75 by combining Ka with the measured rate constant for the hydration of butene,86 for which protonation of the alkene is rate-determining. This rate constant is only 100-fold less than the relaxation limit for water, which is expected to apply to reactions of water as a base as well as a nucleophile. In principle, a rate constant for deprotonation of the carbocation might be measured from the ratio of alkene to alcohol formed from solvolysis of a secondary alkyl chloride, or other substrate with a good enough leaving group to yield the carbocation without competing SN2 substitution. The ratio of alkene to alcohol formed should correspond to a rate constant ratio to which the rate constant for forming the alcohol can be assigned as 1011 s1 and acts as a ‘‘clock’’ similar to diffusion-based clocks. However, in so far as reaction of the carbocation is likely to occur within an ion pair, the yield of alkene may be enhanced by the leaving group acting as proton acceptor and also by protecting one face of the cation from nucleophilic attack.99 The estimated rate constant for loss of the proton would then represent an upper limit compared with reaction in a fully aqueous environment. In practice, it is also possible to take advantage of the closeness of these rate constants to their relaxation limit and interpolate/extrapolate values from a correlation between deprotonation rate constants and pKas. The rate constants for such a correlation come from measurements for secondary or
STABILITIES AND REACTIVITIES OF CARBOCATIONS
37
tertiary benzylic carbocations (Scheme 3) for which pKR has been determined and pKH2 O has been measured or can be estimated.5,25,73,93 Before attempting to derive values for primary and secondary alkyl cations on the basis of such a correlation, however, it is convenient to consider application of the correlation to measurements of pKa and their combination with pKH2 O to derive values of pKR for arenonium ions.
ARENONIUM IONS
Evaluation of pKR from measurements of rate and equilibrium constants for the protonation of carbon–carbon double bonds of alkenes suggests the possibility of a similar approach for aromatic double bonds. Protonated aromatic molecules are the parent structures of the arenonium ion intermediates of electrophilic aromatic substitution. For these cations the equilibrium constant KR refers to equilibria with the corresponding aromatic hydrates, as is illustrated in Scheme 5 for the benzenonium ion (cyclohexadienyl cation) 9 for which the hydrate is cyclohexadienol 10. Cyclohexadienol was prepared by Rickborn in 1970 from reaction of the epoxide of 1,4-cyclohexadiene with methyl lithium.100 A hydrate of naphthalene, 1-hydroxy-1,2-dihydro-naphthalene was prepared by Bamberger in 1895 by allylic bromination of O-acylated tetralol (1-hydroxy-1,2,3,4tetrahydronaphthalene) followed by reaction with base.101 Hydrates of naphthalene and other polycylic aromatics are also available from oxidative fermentation of dihydroaromatic molecules, which occurs particularly efficiently with a mutant strain (UV4) of Pseudomonas putida.102,103 The hydrates are alcohols and they undergo acid-catalyzed dehydration to form the aromatic molecule by the same mechanism as other alcohols, except that the thermodynamic driving force provided by the aromatic product makes deprotonation of the carbocation (arenonium ion) a fast reaction, so that in contrast to simple alcohols, formation of the carbocation is rate-determining (Scheme 6).104,105 OH
+
+ H+
+ H2O 10
9
Scheme 5 OH2+
OH + H
Scheme 6
+
Slow
+ + H2O
Fast
+ H3O+
38
R. MORE O’FERRALL +
kA
+ H3O+
+ H2O kp
Scheme 7
In principle, a value of Ka for the benzenonium ion may be obtained from the ratio of rate constants for protonation of benzene, kA, and proton loss from the ion, kp, as shown in Scheme 7. A value of kA is available from measurements of hydrogen isotope exchange (kx) corrected for primary and secondary isotope effects. This is illustrated in Scheme 8 for the detritiation of tritiated benzene. In the lower part of the scheme, the reacting isotope of the benzenonium ion intermediate (9-t) is indicated as a superscript on the rate constant kp and a secondary isotope effect is neglected. Rate constants for deuterium or tritium exchange of benzene, naphthalene, and other aromatic molecules have been measured in concentrated solutions of sulfuric or perchloric acid. Conveniently, Cox has extrapolated values to aqueous solution from plots of log kx against Xo and corrected them for 72 T isotope effects (e.g., kH p =kp ) to yield kA. For benzene, it has not been possible to measure directly the rate constant kp for deprotonation of the benzenonium ion in order to complete the determination of Ka (= kp/ka). However, this has been possible for 1-protonated naphthalene,106 9-protonated phenanthrene,25 9-protonated anthracene, and 2-protonated benzofuran.75 In the case of the naphthalene, Thibblin and Pirinccioglu showed that the naphthalene hydrate is sufficiently reactive to form the naphthalenonium ion in aqueous azide buffers (pH 4–5).106 Formation of this ion leads to competition between loss of a proton and trapping by azide ion to form the 2-azido-1,2-dihydronaphthalene. From the trapping ratio kp is determined as 1.61010 s1 by the usual ‘‘clock’’ method. The hydrates of phenanthrene (13), anthracene, and benzofuran are not sufficiently reactive to form carbocations at the mild pH of azide buffers. However, the cation may be generated by solvolysis of their acetate or chloroacetate esters. Trapping of the cation by azide ions then occurs in the normal way.25,75 Moreover, the solvolytically generated cations react in these cases not only through loss of a proton to form the aromatic product but by nucleophilic T
T
H +
kA + H3O+
k pT
+ H2TO+
k pH 9-t
kx = kA/(1 + kpH / kpT)
Scheme 8
kA = kx(1 + kpH / kpT)
STABILITIES AND REACTIVITIES OF CARBOCATIONS
39
trapping with water to regenerate the hydrate, which in the absence of acid does not undergo dehydration. Competing formation of the hydrate reflects the lower aromaticity and reduced thermodynamic driving force for formation of the aromatic product compared with benzene or naphthalene. These reactions are illustrated for solvolysis of the dichloroacetate of 9-hydroxy-9,10-dihydrophenanthrene (9,10-phenanthrene hydrate) 11 in Scheme 9, for which the products of deprotonation and azide trapping of the carbocation 12 are phenanthrene (phen) 13 and azido dihydrophenanthrene 15, respectively. All three products in Scheme 9 can be monitored by HPLC. If the product ratio of azide (15) to phenanthrene, [RN3]/[phen], is plotted against the concentration of the azide ion trap, the slope of the plot corresponds to kAz/kp. Assigning kAz the value of 5109 M1 s1 for diffusion leads to kp = 3.71010 s1. A value of kA (the rate constant for protonation of phenanthrene at the 9-position) has not been determined directly in aqueous solution but can be found by combining a partial rate factor for exchange of tritiumlabeled phenanthrene in trifluoroacetic acid with a rate constant for protonation of benzene and assuming that the ratios of rate constants are unaffected by the change in solvent. This gives kA = 5.0 1011 M1 s1. Combining it with kp gives pKa = –log(kp/kA) = –20.9.25 The value of kp obtained in this way for the phenanthreneonium ion is not far from the limit set by the rotational relaxation of water. For such fast reactions, Richard has pointed out that azide trapping could be influenced by preassociation.6 Preassociation has been well characterized in a number of nucleophilic reactions of reactive carbocations with water6 but its impact on deprotonation has not been fully clarified.5,6 In so far as preassociation
+ H+ 13 Phen
kp
O OCCHCl2
+ Cl2CHCOO–
11
12
=
kp k H2O
[ROH]
kH
2O
14 ROH
k Az[N3–]
[Phen] N3
15 RN3
Scheme 9
[Phen] OH
+
[RN3]
=
kp k N3[N3–]
40
R. MORE O’FERRALL
increases the rate of the reaction with azide ion, the inferred value of kp is underestimated and the pKa may be a little less negative than that assigned. However, kp is so close to its limit that the discrepancy must be small. It might seem surprising that a nucleophilic reaction with water competes with proton loss from the phenanthrenonium ion considering the stability of the aromatic product. As discussed by Richard24 (and considered further below) this reflects a higher intrinsic reactivity of the cations toward nucleophilic attack which compensates for the thermodynamic disadvantage of this reaction. For the phenanthrenonium ion the ratio of for rate constants deprotonation and nucleophilic attack on the cation kp =kH2 O is 25;25 for the 1-protonated naphthalene it is 1600,106 for 9-protonated anthracene, 1.8.75 In all these cases it is possible to determine KR directly by combining kH2 O with kH, the rate constant for carbocation formation. The latter constant is readily determined spectrophotometrically by monitoring acid-catalyzed dehydration of the aromatic hydrate to the corresponding aromatic product. In principle, as we have seen, when the dehydration product is aromatic, carbocation formation is the rate-determining step of the reaction. However, the finite values of kp =kH2 O for the phenanthrenonium ion and other arenonium ions leading to moderately stable aromatic products imply a small correction for reversibility of this reaction step. For phenanthrene hydrate the derived value of pKR is 11.6. This is comparable to values for the benzhydryl (–12.5) or p-methylphenethyl (–12.8) cations.22,69,73 The evaluation of pKR as well as pKa allows derivation of pKH2 O ¼ pKR pKa ¼ 9:3. This equilibrium constant offers a measure of the stability of the 9,10-double bond of phenanthrene and thus the aromaticity of its central benzene ring. Comparison with the double bond of 2-butene, for which pKH2 O ¼ 3:94,86 indicates a 1013-fold greater stability, for the aromatic double bond. It should be noted that the value of pKH2 O does not depend on azide trapping. In the difference between pKR and pKa the rate constant kAz cancels out and KH2 O ¼ kA kH2 O =kH kp . The equilibrium constants Ka, KR, and KH2 O are conveniently summarized in Scheme 10 in the form of a cycle similar to that shown above for the a-phenethyl and t-butyl cations (Schemes 1 and 4). It is worth noting that pKH2 O measures the stability of the double bond relative to the alcohol (hydrate). If pKR was converted to HIA, pKH2 O in the cycle would be replaced by the energy of hydrogenation. The latter provides the conventional measure of double bond stability, save that here free energy in aqueous solution is measured rather than the more usual heat of hydrogenation in the gas phase. We will return to a comparison of values of these equilibrium constants for different carbocations, but first pursue pKa and pKR for the benzenonium ion. In azide buffers this cation reveals no trapping by azide ion. This poses the problems, how do we (a) find a value of kp to combine with kA to obtain pKa and (b) determine pKH2 O to derive pKR? We consider first pKH2 O and then kp.
STABILITIES AND REACTIVITIES OF CARBOCATIONS
41
+ H2O + pK R = –11.6
pK a = –20.9
OH pK H2O = 9.3 H2O + H+ +
+ H+
Scheme 10
Equilibrium constants for hydration As already indicated, a number of values of pKH2 O have been measured experimentally, including those just described. Many more can be evaluated from a combination of free energies of formation of alcohols and the relevant alkenes in aqueous solution [DGf (aq)].47 This is illustrated in Scheme 11 in which 1.364 corresponds to 2.303RT at 25C in kcal mol1 and DGf (aq) is abbreviated as DGf . In cases where DGf (aq) for the alcohol is not known, usually it can be found from DGf (aq) for the corresponding hydrocarbon and an estimate of the change in free energy of formation upon replacing H by OH. The value of the latter quantity (DGf (aq)ROH – DGf (aq)RH), designated DGOH, depends on the molecular environment of the OH group. Scheme 12 shows increments, DGOH, to be added to a reference value of DGOH = –39.5 kcal mol1, chosen for the replacement of H by OH in ethane to give ethanol, for a selection of other alcohols. For cyclohexadienol 10 for example the value of DGf (aq) may be estimated from the corresponding value for cyclohexadiene 39.5 (DGOH for EtOH) 1.2 (the increment DGOH for cyclohexen-3-ol), plus a correction of 1.0 kcal mol1 for the unfavorable inductive interaction between the OH group and the remote double bond of the dienol. In so far as DGf (aq) for benzene is known, pKH2 O for addition of water to benzene [Equation (16)] can now be estimated as 22.2.
Scheme 11
42
R. MORE O’FERRALL MeOH
EtOH
PrOH
t-BuOH
5.5
0
0.2
–4.9
OH
OH
–2.0
–1.2
OH
i-PrOH –2.9
–0.6
Scheme 12
OH
pK H2O = 22.2 + H2O
(16) 10
In the cases of naphthalene, phenanthrene, and anthracene similarly calculated values of pKH2 O are 14.2, 9.2, and 7.4 respectively.47 These values may be compared with experimental values of 13.7, 9.3, and 7.5, determined75 as described above for phenanthrene. The good agreement between calculation and experiment, and the systematic dependence of pKH2 O on the stabilization energy of the aromatic rings, lends credence to the value for benzene. It may be noted that the variation in increments shown in Scheme 12 represents differences in interaction energies between the OH group and the hydrocarbon fragment of the alcohol molecule. When pKR values are compared between different carbocations, they include the effect of the structural change upon the alcohol. Thus the difference in values for t-butyl and isopropyl cations underestimates the relative stabilities of the carbocations as measured by their HIAs by 1.5 log units (2.0/1.364). Rate–equilibrium correlations for the deprotonation of carbocations To complete the evaluation of pKa and pKR for protonated benzene, it is necessary to determine a rate constant kp for deprotonation. In so far as there is a substantially greater thermodynamic driving force for deprotonation of the benzenonium ion than for other ions leading to aromatic products, the rate constant must be greater than the values of 2.91010 s1 for the phenanthrenonium ion or 1.61010 for the naphthalenonium ion, and there can be little error in assigning it as 1011 s1. However, it is of interest to examine the variation in kp more rigorously based on a correlation of values of log kp and pKa which takes account of the limiting value of kp at highly negative values of pKa. This correlation is shown for a range of carbocation structures in Fig. 1, with the arenonium ions shown as filled circles. The correlation includes protonated mesitylene, studied by Marziano,107 and earlier measurements of the protonation of methoxy-substituted benzenes108 and azulenes.109 It also
STABILITIES AND REACTIVITIES OF CARBOCATIONS
43
14 12 10
log kp
8 6 4 2 0 –2 –25
–20
–15
–10 pKa
–5
0
5
Fig. 1 A plot of logs of rate constants for deprotonation of carbocations against pKa in aqueous solution at 25C.
includes secondary benzylic cations, including those in Scheme 3 (and Table 4 on p. 59 below), shown as open circles, and tertiary alkyl or benzylic cations shown as squares. The different groups of compounds in Fig. 1 show some dispersion and the correlation line is based on the arenonium ions only. The equation for the line drawn through the points comes from an analysis by Richard of protonation of carbanions which leads to Equation (18). This equation is based on the reaction shown as Equation (17), in which the rate constant for relaxation of the solvent is denoted kreorg. The structure R+H2O represents the carbocation with a solvent shell as initially formed from the alcohol, and H2O R+ represents the carbocation with a ‘relaxed’ solvation shell, which reacts with the loss of a proton. Solvent relaxation becomes rate determining when deprotonation of the carbocations is sufficiently fast. The rate constant ki is an ‘‘intrinsic’’ (microscopic) rate constant for deprotonation. This is unaffected by solvent relaxation, and except for very reactive cations (i.e., for which ki approaches kreorg) is equal to the experimentally measured rate constant kp [which is expressed in terms of ki and kreorg in Equation (18)]. It is assumed that the dependence of log ki upon pKa is linear. With kreorg = 1011 s1, a best fit to the filled circles in Fig. 1 to Equation (18) is obtained with log ki = –0.41pKa þ 1.51. kreorg
ki
Rþ H2 O Ð H2 O Rþ ! Arene kreorg
ð17Þ
44
kp ¼
R. MORE O’FERRALL
kreorg ki ki þkreorg
ð18Þ
It might seem surprising at first that a rate–equilibrium relationship covering such a wide range of reactivity should be assumed to be linear. Although the origin of such linearity is not fully understood it is commonly observed for free energy relationships and is discussed later in the chapter. Certainly, any curvature in Fig. 1 falls within the limits of scatter of the points over the large range of pKa values encompassed (25 log units). As the pKa becomes sufficiently negative, ki can be expected to reach its own vibrationally controlled limit but at a substantially larger value than 1011 s1. Values of kp and pKa for benzene may be obtained from Fig. 1 by substituting the rate constant for protonation of benzene by H3Oþ, kA =2.6 1015 M1 s1 (extrapolated to aqueous solution from kinetic measurements in concentrated solutions of strong acids),72 into the relationship Ka = kp/kA. Taking logs gives pKa = –log kp – 14.36, a relationship which can be plotted as the dashed straight line in Fig 1, which intercepts the correlation line to give pKa = –24.5 and kp = 91010 for protonated benzene. From this value of pKa, and pKH2 O ¼ 22:2, a value of pKR can be derived as pKa þpKH2 O ¼ 2:3.25 A similar analysis for 2-protonated naphthalene 16 complements Thibblin’s measurements106 for the 1-protonated isomer and gives kp = 6.51010 and pKa = –22.5. Table 2 summarizes pK measurements for the simplest protonated aromatic hydrocarbons. The columns to the right and left of the benzenonium ion correspond to benzoannelation of ions subject to protonation at the 2- and 4-positions of the benzene ring, respectively. In the parent ion the two positions correspond to resonance forms (one of which has been rotated through 120 in the table). The naphthalenonium ion 17 is shown as being formed from the 1,4-water adduct (hydrate) of naphthalene. It may also be formed from the isomeric ‘‘2,1’’ hydrate (1,2-dihydro-2-naphthol) with pKR = –6.7 and pKH2 O ¼ 13:7. Table 2 Values of pKH2 O , pKa, and pKR for arenonium ions +
+
7
pKH2 O pKa pKR
7.5 13.5 –6.0
17
16.9 –20.4 –3.5
+
9
22.2 –24.5 –2.3
+
+
+
16
12
14.5 –22.5 –8.0
9.3 –20.9 –11.6
STABILITIES AND REACTIVITIES OF CARBOCATIONS
45
From the tabulation it is evident that for aromatic molecules pKa and pKR provide very different measures of stability. From our earlier discussion (p. 23–28), it is clear that pKR provides the more appropriate measure of the stability of the carbocations and that pKa strongly reflects the stability of the aromatic molecule, which indeed is directly measured by pKH2 O . Thus the nearly invariant pKa for four of the cations arises from compensation between changes in the stability of the cation and of the aromatic molecule. It is noteworthy that as judged by pKR protonated benzene is a particularly stable carbocation. The value of 2.3 is obtained indirectly, as described above, but is consistent with pKR = –3.5 measured by McClelland for the phenylsubstituted dimethyl analog 18.110 A surprising observation is that benzoannelation is quite strongly destabilizing for the cations. We will return to the significance of this later in the chapter, as well as to the fact that the effect of benzoannelation on the pKas is opposite to that on pKR. The latter behavior implies that the unfavorable effect of benzoannelation on the stability of the reacting double bond of the aromatic molecules is greater than that on the stability of the carbocations.
Ph +
Me
Me
18
Cox’s extrapolation of rate constants for protonation of a number of ringsubstituted benzenes72 can be combined with the correlation of Fig. 1 to derive pKas in the same way as for benzene and naphthalene. The pKas include p-protonated bromobenzene 24.3, toluene, 20.5, and anisole 15.0. Cox noted the activating effect of bromine on hydrogen isotope exchange, which is partially concealed by a statistical factor of six which increases the basicity of benzene. In principle, the pKa for anisole might be considered the least well defined of the pKas as the inferred value of kp = 3.0108 is further removed from its limiting value. On the other hand, there is less uncertainty in the extrapolated value of kA than for the less basic aromatics. The only conjugate acid of a substituted benzene for which pKR can reasonably be estimated is the protonated toluene. A value of DGf (aq) for the corresponding hydrate is readily estimated from the likely effect of methyl substitution on the stability of 1,4-benzene hydrate,47 and this can be used to estimate pKH2 O as described above, while pKR is obtained from pKR = pKH2 O þ pKa. The resulting pK values are compared below with those for the corresponding methyl-substituted naphthalenium 19 and anthracenium 20 ions, for which reactions of the hydrates (or their methyl ethers) have been
46
R. MORE O’FERRALL
studied by Thibblin.111,112 For 1-methylnaphthalene, pKH2 O may be estimated in the same way as for toluene and a pKa may be obtained by combining azide clock measurements of kp with a value of kA derived from a partial rate factor in trifluoroacetic acid.75,113 For the 9-methyl-9-anthracenium ion, Zia and Thibblin’s measurements of rate constants from azide trapping and acidcatalyzed reaction of the hydrate yield pKR directly. Azide trapping also provides kp which when combined with a partial rate factor-based kA114 gives pKa and thence pKH2 O . The results listed below are generally consistent with expectations based on pK values for the parent ions, save that it is noticeable that, in contrast to the situation for the benzenonium and naphthalenonium ions, methyl substitution de-stabilizes the anthracenonium ion. This is plausibly attributed to interaction of the methyl group with the peri-hydrogen atoms of the flanking benzene rings. It is perhaps surprising at first that methyl substitution increases the equilibrium constants for hydration (cf. Table 2). This is at least partly due to a geminal stabilizing interaction (2–3 kcal mol1) between the methyl and OH group of the hydrate.
CH3
CH3
CH3
+
+
+
H
H
H
H 19
pKH2 O pKa pKR
21.6 –20.5 1.1
16.0 –17.0 –1.4
H
H 20
6.1 –12.7 –6.6
ALKYL CATIONS
Having introduced the correlation of Fig. 1, we may return to the stabilities of alkyl cations. Rate constants for the hydration of secondary and primary alkenes have been measured in concentrated solutions of aqueous sulfuric acid by Lucchini and Modena97 and by Tidwell and Kresge42 using proton nuclear magnetic resonance (NMR) or UV to monitor progress of the reactions. It is conceivable that the reactions involve a concerted addition of a proton and water molecule to the alkenyl double bonds. However, the very weak basicity of water under the conditions of reaction makes this unlikely, and the steep acidity dependences of the reactions (e.g., m* = –1.65) is
STABILITIES AND REACTIVITIES OF CARBOCATIONS
47
inconsistent with substantial localization of charge on an oxygen atom. Other arguments in favor of rate-determining protonation of the alkenes to form carbocations as discrete short-lived intermediates have been advanced over a number of years by Lucchini and Modena97 and by Tidwell.98,115 The rate constant for the protonation of ethylene, 8.51015 M1 s1, is even smaller than that for protonation of benzene, and there can be little doubt that deprotonation of the ethyl cation in the absence of high concentrations of acid is at or close to the solvent relaxation limit. Assigning this value gives pKa = –25.1 for the ethyl cation, and combining this pKa with pKH2 O ¼ 4:8 for hydration of ethylene gives pKR = –29.9. For 2-propene, the rate constant is considerably larger, 2.4 109 M1 s1, and a derivation of pKa depends on the assignment of kp using the correlation of Fig. 1. There is sufficient dispersion of points in Fig. 1 to suggest some ambiguity in this assignment. Thus the (four) points for protonation of a double bond with a terminal methylene group fall below the correlation line but show a steeper slope. Since the relevant pKa is close to the point at which the two correlations might coincide we derive the value as before from the measured kA = 2.4109 to obtain 17.9, after correction for the statistical effect of six equivalent hydrogens in the isopropyl cation. Combination with pKH2 O ¼ 4:23, then gives pKR = –22.1. The possible uncertainty in this value is indicated by deriving alternative values of pKa and pKR for the isopropyl cation starting with kA = 4.5109 M1 s1 for protonation of 2-butene (sic).42 Proceeding as before we deduce pKa = –16.8 for the 2-butyl cation forming 2-butene and thence pKa = –15.0 for formation of the 1-butene, based on the equilibrium constant for isomerization of the alkenes. Now the identity of the rate constants for protonation of 1-butene and 1-propene suggests that the pKas of the 2-butyl and 2-propyl cations are the same, barring statistical factors, and combination with values of pKH2 O gives pKR = –20.3 and 20.0 respectively. The value of pKR = –20.0 for the isopropyl cation is 2.1 log units more positive than the value derived from protonation of propene directly. In its favor, protonation of 2-butene occurs at a ‘‘secondary’’ rather than (as for 2-propene) a ‘‘primary’’ vinylic carbon atom, as is also true of formation of the cations correlated in Fig. 1. However, that correlation refers to benzylic rather than alkyl cations and there is no good reason to suppose their behavior is strictly comparable. The more negative pKR is preferred for two reasons. Firstly, as will be clear below, it is correlated better with the gas-phase stability of the isopropyl cation. Secondly, derivation of pKR = –16.5 for the cyclohexyl cation from the rate constant for protonation of cyclohexene98 gives a value which, for a secondary alkyl cation, seems too close to that of the t-butyl cation (pKR = –16.4), even though the difference is increased by 2.1 log units if allowance is made for the more favorable geminal interactions of an OH
48
R. MORE O’FERRALL
bond in a tertiary than a secondary alcohol (i.e., by replacing pKR by its HIA counterpart pKRH). These points have been pursued in detail for two reasons. The first is to indicate the level of uncertainty in deriving pKas when the rate of deprotonation falls significantly short of its relaxation limit and the structure-reactivity correlation for the alkene conjugate base of the cation is insufficiently defined. The second is that the identity of the rate constants for 2-propene and 2-butene still imply a difference of 0.3 log units between 2-propyl and 2-butyl cations. In so far as this difference corresponds with the small difference in geminal interaction of the OH groups, the implication is that as measured by their HIAs the two ions have the same stability (cf. discussion on p. 25). In conclusion, the preferred pKR for the 2-propyl cation is listed below with the more secure values for the t-butyl and ethyl cations.
pKRS
(CH3)3Cþ
(CH3)2CHþ
CH3 CH2þ
–16.4
–22.1
–29.9
VINYL CATIONS
Lucchini and Modena also measured rate constants for the hydration of acetylene and methyl acetylene.97 Accepting that the initial and rate-determining step of this reaction is formation of the corresponding vinyl cations, we may analyze the measured rate constants in the same way as for protonation of the alkenes. The rate constants for the two substrates are similar to those for ethylene and propene and lead to pKa values of 25.2 and 18.3.75 Values of pKR can now be derived by recognizing that hydration of acetylene and methylacetylene yield enols of acetaldehyde and acetone, respectively. Values of pKH2 O are accessible because free energies of formation in aqueous solution of the enols can be obtained from the keto–enol equilibrium constants and free energies of formation of the aldehyde and ketone.38,116 Combining these with those of the acetylenes yields values of pKH2 O and thence pKR. The cycle for acetylene, which includes the unsusbstituted vinyl cation, is shown in Scheme 13, from which it can be seen that pKR = –40.2. The pKR for the a-methyl vinyl cation is estimated as 31.7. H2O + H2C CH+ –40.2
–25.2 H2O + H+ + HC CH
Scheme 13
–15.0
H2C CH OH + H+
STABILITIES AND REACTIVITIES OF CARBOCATIONS
49
The value of pKR = –40.2 makes the vinyl cation the most unstable carbocation for which equilibrium measurements are available. It is remarkable that while the vinyl cation and benzenonium ion have similar pKas, their pKR values differ by 38 log units. This is an indication of the sensitivity of pKa to the stability of the conjugate base of the cation, and specifically to the very different energies of p-bonds in acetylene and benzene. Measurements by Okuyama indicate that while secondary (alkyl substituted) vinyl cations are viable intermediates in the solvolysis of vinylic precursors with sufficiently reactive leaving groups,117 the same is not true of primary vinyl cations even in solvents as highly ionizing and poorly nucleophilic as TFE and hexafluorisopropanol.118 Thus Lucchini and Modena’s access to the parent vinyl cation clearly depends on the high energy of the triple bond of their alkyne reactant. Calculations suggest that the most stable form of the vinyl cation is likely to be that in which the proton is coordinated to a p-bond of acetylene rather than forming a -bond with a terminal carbon atom.10,119,120 An extensive mechanistic chemistry of vinyl cations has been developed120 including studies of the rate and stereochemical course of reactions of cations generated by flash photolysis.84,121–124 Nevertheless, although stabilities of the cations have been measured and calculated in the gas phase120 and stabilities in solution have been assessed from rate constants for solovolysis based on the use of leaving groups as reactive as triflate and iodobenzene,117,118,125 the kinetic measurements do not at present provide access to thermodynamic data. This is partly because of the difficulty of measuring rate constants for the reverse of the reactions of vinyl cations with water or alcohols in competition with tautomerization or hydrolysis of the relevant enol or vinyl ether reactants.
THE METHYL CATION: A CORRELATION BETWEEN SOLUTION AND THE GAS PHASE
There exists a further potential source for assignment of stabilities of carbocations. That is to exploit the wider range of stabilities available in the gas phase than in solution through an appropriate correlation between the two. There have been a number of attempts at such correlations126–128 which in the past have been limited partly by the smaller number of measurements available in solution. For sufficiently homogeneous series of structures, correlations certainly exist. Richard and Mishima compared pKas for protonation of ring-substituted a-methylstyrenes in TFE–H2O mixtures and the gas phase and found the slope of a plot of solution against gas phase values to be 0.70.89 They compared this slope with that of 0.40 for the protonation of pyridines129 and ascribed the lower slope in that case to the importance of hydrogen bonding in solvating the pyridinium ions.127 Undoubtedly, more disparate structures lead to greater dispersion of points. Now that more solution values are available the structure
50
R. MORE O’FERRALL
dependence of these correlations would benefit from closer investigation. Such an analysis is beyond the scope of this review, but Keeffe and the author have explored the possibility of extrapolating a pKR for the methyl cation from a correlation of methyl substituent effects between gas phase and solution.26 Figure 2 shows plots of hydride ion affinities HIA in the gas phase against solution values for (a) ethyl, isopropyl, and t-butyl, (b) methoxymethyl, methoxyethyl, and methoxyisopropyl, and (c) benzyl, aphenyl ethyl, and cumyl cations. Also shown are the vinyl cation and methylvinyl cation. The gas-phase HIAs for the benzyl cations are based on heats of reaction, HIAs for the other cations are based on free energies. Despite deviations of the benzyl and vinyl cations from the other values, the satisfactory correlation of the alkyl and methoxyalkyl cations with slope 1.52 implies a consistent behavior within this limited structural family. The inverse of the slope of the plot is 0.67, which is close to the value for the protonation of the a-methylstyrenes. This level of agreement encourages a speculative extrapolation of pKR = –43 for the methyl cation based on the measured value of its HIA in the gas phase.
60
CH2 = CH+
ΔHIA gas phase
40
CH3CH2+
20
(CH3)2CH+ MeOCH2+ PhCH2+
0
–20
–40 –20
–10
0 10 ΔHIA aqueous solution
20
30
Fig. 2 Plot of hydride affinities (HIA) in the gas phase against values in aqueous solution at 25C. Filled circles, alkyl cations; open circles, methoxyalkyl cations; triangles, vinyl cations.
STABILITIES AND REACTIVITIES OF CARBOCATIONS
51
This concludes the discussion of the stabilities of carbocations with hydrocarbon-based structures and also of different methods for deriving equilibrium constants to express these stabilities. The remainder of the chapter will be concerned mainly with measurements of stabilities for oxygen-substituted and metal ion-coordinated carbocations. Consideration of carbocations as conjugate acids of carbenes and derivations of stabilities based on equilibria for the ionization of alkyl halides and azides will conclude the major part of the chapter and introduce a discussion of recent studies of reactivities.
OXYGEN-SUBSTITUTED CARBOCATIONS
Oxygen substitution has a radical effect on the stability of a carbocation, which is manifested in the chemistry of carbohydrates, benzopyran pigments, and the extensive acid-dependent reactions of carbonyl compounds. The greatest effects are from a-oxygen substituents but effects of substituents in the aromatic ring of benzylic carbocations are also large. As we shall see, there is a surprising influence of b-oxygen substituents upon the stabilities of arenonium ions. a-oxygen substituents For several a-alkoxy carbenium ions rate constants for reaction with water were determined by Jencks and Amyes from the partial reversibility and associated common ion rate depression of hydrolysis of the corresponding azidoacetals, as is illustrated in Scheme 14.130 Jencks and Amyes measurements gave ratios kAz =kH2 O for reactions of the carbocations with water and azide ions from which values of kH2 O could be derived in the usual way by assigning a diffusional rate constant, 5109 M1 s1, to kAz, save in the case of the methoxymethyl cation for which kH2 O was presumed to have achieved it relaxation limit (1011 s1). The reverse of the water trapping reaction is acid-catalyzed conversion of a hemiacetal to the carbocation. The rate constant for this reaction, kH, was assigned on the assumption that it was 0.57 times that for the corresponding ethylacetal or 0.8 times that for the methylacetal.130–132 Values of KR were then derived in the usual way as KR ¼ kH2 O =kH .132
R MeOCH N3
k1
+ MeOCH
k H2O
R RCHO + MeOH
MeOCH OH
k Az kobs =
Scheme 14
R + N3–
k1 ( 1 + k Az[N3–]/k H2O )
52
R. MORE O’FERRALL
For di- and trimethoxy carbocations, for which rate constants for reaction of the cations with water have been measured by McClelland and Steenken,4,133 rate constants for the back reactions of the hemiorthoester and hemiorthocarbonate were assigned in the same way as for the hemiacetals from the corresponding methyl or ethyl ethers.134–136 Estimates of pKR for representative methoxy and dimethoxy carbocations are shown in the first two rows of structures at the bottom of the page. The structures and pKR values shown summarize the influence on carbocation stability of (a) accumulating methoxy substitution, (b) the difference between methoxy and ethoxy substituents and between cyclic and acylic structures (with five-membered ring cyclic structures indicated as (CH2O)2C+R) and (c) the influence of methyl and phenyl substituents. From the first two rows, it is clear that a methoxy group has a very strong stabilizing effect on a carbocation and that this effect is attenuated as the stability of the carbocation increases. As pointed out by Kresge and McClelland, relative to methyl, a phenyl group stabilizes a cyclic but destabilizes an acyclic dialkoxy cation.4 This is plausibly attributed to steric hindrance to conjugation of the alkoxy oxygen atom. Of interest is a comparison of a-methoxy with a-hydroxy substituents. The a-hydroxy carbenium ions correspond to protonated ketones and their pKR values may be derived from a combination of a hydration equilibrium constant and a pKa for protonation of the ketone, as illustrated by the thermodynamic cycle based on acetophenone in Scheme 15.137,138 Corresponding data are available for benzaldehyde138,139 and acetone70,140,141 and lead to the values of MeOCHþ 2
(MeO)2CHþ
–15.9
–5.6 þ
(MeO)3Cþ
(EtO)2CHþ
–1.5 þ
–5.7
(MeO)2C Me (MeO)2C Ph (CH2O)2C Me (CH2O)2CþPh –1.3 þ
PhCH –O 14.7
þ
–3.0
PhCHOH –2.4
–2.0 þ
–1.0
PhCHþ 2
PhCHOMeþ
(–21)
–7.5
PhC(OH) OMeþ 3.0
OH+ H2O + Ph
C
1.31
–3.87 H2O + H+ + PhCOMe
Scheme 15
CH3
5.18
PhC(OH)2Me + H+
PhCðOHÞþ 2 7.4
STABILITIES AND REACTIVITIES OF CARBOCATIONS
53
pKR below the third row of structures on the previous page. Measurements are also available for methyl benzoate,138,142 for which the protonated ester and hydrate adduct are intermediates in acid-catalyzed ester hydrolysis. Extrapolating from the ester, a value may also be estimated for protonated benzoic acid, for which a pKa143 is combined with a value of DGf (aq) for PhC(OH)3 derived from the corresponding value for PhC(OH)2OMe142 by Guthrie’s method.144 Comparisons of structurally related hydroxy- and methoxy-substituted cations show that hydroxy is more stabilizing by between 4 and 5 log units. This difference was recognized 20 years ago by Toullec who compared pKas for protonation of the enol of acetophenone and its methyl ether145 (–4.6 and 1.3, respectively) based on a cycle similar to that of Scheme 15, but with the enol replacing the hydrate, and a further cycle relating the enol ether to a corresponding dimethyl acetal and methoxycarbocation.146 Toullec concluded, understandably but incorrectly, that there was an error in the pKa of the ketone (over which there had been controversy at the time).147,148 In a related study, Amyes and Jencks noted a difference of 105-fold in reactivity in the nucleophilic reaction with water of protonated and O-methylated acetone and concluded that the protonated acetone lacked a full covalent bond to oxygen.130 It seems clear that the explanation of these differences lies in the advantage in solvation energy conferred by an OH group attached to a charge center. The importance of this solvation is indicated by the low m* values for the protonation of most ketones52,71,138 and the lower m* value and greater basicity of carboxylic acids than their esters, for example, pKa = –4.43 and m* = 0.51 for benzoic acid143 compared with pKa = –7.05 and m* = 0.82 for methyl benzoate.138 Other examples of the superior solvation of OH relative to MeO groups conjugated with a positive charge are mentioned below (p. 56) The value of pKR = 7.4 for protonated benzoic acid (PhCðOHÞ2þ on the previous page) is of interest in that it allows comparison with the corresponding value of pKR = 8.8 for the isoelectronic phenylboronic acid PhB(OH)2149. Considering the presence of the positive charge on the carbon acid and absence of a charge on the boronic acid, the difference in Lewis acidities is remarkably small. Presumably, this reflects the greater stability of boron–oxygen than carbon–oxygen bonds. The last row of structures on the previous page includes the effect of an a–O substituent on the stability of a benzyl cation. This comes from considering an aldehyde or ketone as an O-substituted carbocation. A pKR is then obtained from the equilibrium constant for addition of hydroxide ion to the ketone to form the conjugate base of its hydrate. This can be derived from the cycle including the hydrate shown for benzaldehyde in Scheme 16. The cycle includes the equilibrium constant for hydration of the carbonyl group pKhyd and a pKa for ionization of the hydrate.139 In practice, KR is obtained by measuring the equilibrium constant for addition of hydroxide ion Kc150 [Equation (2) on p. 21] and the relationship KR = KcKw. As expected, O is even more
54
R. MORE O’FERRALL H2O + PhCHO pK R = 14.74
pK hyd = 2.10 12.64 PhCH(OH)2
PhCH(OH)O– + H+
Scheme 16
stabilizing than OH. In general, the relative effects of substituents across the structures shown on p. 52 present a consistent pattern. Acid-catalyzed reactions of aldehydes with nucleophiles offer a further method for determining pKR. This is illustrated by the reaction of 9formylfluorene (FlCHCHO) with hydroxylamine to form the oxime shown in Scheme 17. The kinetic dependence of the reaction on concentrations of acid and hydroxylamine suggests that this reaction proceeds by rate-determining attack of hydroxylamine on the O-protonated aldehyde35. If the attack of hydroxylamine is diffusion controlled, the measured first-order rate corresponds to kobs = (kdiff/Ka)[NH2OH], where kdiff = 3.0109 M1 s1 is the rate constant for diffusion and Ka is the acid dissociation constant of the protonated 9-formylfluorene. Despite the diffusion rate, reaction of the protonated aldehyde with hydroxylamine is relatively slow because of the low concentration of unprotonated hydroxylamine at the prevailing acid concentration. Thus, protonation of the aldehyde is readily reversible. Division of the measured rate constant kobs by the rate constant for diffusion and the concentration of hydroxylamine gave pKa = –4.5 for the protonated formylfluorene. Combination of this equilibrium constant with that for hydration of the carbonyl group then gave pKR = –5.3. In general, diffusion control of the reactions of protonated carbonyl groups with nucleophiles is more likely to apply for reactions of aldehydes than ketones because of the less negative pKR and lower reactivity of the conjugate acids of latter. Thus pKR = –5.3 for the protonated 9-formylfluorene may be compared with pKR = 0 and 1.3 for protonated acetone and acetophenone, respectively. For these ketones protonation equilibria can be measured directly138 and reactions of the protonated ketones with hydroxylamine were shown to occur below their diffusion limits.35 For aliphatic aldehydes, direct determination of pKas is usually not
+
O +
H + FlCH
C
OH
1/K a H
FlCH
C
OH
k diff[NH2OH] H
C
FlCH +
Scheme 17
H
NH2OH
FlCHCH
NOH + H2O + H+
STABILITIES AND REACTIVITIES OF CARBOCATIONS
55
feasible, because of the combination of a lack of strong UV chromophore, low basicity, and extended range of acid concentrations over which protonation occurs, reflected in low m* values. However, as described below (p. 57) the diffusion method has been used to infer a pKa for the protonation of a quinone methide. Oxygen substituent effects on arenonium ions It is also possible to examine the effect of oxygen substituents on the stability of arenonium ions. Wirz has studied keto–enol equilibria for phenol,151 naphthol (Wirz J, Personal communication), and anthrol.152,153 The tautomeric constants may be combined with pKas for protonation of the keto tautomer and ionization of the phenol to provide pKas for protonation of the aromatic ring of phenol and the phenoxide ion. As illustrated in Scheme 18 the unstable keto tautomer of phenol 22 was produced by photolysis of the bicyclooctene dione 21. Except in the case of the anthrone a pKa for protonation of the keto tautomer has not been measured directly. However, values can be estimated from the pKa for protonation of the 4,4-dimethylated analog136 with a correction for the substituent effect of the methyl groups. The pKas for C-protonation of the phenols and phenoxide ions are compared with values for the unsubstituted aromatic molecules in Table 3. The focus on pKa rather than pKR is because the equilibrium constants for hydration of the keto tautomers of the phenols have not been measured or estimated. The values and DpKO of DpKOH a a show the magnitude of the oxygen substituent effects relative to the parent aromatic molecules. Again the substituent effects are large, and much larger for O (more then 20 log units) than OH (10 log units). At first, it is surprising that the effects are so similar for the benzene, naphthalene, and anthracene. Once more this arises because the pKa reflects the stability of OH+
O
hν –(CH2CO)
O
–13.2
–2.1
OH pK E = –12.73
O 21
22 –2.89
Scheme 18
O– 9.84
56
R. MORE O’FERRALL
Table 3 Acid dissociation constants of arenonium ions and their a-HO and a-O derivativesa + +
+
+ +
+ H
H
H
H
H
pKa a-H a-OH a-O
–24.5 –13.2 –1.1
–20.5 –8.3 3.1
–13.4 –3.2 10.0
DpKa a-OH a-O
11.3 23.4
12.2 23.6
10.2 23.4
a
Me
H H
H
H
H
–22.2
–24.5
2.1
–2.9
–15.7 4.1 19.3
24.3
21.6
19.8 35.0
The oxygen substituents are located at the positions shown with a formal positive charge in the parent cation.
both the protonated and unprotonated aromatic molecule. In practice, the aromatic rings delocalize charge and moderate the influence of the substituents. This is indicated by comparison with the quite different and larger effects of HO and O on the carbon basicity of the enol and enolate anion of acetophenone, which are also shown in Table 3. For phenol one can compare the effects of hydroxy and methoxy substituents. Scheme 19 shows effects of O-methyl substitution on pKas for protonation of a benzene ring containing one, two, and three hydroxy substituents. The pKas for di- and trihydroxy-substituted and methoxy-substituted benzenes were measured directly by Kresge et al.68 Again the stabilities of the hydroxysubstituted cations in water are consistently greater than methoxy. The importance of solvation in controlling these effects is demonstrated by the inversion of relative pKas of trihydroxy and trimethoxy benzene in concentrated solutions of perchloric acid.68 Thus the difference in pKas is matched by a
H
pKa
Scheme 19
R=H R = Me
OR
OR
OR
+
+
+
H
–13.2 –15.0
H
H
–6.3 –7.5
OR
RO
H
H
–3.35 –5.2
OR
STABILITIES AND REACTIVITIES OF CARBOCATIONS
57
corresponding difference in m* values, for example, pKa = –5.2 and m* = 1.65 for trimethoxybenzene and pKa = –3.35 and m* = 0.87 for trihydroxybenzene. Oxygen ring substituents: quinone methides Effects of oxygen substitutents in an aromatic ring upon an exocyclic rather than endocyclic carbocation charge center have also been measured. The possibility of comparing HO, MeO, and O substituent effects for the benzylic cations is provided by recent studies of quinone methides, including the unsubstituted p-quinone methide 23, which may be considered as a resonancestabilized benzylic cation with a p-oxyanion substituent.
CH2
CH2+
O
O– 23
Such structures can be generated by flash photolysis of p-hydroxybenzyl alcohol or its derivatives such as p-hydroxybenzyl acetate.154 Kresge has studied the subsequent reaction of the quinone methide with water to yield the corresponding hydroxy-substituted benzyl alcohol 25, as shown in Scheme 20.155 The hydrolysis shows an acid-independent reaction at neutral pH and an acid-catalyzed reaction at lower pH, consistent with attack of water on the neutral and O-protonated (24) quinone methides, respectively. Other nucleophiles show similar acid-dependent and acid-independent reactions. By assuming that for the acid-catalyzed reaction with thiocyanate anion (to form the trapped product 26) attack of the thiocyanate ion is both rate determining and diffusion controlled with a rate constant 5109 M1 s1,156 Kresge was able to derive a pKa = –2.0 for the initial protonation reaction from the
H2O H+ O
CH2 23
25
CH2+
HO 24
CH2OH + H+
HO
SCN–
HO
CH2SCN 26
Scheme 20
58
R. MORE O’FERRALL
relationship kobs = kd/Ka (cf. the similar determination of a pKa for protonation of 9-formylfluorene, p. 54). This also allowed assignment of rate constants kH2 O ¼ 3:3 s 1 and 5.8106 s1 for reactions of the neutral and protonated quinone methide, respectively. The O-protonated quinone methide corresponds to the p-hydroxybenzyl cation 24. Richard measured the rate constant kH for acid-catalyzed formation of this cation from p-hydroxybenzyl alcohol by monitoring formation of a thiol-trapped product by HPLC.157 Combining this rate constant with kH2 O yields pKR = –9.6 for the cation from the usual relationship KR = kH2 O /kH. This equilibrium constant may be combined with the pKa for the protonated quinone methide and an estimated pKa = 9.9 for p-hydroxybenzyl alcohol to give pKR = 2.3 for the p–O-substituted alcohol based on the cycle of Scheme 21. Combining the above values of pKR with the value for the p-methoxybenzyl cation measured by Toteva and Richard158 allows the effect of the three oxygen substituents on the stability of the benzyl cation to be compared in Scheme 22. The values of pKR may also be compared with effects of similar oxygen substitutions at the a-position of the benzyl cation from Table 3, which are also shown in Scheme 22. As expected, the relative magnitudes of the O, HO, and MeO substituent effects exhibit similar patterns in the a- and pK R = –9.6 H2O + HO
CH2+
CH2OH + H+
HO
pKa = 9.9
pKa = –2.0 pK R = 2.3 H+ + H2O + O
CH2
–
CH2OH + 2H+
O
Scheme 21
CH2+
pKR
(–21) PhCH2+
pKR
(–21)
Scheme 22
CH2+
CH2+
CH2+
OMe
OH
O–
–9.6
2.3
PhCHOH +
PhCH=O
–2.4
14.7
–12.4 PhCHOMe+ –7.5
STABILITIES AND REACTIVITIES OF CARBOCATIONS
59
p-positions but the a-effects are larger. Nevertheless, it is evident that even when separated from the carbocation center by an aromatic ring, the stabilizing effects of oxygen remain very large. Measurements of stabilities of benzylic carbocations with o-oxygen substituents show smaller effects than their p-counterparts. This is apparent from the examples 27–30, for which differences in pKR from replacing MeO by Me (or, in cyclic structures, O by CH2) are shown in Table 4.73 For the o-methoxy substituent, the relatively small increment in pKR (DpKR = 2.3 compared with 3.9 for p-MeO) can be understood in terms of steric hindrance to resonance interaction and to the more favorable accommodation of resonance structures by a benzene ring in the p- than o-case in line with greater stability of p- than o-benzoquinone.159 Perhaps more surprising is that the substituent effect is also small when the oxygen is situated in a fused cyclic ring structure as in 29 and 30 (DpKR = 2.4 and 0.1). Presumably, this represents a conformational restraint of the ring, which is greater for a six- than five-membered ring. It should be mentioned that neutral and acid-catalyzed hydrolyses of the o-quinone methide of benzene have also been studied.155 So far, no value of pKR has been reported. b-Oxygen substituents: hyperaromaticity of arenonium ions Carbocations with b-oxygen substituents have received less attention in the literature than those with a-oxygen substituents. Nevertheless, they have been extensively studied as intermediates in the acid-catalyzed ring opening of epoxides,160 especially, of arene oxides and dihydroarene oxides, which are implicated in the mutagenic metabolism of polycylic aromatic hydrocarbons.161 The structures of deoxy analogs of the carbocations have been investigated under stable ion conditions162 but not the b-hydroxy- or alkoxysubstituted ions themselves. At first sight, there is nothing remarkable in the kinetic or equilibrium effects of b-oxygen substituents. A b-hydroxy group normally decreases the Table 4 Effects of oxygen substituents on stabilities of cyclic benzylic carbocations +
+
27
pKR(H2O) DpKR a b
8.9 3.9
Relative to methyl substituent. Relative to carbocyclic cation.
O
OMe
MeO 28
11.7 2.1a
+
+
29
9.3 2.4b
O 30
12.0 0.1b
60
R. MORE O’FERRALL
rate of carbocation formation163 and the stability of the carbocation. A comparison of pKR values is provided by the 9-phenanthrenonium ion (pKR –11.6) and its 10-hydroxy analog 31 (pKR = –14.4). The KR values indicate a103-fold less favorable equilibrium constant for formation of the carbocation from addition of the b-hydroxyl group.88 HO +
31
What is remarkable, however, is the stereochemical influence of a bhydroxyl group. b-hydroxycarbocations such as 31 are formed not only from arene oxide as precursors but from arene dihydrodiols. As shown for the parent benzene dihydrodiols in Scheme 23, arene dihydrodiols exist as cisand trans-isomers. The cis-isomers are obtained as products of the action on the aromatic molecule of dioxygenase enzymes and have been prepared on a large scale by fermentation.92 The trans-isomers are normally accessible by straightforward synthesis, for example, from the arene oxide. Both isomers undergo acid-catalyzed dehydration to the parent aromatic molecule, as is also shown in Scheme 23. It is clear that their reactions should involve a common carbocation intermediate,163,164 and in so far as there is little difference in the stabilities of the isomers,165 their difference in reactivities might have been expected to be small. On the contrary, the cis-benzenedihydrodiol is found to react 4500 times more rapidly in the presence acid than the trans. Moreover, as shown below, this ratio falls to 440 for naphthalene dihydrodiols, to 50 for phenanthrene dihydrodiols, and less than 10 for a nonaromatic analog such as the acenaphthylene or dihydronaphthalene dihydrodiols.164 These rate ratios are shown on the following page and suggest that the effect is linked to the aromaticity of the ultimate product of the reaction. Trapping experiments with the 10-hydroxyphenanthrenonium ion 31 indicate that the ratio of
OH H+ OH
H+
Scheme 23
–H
+
OH OH
OH
OH
+
STABILITIES AND REACTIVITIES OF CARBOCATIONS
61
cis/trans dihydrodiol products formed from nucleophilic trapping with water in the microscopic reverse reaction is >30. This demonstrates the consistency of the forward and back reactions for cation formation. The behavior is little affected if the b-hydroxy group is changed to b-methoxy.88 HO
OH
OH OH
OH
OH
OH
OH
kcis /ktrans
440
4500
7
50
The interpretation offered for this surprising behavior is that the arenonium ions are stabilized by C–H hyperconjugation, the effect of which is enhanced by the contribution of an aromatic structure to the no-bond resonance form shown for the benzenonium ion 32 below.164 The difference between cis- and trans-diols then arises because reaction of the trans-diol leads initially to a carbocation in which a pseudoaxial C–OH rather than C–H bond is orientated for hyperconjugation (34 rather than 33). The difference in energies of the two conformations and its dependence on the aromaticity of the no-bond structures is confirmed by calculations, which show 9 kcal mol1 difference between the two conformations of the 2-hydroxy benzenonium ions and only 0.5 kcal mol1 for the corresponding 6-hydroxycyclohexenyl cations with one less double bond.164 + H+
H 32 OH2+ OH
H cis
OH2+ OH
+
H
+
H
H 33
H
H OH 34
trans
OH
Stabilization conferred by ‘‘aromatic’’ hyperconjugation resolves a puzzle concerning the relative stabilities of arenonium ions. As judged by rates of solvolysis reactions, normally a phenyl group is more effective than vinyl in stabilizing a carbocation center.166 This difference is moderated for cycloalkyl substrates, so that benzoannelation has little effect, for example, on the rate of hydrolysis of 3-chlorocyclohexene (Cagney H, Kudavalli JS, More O’Ferrall
62
R. MORE O’FERRALL
RA, unpublished data). By comparison, the large and unfavorable effect of benzoannelation on the stability of the benzenonium ion as reflected in its small negative pKR value (–2.3) compared with the larger negative values for the 1-naphthalenonium ion (–8.0) and 9-phenanthrenonium ion (–11.6) is surprising (cf. Table 2, p. 44). The order is explained, however, if it reflects the relative magnitudes of the hyperconjugative stabilization of the ions, which in turn depends on the aromaticity of their no-bond resonance structures. That the observed effect of benzoannelation is consistent with the aromatic character of the benzenonium ion is confirmed by comparison with corresponding effects on the stabilities of tropylium49,167 and pyrylium ions168,169 shown in Scheme 24. In both cases the stabilities of the ions are severely reduced by the additional benzene rings. Indeed, the effect may be compared with the effect of benzoannelation on the aromatic stabilization of benzene itself, which is characteristically decreased by conversion to naphthalene and phenanthrene or anthracene. The fact that, in contrast to pKR, the pKa of the benzenonium ion is increased by benzoannelation implies that benzoannelation does not have as large an effect on the ‘‘aromaticity’’ of the benzenonium ion as on benzene itself. A further indication of ‘‘aromatic’’ stability is provided by measurement of pKR for the cycloheptadienyl cation 35. This ion is a homolog of the cyclohexadienyl cation (pKR = –2.3) and might have been expected to have a similar stability. In practice, measurements in aqueous solution using the azide clock show that pKR is 11.6, which corresponds to a decrease in stability of 12.5 kcal mol1.88 It seems unlikely that this difference arises solely from strain in the cycloheptadienyl ring. Moreover, for the dibenzocycloheptadienyl cation, 36, a pKR = –8.7 can be deduced from measurements in aqueous trifluoroacetic acid (Scheme 25).170 Despite the difference in solvents it seems clear that in this case and in contrast to its effect in Scheme 24 dibenzoannelation strongly stabilizes the cation.
+
pK R
4.7
+
+
1.6
–3.7
pK R
Scheme 24
<5
+ O
+ O
+ O
–2.0
–6.0
STABILITIES AND REACTIVITIES OF CARBOCATIONS
pK R
+
+
35
36
–11.6
–8.7
63
Scheme 25
Hyperconjugation was invoked by Koptyug’s group in the 1960s to explain the structures and spectroscopic properties of methylated benzenonium and other arenonium ions under stable ion conditions.171 The X-ray structure of protonated hexamethyl benzene shows that the ring is close to planar with an internal bond angle nearer to trigonal than tetrahedral at the formally sp3 carbon atom.172 The stretching frequency of the hyperconjugating C–H bond increases from benzenonium to naphthalenonium to phenanthrenonium ions.173 A further surprising observation explained by hyperconjugation is the greater reactivity of benzene oxide 37 toward acid-catalyzed ring opening in aqueous solution than dehydration of benzene hydrate 10.105 Both reactions occur with rate-determining carbocation formation, but normally an epoxide reacts 106 times as rapidly as a structurally related alcohol. The anomalous behavior of the oxide and hydrate of benzene can be attributed partly to homoaromatic stabilization of the arene oxide,174 but it is likely that initial formation of an unfavorable conformation of a carbocation with a pseudoaxial hydroxyl group b- to the charge center also plays a significant role. OH H+ 10 k H = 190 M–1 s–1
+
O
+ H2O 37
H+
+ OH
k H = ~20 M–1 s–1
Protonated aromatic molecules are intermediates in aromatic hydrogen isotope exchange. The stabilization they experience presumably applies to other Wheland-type intermediates. From the work of Eaborn in the 1950s and 1960s, it is known that trimethylsilyl and other leaving groups conducive to -bond delocalization are highly reactive toward displacement from an aromatic ring,175,176 and this has been attributed to hyperconjugation.114,177 Taking account of the contribution of an aromatic resonance structure to this enhanced hyperconjugation, it seems appropriate to characterize the phenomenon as ‘‘hyperaromaticity.’’ This term is suggested by an obvious analogy with the more familiar homoaromaticity.178 The analogy is illustrated
64
R. MORE O’FERRALL
by comparison with the homoaromatic norcaradiene 38. Both the benzenonium ion 32 and norcaradiene are characterized by resonance of and p valence bond structures. For 32 the resonance involves an exocyclic -bond and endocyclic p-bond, whereas for 38 the –p resonance is endocyclic. Use of the prefix ‘‘hyper’’ might seem inappropriate for an effect which is less stabilizing than the normal n- and p-aromatic resonance. However, the term ‘‘hyperconjugation’’ was justified by Mulliken on the grounds that it implied ‘‘conjugation over and above that usually recognized,’’179 which would seem appropriate for hyperaromaticity also. Homo
38
METAL-COORDINATED CARBOCATIONS
The effect of metal coordination on the structure and stability of carbocations is great enough to call into question the characterization of many metal complexes as carbocations.180,181 At least two types of metal coordination are common. In one a sigma bond or pair of electrons on a metal contributes a hyperconjugative or neighboring group interaction with a carbocation center. The other involves direct coordination of the metal to a p-system which includes the formal charge center, usually through an 5 or 7 interaction. In such cations the charge may be located primarily on the metal, with little evidence of carbocation behavior other than proneness to nucleophilic reaction at the formal charge center on carbon. For the Cr(CO)3-coordinated benzylic carbocation 39, for example, Cr(CO)3 exhibits both an 6 interaction with benzene ring and a hyperconjugative (-bond) interaction with the benzylic carbon.
+ CH2 Cr OC
CO CO 39
There have been a limited number of quantitative measurements demonstrating the effects of metal coordination. A communication by Petit in 1961 reported pKR values for Fe, Cr, and Mo tricarbonyls coordinated to tropylium and cyclohexadienyl cations,182 but a full paper was not published and some of
STABILITIES AND REACTIVITIES OF CARBOCATIONS
65
his values appear to be in error. Measurements of pKR prior to 1982 were reviewed by Watts180 and these showed that a ferrocenyl substituent and its ruthenium analog are strongly stabilizing toward an adjacent carbocation center and that a benzylic cation is significantly stabilized by coordination of Cr(CO)3 to the phenyl ring. Values of pKR for these cations are compared with those of benzyl and benzyhydryl cations below and illustrate stabilization by neighboring group interactions. The effect of a ferrocenyl substitutent is characteristically greater than that of a Cr(CO)3-coordinated phenyl ring. Some of the stabilization from ferrocene may be through a p-interaction of the carbocation charge center with the cyclopentadienyl ring. However, crystal structures of the ions reveal geometries consistent with substantial bonding between the metal and the cation center and reactions with nucleophiles show a marked selectivity for the opposite face of the cation from the metal (cf. 39).183 PhCH2 þ Ph2CHþ FeCp2 CH2 þ (FeCp2)2CHþ RuCp2 CH2 þ Ph CrðCOÞ3 CH2 þ (–21)
–12.5
–1.2
4.1
1.2
–11.8
There have been extensive kinetic measurements of reactions of p-coordinated carbocations with nucleophiles. These were reviewed in 1984 by Kane-Maguire and Sweigart who compared reactivities of Fe, Ru, Mn, Os, Cr, Mo, W, and Re coordinated to cyclohexadienyl, tropylium, and other unsaturated cyclic cations with or without carbonyl or triphenylphospine ligands for the metals.184 More recent studies have been carried out by Mayr,185,186 including a comparison between reactivities and pKR values for metal-coordinated and uncoordinated ions.187 Based on that correlation (cf. Fig. 10 on p. 106) substitution of a b-hydrogen atom of the ethyl cation by FeCp(CO)2185 increases pKR from 30 to approximately þ10. It should be noted that the attachment here is through the iron atom, whereas for the cations above the CH2þ moiety is bound to the cyclopentadienyl ring (e.g., in FeCp2 CH2 ). There has been interest in the stabilizing effect of coordination of a dicobalt hexacarbonyl on propargyl cations, for which it can act as a protecting group187,188 in the reaction named after Nicholas.189 This stabilization is significantly greater than that of a Cr(CO)3-coordinated phenyl group190 and values of pKR in the range 6.8 to 7.4 have been reported for the ions (e.g., 40).189 It is noteworthy that substituents (R) at the methylene group are practically without effect, implying complete dispersion of charge from the formal carbocation center.187,191 Jaouen has reported pKR values indicating a much greater stabilization of the propargyl cations by Mo2Cp2(CO)4 than Co2(CO)6,192 and Mayr has shown that replacement of CO by Ph3P is also
66
R. MORE O’FERRALL
strongly stabilizing.187 The structure of the propargyl reactant complex reflects the electron deficiency of the bonding to cobalt.193 CH2OH
Co2(CO)6 R
CH2OH
R (CO)3Co
CH R
Co(CO)3
(CO)3Co
Co(CO)3 +
40
Watts and Bunton examined the effect of Cr(CO)3 coordination on pKR for the tropylium ion.194 Because of a competing reaction at high pH in water, the study was conducted in methanolic solutions in which pKR is decreased by up to 5 log units.195 This allowed determination of pKR = 6.6, in methanol which translates to perhaps 9.5 in water. For the uncoordinated tropylium ion pKR is reported as 2.15 in methanol compared with 4.7 in water.195 The moderate stabilization of the tropylium ion by coordination of Cr(CO)3 is pertinent to Schleyer’s conclusion that coordination of Cr(CO)3 does not impair the aromaticity of benzene.181 A very different pKR applies to tropylium ion coordinated to an Fe(CO)3 group, 41. The value has not been determined experimentally but calculations for an isodesmic reaction relating 41 to the uncomplexed tropylium ion imply a pKR in the region of 5.196 The relative instability of this ion must reflect sacrifice of aromatic stabilization in the 5 coordination imposed by the Fe(CO)3. ΔHcalc = –13 kcal mol–1 +
+
+
Fe(CO)3
+ Fe(CO)3
41
Likewise, a neighboring group interaction from Cr(CO)3 coordinated to a benzene ring of the dibenzotropylium ion 42 is destabilizing toward the ion, whereas the same interaction in the corresponding nonaromatic dibenzocycloheptadienyl cation 43 is stabilizing. Changes in pKR accompanying coordination of Cr(CO)3 are indicated under the structures below.170
+ 42 ΔpKR
–2.4
Cr(CO)3
+ 43 +3.5
Cr(CO)3
STABILITIES AND REACTIVITIES OF CARBOCATIONS
67
OH
pK R = 4.7
(CO)3Fe
+ H+
+
(CO)3Fe 44
(CO)3Fe
+ H+
pK a = ~9 (computed)
Scheme 26
By contrast, measurement of pKR = 4.7 for the Fe(CO)3-cooordinated cyclohexadienyl cation 44 (Scheme 26) indicates a 107-fold more favorable equilibrium constant for carbocation formation than for the uncoordinated cation.197 However, a more dramatic effect of coordination is to render nucleophilic reaction with water more favorable than loss of a proton. A pKa = 9 can be estimated by computing the energy differences between coordinated and uncoordinated benzene and coordinated cyclohexadiene. This compares with the value of 24.5 for the uncoordinated cyclohexadienyl cation. The large difference must reflect the unfavorable effect of Fe(CO)3 coordination on benzene, an effect analogous to that found by Mayr for Fe (CO)3 coordination on the tropylium ion.196 As expected, both the coordinated cyclohexadienyl and tropylium ions are highly stereoselective toward exo attack by water. For the corresponding five-membered ring, in which Fe(CO)3 is formally coordinated to a cyclopentadienyl cation,198,199 there are indications that the complex has the character of a cylopentadienyl anion coordinated to iron with oxidation state of þ2. This is suggested by the characteristic X-ray structure (Kudavalli JS, More O’Ferrall RA, Muller-Bunz H, unpublished data) of a Ph3P-substituted derivative200 and by attack of nucleophiles at the carbonyl group of the complex in preference to a ring carbon atom.198,199 Fischer carbenes (e.g., 45) are not obviously analogs of carbocations. However Bernasconi has pointed to a similarity between displacement of a nucleophilic group attached to the carbenic carbon and ester hydrolysis, which implies a comparison between the C=metal and C=O double bonds.201 From this point of view, Fischer carbenes can be considered as carbocations stabilized by a negatively charged metal ion. There is an obvious analogy with a view of C=O as a carbocation stabilized by a negatively charged oxygen (p. 53). As discussed by Bernasconi, pKR is not directly measurable, but equilibrium constants for addition of methoxide ion in methanol indicate that addition is 106 times more favorable than to a comparably substituted C=O group, which implies values of pKR more positive by six units for an otherwise
68
R. MORE O’FERRALL
comparable ester structure. In so far as pKR for methyl benzoate has been estimated as 21.1 by Guthrie and Cullimore144 the value for 45 should be about 15. This implies that an adduct would be formed in fairly concentrated aqueous sodium hydroxide. Again little difference is expected between Cr, Mo, and W. OMe (CO)5Cr Ph 45
CARBOCATIONS AS PROTONATED CARBENES
Proton loss from carbocations normally occurs from a b-carbon atom to form an alkene, and it is to this process that measurements of pKa for carbocations normally refer. However, in principle, loss of a proton can also occur from an a-carbon atom to yield a carbene. The isolation of the first stable cyclic dinitrogen-substituted carbenes sparked numerous studies of related structures but few experimental attempts to measure pKas.202 However, Alder203 and Streitwieser204 measured pKas for protonation of imidazolyl carbenes to give imidazolium ions in DMSO and these measurements have been extended by Chu and coworkers.205 Recently Amyes has reported aqueous pKas in the range 17–24 for carbenes derived from the imidazolium, oxazolium, and thiazolium ions shown below (46–48).206 For the imidazolium ions, rate constants for hydrogen isotope exchange catalyzed by hydroxide ion measured by proton NMR were combined with rate constants at the limit of solvent relaxation (1011 s1) for reaction of the carbenes with water. For the thiazolium and oxazolium ions, exchange rate constants were measured by Jencks and Washabaugh207 and estimated, respectively. H
H
H
N+
N+
N+
H N H pK a
23.8
46
H
H N+ H
H
O
S
N
47
48
H
16.9
19.5
~24
49
Amyes et al. point out that the difference in pKas for C- and N-protonation of these carbenes provides the difference in stability of the carbene and parent heterocyle as shown by the cycle of Scheme 27 for the imidazolyl carbene 50. Interestingly, Yates and coworkers have calculated similar pKas for the imidazolium ion 46 and its saturated imidazolinium counterpart 49.208 This
STABILITIES AND REACTIVITIES OF CARBOCATIONS
H+ + 50
H N
H N
H N
16.7
69
:
H + H+
:
N H
N
N H 23.8
H N
51
7.1 H
N+ H
Scheme 27
implies that the aromatic stabilization of the imidazolium ion is similar to that of the carbene, although by other criteria the aromatic character of the ion is greater.209 The magnitude of the stabilization of the carbenes is revealed most directly by their hydrogenation energies as shown in Equation (19).210 This has an obvious analogy with the use of hydrogenation energies to measure the stabilities of aliphatic and aromatic p-bonds.211 The heat of hydrogenation of imidazolyl carbene 50 is calculated to be 17.7 kcal mol1 greater than that of the imidazolinyl carbene 51212 which indicates the magnitude of the aromatic stabilization of the former carbene206,209,210 (although whether the stabilization is solely aromatic has been a subject of discussion). R2 C : þ H2 ¼ R2 CH2
ð19Þ
A variation on Scheme 27 and Equation (19) has been utilized by Keeffe and the author to evaluate pKas of alkyl, aryl and alkoxy carbenes.26 For carbocations for which the pKa for loss of a proton from a b-carbon atom is known, combination of this pKa with the experimental or calculated energy difference between alkene and carbene conjugate bases leads to the pKa for protonation of the carbene, provided it can be assumed that the energy difference between alkene and carbene is insensitive to solvent. Where a pKa for loss of a b-hydrogen of the carbocation is not accessible, for example, for carbenes lacking a b-hydrogen, pKR can be used instead. Thus the cycle of Scheme 28 relates a pKa for protonation of the carbene to an experimentally measured
pK a
R2CH+
R2CHOH + H+
H+ + R2C pK H2O
Scheme 28
pK R
70
R. MORE O’FERRALL
value of pKR and calculated value of pKH2 O for conversion of the carbene to the corresponding alcohol. The value of pKH2 O for the hydration of the carbene provides a measure of carbene stability comparable to the heat of hydrogenation. As already noted both have analogies with the similar measures of stabilization of p-bonds. Keeffe and the author calculated energies of a number of carbenes for which pKR measurements for the corresponding cations are available.26 By assuming that the solvation energy of the carbene was the same as for its alkene isomer, or a related structure, it was possible to derive the desired value of pKH2 O , and thence a pKa for loss of an a-proton from the cation. These values of pKa are listed in Table 5 together with values of pKR for the carbocations derived by protonation of methyl-, phenyl-, and methoxy-substituted carbenes. Also shown are values of pKH2 O for hydration and DH for hydrogenation of the carbene. It is noteworthy that the stabilizing effects of methyl and phenyl substituents are similar for the carbocation and carbene and that pKas for protonation of these carbenes fall in the narrow range 29–33. The similarity of this stabilization is consistent with the comparable aromatic stabilization of the imidazolium ion and corresponding carbene noted by Amyes.206 A surprising conclusion from Table 2 is that methoxy substituents are more strongly stabilizing for a carbene than a carbocation, and yield smaller than normal pKas, comparable to those for the imidazolium and related ions (46–49). This is consistent with Kirmse’s finding that relative rates of protonation of carbenes fall in the order Ph2C > Ph(MeO)C > R(MeO) C > (MeO)2C. As Kirmse and Steenken pointed out, this does not correspond to the order of stability of the carbocation products.213 In principle, the effects of oxygen substituents are consistent with CF2 being a relatively stable carbene despite the corresponding carbocation being quite unstable. This is understandable if the dipolar structure produced by resonance interaction in the carbene (52) is compensated by an inductive ‘‘back donation’’ of electrons in the -bonds. In the cation (53), back donation accentuates rather than compensates charge separation arising from resonance
Table 5 A comparison of stabilities of singlet carbenes (pKH2 O ) and carbocations (pKR) in aqueous solution at 25C Carbocation
pKa
pKR
pKH2 O
DHhydrogen
Carbene
CHþ 3 CH3 CHþ 2 PhCHþ 2 þ Ph2CH MeOCHþ 2 ðMeOÞ2 CHþ
28 30 31 29 19 13a
–42 –29.6 –21 –12.5 –15.9 –5.7
–70 –59.3 –51.8 –41.0 –34.6 –18.6
–119.1 –107.9 –98.9 –84.3 –70.2 –40.8
CH2 CH3CH PhCH Ph2C MeOCH (MeO)2C
a
Value differs from that in Guthrie et al.132,26
STABILITIES AND REACTIVITIES OF CARBOCATIONS
71
interaction with an oxygen atom. Such a -bond interaction would also account for the fact that the resonance appears not to produce a strongly dipolar electron distribution for the carbene. + – MeO CH
MeO CH 52
+ MeO CH2
+ MeO CH2 53
HALIDE AND AZIDE ION EQUILIBRIA
So far we have considered only pKR and (occasionally) HIA as measures of carbocation stability. However, equilibrium constants for the reaction of carbocations with a variety of nucleophiles other than water have been measured. Ritchie especially has measured195 and reviewed15 values for reactions of relatively stable cations, such as trityl ions with electron-donating substituents or aryl tropylium ions, with alcohols, amines, and oxygen or sulfur anions. More recently, there has been interest in less stable cations which can be formed from solvolysis of precursors possessing good leaving groups such as chloride or azide ions. When written in the associative direction, equilibrium constants for these reactions measure the relative stabilities of the carbocations in terms of chloride or azide ion affinities. This is shown in Equation (20) in X which X is Cl or N 3 and KR is the equilibrium constant for the association reaction. RX ¼ Rþ þX ;
KX R¼
½RX ½Rþ ½X
ð20Þ
Chloride ions Values of KCl R for chloride ions have been determined by combining a rate constant for solvolysis ksolv (for reactions for which the ionization step is ratedetermining) with a rate constant for the reverse reaction corresponding to recombination of cation and nucleophile. The latter constant may be found (a) by generating the cation by photolysis and measuring directly rate constants for reactions with nucleophiles or (b) from common ion rate depression of the solvolysis reaction coupled with diffusion-controlled trapping by a competing nucleophile used as a clock. A further possibility arises where the carbocation intermediate of the solvolysis is so unstable as to react with water at the limiting rate of solvent relaxation with a rate constant of 1011 s1. It is then likely that the reaction with water occurs at the stage of a carbocation anion pair and that the back
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reaction of the ion pair to reform the reactant occurs more rapidly than the solvent relaxation, with a rate constant that may be as large as 1013 s1. Provided the back reaction is significantly faster than reaction with the solvent the measured rate constant for solvolysis should correspond to 1 1011/ K X Rs . Quite often values of K X R have been measured for cations for which pKR is not known. Thus combining Equation (20) with Equation (1) for KR (p. 21, with Hþ replacing H3Oþ) gives the ratio of equilibrium constants as Equation (21). Rewriting this ratio as pKR – pKCl R allows the difference in pK’s to be expressed in terms of free energies of formation in aqueous solution at 25 (DGf ) for the relevant alcohol and alkyl chloride as shown in Equation (22).38,43,214 KR ½Hþ ½Cl ½ROH ¼ ½H2 O½RCl KRCl pKR pK RCl ¼
DGf ðHþ ; Cl ÞþDGf ðROHÞ DGf ðH2 OÞ DGf ðRClÞ 1:364
ð21Þ
ð22Þ
Experimentally, the simplest evaluation of K RCl is based on measurement of a rate constant in water for solvolysis of an alkyl halide for which reaction of the carbocation with water is at its solvent relaxation limit. An example is provided by the solvolysis of t-butyl chloride. A rate constant for solvolysis in water at 25 was measured by Fainberg and Winstein215 as 2.88102 s1. This yields pK RCl = –12.5. Substitution of the appropriate free energies of formation into Equation (22),38,214 together with an estimate of the free energy of transfer from gas to aqueous solution for t-butyl chloride,43 gives pKR – pKCl R = 4.7 and pKR = –17.2. This value is impressively close to pKR = –16.4 determined by Toteva and Richard.158 Indeed, the agreement is improved by recognizing that K RCl refers to the formation of an ion pair. Thus, taking Richard and Jencks’s value of 0.3 M1 for an ion pair association constant in water85 allows correction of pKR to 16.7. The level of agreement between values is probably fortuitous considering possible sources of discrepancy, such as a difference in solvent relaxation for an ion pair and a cation generated without a counter ion by protonation of an alkene by H3Oþ. A similar estimation for isopropyl chloride leads to a value of 17.3, which seems too low compared with 22.1 from the protonation of propene (p. 48). This is consistent with the expected intervention of an SN2 mechanism.216 The method should work better for adamantyl chlorides or norbornyl chloride for which SN2, and, presumably, preassociation processes are precluded. Speculative values of pK RCl and pKR for the relevant carbocations 54–56 are listed below based on a solvolysis rate constant in water for the
STABILITIES AND REACTIVITIES OF CARBOCATIONS
73
1-adamantyl chloride217 and ratios of values in aqueous acetone for the 1- and 2-adamantyl isomers and exo-norbornyl chloride.218 Although DGf (aq) for the alcohols and chlorides in these cases are not available, good estimates of DGf (ROH) – DGf (RCl) can be made by examining the structure dependence of Cl for OH substitutions for representative alcohols and alkyl chlorides for which free energies of formation have been measured.38,43,214
+
+ +
54
K RCl ¼ 1011=ksolv pKR – pK RCl pKR
56
55
1.31013 –4.6 –17.2
2.61016 –4.1 –20.0
2.11012 –4.1 –15.9
From the above results it can be seen that variations in pKR – pK RCl are rather small. The same is true of pK RCl for the ionization of trityl chloride and p-methoxybenzyl chloride, shown in Table 6 below, from which values of pKR – pK RCl are 4.7 and 4.75 log units, respectively.19,78,219 However, this level of uniformity is not expected of all nucleophiles and substrates. An extreme example of variation in DpKXR is provided by comparison of chloride and dimethyl sulfide as nucleophiles reacting, respectively, with the p-methoxybenzyl cation and the structurally very different electrophile, the di-trifluoromethyl quinone methide 57.220 In the case of the p-methoxybenzyl cation the addition of Me2S is more favorable than addition of chloride ion by a factor of 107-fold; for the quinone methide it is 100 times less favorable. Toteva and Richard attribute the difference to the large and unfavorable steric and polar interactions between the positively charged SMe2þ
Table 6 Comparison of pK RCl , pKR Ph3C+
, and pKR + CH2
MeO
O
C(CF3)2 57
pKR pK RCl 2þ pK RSMe
–6.6 –1.85
–13.4 –8.7 –15.7
– 4.4 6.5
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Me2Sþ group and the two CF3 groups in the adduct of the quinone methide. This more than balances the greater carbon affinity of the sulfur nucleophile expressed in the reaction with the p-methoxybenzyl cation. This behavior is exceptional. Nevertheless, the assumption that pKR and pK RCl measure equivalent trends in carbocation stability needs to be treated with caution. Richard and coworkers measured values of pK RCl to assess the influence of b-fluoro substituents on the stability of the a-methyl p-methoxybenzyl cation 58 (R = Me). As indicated in Scheme 29, replacement of an a-methyl by an a-trifluoromethyl group decreases the stability of the 221 carbocation by 7 powers of 10 in K Cl R. Cl However, measurements of pK R in this case lead to a lesser dependence of the equilibrium constant upon carbocation stability than pKR. Guthrie has calculated relative values of pK RCl and pKR and shown that an unfavorable geminal interaction between Cl and CF3 reduces the difference between þ Cl ArCHþ 2 and ArCHCF3 on the pK R scale by about 7 log units compared with pKR. This implies that replacing CH3 by CF3 in the p-methoxybenzyl cation decreases pKR by 14 units. Based on the value of pK RCl = –8.7 for the p-methoxybenzyl cation, pKR for the a-CF3 cation should be close to 23.5. However, note that the values of pK RCl in Scheme 29 were measured in 50–50 v:v TFE–water mixtures rather than water. In general, for anionic nucleophiles pK X R is expected to be highly sensitive to solvent. Results of Pham and McClelland222 indicate that pKR – pK RCl increases by 8 log units between water and 2% aqueous acetonitrile. The effect of a change from water to TFE–water will be much less than this, but a comparison for the p-methoxybenzyl cation shows that pK RCl decreases by 1 log unit.223 Thus neglecting any difference between pKR values in the two solvents the estimate of pKR for the a-trifluoromethyl-substituted p-methoxybenzyl cation is increased to 22.5. This value has been considered at some length because equilibrium measurements for the ions summarized as 58 are relevant to the effects of a-trifluoromethyl substituents on reactivity discussed later in the chapter (p. 80).
+ CH R
MeO 58
Cl pK R
Scheme 29
R
=
(TFE —H2O)
=
H
CH3
–9.5 –6.3
CH2F
CHF2
CF3
–9.4
–12.1
–13.4
STABILITIES AND REACTIVITIES OF CARBOCATIONS
75
Bromide and fluoride ions From the few measurements of bromide ion affinities it appears that pKBr R is similar to pK RCl . E.g. for the p-hydroxybenzyl cation, for which pKR = –9.6, pK RBr = –5.7.156 For the trityl halides on the other hand, chloride has a one log unit advantage, perhaps from a steric effect189,222,224 Probably, for the same reason, fluoride has a 107-fold greater affinity for the trityl cation19 than has the chloride ion (and is similar to that of acetate19), whereas for the p-methoxybenzyl cation the difference is only 4-fold.158 Azide ions There have been more equilibrium measurements for reactions of carbocations with azide than halide ions. Regrettably, there is little thermodynamic data on which to base estimates of relative values of pK RAz and pKR using counterparts of Equations (17) and (18) with N3 replacing Cl. Nevertheless, a number of comparisons in water or TFE–H2O mixtures have been made87,106,226,230 and Ritchie and Virtanen have reported measurements in methanol.195 The measurements recorded below are for TFE–H2O and show that whereas pK RCl is typically 4 log units more positive than pKR, pK RAz is eight units more negative. The difference should be less in water, perhaps by 2 log units, but it is clear that azide ion has about a 1010-fold greater equilibrium affinity for carbocations than does chloride (or bromide) ion. + + CHMe
MeO
pK RAz pKR
–13.3 –5.1
+ CMe2
MeO
–16.6 –8.6
–14.2 –5.9
A different picture emerges if we extend the comparison to cations with an a-methoxy substituent, as shown below.130 Now the difference between pKR and pKAz R is in the range 3–4.4 log units, which is much smaller than the eight units above. A small part of the difference may be due to a change in solvent from TFE–H2O to water, but the greater part must represent stabilization of the hemiacetal product of the KR equilibrium by the favorable interaction of geminal oxygen atoms.45,47,225 We have noted earlier that favorable interactions between OH and alkyl groups leads to differences between pKR and HIA. The oxygen–oxygen interactions are much larger.13,45
pKAz R pKR
PhCþ(OMe)Me
Me2CþOMe
PhCHþOMe
EtCHþOMe
–7.9 –4.6
–9.8 –5.4
–10.3 –7.3
–13.3 –10.3
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Azide equilibrium measurements have also been used to demonstrate that in addition to N3 having a high affinity for carbocations, N3 as an a-substituent is nearly as strongly stabilizing as a methoxy group. The preparation and solvolysis of gem-diazide derivatives of propionaldehyde and substituted benzaldehydes has allowed Richard and Amyes to study the solvolysis and, through studies of common ion rate depression, the reverse reaction of trapping carbocation intermediates by azide ion.226 Combining solvolysis and trapping rate constants then yields equilibrium constants pK RAz = –16.4 for the a-azido propyl cation compared with pK RAz = –13.2 for the a-ethoxy cation, corresponding to only 4 kcal mol1 greater stabilization by the ethoxy than azido substituent. Comparable differences are found for the substituted a-diazobenzylic and a-methoxy benzylic carbocations. Richard points out that the strong stabilizing effect of the a-azido group has implications for the mechanism of the Schmidt reaction. Were it not for their instability, it seems clear that gem diazides would find wider applications in synthesis. This short review of equilibria for reactions with halide and azide ions illustrates the utility of measures of carbocation stability other than pKR. Provided they refer to aqueous or largely aqueous media and the carbocations do not contain b-substituents which interact strongly with the nucleophile in the cation–nucleophile adduct, such as CF3, RO, or N3, values of pK X R can usually be related to pKR with an uncertainty of less than 1 log unit. On the other hand, they clearly demonstrate the specificity of geminal interactions between the bound nucleophile and electronegative a-substituents in determining relative values of pK X R and pKR.
3
Reactivity of carbocations
An important role of equilibrium measurements is in providing a framework for studies of reactivity and, in the present context, particularly reactivities of carbocations toward nucleophiles and bases. The reactivity of carbocations is too large a topic to deal with comprehensively here, but it may be helpful to attempt an overview of selected topics. Again, important areas, including reactions of vinyl cations120–124 and of b-hydroxy-carbocations formed from acid-catalyzed ring opening of epoxides,160,161 will not be covered, partly because of a lack of equilibrium measurements. Particularly extensive data exists for the reaction of carbocations with water and it is convenient to consider this first and to progress then to a wider range of nucleophiles. Thus we make the same division as for equilibria, but whereas the equilibrium data are dominated by reactions with water, a greater proportion of the kinetic data relates to nucleophiles other than water.
STABILITIES AND REACTIVITIES OF CARBOCATIONS
77
NUCLEOPHILIC REACTIONS WITH WATER
The starting point for most discussions of reactivity is a correlation of rate and equilibrium constants. One such correlation is shown in Fig. 1 of this chapter. It applies not to reactions of the carbocation with water as a nucleophile but to water acting as base, that is, the removal of a b-proton from the carbocation to form an alkene or aromatic product. We will consider this reaction below, but here note that for most of the carbocations in Fig. 1 values of kH2 O , the rate constants for reaction of the carbocation with water as a nucleophile are also available.25 Figure 3 shows a plot of values of log kH2 O against pKR for the carbocations of Fig. 1, namely, arenonium ions, cyclic and noncyclic secondary benzylic carbocations, and tertiary alkyl and benzylic cations.25 The plot is very similar to that reported by McClelland for other groups of carbocations including, benzhydryl, trityl, aryltropylium, and dialkoxyalkyl.3,4 One feature of Fig. 3 is that it incorporates the limiting rate constant of 1011 s1 corresponding to the rotational relaxation of water. Another is the grouping of different structural families on distinct correlation lines. Thus the tertiary alkyl cations show a steeper slope than the secondary cations. This is consistent with McClelland’s 12
log kH2O
10
8
6
4
–18
–16
–14
–12
–10
–8
–6
–4
–2
0
pKR
Fig. 3 Plot of log kH2 O against pKR. The main correlation line based on arenonium ions and secondary benzylic carbocations; the dashed line and filled circles are for tertiary cations.
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more extensive results for which the slopes range from 0.68 to 0.54. The slopes of the lines in Fig. 3 are 0.55 and 0.44. A further characteristic of Fig. 3, and of McClelland’s data, is that within structurally related reaction families the plots are quite linear, even where some of the rate constants closely approach their limiting values. This is contrary to a simplistic view that selectivity (represented by the slope of the plot) should depend on reactivity. The linearity of such plots has been analyzed in detail by Richard8 who attributes it to compensation between effects on reactivity of changes in thermodynamic driving force and changes in an intrinsic kinetic barrier to reaction. Much of this section will be devoted to explaining this proposal. Marcus analysis The idea of an intrinsic energy barrier for a reaction, or family of reactions, is embodied in Marcus’s treatment of the relationship between reaction rates and equilibria.227–229 For a family of reactions within which it remains constant an ‘‘intrinsic’’ barrier corresponds to the activation energy of a thermoneutral reaction (DG = 0). For other reactions ‘‘within the family’’ the experimental activation energy is sensitive to the thermodynamic driving force. This is represented schematically in Fig. 4, in which a change in equilibrium constant arises from a structural change (substituent effect) stabilizing the product of the reaction (by free energy DG). The effect of this change diminishes steadily along the reaction coordinate so that it has no effect on the reactant. A consequence is that the barrier to reaction is reduced and its energy maximum
Λ
x=0
x = 0.5
x = 1.0
ΔG °
Fig. 4 Marcus potential energy barrier G = 4x(1 – x)L perturbed by a substituent stabilizing the product by DG.
STABILITIES AND REACTIVITIES OF CARBOCATIONS
79
(transition state) is moved closer to the reactants. For simple analytical representations of the barrier, it is easy to show that the position of the maximum is reflected in the slope of a plot of activation energy DG6¼ against energy of reaction DG, which is the same as the slope of a rate–equilibrium relationship in which logs of rate constants are plotted against logs of equilibrium constants. Equations (23) and (24) summarize the relationships between DG6¼ and DG and between the slope = dDG6¼/dDG and DG for the linear perturbation of the inverted parabola shown in Fig. 4. The parabola is represented analytically by G = 4x(1 – x)L, where L is the usual mnemonic symbol for the intrinsic barrier (DG6¼ when DG = 0) and x represents the position along the reaction coordinate between 0 for reactants and 1.0 for products. For the perturbed parabola G = 4x(1 – x)L – xDG, and DG6¼ is G when dG/dx = 0. It should be noted that, in principle, G represents free energy (which is the quantity measured experimentally) but that it is treated as if it were potential energy. It is not difficult to see that if the intrinsic barrier L remains constant Equations (23) and (24) imply that a plot of DG6¼ against DG (or log k against log K) is curved, and that the curvature, which is given by d/dDG = 1/8L, depends (inversely) on the magnitude of the intrinsic barrier. In other words log k versus log K plots for reaction families with common intrinsic barriers should be strongly curved for fast reactions and show little curvature for slow reactions. On the other hand, it can also be seen that if an increase in intrinsic barrier compensates the decrease in barrier arising from the contribution of DG2/16L as the energy of reaction (and thermodynamic driving force) becomes more favorable, then the value of in Equation (24) and hence the slope of the correlation could remain nearly constant, or at least not decrease as much as expected. ðDG Þ2 16L
ð23Þ
dDG6¼ DG ¼ 0:5þ dDG 8L
ð24Þ
D G6¼ ¼Lþ 0:5DGþ
ð¼xÞ ¼
Intrinsic barriers for carbocation reactions The origin of intrinsic barriers to reactions of carbocations has been discussed by Richard.8 He suggests that reaction of water with a carbocation possessing a strongly localized positive charge such as CH3 þ will not only be favorable thermodynamically but possess a very low intrinsic barrier. By contrast, a high intrinsic barrier is associated characteristically with an SN2 reaction, in which
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H2O
CH3
H2O
CH2
+ Me O H + OMe
Scheme 30
there is strong coupling between making and breaking of bonds to an incoming nucleophile and departing leaving group. Richard points to an analogy between bond breaking to the leaving group in an SN2 reaction and the internal displacement of electrons accompanying attack of a nucleophile on a delocalized carbocation (Scheme 30). He suggests that high intrinsic barriers are associated with reactions of carbocations subject to extensive delocalization of carbocationic charge. A striking instance of such delocalization has been provided by Richard in a study of the reactions with water of p-methoxybenzyl carbocations 58 bearing a-substitutents CH3, CH2F, CHF2, and CF3.230–232 Equilibrium measurements described above (p. 54) showed that the stability of the carbocations along this series of substituents decreases by 7 log units as measured by the equilibrium constant for association of the carbocation with chloride ion pK RCl (and double that on a pKR scale). Remarkably, despite this large change in stability, rate constants for attack of water for the same series of carbocations are practically unchanged (Scheme 31). Indeed, addition of a second aCF3 group actually decreases the rate constant. Richard interprets these measurements as implying an increase in delocalization of charge and increase in double bond character at the benzylic carbon atom of the carbocation as the number of electron withdrawing fluorine substituents increases. This is consistent with a changing balance of contributions of the valence bond resonance forms 59 and 60.
+ CH R
MeO 58
R
=
10–7 × kH2O =
Scheme 31
CH3
CH 2F
4.8
10.0
CHF2
10.0
CF3
5.3
ArC+(CF3)2 0.45
STABILITIES AND REACTIVITIES OF CARBOCATIONS
+ CH CX3
MeO 59
+ MeO
CH CX3
81
(X = H or F)
60
The increase in double bond character is assumed to increase the intrinsic barrier for reaction at the a-carbon atom. As this increase is greatest for the thermodynamically least stable (CF3-substituted) carbocation, changes in thermodynamic driving force and intrinsic barrier oppose each other. The constancy of the values of kH2 O thus reflects a change in intrinsic barrier overriding the second and third terms in the Marcus expression of Equation (20). This is a more radical effect than the lesser variation preserving the linearity of the plots for the reaction families in Fig. 3 (p. 77), for which only the third term is overridden. An alternative interpretation of the dependence of intrinsic barrier on charge delocalization has been provided by Bernasconi.233 Bernasconi emphasizes that in the transition state for reaction or formation of a carbocation delocalization of charge is less effective than in the carbocation itself. How this arises has been well explained by Kresge.234 Supposing that a carbocation in Scheme 31 is formed from a benzyl halide precursor and that the carbon– halogen bond is half broken in the transition state, Kresge pointed out that the charge in the transition state must be delocalized less efficiently than in the product. This is because rehybridization of the breaking sp3 C–Cl bond to generate an empty p orbital at the charge center of the carbocation will have progressed only to the extent of 50%. It follows that if (say) a charge is 80% delocalized in the fully formed cation, it will be delocalized only to the extent of 40% in the transition state. Correspondingly, there will be a greater localization of charge at the formal carbocation center in the transition state than in the product (carbocation). This phenomenon is referred to by Bernasconi as an ‘‘imbalance’’ in charge distribution between the transition state and reactants and products. In so far as delocalization is associated with stablization of charge, it is reasonable that its impairment decreases the (intrinsic) energy barrier to reaction. This modified charge distribution in the transition state leads to a mismatch between substituent effects on the rate of reaction and on the equilibrium constant. With respect to the fluorine substituents in Scheme 31, these decrease both the stability of the carbocation and the stability of the transition state. However, while there must be less carbocation character in the transition state than in the carbocation itself the positive charge is located to a greater degree on the benzylic carbon atom and therefore will be more sensitive to stabilization by substituents. If substituent effects at the a-carbon atom in the carbocation and in the transition state are then of comparable magnitude, there will be no net effect on the rate of reaction, as is observed.
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On the other hand, because of the poor delocalization of charge, substitutents in the benzene ring will have a small effect on the stability of the transition state. Their dominant effect will be stabilization or destabilization of the delocalized charge of the carbocation itself, leading to large changes in reactivity. Thus Richard reports a relatively large value of þ = –4.8 for reaction of the ring-substituted a-trifluoromethyl benzylic carbocations (e.g. 59, X=F) with water.232 It should also be noted that while an increase in the number of fluorine substituents leaves the rate of reaction of the cation with water unaffected, the reverse reaction is profoundly affected. In the latter direction the full equilibrium effect of the substituent is felt on the rate. This is because now the effects of changes in thermodynamic driving force and intrinsic barrier complement each other. The corresponding relationship between substituent effects in forward, reverse, and equilibrium reactions and transition state ‘‘imbalance’’ in carbanion reactions, of which the nitroalkane anomaly235 is a prime example, has been discussed in detail by Bernasconi.233 Linearity of log kH2 O – pKR plots If we return now to the plot of log kH2 O against pKR of Fig. 3 (p. 77), we find that the structural changes leading to charge delocalization and changes in rate and equilibrium constants are more various than in Richard’s examples (Scheme 31). However, it remains true that delocalization of charge is the main factor affecting the stability of the carbocation and that this again is expected to lead to an imbalance between the charge distribution in the reactants and transition state. The delocalization stabilizes the carbocation and, less effectively, stabilizes the transition state, so that changes in thermodynamic driving force and intrinsic barrier again complement each other. It is perhaps less obvious in this case how the two factors combine to give a linear rather than a curved free energy relationship than when the effects are opposed. However, in the reverse reaction, the changes do oppose each other. Then, in so far as the slopes of the two log k–log K plots sum to unity, and the degrees of (positive and negative) curvature of the two plots must be the same, linearity of the plot in one direction implies linearity in the other. A way in which compensation between changes in intrinsic barrier and thermodynamic driving force can be expressed in terms of Marcus’s equation has been suggested by Bunting. Bunting and Stefanidis showed that if an intrinsic barrier is taken to vary linearly with DG, that is, L = Lo(1 þ mDG), then the curvature of a plot of log k against log K is reduced.236,237 The reduction in curvature is apparent from modifying the expression for the slope of the plot deriving from Marcus’s equation, that is = 0.5 þ DG/8L in Equation (24), which on combining with Bunting and Stefanidis’s expression for L236 is transformed to Equation (25).
STABILITIES AND REACTIVITIES OF CARBOCATIONS
DG a ¼ 0:5 þ mLo þ 8Lo
1þmDG=2 ð1þmDG Þ2
83
! ð25Þ
While Equation (25) appears complicated, a straightforward implication is that when DG = 0, a is no longer 0.5 but 0.5 þ mLo. Moreover the term which controls the variation of a in Equation (24), (DG/8L), which increases as DG increases, is moderated in Equation (25) by a factor which reduces as DG increases. It should be noted that m may be positive or negative and that the sign depends on whether L increases or decreases with increasing DG, which in turn depends on the direction of reaction. Values of mLo typically fall in the range () 0.1–0.5. Thus the lack of effect of b-fluorine substituents on the rate of the a-methyl p-methoxybenzyl cations with water (Scheme 31) implies that a = 0 and mLo = –0.5. The sensitivity of a to DG can readily be assessed for different values of m by substituting integral multiples of Lo for DG in Equation (25). In conclusion, it can also be pointed out that in principle a large value of L is itself sufficient to account for an extended linear free energy relationship. However, as Mayr has noted this is only true if the slope of the plot is 0.5.238 Moreover, if the Marcus expression offers a quantitative guide to the degree of curvature of a free energy relationship (and it is by no means clear that it does),228 it is evident that the intrinsic barriers to reactions of carbocations with familiar nucleophiles are insufficiently large to account for the lack of curvature. Mayr has also commented on the need for compensation for Marcus curvature in an extended free energy relationship. In the context of a discussion of the reactions of carbocations with alkenes, he suggests the alternative possibility that this compensation might arise from a log K-dependent change in the relative energies of frontier orbitals on the carbocation and the nucleophile.30
Estimates of intrinsic reaction barriers Notwithstanding the possibility of variation of an intrinsic barrier within a reaction series, for comparisons between different reactions it is often convenient to assume that an unmodified Marcus expression applies. This approximation is justified partly by the high intrinsic barriers and small amounts of curvature characteristic of most reactions at carbon, including reactions of carbocations. The Marcus relationship then provides a common framework for comparisons between reactions based on the measurement of even a single combination of rate and equilibrium constants. Thus, calculation
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of an intrinsic barrier using Equation (23) (p. 79) offers greater insight into comparisons between reactions than is provided by the individual measurements. It should be noted, however, that calculation of an intrinsic barrier requires modification of a measured rate constant by kBT/h, where kB is Boltzmann’s constant and derives from Eyring’s expression for DG6¼, that is L = RT ln{ko/(kBT/h)}, where ko is the rate constant for the hypothetical thermoneutral reaction (log K = 0).239 A common practice is to refer to ko as an intrinsic rate constant and to compare values of log ko between reactions in place of L. An example of the use of values of pKR and kH2 O to calculate and compare intrinsic barriers is provided by Richard’s measurements for carbocations 61–64. The objective of Richard’s study was to compare reactions in which oxygen substituents are directly attached to a charge center with similar reactions in which the charge and substituent are separated by an aromatic ring.157 In the case of formaldehyde 64 and the quinone methide 63, the ‘‘carbocation’’ corresponds to the resonance form in which charge separation places a negative charge on the oxygen atom and positive charge on carbon. In estimating these barriers Richard addresses a problem that so far has been avoided. When discussing the correlation of log kH2 O with pKR in Fig. 3, it was implied that the rate and equilibrium constants refer to the same reaction step. That is not strictly true, because attack of water on a carbocation yields initially a protonated alcohol which subsequently loses a proton in a rapid equilibrium step. As we are reminded in Equation (26) the equilibrium constant KR refers to the combination of these two steps. To calculate an intrinsic barrier for reaction of the carbocation with water therefore the equilibrium constant KR should be corrected for the lack of stoichiometric protonation of the alcohol. Fortunately, there have been enough measurements of pKas of protonated alcohols240 (e.g. pKa = –2.05 for CH3 OH2þ ) for the required corrections to be made readily. þ Rþ þ H2 OÐROHþ 2 ÐROH þ H
ð26Þ
With the appropriate equilibrium constants in hand Richard was able to calculate the intrinsic barriers for attack of a water molecule (L, kcal mol1) shown under the carbocation structures below.157 From comparing the values it can be seen that interposing a benzene ring between the oxygen substituent and carbocation center substantially increases the barrier, consistent with the expectation that the height of an intrinsic barrier depends on the extent of delocalization of charge. Interestingly, the increase between neutral oxygen and O as a substituent is rather small, despite the fact that charge delocalization must be substantially greater in the latter case.
STABILITIES AND REACTIVITIES OF CARBOCATIONS
+ MeO
L (kcal mol1)
+ EtO
CH2
CHEt
O
85
O CH2
CH2
61
62
63
64
11.5
6.6
13.2
8.7
Richard has also shown that intrinsic barriers for carbocation reactions depend not only on the extent of charge delocalization but to what atoms the charge is delocalized. In a case where values of pKR for calculation of L were not available, comparisons of rate constants for attack of water kH2 O with equilibrium constants for nucleophilic reaction with azide ion pKAz for 65–67 showed qualitatively that delocalization to an oxygen atom leads to a lower barrier than to an azido group which is in turn lower than to a methoxyphenyl substituent.226 + EtO Order of Λ:
CHEt
65
N
+ N N CHEt
<
+ MeO
CHMe
<
66
67
It is not intended to extend this discussion of reactions of carbocations with water to consideration of the alcoholic solvents trifluoroethanol (TFE) and hexafluoroisopropanol (HFIP), which have been extensively studied and reviewed by McClelland and Steenken.3 However, an important point of interest of these solvents is that their reactivities toward carbocations are greatly reduced compared with water (by up to a factor of 104 in TFE and 108 in HFIP) and that differences in rate constants can be observed between cations which would react indiscriminately at the solvent relaxation limit in water. The following comparisons of rate constants for carbocations with similar pKR values reacting with hexafluoroisopropanol241,242 reinforces the conclusion that structural variations in the cation lead to changes in intrinsic barrier and, for example, that phenyl substitution is probably associated with such an increase in going from benzyl to benzhydryl (although the benzyl cation itself is not shown).
Ph2CH+
pKR
–12.5
log k (HFIP)
0
Me + Me
CH2+
MeO
–12.4
–12.5
2.48
3.95
+
–15.7 4.3
H
+ CH-Me
–15.7 5.78
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No barrier calculations It would not be appropriate to conclude this discussion without recognizing Guthrie’s efforts to evaluate intrinsic barriers using ‘‘no barrier theory.’’243 Guthrie supposes that a chemical reaction involves a combination of energy changes that can be described by a quadratic dependence on a reaction coordinate (which for convenience is taken to vary from 0 to 1.0 between reactants and products). The term ‘‘no barrier’’ arises because the quadratic dependence implies the absence of a barrier for any single energy term. A barrier arises, nevertheless, from the combination of two or more such energy changes. Thus for a methoxybenzyl carbocation reacting with a nucleophile one energy change would correspond to bond formation, and two others to (a) rehybridization from sp2 to sp3 at the reacting carbon and (b) a change in geometry corresponding to loss of resonance of the benzene ring and methoxy group with the charge center of the carbocation as it is transformed to the nucleophilic adduct. What is required to evaluate a barrier is to estimate the energy of ‘‘reactants’’ and ‘‘products’’ of these independent transformations. The process is visualized most easily for two coordinates at right angles which define two sides of a square in which the reactants and products are at opposite corners. The energy is represented vertically and with the two geometric coordinates forms a ‘‘box.’’ The energy surface is generated by taking the two geometric coordinates, say bond breaking and rehybridization, and assigning one-dimensional quadratic energy profiles to the sides of the box, by considering both bond breaking followed by rehybridization and rehybridization followed by bond breaking. A further assumption is that for any section through the diagram for which only one of the geometric coordinates varies (i.e., parallel to one of the sides of the box) the energy is a quadratic function of that coordinate, with the minimum at the low-energy end. This suffices to generate an energy surface with a saddle point, as illustrated in Fig. 5. For the reaction of p-methoxybenzyl cations, Guthrie has estimated energies for the six species at the limits of the three geometric changes corresponding to bond breaking, rehybridization, and electron delocalization. Important anchors in the process are the fully reconstituted reactants and products, which means that the equilibrium constant for the reaction is an essential input into the calculation. He is successful in predicting barriers for the methoxybenzylic carbocations 57 within 2 kcal and has done the same with nucleophilic addition to the carbonyl and protonated carbonyl groups which are considered in an analogous manner to the carbocations proper. In principle, the success of the method depends on identifying the factors contributing to the intrinsic barrier and associating energies with their reactant and product-like geometric limits. Whether or not an energy change contributes significantly to the barrier can be assessed by including and then omitting it.
STABILITIES AND REACTIVITIES OF CARBOCATIONS
87
Free energy (kcal / mol–1)
20.
10.
0.
–10.
–20. 0.0
1.0
0.2
0.4
0.6
0.8
1.0 0.0
0.5 tor dis al c i tr me
n
tio
o
Ge
Bond change
Fig. 5
Construction of Guthrie’s ‘‘no barrier’’ plot.
Poor agreement between calculation and experiment implies that an important energetic contribution has been omitted. At the least, Guthrie’s analysis is a useful contribution to analyzing the origin of barriers to reactions. It is also remarkably successful quantitatively.
REACTIONS WITH WATER AS A BASE
Reactions of carbocations with water as a base removing a b-proton to form an alkene or aromatic product have been less studied than nucleophilic reactions with water. Nevertheless, the correlations included in Fig. 1 (p. 43) represent a considerable range of measurements and these can be further extended to include loss of a proton a to a carbonyl group.116 Indeed, if one places these reactions in the wider context of proton transfers, it can be claimed that they constitute the largest of all groups of reactions for which correlations of rate and equilibrium constants have been studied.116,244,245
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A notable difference between reactions of carbocations with water as a nucleophile and a base is the significantly higher intrinsic barrier for the latter. This difference has been demonstrated most explicitly by Richard, Williams, and Amyes22,246 for reaction of the a-methoxyphenethyl cation 68 with methanol (rather than water) acting as the base and nucleophile. The two reactions and the intrinsic barriers calculated from their rate and equilibrium constants are shown in Scheme 32. Values of L = 6.8 and 13.8 kcal mol1 are found for the substitution and elimination, respectively. The present author noted that the ratio of alcohol to alkene products formed from reactions of carbocations with water are correlated with the equilibrium constant for hydration of the double bond of the alkene product, KH2 O . This can be seen to arise if there is a rate-equilibrium relationship between log kH2 O and pKR and also between the deprotonation rate constant log kp and the pKa of the carbocation. Combing the two relationships, the log of the product ratio of alkene to alcohol log(kp/kH2 O ) might be expected to correlate with pKR – pKa, which, as we have seen, is equal to pKH2 O . Strictly speaking, the relationship holds only if the slopes of the constituent rateequilibrium plots are the same. However, comparison of Figs. 1 and 3 indicate that this is approximately true, and Fig. 6 shows that there is indeed a good linear dependence of log(kp/ kH2 O ) on pKH2 O .25 As noted above, this correlation and that of Fig. 1 are deficient in not recognizing that the product of the nucleophilic reaction is not the alcohol, as implied by the correlation with pKR, but the protonated alcohol. However, it is reasonable to suppose that variation of the pKas for O-protonation of the alcohols, which are required to correct values of KR, are small compared with variations in pKR itself (and thus pKH2 O ) and would not significantly affect the quality of the correlation. It is also true that the correlation is dominated by the large and variable values of pKH2 O for aromatic products of deprotonation. These tend to obscure variations in product ratios for tertiary alkyl and secondary benzylic cations which are the focus of a previous discussion of this partitioning by Richard.5
Ph
MeO Λ = 6.8 kcal mol + MeOH + MeO 68
C
–1
MeO
+ H+
CH3
Ph C CH3 MeO
Λ = 13.8 kcal mol–1
Scheme 32
CH2 + H+ + MeOH Ph
STABILITIES AND REACTIVITIES OF CARBOCATIONS
89
8 6
2
log kp /kH O
4 2 0 –2 –4 –6 –5
0
5
10 pKH2O
15
20
25
Fig. 6 A plot of log (kp/kH2 O ) for reactions of secondary (O) and tertiary (&) carbocations with water as a nucleophile and base against pKH2 O for hydration of the p-bond of the deprotonation product; (points close to or above the dashed line correspond to reactions for which deprotonation leads to an aromatic product).
A clear manifestation of the difference in intrinsic barriers for the nucleophilic and deprotonation reactions is apparent in Fig. 6.25 The horizontal dashed line in the figure corresponds to equal rate constants for formation of substitution and deprotonation products. It can be seen that this corresponds to pKH2 O 7, that is, when dehydration of the alcohol to the alkene is favored by 10 kcal mol1. It implies that a greater thermodynamic driving force by 10 kcal mol1 is required for the alkeneforming pathway to overcome the advantage conferred on the substitution reaction by a more favorable intrinsic barrier. Similarly, when KH2 O = 1, deprotonation occurs 104 times more slowly than the rate of formation of the alcohol product. In so far as in aqueous solution dehydration of alcohols to form alkenes is normally disfavored thermodynamically, it is clear why the rate-determining step in the acid-catalyzed dehydration (or hydration of the alkenes) is normally proton transfer. Only when the double bond of the product is strongly stabilized, for example by forming part of an aromatic ring, does deprotonation become faster than carbocation formation. The correlation of Fig. 6 is dominated by carbocations which undergo deprotonation to form aromatic products. The positive deviations of tertiary alkyl cations have already been mentioned (p. 43). As discussed by Richard7 these
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R. MORE O’FERRALL
may be due partly to the close approach of the rate constant for the nucleophilic reaction with water to its limiting value. This would mean that it no longer increased with increasing instability of the cation, while the rate constant for the elimination reaction, with its higher intrinsic barrier, would continue to increase. If both reactions had reached their limit, the point in Fig. 6 would lie on or close to the dashed line corresponding to log(kp/kH2 O ) = 0. There are other instances, however, where unusually large extents of elimination are encountered which cannot be explained in this way. An example is provided by a study of the nucleophilic and elimination reactions of the dipentamethyl benzhydryl cation 69.247 Comparisons of pKR values (from extrapolations based on the HR acidity function) with those of the unmethylated and partially methylated benzhydryl cations shown below, indicate that methylation cumulatively stabilizes the cation relative to the alcohol (possibly in part because the latter is destabilized by steric congestion). pK a = – 6.0 + H+ + 70
69
(C6H5)2CH+
(2-CH3C6H5)2CH+
(4-CH3C6H5)2CH+
Mes2CH+
–13.3
–12.7
–10.4
–6.8
69 –4.8
Somewhat surprisingly the di-pentamethylbenzhydryl cation undergoes deprotonation at an o-methyl group to give the alkene possessing the xylylene structure 70. From measurement of the alcohol–alkene equilibrium constant ( pKH2 O = 1.2), the pKa of the carbocation is deduced as pKR – pKH2 O = –5.6. The relative stability of the xylylene again must reflect steric congestion in the alcohol. However, the ratio of rate constants for deprotonation to nucleophilic trapping is also 100 times higher than expected from the correlation of Fig. 6, and it is not hard to attribute this to an even greater steric congestion in the transition state for nucleophilic attack of a water molecule than in the product. A similar reason for a higher than expected alkene-to-alcohol product ratio from reaction of the o-dimethyl cumyl carbocation248 has been proposed by Richard.5,249 REACTIONS OF NUCLEOPHILES OTHER THAN WATER
We will deal more briefly with reactions of carbocations with nucleophiles other than water, and then consider correlations in which the nucleophile rather than (as hitherto) the carbocation is varied. Fig. 7 shows a plot of
STABILITIES AND REACTIVITIES OF CARBOCATIONS
91
12
10
Ν3−
log k
8
6
4 H2O 2
0 –12
–10
–8
–6
–4
–2
0
2
pKR
Fig. 7 Plots of log k against pKR for nucleophilic reactions of water, azide ions and chloride ions (D) with benzhydryl and trityl cations.
logs of rate constants for reactions of azide ions with benzhydryl and trityl cations against pKR.77,250 Also shown for comparison are logs of rate constants (s1) for reaction of water with same cations. The plot shows the much greater reactivity of azide ions and the tendency of their reactions to be diffusion controlled over a considerable range of pKR for which, for the water reaction, the chemical step remains rate-determining. As has been discussed elsewhere, Fig. 7 demonstrates the basis for using reactions with azide ion as a clock for determining values of log kH2 O in the range pKR = –5 to 15. However, the discussion above cautions against too narrow an interpretation of this figure. The correlations apply to benzhydryl cations and trityl cations and, as we have seen, other families of cations can lead to less ‘‘ideal’’ dependences of kH2 O and, presumably, kAz on pKR. Choride ion is considerably less reactive than the azide ion. Thus, although values of kCl/ kH2 O have been quite widely available from mass law effects of chloride ion on the solvolysis of aralkyl halides, normally the reaction of the chloride ion cannot be assumed to be diffusion controlled and the value of kH2 O cannot be inferred, except for relatively unstable carbocations (p. 72). Mayr and coworkers251 have measured rate constants for reaction of chloride ion with benzhydryl cations in 80% aqueous acetonitrile and their values of log k are plotted together with a value for the trityl cation19 in Fig. 7. There is some scatter in the points, possibly because of some steric hindrance to reaction of the trityl cations. However, it can be seen that chloride ion is more
92
R. MORE O’FERRALL
reactive than the aqueous solvent. As Mayr points out, this is consistent with the ionization step being rate determining in solvolysis reactions of aralkyl halides in largely aqueous solvents. However, as the proportion of acetonitrile in the solvent increases, or in a less basic solvent such as TFE, carbocation formation becomes reversible (although for more reactive cations the reversibility may be compromised by encroachment of the diffusion limit to reaction of the chloride ion).251 Compared with chloride, the bromide ion is more reactive by rather less than a factor of 10 with respect to the benzhydryl cations and by less than a factor of 2 for the trityl cation. Fluoride and acetate ions are a little less reactive than chloride ion toward the trityl cation (less than a factor of 10) but their equilibrium affinities for the ion are more than 106-fold greater.19,219 Correlations of nucleophilic reactivity We conclude this chapter with a review of attempts to correlate reactivities of nucleophiles toward carbocations. An obvious difficulty is that for any wide variation in the nature of the nucleophile the identity of the reacting atom changes. This brings us to the limit of reasonable attempts to establish structure–reactivity relationships which, for their success, normally depend on structural changes being made away from the reaction site. It is perhaps not surprising therefore that for reactions of a carbocation with a series of nucleophiles, unless the nucleophiles form a structurally homogeneous family sharing a common reacting atom, simple rate–equilibrium relationships fail. The extent of this failure is evident from comparisons of experimental measurements of rate and equilibrium constants. One comparison in the literature is provided by Ritchie and coworkers’ study of the relatively stable cation, pyronin (the 3,6-bis(dimethylamino)xanthylium cation 71) with a series of nucleophiles.252 Another example is McClelland’s measurements of rate and equilibrium constants for the reactions of halide and acetate ions with the trityl cation.19 As already mentioned fluoride and acetate are less reactive than bromide and chloride despite their equilibrium affinities being much greater. This is reflected indeed in the much lower rates of solvolysis of the fluoride and acetate than bromide or chloride as leaving groups Me2N
+ O
NMe2
71
. Rate and equilibrium constants for reactions of the trityl cation are summarized in the first two columns of Table 7 and clearly indicate that no simple rate–equilibrium relationship exists. The mild decrease in rate constants kX for
STABILITIES AND REACTIVITIES OF CARBOCATIONS
93
Table 7 Rate and equilibrium constants and intrinsic barriers for the reaction of the trityl cation with halide and acetate anions in aqueous acetonitrile (2:1) at 20Ca
Br Cl F AcO a
kX
pKRX
L
5.0106 2.2106 8.6105 4.0105
–0.8 –1.8 –8.0 –7.8
8.9 10.0 14.6
Data from McClelland et al.19
nucleophilic attack along the series Br > Cl > F > AcO contrasts with the large change in equilibrium constants pK X R between the first and second pairs of nucleophiles. Comparable results for the reactions of acetate and halide ions with the quinone methide 57 have been reported by Richard and coworkers.219
O
C(CF3)2 57
A similar picture holds for other nucleophiles. As a consequence, there might seem little hope for a nucleophile-based reactivity relationship. Indeed this has been implicitly recognized in the popularity of Pearson’s concept of hard and soft acids and bases, which provides a qualitative rationalization of, for example, the similar orders of reactivities of halide ions as both nucleophiles and leaving groups in (SN2) substitution reactions, without attempting a quantitative analysis. Surprisingly, however, despite the failure of rate–equilibrium relationships, correlations between reactivities of nucleophiles, that is, comparisons of rates of reactions for one carbocation with those of another, are strikingly successful. In other words, correlations exist between rate constants and rate constants where correlations between rate and equilibrium constants fail. Mayr has amusingly described the ebb and flow of optimism and pessimism in a history of attempts to establish correlations based on varying the nature of a nucleophile.253 Initially, it was natural to seek a correlation for SN2 or other nucleophilic reactions of stable organic substrates, because there were few opportunities for measuring rate constants for reactions between nucleophiles and carbocations directly. Thus in 1953 Swain and Scott254 proposed the relationship of Equation (27) in which the parameters s and n refer to substrate (electrophile) and nucleophile, respectively. Methyl bromide was chosen initially as the reference substrate and, perhaps not altogether wisely, water was taken as the reference nucleophile. Subsequently, Pearson and Songstad measured nucleophilicity parameters nCH3 I for a wider range of nucleophiles using methyl iodide in methanol as electrophile and solvent.255
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R. MORE O’FERRALL
log
k kH2 O
¼ sn
ð27Þ
Swain and Scott found satisfactory correlations with Equation (27) which provided s values for a number of reactants. However, as indicated in Scheme 33, for the limited number of substrates conveniently studied,158,186 variations in s did not show a clearly discernible pattern (and no obvious correlation with reactivity). Moreover, Pearson and Songstad demonstrated that the correlations break down if extended to extremes of ‘‘soft’’ and ‘‘hard’’ electrophilic centers such as platinum, in the substitution of trans-[Pt(pyridine)2Cl2], or hydrogen in proton transfer reactions.255 Despite this, Swain and Scott’s equation has stood the test of time and it is noteworthy that a serious breakdown in the correlations occurs only when the reacting atoms of both nucleophile and electrophile are varied. In this chapter we will restrict ourselves to carbon as an electrophilic center, and particularly, although not exclusively, to carbocations. Although before the mid-1980s reactions of other than highly stabilized carbocations were not accessible to kinetic measurements, it was possible to measure ratios of products from partitioning between nucleophiles of more reactive carbocations generated in solvolysis reactions. Particularly studied was the competition between water and azide ions for carbocation intermediates produced in reactions of alkyl halides in aqueous organic solvents.28 These measurements provided values of kAz/kH2 O , determined from the ratio of azido to alcohol products. The ratios varied from 3 to 600 and showed a striking dependence on the rate constants for the solvolysis reactions, which varied over 13 powers of 10.256 In principle, these measurements represent an application of the Swain– Scott relationship to two nucleophiles only. This is apparent from Equation (28), in which nAz corresponds to n for the azide ion and the electrophilic parameter s is seen to measure the selectivity of the carbocation between azide
OTs
ArCH2 CH Me
0.27
0.34
0.43
O
O
0.77
0.87
EtOTs 0.66
OH
+
PhCH2Cl
Scheme 33
I
ArCH2 CH Me
s=
s=
Br
ArCH2 CH Me
S
0.95
Me-Br
PhSO2Cl
1.0
1.25
PhCOCl 1.43
STABILITIES AND REACTIVITIES OF CARBOCATIONS
95
and water nucleophiles. Thus the substrates for which s was measured in Scheme 33 are replaced by carbocations, including, for example, Ph2CHþ, t-Buþ and 1- and 2-adamantylþ.256 log
kAz ¼snAz kH2 O
ð28Þ
Apparently, these results implied an inverse relationship between reactivity and selectivity, with the reactivity of the carbocation measured by the inverse of the rate constant for solvolysis. This indeed was not unexpected in the context of a general perception that highly reactive reagents, especially reactive intermediates such as carbocations, carbanions, or carbenes are unselective in their reactions.257–259 Such a relationship is consistent with a natural inference from the Hammond postulate258 and Bell–Evans–Polanyi relationship,260 and is illustrated experimentally by the dependence of the Bronsted exponent for base catalysis of the enolization of ketones upon the reactivity of the ketone,261,262 and other examples21,263 including Richard’s careful study of the hydration of a-methoxystyrenes.229 However, as has again been well summarized by Mayr,253 a striking antithesis was then established between the variation in these values of kAz/ kH2 O and measurements by Ritchie of rate constants for reactions of a wide range of nucleophiles with relatively stable carbocations such as crystal violet 72, pyronin 71, the p-dimethylaminophenyltropylium ion or the p-nitrophenyldiazonium ion. For such stable cations, direct kinetic measurements were possible using conventional spectrophotometric monitoring or, for faster reactions, a preliminary mixing of reagents by stopped flow. NMe2
+
Me2N
72 NMe2
Far from confirming a dependence of nucleophilic selectivity on the reactivity of the carbocations, Ritchie observed that selectivities were unchanged over a 106-fold change in reactivity.15 He enshrined this result in an equation (29) analogous to that of Swain and Scott, but with the nucleophilic parameter n modified to Nþ to indicate its reference (initially) to reactions of cations, and with the selectivity parameter s taken as 1.0, that is, with no dependence of the selectivity of the cation on its reactivity (as measured by the rate constant for the reference nucleophile, kH2 O for water).
96
R. MORE O’FERRALL
log
k kH2 O
¼Nþ
ð29Þ
This lack of variation of selectivity with reactivity was confirmed in an independent study by Kane-Maguire and Sweigart who found that relative reactivities of amine and phosphine nucleophiles toward a range of organometallic cations were also independent of the nature of the electrophile.184,264 The dilemma presented by these conflicting results was resolved by TaShma and Rappoport.265 They pointed out that the apparent dependence of kAz/ kH2 O upon the reactivity of the carbocation arose because even the most stable cation reacting with azide ion did so at the limit of diffusion control. Thus while kH2 O remained dependent on the stability of the cation in the manner illustrated in Fig. 7 the rate constant for the azide ion remained unchanged. Thus the most stable cation formed in the solvolysis reactions was the trityl ion, for which direct measurements of kH2 O = 1.5105 s1 and kAz = 4.1109 now show that even for this ion the reaction with azide ion is diffusion controlled.22 The advent of laser flash photolytic studies, and the correct use of product ratios to assess reactivities of nucleophiles competing with azide ions reacting at the diffusion limit, led to direct measurements of rates of nucleophilic reactions for a much wider range of carbocation stabilities. Much of this work, which was carried out by the research groups of McClelland and Steenken and Richard and Amyes, has already been cited. We will return to these studies in the context of a further discussion of reactivity and selectivity and the failure of rate constants of reactions of nucleophile to correlate with equilibrium constants at the end of this chapter. First, however, we turn to a further investigation of carbocation reactions undertaken by Mayr and his research group in Munich. In a comprehensive series of studies Mayr has extended Ritchie’s observations and placed them in a wider context, including applications to organic synthesis. As will be seen, together with the studies of McClelland and Richard this work leads at least in outline to a coherent view of reactivity, selectivtiy and equilibrium in carbocation reactions. Nucleophile–electrophile reactions and synthesis Rappoport and TaShma’s work removed a major difficulty for Ritchie’s analysis and helped pave the way for Mayr to exploit fully the wide applicability and simplicity of Equation (29) for predicting rates of reactions of electrophiles with nucleophiles. Mayr pointed out that Equation (29) could be rewritten as Equation (30), in which log ko corresponds to the rate constant for reaction of the electrophile under study with a reference nucleophile266 (chosen as water by Ritchie) which, in so far as it is characteristic of the
STABILITIES AND REACTIVITIES OF CARBOCATIONS
97
electrophile, is sensibly denoted E. We can then rewrite Equation (30) as Equation (31), in which the measured rate constant for reaction is expressed as the sum of one parameter for the nucleophile and one for the electrophile. Log k¼log ko þNþ
ð30Þ
Log k¼EþN
ð31Þ
In Equation (31), Ritchie’s parameter Nþ is replaced by N because, as will become clear, there is a difference in the definition of these parameters, including the choice of reference nucleophile. However, the striking simplicity of the relationship in representing reactions in which the nucleophile and electrophile are equal partners is apparent. It implies that reactivity of electrophile–nucleophile combination reactions might be predicted from two parameters. The challenge of presenting this as a practical aid to organic synthesis was taken up by Mayr’s research group.267 The starting point for Mayr’s work in the mid-1980s was very different from Ritchie’s studies of mainly oxygen and nitrogen nucleophiles. Mayr’s initial aim was to measure rate constants for the synthetically important alkylation reactions of alkenes.27,268,269 As representative alkylating agents, he chose p-substituted benzhydryl cations to provide a homogeneous family of electrophiles. These ions could be generated by the addition of the appropriate benzhydryl chloride to dry methylene chloride containing BCl3. The reactions with alkenes were carried out at 70C and monitored spectrophotometrically or conductimetrically under conditions for which the rate-determining step of the reaction was attack of the electrophile on the alkene.270 The temperature dependences of the reactions were studied to extrapolate rate constants at 20C, and rate constants for a fraction of the reactions were measured directly at this temperature, with the carbocations generated from the benzhydryl chlorides by flash photolysis.27,83 Mayr initially defined a set of electrophilic parameters for the benzhydryl cations using a reference nucleophile, which was chosen as 2-methyl-1pentene.268,269 Values of E were then defined as log k/ko, where ko refers to a reference electrophile (E = 0), which was taken as the 4,40 dimethoxybenzhydryl cation. Plots of log k against E for other alkenes are thus analogous to the plots of log k against pKR in Fig. 7 except that the correlation is referenced to kinetic rather than equilibrium measurements. However, they differ from plots based on the Swain–Scott or Ritchie relationships in which log k is normally plotted against a nucleophilic parameter, that is, n or Nþ, rather than E. In practice, rate constants for only a limited range of benzhydryl cations could be measured for 2-methyl-1-pentene itself. However, it became apparent that if reaction of the cation occurred at a methylene group (=CH2) plots of
98
R. MORE O’FERRALL
log k versus E were almost parallel for alkenes of widely differing reactivity. This allowed E values for benzhydryl cations varying in reactivity from p,p0 -dichloro to p,p0 -bis(dimethylamino) to be assigned. When the structure of the p-nucleophile was varied more widely to include nonterminal alkenes, alkenes with O, N, or other b-substituents, alkynes, and aromatic molecules, a greater variation in the slopes of the plots was found. Fig. 8 shows plots of log k versus E for a representative group of alkene structures as well as for arenes.271 To accommodate the more reactive nucleophiles, the electrophilicity range of the benzhydryl carbocations was extended by inclusion of p-amino substituents for which the electron-donating ability of the amino group was amplified by incorporation in a tricyclic ring structure.272 Variations in slope are not large but are sufficient to merit addition of a slope parameter for each nucleophile. The logic of choosing a structurally homogeneous set of electrophiles is now evident. These can be reacted with
O N
N
OSiMe3
8
OSiMe3
O
OSiMe3 OSiMe3
OSiMe3
OPh
with s = 1
6
SiMe2Cl 4
log k
2
N = –E
0
–2
–4 –10
–8 + CH
N
2
–6
–4
+ CH
+ CH
NMe2 2
NPh2 2
–2 + CH
Ph
N
CF3 2
0 + CH
OMe 2
2
4 + CH
6 + CH
Me 2
Cl
2
with E = 0
Electrophilicity(E )
Fig. 8
Plots of log k versus E for the reaction p-nucleophiles with benzhydryl cations.
STABILITIES AND REACTIVITIES OF CARBOCATIONS
99
nucleophiles of very different structure and differences in slope can be assigned to steric or other effects associated exclusively with the nucleophile. One way to modify Equation (31) to allow for the different slopes is to multiply the electrophilicity parameter E by a variable s as shown in Equation (32). Note again that s here differs from s in the Swain–Scott equation which refers to the slope of a plot of log k versus the nucleophilicity parameter n (or N) rather than electrophilicity parameter (E). However, the equation that Mayr adopts is not Equation (32) but Equation (33),269 in which s multiplies not only E but both E and N. This is formally equivalent to Equation (32), because s is still determined by the slope of the plot of log k against N, that is, by the dependence of log k on the nucleophile only. However, multiplication of N by s leads to some subtle changes which suit the original purpose of the study, namely, to develop synthetically useful predictions of rates of reactions of electrophiles with nucleophiles. It is an unusual but interesting and practical manipulation of an otherwise conventional free energy relationship. Log k ¼ sE þ N
ð32Þ
Log k ¼ sðN þ EÞ
ð33Þ
One virtue of Equation (33) is that it avoids long extrapolations of values of N measured for electrophiles with E values far removed from zero. This can be seen from Fig. 8 which includes plots of log k versus E for highly unreactive p-nucleophiles such as toluene and highly reactive ones such as vinyl acetals and enamines. According to Equation (33), the value of N corresponds to the intersection of the plot of log k versus E not with the vertical line (ordinate) for E = 0 but, as shown in the figure, with the horizontal line corresponding to E = –N. This intersection has the physical significance that the rate constant for combination of the relevant nucleophile and electrophile (i.e. at the E value of the intersection) is 1.0 M1 s1. Mayr points out that an advantage of this definition is that it prevents crossover of correlation lines which in some instances occur if the extrapolations are extended beyond the reactivity ranges likely to lead to reaction. Thus the relative magnitudes of N properly reflect relative reactivities of nucleophiles under realistic reaction conditions. Although not well illustrated in Fig. 8 the potential for crossover is implicit in the lack of parallelism of the correlation lines. Of course, if all lines were parallel with unit slope the relative magnitudes of N would be the same whether defined by Equation (32) or (33). In the most recent correlation analysis based on Equation (33) a ‘‘basis set’’ of 23 benzhydryl cations and 39 p-nucleophiles, for which extensive measurements are available, were selected to provide a set of reference parameters which would not require further modification as data was acquired for new
100
R. MORE O’FERRALL
nucleophiles, and indeed new electrophiles.272 As before the p,p0 dimethoxybenzhydryl cation was assigned the value E = 0 and the slope parameter s for 2-methyl-1-pentene was defined as 1.0. One might query the robustness of anchoring the correlation to a single s value, but the effectiveness of this is endorsed by the good overlap of plots for nucleophiles ranging from the most to the least reactive, as is evident in Fig. 8. Moreover, a comparable analysis of slopes and intercepts of plots of pKa against Xo for a ‘‘basis set’’ of weak bases undergoing protonation in strongly acidic media shows little difference from an alternative analysis in which a common slope parameter is assigned to structurally similar bases covering a range of base strengths.52,53,55 The origin of the variation in s values for the different alkenes encompassed by Equation (33) is not entirely clear but steric effects have an obvious influence. Thus, as shown in Scheme 34, alkylation of tetramethyl ethylene gives s greater than 1.0 (1.44) consistent with increased selectivity as a result of hindrance to attack of an electrophile by the methyl substituents.27 Aromatic p-systems also have high s values, especially where reaction occurs at an o-position.271 However, b-oxygen and allylic silicon, germanium, or tin substituents decrease s,269,273 while for phenylacetylene s also appears to be low.269 A tendency for less reactive nucleophiles to have larger s values may imply a mild dependence of selectivity on reactivity, but the variations in s are small and changes in reactivity large. Just as N for a nucleophile can be determined from a plot of log k against E for a series of electrophiles, in principle, the value of E for an electrophile can be determined from the intercept (at E þ N = 0) of a plot of log (k/s) versus N for a series of nucleophiles (or indeed, if need be, from the measurement for a single nucleophile). In this way E values have been determined for many electrophiles other than benzhydryl cations, including metal-coordinated cations,186 BF3-coordinated aldehydes,274 tropylium ions, and many benzylicand heteroatom-substituted carbocations. In the low reactivity range
0.98
0.94 SiMe3
0.94
OSiMe3
1.32
OPh
1.17 1.62 OSiMe3 OMe
SiMe3 1.40
Scheme 34
0.70 0.98
1.17
Ph
STABILITIES AND REACTIVITIES OF CARBOCATIONS
101
electrophiles extend to neutral molecules. These may also be included within the benzhydryl calibration framework by choosing quinone methides such as 73 in which nucleophilic attack is directed to an electrophilic carbon–carbon double bond by bulky substituents flanking the carbonyl group.275 Such quinone methides have been important in establishing N values for reactive nucleophiles such as nitroalkyl276 and other stabilized carbanions275,277 including phosphorus ylids.278 With a further extension of nucleophiles to include organometallic reagents, the range of processes embraced within the nucleophile–electrophile combinations includes Friedel–Crafts alkylations, Wittig and Mannich reactions, Nicholas propargylation, and Mukaiyama aldol cross couplings among other synthetically useful reactions.27
Me2N
O 73
It should be noted that although the core E and N values are defined for CH2Cl2 as solvent, rates of reactions between positively charged and nonhydrogen-bonded neutral reagents are normally only weakly sensitive to solvent27,270,279 so the values should provide a reasonable approximation over a range of solvents. On the other hand, for reactions of carbocations with carbanions, especially where negative charge is delocalized to oxygen, a much greater solvent sensitivity is observed and different N parameters have been determined in water and DMSO as solvents. It should be noted that the effect of solvent is expressed in the N values and that to a good approximation the E values for nonpolar solvents can be retained. The simplest demonstration of the synthetic utility of the E and N parameters follows from the approximation that all the slope parameters s in Equation (33) are 1.0 and that log k = E þ N. It is then possible to plot E parameters against N parameters to give the reactivity box shown in Fig. 9.280 A diagonal of this box corresponds to E þ N = 0 and k = 1 M1 s1. Lines parallel to this diagonal correspond to constant values of log k indicated by the appropriate (constant) value of E þ N. If the E and N values of two reagents are known or can be guessed then a reasonable assessment of the time for reaction can be made. Reactions with E þ N in the upper left of the box (i.e., with large negative values) will be relatively slow, and this area, for which k is predicted to be <106 M1 s1, is partitioned off. Reactions represented in the lower section of the box will be fast, and the right hand diagonal indicates the limit of reaction under diffusion control, with k = 1010 M1 s1. As is also indicated, reactions in the upper right-hand corner represent attack of a carbanion at an (electrophilic) double bond and, at the lower left, attack
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R. MORE O’FERRALL Cl
CN N
O
N
OSiMe3
CN
O O
NO2 COOEt COOEt
MeO
–20
k < 10 –6 M–1s–1
COOEt
o
No reaction at 20 C
COOEt
O2N Ph + Pd(PPh ) 3 2
E –10
E+N=0
N2+
Me + N CH2 Me
–1 –1
k = 1.0 M s
+
0
+
+
k > 1010 M–1s–1
Co2(CO)6 OMe +
No reaction at 20oC Me3C +
10 –10
0
10
20
N Fig. 9 Semiquantitative model of reactivity in electrophile–nucleophile reactions.
of a carbocation on a relatively unreactive double bond. Ionic polymerizations of vinyl derivatives are further important reactions for which Fig. 9 provides a valuable guide.281 Although for many reagents determining values of E or N may not be feasible, often an approximate value may be interpolated from comparison with the wide range of structures for which values are known. Extensions of Mayr’s work In addition to their reactions with alkenes and carbanions as nucleophiles benzhydryl cations react with hydride donors.282–284 These hydride transfer reactions show the same linear dependence of log k upon E as the reactions with alkenes and the same constant relative selectivity, that is with slopes of plots s close to 1.0, for structures ranging from cycloheptatriene to the
STABILITIES AND REACTIVITIES OF CARBOCATIONS
103
borohydride anion and dihydropyridines and solvents from methylene chloride to DMSO or aqueous acetonitrile. As with the reactions with alkenes the measurements were shown to be rather insensitive to changes in solvent. It might appear that this discussion has departed far from the original consideration of nucleophiles which was focused on anions in hydroxylic solvents. However, a feature of Mayr’s scheme is the wide range of its application. Of obvious interest is its extension to nucleophilic centers other than carbon or hydrogen and to water as a solvent. Reactions of strong nucleophiles in water are not easily observable for the more unstable benzhydryl carbocations, but are readily monitored with highly stabilized aminosubstituted cations such as those shown in Fig. 8, which were developed by Mayr as part of the benzhydryl series of compounds for this purpose. For these ions, reactions with water, hydroxide ion, other oxyanions, amines, amino acids,285 azide ion,286 and a thiolate ion have been studied.266,287 Plots of log k against E are again linear, and confirm that a consistent nucleophilic behavior is observed between p-nucleophiles and n-nucleophiles as different as olefinic hydrocarbons and the hydroxide ion. These measurements allow a comparison with the earlier analyses of reactions of n-nucleophiles in water in terms of Ritchie’s Nþ equation. A significant finding is that although plots of log k against E are linear, the slopes are significantly less than 1.0, falling consistently in the range 0.52–0.71 except for water (0.89) and –OOCCH2S (0.43). The exceptional behavior of water is consistent with difficulties Ritchie encountered in taking this as a reference nucleophile for the Nþ relationship and is in line with values for other hydroxylic solvents.288 On the other hand, the narrow range of s and N values for other nucleophiles becomes compatible with the Nþ relationship if Nþ = 0.6N. We will return to the significance of this, but note that assignment of s and N values to nucleophiles on which the Nþ relationship was based allows, in turn, assignment of E values to cations studied by Ritchie, notably trityl cations and substituted xanthylium ions and tropylium ions. It is remarkable that Mayr’s study, which originated with a very different reaction and solvent, is able to correlate satisfactorily data for nucleophilic reactions of carbocations in aqueous solution. In principle, any carbocation for which a rate constant for reaction with water below the relaxation limit has been measured, either directly by flash photolysis or indirectly by the azide clock, may be assigned an E value based on the values of N = 5.11 and s = 0.89 for water (although where possible E values are better based on reactions with more nucleophiles). On the other hand, it is to be expected that on moving beyond the structural constraints of the benzhydryl cations, the assigned E values will have less generality, if only because of the influence of steric effects. Thus the E values assigned to trityl cations overestimate by several orders of magnitude their reactivities toward alkenes. This is consistent with the known steric demands of the trityl cation289 and the likelihood that steric effects would be qualitatively different for reactions with alkenes and nitrogen or oxygen bases.
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Likewise, although N values for alkenes and hydride donors are practically independent of the solvent, hydrogen bonding to oxygen and nitrogen nucleophiles renders their N values sensitive to the nature of the solvent. This solvent dependence has been examined in some detail for the reactions of benzhydryl cations with halide ions, for which the cations were generated by flash photolysis.251 As might be expected, a reduction in the solvent ionizing power, as judged by solvent Y values, increases reactivity. More than a 100-fold difference was found between ethanol and TFE as solvent, and intermediate values were found for water and water–acetonitrile mixtures. In a striking application of this data, combination of N and s values for solvent288 and halide ions with E values for carbocations, allows an effective analysis of the detailed course of SN1 solvolyses, especially if allowance is made for encroachment of the diffusion limit for reactions of more reactive carbocations with halide ions.251 These results are by no means unrelated to the synthetic motivation of the earlier studies of alkylation reactions in CH2Cl2 as solvent. Comparisons of N and s values of alkenes and aromatics with those of hydroxylic solvents offer a guide to the conduct of Friedel–Crafts and other electrophilic carbon-carbon bond-making reactions in hydroxylic solvents. Not surprisingly, TFE is a particularly favorable solvent for such reactions and if allowance is made for a minor solvent dependence of N values for arenes and alkenes a good estimate of the likely feasibility of such reactions can be made.290–293 Remarkably, despite earlier suggestions to the contrary294 a good correlation exists between nucleophilic parameters for reactions of carbocations and those for SN2 substitutions. This is true of the Swain–Scott parameters (or Pearson and Sonntag’s nCH3 I values), and a particularly good correlation exists between Mayr’s N values and rate constants for SN2 displacements of neutral dibenzothiophene from the S-methyldibenzothiophenium ion 73, both for a range of hydroxylic solvents studied by Kevill295 and by oxygen, amine, and even phosphorus nucleophiles measured by Mayr and coworkers.253
+ S Me
74
However, the slope of the plot of log k against N for these reactions is not 1.0 but close to 0.6. This implies that increased nucleophilicity is nearly twice as effective in promoting reaction with a carbocation as with an SN2 substrate. Although the mechanisms of these reactions are different, it is perhaps
STABILITIES AND REACTIVITIES OF CARBOCATIONS
105
surprising that a highly reactive carbocation should be less selective than relatively unreactive alkylating agents such as methyl bromide correlated by the Swain equation. This point has been discussed by Richard, Toteva, and Crugeiras, who point to a likely difference in intrinsic reactivity associated with the closed rather than open electron shell of the reaction site for reactions at a saturated carbon center.219 In recognition of the excellent correlation that exists between his own and Swain and Scott’s (or Kevill’s) parameters, Mayr suggests modifying Equation (33) to include a further electrophilic constant distinguishing reactions at sp2 and sp3 carbon atoms.29,253 He denotes this constant sE to indicate that it refers specifically to the electrophile, and introduces the subscript ‘‘N’’ for the parameter s which has so far referred to the nucleophile. Again, instead of adopting the expected conventional form of log k = sNE þ sEN he chooses Equation (34), in which values of E and N correspond to intercepts on the abscissa rather than the ordinate of plots of log k versus E or N. Of course, the original Equation (33) and indeed the Swain–Scott equation (Equation 27) are special cases of Equation (34). log k¼sE sN ðE þ NÞ
ð34Þ
In Equation (34), Mayr has not only provided a simple and comprehensive relationship embracing nucleophilic reactions at carbon, but has tested the relationship with hundreds of examples. The equation and measurements provide a practical basis for semiquantitative prediction of reaction rates embracing a large number of synthetic organic and organometallic reactions, as we have seen. Many incidental problems have also been addressed, including the choice of amine catalysts for organocatalysis,296,297 partitioning of carbocations between solvent and nucleophiles,288 competition between alkylation and hydride abstraction,283 carbocationic and carbanionic polymerizations,298 quantitative free energy profiles for SN1 nucleophilic substitutions,251 and the nature of the borderline between SN1 and SN2 mechanisms.299 An analog of Equation (33) has been applied to estimating rate constants for SN1 solvolyses in terms of parameters representing reactivities of leaving groups and incipient carbocations.300
REACTIVITY, SELECTIVITY, AND TRANSITION STATE STRUCTURE
In addition to the work on carbocation reactions already described Mayr,28 together with Richard and McClelland, has been concerned with problems raised by the lack of dependence of selectivity on reactivity apparent both from the normal constancy and specific variations in values of the slope parameters sN (and sE).28 We conclude this chapter, therefore, with a brief discussion of
106
R. MORE O’FERRALL
this problem and of additional questions raised by the lack of correlation of rate with equilibrium constants when the reacting atom of the nucleophile is varied between anionic or neutral oxygen, nitrogen, sulfur, phosphorus, or halogen atoms. We begin by considering a plot of Mayr’s E parameters against pKR in Fig. 10. For the benzhydryl cations shown as open circles the correlation is excellent. For other cations there is dispersion into structurally related groups such as trityl cations and tropylium ions. This behavior shows a close analogy with plots of log kp and log kH2 O against pKa and pKR in Figs. 1 and 3 (pp. 43 and 77) and may be considered normal for what amounts to a rate–equilibrium relationship. The slope of 0.68 for the plot is also comparable to that for plots of log kH2 O against pKR.4 There is little or no indication of curvature in Fig. 10 and in this respect the plot is again similar to those of Figs. 1 and 3. The behavior may be interpreted in terms of compensation between changes in thermodynamic driving force for the reaction and variations in intrinsic activation barrier, both depending on changes in equilibrium constant for the reaction, as discussed already (pp. 77–90). An important point made by Mayr, is that the constant slope for these relationships by no means implies a static transition state.282 This was
5
E
0
–5
–10
–10
–5
0 pKR
5
10
Fig. 10 Plot of E parameters against pKR: open circles, benzhydryl cations; filled circles, trityl cations; squares, organometallic cations; filled triangles, tropylium ions; open triangles, flavylium, xanthylium and other O-, S-, or N-conjugated cations.
STABILITIES AND REACTIVITIES OF CARBOCATIONS
107
demonstrated in model calculations for hydride transfer between carbocation centers, which showed a systematic dependence of the degree of hydrogen transfer at the transition state upon the energy of reaction. The calculations also demonstrated that changes in intrinsic barrier occurred and were associated with a marked imbalance in charge distributions between reactants and transition state. When calculated values of the activation energy were plotted against the energy of reaction, they furnished slopes = 0.72 for structural changes leading to changes in energy of the carbocation acting as hydride acceptor and = 0.28 for corresponding changes in the hydride donor. These values are close to the values of 0.75 and 0.25 one might expect for a symmetrical transition state in which the hydrogen is half transferred and rehybridization of the reacting bonds had occurred to the extent of 50%, as envisaged in Kresge’s idealized model discussed above (p. 81).234 As expected the intrinsic barrier is increased by electron donating substituents (which stabilize the carbocations through delocalization of the charge) in the hydride donor and acceptor. For the carbocation, the effects of substituents on the energy of reaction and intrinsic barrier are complementary and for the donor, they are opposed. Mayr’s calculations are consistent with his experimental demonstrations that for hydride transfer the magnitudes of N and E are independent of each other. It seems likely that the same is true of reactions of carbocations with alkenes, which again yield a carbocation as immediate product of the reaction. In these reactions then, the lack of dependence of selectivity on reactivity can be interpreted in terms of the compensation between thermodynamic driving force and variable intrinsic barrier, as already discussed, which receives substantial reinforcement from Mayr’s calculations. On the other hand, it seems less likely that the relative reactivities of nnucleophiles should be independent of the reactivity of a carbocation. At least when they act as bases, there is little or no evidence that changes in structure of n-nucleophiles lead to changes in intrinsic barrier.301 One might expect therefore that carbocations of different reactivities reacting with a structurally related group of nitrogen or oxygen nucleophiles would show different slopes of plots of log k versus log K. There are some difficulties with testing this experimentally. The first is that it is not easy to match the same set of bases to electrophiles of quite different reactivity. A second is that the most readily available equilibrium constants characterizing the nucleophiles are pKas of the conjugate acids, which do not necessarily correlate reactivities toward carbocations. Thirdly, one should avoid reactions influenced by diffusion control. Finally, care has to be taken with steric and solvent effects. McClelland has studied the reaction of four primary amines with benzhydryl and trityl cations.4,302 Rate constants for reactions of most of the benzhydryl cations were close to their values for diffusion control. However, he was able to measure diffusion free rate constants for substituted trityl cations. There was a further complication, consistent with earlier measurements by Berg and
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R. MORE O’FERRALL
Jencks303 in so far as there is a significant influence from a preequilibrium desolvation of the amine, which is larger for more basic amines. Nevertheless, based on careful measurements, McClelland was able to correct for this and demonstrate a clear dependence of slopes ( nuc) of plots of log k against the pKa of the ammonium ion upon the stability of the trityl cation as shown in Fig. 11. Interestingly, no leveling of the plot was observed for trityl cations such as crystal violet conforming to Ritchie’s equation. These measurements are consistent with earlier studies by McClelland of the trityl and xanthylium ions for which plots of log k against Nþ for a wide range of nucleophiles were recorded. The correlations showed some scatter, with a strong positive deviation of the azide ion, but it was clear that the slopes of the best straight lines through the points were considerably less than unity, being 0.33 for the trityl cation19 and 0.65 for the xanthylium ion.304 Again, the distinguishing feature of these cations compared with those studied by Ritchie was their much higher reactivity. A further dependence of the selectivity between different nucleophiles on the stability and reactivity of carbocations was found by Richard and Amyes in a study of reactions of alcohols and carboxylate anions with p-substituted a-trifluoromethyl benzyl cations (75, X = Me, OMe, SMe, N(Me)CH2CF3, and NMe2) monitored using the azide clock.305 Apart from the methylsubstituted substrate, for which the reactions approached diffusion control,
0.7
β nuc
0.6
0.5
0.4
0.3
–10
–5
0
5
pKR
Fig. 11 Plot of nuc against pKR for reaction of primary amines with trityl cations ( values corrected by 0.2 to allow for desolvation of amines).
STABILITIES AND REACTIVITIES OF CARBOCATIONS
109
there was a strong dependence of selectivity upon the stability of the cation. The selectivities were measured from ratios of products of reactions of ethanol and TFE with the carbocations (or Bronsted exponents for reaction of carboxylate anions) and the stability was measured by the rate constant kS for reaction of the carbocation with the aqueous TFE as solvent. The variation in selectivity (kEtOH/kTFE) became saturated for the most stable p-aminosubstituted cations, for which selectivities are practically independent of the nature of the amino group. This behavior is indicated below by the substituent dependence of kEtOH/kTFE product trapping ratios, which vary by a factor of 100 between Me and Me2N. CH+
X
CF3
75
X
Me
MeO
MeS
CF3CH2(Me)N
Me2N
kEtOH/kTFE
3.1
55
71
270
330
kS (s1)
11010
5107
1.2107
2104
<800
It seems clear therefore that more reactive cations than those for which Ritchie’s Nþ relationship was developed, show a distinct dependence of selectivity between nucleophiles upon the stability and reactivity of the carbocation. Richard has confirmed that for a very stable benzylic ‘‘carbocation,’’ represented by the bis-trifluoromethyl quinone methide 57, the Nþ regime is restored and that a plot of log k against Nþ for reactions of nucleophiles, including amines, oxygen and sulfur anions, the azide ion, and a-effect nucleophiles, shows a good correlation with Nþ.219 CF3 O
C CF3 57
This is further confirmation that there is scope for constant selectivity regimes. Richard comments that the sharp dependence of selectivity upon reactivity he and McClelland found for relatively reactive cations must be moderated for more strongly stabilized ions if a limiting value of nuc near to 1.0 is not to be exceeded. As Richard points out, the low reactivity and high intrinsic barriers for highly stabilized electrophiles will necessarily be
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R. MORE O’FERRALL
associated with a weak dependence of selectivity on reactivity and in this respect is consistent with expectations based on the Marcus equation. It should be emphasized that the dependence of selectivity on reactivity established for electrophiles of intermediate reactivity is by no means at odds with Mayr’s assignments of ‘‘constant’’ N values to n-nucleophiles. Thus in Mayr’s study of amines, changes of selectivity between different nucleophiles can be highlighted by log k–log K plots for different electrophiles reacting with a common group of nucleophiles. For two nitrogen-substituted carbocations differing in reactivity by 300-fold the ratio of nuc values was estimated as 0.85 (Mayr and Ofial unpublished data). However, because systematic variations in selectivity with reactivity appear to be quite mild (a) they are likely to be revealed only by large changes in reactivity and (b) N values still provide a reliable basis for semiquantitative assessments of reactivities. Thus the range of reactivities of electrophiles chosen by Mayr for defining N-values for n-nucleophiles fall within experimentally measurable ranges, and these are likely to be of most relevance to predictions of the feasibility of electrophile– nucleophile combination reactions.
HARD AND SOFT NUCLEOPHILES
The nucleophiles discussed so far have been either carbon nucleophiles, or homogenous sets of amine or neutral oxygen nucleophiles. The Nþ relationship embraces a wide variety of anionic nucleophiles with different reacting atoms. As already demonstrated, reactivities of these nucleophiles strikingly fail to correlate with equilibrium constants for their reactions. The interpretation of reactivities here provides a particular challenge, because differences in solvation and bond energies contribute differently to reaction rates and equilibria. Analysis in terms of the Marcus equation, in which effects on reactivity arising from changes in intrinsic barrier and equilibrium constant can be separated, is an undoubted advantage. Only rather recently, however, have equilibrium constants, essential to a Marcus analysis, become available for reactions of halide ions with relatively stable carbocations, such as the trityl cation, the bis-trifluoromethyl quinone methide (49), and the rather less stable benzhydryl cations.19,219 A comparison of reactions of halide and acetate ions with quinone methide 57 has been provided by Richard, Toteva, and Crugeiras.219 The lack of correlation between rate and equilibrium constants is highlighted by the fact that iodide ion is 1400 times more reactive than acetate despite the reaction being thermodynamically less favorable by 6 kcal mol1. This is characteristic of a comparison of soft and hard nucleophiles, of which the former show lower intrinsic barriers306,307 The consistent behavior between different (Nþ)
STABILITIES AND REACTIVITIES OF CARBOCATIONS
111
electrophiles is signaled by differences in intrinsic barrier between the quinone methide 57 and the trityl cation being independent of the nature of the nucleophile. (Intrinsic barriers for the reactions with the trityl cation are shown in Table 7 on p. 93.) Richard points to two factors likely to affect the comparison between acetate and halide ions (F, Cl, and I). One is that the observed differences in intrinsic barriers parallel differences in solvation energy. In Marcus’s original rate–equilibrium relationship a contribution from a preequilibrium step involving desolvation was explicitly included. In practice, however, it is difficult to separate contributions from this step from changes in intrinsic barrier. Where desolvation is not specifically recognized therefore it will be expressed as a contribution to the intrinsic barrier. Correspondingly, any desolvation of the anions that occurs before covalent interaction of the nucleophile with the carbocation will tend to reduce the difference in intrinsic barriers for the bonding-making reaction step. Put another way, differences in intrinsic barriers between the four ions might be expected to be considerably smaller in the gas phase than in solution. The second factor is the dependence of bonding interactions between the nucleophile and carbocation at the transition state upon the distance between the charge centers. The importance of this is suggested by a comparison of rate and equilibrium constants for the reactions of chloride ion and Me2S with the quinone methide 57 and p-methoxybenzyl cation. For the p-methoxybenzyl cation the equilibrium constant for reaction with the sulfur nucleophile is more favorable than that for the chloride ion by a factor of 107. As already discussed on p. 73 (cf. Table 6) this is a normal reflection of the greater carbon basicity of sulfur than chlorine. However in the case of the quinone methide the relative magnitudes of the equilibrium constants is reversed, with KMe2 S /KCl = 0.008. Toteva and Richard attribute this to the unfavorable steric and electrostatic interactions between the CF3 groups of the quinone methide adduct and the positively charged sulfonium ion. The significance of these results for differences in reactivities of nucleophiles is that, despite the unfavorable relative equilibrium constants, Me2S is more reactive toward the quinone methide than chloride ion by a factor of nearly 3000. This mismatch of rate and equilibrium effects is summarized in Scheme 35. It must imply (a) that there is a relatively long partial bond between sulfur and carbon in the transition state so that the unfavorable steric and electrostatic effects are not developed and (b) that the favorable carbon–sulfur bonding interaction is well developed despite the long bonding distance. It is not intended to pursue this discussion to a firmer conclusion. However, it is reasonable to infer that our understanding of reactivity and selectivity in carbocations has been brought to a point where the origins of differences in reactivities of hard and soft nucleophiles and of lack of correlation of rate and equilibrium constants have been greatly clarified. Particularly, in the hands of
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R. MORE O’FERRALL
–
Me2S
O
CF3
CF3 SMe2+ CF3 K Me2S /K Cl = 0.008
O CF3
Cl–
–
O
CF3 Cl CF3
k Me2S /kCl = 2700
Scheme 35
Richard, the Marcus analysis, allied to the concept ‘‘imbalance’’ of bond making and charge development at the transition state, has provided an effective framework for tackling one of the outstanding problems for a general interpretation of reactivity. A reasonable conclusion might be that further measurements of equilibrium constants will be required to support and test the level of understanding achieved so far, and to probe more deeply the interpretation of ‘‘hard and soft’’ nucleophilicity in its application to reactions of electrophilic carbon atoms.
SUMMARY AND CONCLUSIONS
It seems clear that for reactions of carbocations with nucleophiles or bases in which the structure of the carbocation is varied, we can expect compensating changes in intrinsic barrier and thermodynamic driving force to lead to relationships between rate and equilibrium constants which have the form of extended linear plots of log k against log K. However, this will be strictly true only for structurally homogeneous groups of cations. There is ample evidence that for wider structural variations, for example, between benzyl, benzhydryl, and trityl cations, there are variations in intrinsic barrier particularly reflecting steric effects which lead to dispersion between families of cations. On the other hand, for carbocations reacting with n-nucleophiles such as amines or alcohols a systematic dependence of selectivity on reactivity becomes apparent. As usual, this is not readily detected as curvature of a free energy relationship for a single carbocation reacting with a series of nucleophiles, because it is difficult to find a structurally homogeneous family covering a sufficiently wide range of reactivity. It is apparent, however, from plots of log k against pKa (or other measure of reactivity or stability) for reaction of a more a limited range of nucleophiles with a series of different carbocations. The slopes of the plots show a systematic relationship between the reactivity of the carbocation and its selectivity between different
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nucleophiles. Ironically, the measurements of McClelland and Richard reestablish the conclusion incorrectly drawn from measurement of selectivities between water and azide ion for carbocations reacting with azide ions under diffusion control, namely that there is an inverse relationship between reactivity and selectivity. These results have been assessed from different points of view. In an article entitled ‘‘The Reactivity-Selectivity Principle: An Imperishable Myth in Organic Chemistry’’ Mayr and Ofial comment that except where it is an artifact of competition between chemically activated and diffusion-controlled reactions examples of an inverse relationship between reactivity and selectivity are relatively rare, and they cite extensive earlier literature making this point.30 From an alternative point of view, one can consider such relationships as representing ‘‘ideal’’ behavior consistent with the Hammond postulate and Bell–Evans–Polanyi principle,259 from which real relationships depart, because of variations in intrinsic barrier and associated ‘‘imbalance’’ of bond making and bond breaking in transition states. Expositions of the ‘‘imbalance principle’’ and its application to different reactions are contained in articles by Jencks on carbonyl reactions,263 by Richard8 and Bernasconi,233 on carbocation and carbanion reactions and by Gajewski on electrocyclic reactions.308,309 The views of Mayr and Ofial differ from these by less than might at first appear. They invoke variations in frontier orbital interactions to account for departures from Bell–Evans–Polanyi behavior,30 and in an earlier discussion suggest a similar role for variations in intrinsic barrier in hydride transfer reactions.282 Because ‘‘systematic’’ variations in selectivity with reactivity are commonly quite mild for reactions of carbocations with n-nucleophiles, and practically absent for p-nucleophiles or hydride donors, many nucleophiles can be characterized by constant N and s values. These are valuable in correlating and predicting reactivities toward benzhydryl cations, a wide structural variety of other electrophiles and, to a good approximation, substrates reacting by an SN2 mechanism. There are certainly failures in extending these relationships to too wide a variation of carbocation and nucleophile structures, but there is a sufficient framework of regular behavior for the influence of additional factors such as steric effects to be rationally examined as deviations from the norm. Thus comparisons between benzhydryl and trityl cations reveal quite different steric effects for reactions with hydroxylic solvents and alkenes, or even with different halide ions Steric effects provide examples of ‘‘hard cases’’ with respect to predicting reactivities. The same might be said to be true of solvent effects for reactions of n-nucleophiles or carbanions. However, while values of N may vary with solvent the differences can be exploited, for example, in promoting a desired reaction in synthesis. Moreover, in attempting to interpret solvent effects, it is possible that comparing measurements of reaction rates and (preferably)
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equilibria in solvents of widely differing ion-solvating characteristics, such as water, DMSO, and HFIP, will be helpful in separating intrinsic differences in reactivity from specific solvation effects. Marcus’s treatment provides a relatively unexploited framework for such an analysis. A particular difficulty arises for the comparison of hard and ‘‘soft’’ nucleophiles. This difficulty indeed is amplified if one goes beyond carbocation reactions to consider softer or harder electrophilic centers, such as transition metals or protons. Interpreting differences between reacting atoms presents an ultimate challenge for attempts to understand reactivity. Richard has gone a considerable way toward offering a rational analysis of the principal factors to be considered in such an endeavor. However, this is one issue likely to attract attention in the next one hundred years of carbocation chemistry and in the wider field of electrophile–nucleophile combination reactions.
Acknowledgments Many helpful comments from Herbert Mayr, Armin Ofial, and Peter Guthrie and support of much of the author’s own work by The Science Foundation Ireland (Grant No. 04/IN3/B581) are gratefully acknowledged.
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213. Kirmse W, Kilian J, Steenken S. J Am Chem Soc 1990;112:6399–400. 214. Frekel M, Marsh KN, Wilhoit RC, Kabo GJ, Roganov GN. Themodynamics of organic compounds in the gas phase. College Station, TX: Thermodynamics Research Centre, 1994. 215. Fainberg AH, Winstein S. J Am Chem Soc 1956;78:2770–7. 216. Dfietze PE, Jencks WP. J Am Chem Soc 1986;108:4549–55. 217. Bentley TW, Carter GE. J Am Chem Soc 1982;104:5741–7. 218. Raber DJ, Harris JM, Hall RE. J Am Chem Soc 1971;91:4821–8. 219. Richard JP, Toteva MM, Crugeiras J. J Am Chem Soc 2000;122:1664–74. 220. Toteva MM, Richard JP. J Am Chem Soc 2000;122:11073–83. 221. Richard JP, Amyes TL, Bei L, Stubblefield V. J Am Chem Soc 1990;112:9513–9. 222. Pham TV, McClelland RA. Can J Chem 2001;79:1887–97. 223. Amyes TL, Richard JP. J Am Chem Soc 1990;112:9507–12. 224. Richard JP. J Am Chem Soc 1991;113:4588–95. 225. Jagannadham V, Amyes TL, Richard JP. J Am Chem Soc 1993;115:8465–6. 226. Richard JP, Amyes TL, Jagannadham V, Lee Y-G, Rice DJ. J Am Chem Soc 1995;117:5198–205. 227. Marcus RA. J Phys Chem 1968;72:891–9. 228. Lewis ES, Shen CS, More O’Ferrall RA. J Chem Soc Perkin Trans 2 1981; 1084–8. 229. Richard JP, Williams KB. J Am Chem Soc 2007;129:6952–61. 230. Amyes TL, Stevens IW, Richard JP. J Org Chem 1993;58:6057–66. 231. Richard JP. J Org Chem 1994;59:25–9. 232. Richard JP. J Am Chem Soc 1989;111:1455–65. 233. Bernasconi CF. Adv Phys Org Chem 1992;27:119–238. 234. Kresge AJ. Can J Chem 1974;52:1897–903. 235. Bordwell FG, Boyle WJ, Jr. J Am Chem Soc 1972;94:3907–11. 236. Bunting JW, Stefanidis D. J Am Chem Soc 1989;111:5834–9. 237. Yamataka H, Nagase S. J Org Chem 1988;53:3232–8. 238. Schindele C, Houk KN, Mayr H. J Am Chem Soc 2002;124:11208–14. 239. Glasstone S, Laidler KJ, Eyring H. Theory of rate processes. New York: McGraw Hill; 1941. 240. Perdoncin J, Scorrano G. J Am Chem Soc 1977;99:6983–6. 241. McClelland RA, Mathivanan N, Steenken S. J Am Chem Soc 1990;112:4857–61. 242. McClelland RA, Chan C, Cozens FL, Modro A, Steenken S. Angew Chem Int Ed 1991;30:1337–9. 243. Guthrie JP, Pitchko V. J Phys Org Chem 2004;17:548–59. 244. Caldin EF, Gold V, editors. Proton transfer reactions. London: Chapman & Hall; 1973. 245. Stewart R. The proton: applications to organic chemistry. Orlando, FL: Academic Press; 1985. 246. Richard JP, Williams KB, Amyes TL. J Am Chem Soc 1999;121:8403–4. 247. Hegarty AF, Wolfe VE. ARKIVOC 2008; 161–82. 248. Creary X, Hatoum HN, Barton A, Aldridge TE. J Org Chem 1992;57:1887–97. 249. Amyes TL, Mizersi T, Richard JP. Can J Chem 1999;77:922–33. 250. McClelland RA, Kanagasabapathy VM, Steenken S. J Am Chem Soc 1988;110:6913–4. 251. Minegishi S, Loos R, Kobayashi S, Mayr H. J Am Chem Soc 2005;127:2641–9. 252. Ritchie CD, VanVerth JE, Ting JY. J Am Chem Soc 1983;105:279–84. 253. Phan TB, Breugst M, Mayr H. Angew Chem Int Ed 2006;45:3869–74. 254. Swain CG, Scott BS. J Am Chem Soc 1953;75:846–8. 255. Pearson RG, Sobel H, Songstad J. J Am Chem Soc 1968;90:319–26. 256. Raber DJ, Harris JM, Hall RE, Schleyer PvR. J Am Chem Soc 1971;93:4821–8.
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257. Pross A. Adv Phys Org Chem 1977;14:69–132. 258. Hammond GS. J Am Chem Soc 1955;77:334–8. 259. Argile A, Carey ARE, Fukata G, Harcourt M, More O’Ferrall RA, et al. Isr J Chem 1985;26:303–12. 260. Bell RP. The proton in chemistry. 2nd ed. London: Chapman & Hall; 1973. 261. Bell RP, Lidwell OM. Proc Roy Soc A 1940;176:88–113. 262. Kresge AJ. Chem Soc Rev 1973;2:475–504. 263. Jencks WP. Chem Rev 1985;85:511–27. 264. Alavosus TJ, Sweigart DA. J Am Chem Soc 1985;107:985–7. 265. TaShma R, Rappoport Z. J Am Chem Soc 1983;105:6082–95. 266. Minegishi S, Mayr H. J Am Chem Soc 2003;125:286–95. 267. Mayr H, Kuhn O, Gotta MF, Patz M. J Phys Org Chem 1998;11:642–54. 268. Mayr H, Schneider R, Grabis U. J Am Chem Soc 1990;112:4460–67. 269. Mayr H, Patz M. Angew Chem Int Ed 1994;33:938–57. 270. Mayr H, Schneider R, Schade C, Bartl J, Bederke R. J Am Chem Soc 1990;112:4446–54. 271. Mayr H, Bartl J, Hagen G. Angew Chem Int Ed 1992;31:1613–5. 272. Mayr H, Bug T, Gotta MF, Hering N, Irrgang B, Janker B, et al. J Am Chem Soc 2001;123:9500–12. 273. Burfeindt J, Patz M, Muller M, Mayr H. J Am Chem Soc 1998;120:3629–34. 274. Mayr H, Gorath G. J Am Chem Soc 1995;117:7862–8. 275. Lucius R, Mayr H. Angew Chem Int Ed 2000;39:1995–7. 276. Bug T, Lemek T, Mayr H. J Org Chem 2004;69:7565–76. 277. Kaumanns O, Lucius R, Mayr H. Chem Eur J 2008;14:9675–82. 278. Appel R, Loos R, Mayr H. J Am Chem Soc 2009;131:704–14. 279. Richard JP, Szymanski P, Williams KB. J Am Chem Soc 1998;120:10372–8. 280. Lucius R, Loos R, Mayr H. Angew Chem Int Ed 2002;41:92–95. 281. Ofial AR, Mayr H. Macromol Symp 2004;215:353–67. 282. Wurthwein EU, Lang G, Schaple LH, Mayr H. J Am Chem Soc 2002;124:4084– 92. 283. Mayr H, Lang G, Ofial AR. J Am Chem Soc 2002;124:4076–83. 284. Richler D, Mayr H. Angew Chem Int Ed 2003;48:1958–61. 285. Brotzel F, Mayr H. Org Biomol Chem 2007;5:3814–20. 286. Phan TB, Mayr H. J Phys Org Chem 2006;19:706–13. 287. Brotzel F, Chu YC, Mayr H. J Org Chem 2007;72:3679–88. 288. Minegishi S, Kobayashi S, Mayr H. J Am Chem Soc 2004;126:5174–81. 289. Tsuno Y, Fujio M. Adv Phys Org Chem 1999;34:267–385. 290. Hofmann M, Hampel N, Kanzian T, Mayr H. Angew Chem Intl Ed 2004;43:5402–5. 291. Westmaier H, Mayr H. Org Lett 2006;8:4791–9. 292. Westmaier H, Mayr H. Chem Eur J 2008;14:1638–47. 293. McClelland RA, Cozens FL, Li J, Steenken S. J Chem Soc Perkin Trans 2, 1996; 1531–43. 294. Pross A. Theoretical and physical principles of organic reactivity. New York: Wiley; 1995, p. 232. 295. Kevill DN. In: Charton M, editor. Advances in structure-property relationships. Greenwich: JAI; 1996. pp. 81–115. 296. Baidya M, Kobayashi S, Brotzel F, Schmidhammer U, Riedle E, Mayr H. Angew Chem Intl Ed 2007;46:6176–9. 297. Lakhdar S, Tokuyasu T, Mayr H. Angew Chem Int Ed 2008;47:8723–6. 298. Ofial AR, Mayr H. Macromol Symp 2004;215:4076–83. 299. Nolte C, Phan TB, Kobayashi S, Mayr H. J Am Chem Soc 2009;131:11392–401.
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300. Denegri B, Ofial AR, Juric S, Streiter A, Kronja O, Mayr H. Chem Eur J 2006;12:1648–56, 1657–66. 301. Marcus RA. J Am Chem Soc 1969;91:7224–5. 302. McClelland RA, Kanagasabapathy VM, Banait NS, Steenken S. J Am Chem Soc 1992;114:1816–23. 303. Berg U, Jencks WP. J Am Chem Soc 1991;113:6997–7002. 304. McClelland RA. J Am Chem Soc 1989;111:2929–35. 305. Richard JP, Amyes TL, Vontor T. J Am Chem Soc 1992;114:5626–34. 306. Bernasconi CF, Killon RB. J Am Chem Soc 1988;110:7506–12. 307. Bernasconi CF, Ketner RJ, Chen X, Rappoport Z. J Am Chem Soc 1998;120:7461–8. 308. Gajewski JJ. J Am Chem Soc 1979;101:4393–4. 309. Gajewski JJ. Acc Chem Res 1980;13:142–8.
Secondary equilibrium isotope effects on acidity CHARLES L. PERRIN Department of Chemistry & Biochemistry, University of California – San Diego, La Jolla, CA 92093-0358, USA 1 Scope 123 2 Theory 125 3 Methodology 127 pH titration 127 NMR pH titration 127 NMR titration 128 Equilibrium perturbation 132 4 Secondary deuterium isotope effects on acidities in solution 134 OH acids 134 NH acids 136 CH acids 142 5 Heavy-atom isotope effects on acidities 143 6 Secondary isotope effects on Lewis acid–Lewis base interactions 144 7 Secondary isotope effects on gas-phase acidity and basicity 146 8 Secondary isotope effects on conformational equilibrium 148 9 Secondary isotope effects on tautomeric equilibria 150 10 Secondary isotope effects on hydrogen bonding 152 11 Secondary isotope effects in chromatography 153 12 Secondary isotope effects on molecular structure 155 13 Origin of secondary isotope effects on acidity 157 Evidence from vibrational spectroscopy 157 Computations 159 Cause of frequency changes 162 Necessity for an inductive effect? 164 Acknowledgments 167 References 167
1
Scope
This chapter is a review of secondary equilibrium isotope effects (IEs) on acidity, primarily on the comparison of protium with deuterium (and also tritium), but also addressing the IEs of 13C, 14C, 15N, and 18O. Secondary IEs are those where the bond to the isotope remains intact, whereas primary IEs are those where the bond is broken. Primary isotope effects are generally 123 ADVANCES IN PHYSICAL ORGANIC CHEMISTRY VOLUME 44 ISSN: 0065-3160 DOI: 10.1016/S0065-3160(08)44003-0
2010 Elsevier Ltd. All rights reserved
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considerably larger than secondary, which therefore represent a challenge to measure. For hydrogen the distinction between primary and secondary is quite clear, and primary IEs are those involving hydrogen transfer. Many of those are solvent IEs, and there is a considerable literature on this topic, including fractionation factors.1 We ignore all kinetic IEs,2 although we include some equilibrium IEs that were measured along with kinetic IEs for purposes of comparison. Also, it must be noted that any IE on acidity must also be one on basicity, because acidity and basicity are affected in equal and opposite amounts by an isotope. IEs provide a discriminating insight into molecular structure and reactivity. They involve only a minimum perturbation, and they can be directed at specific positions within a molecule. Molecules that differ in the position of an isotope are called isotopomers, although the usual IEs are between isotopologues, molecules that differ in the number of isotopic substitutions. This review updates a classic and influential review by Halevi.3 What makes the current review timely is the recent development of a nuclear magnetic resonance (NMR) titration method capable of exquisite accuracy and not subject to the systematic error associated with possible impurities in one of the samples and not in the other. New values can now be compared with previous ones. The subject of acidity is viewed broadly, and examples are not restricted to IEs on protonation reactions. Among the generalizations are IEs on Lewis acidity and basicity, IEs on conformational and tautomeric equilibria that can be converted into IEs on acidity, and IEs in chromatographic separations that depend on IEs on acidity. IEs on enzyme-catalyzed reactions are omitted, because their emphasis is ordinarily on kinetic IEs, which are used to determine mechanisms.4 However, it should be recognized that equilibrium IEs are operative in the association of substrates with enzyme active sites.5,6 One of the questions that is addressed in this chapter is the origin of the secondary IEs. Certainly, zero-point energies must be involved, but are they the only origin or can an inductive effect arising from anharmonicity of bond vibrations also contribute? An example of this controversy is typified by a recent statement that IEs ‘‘result from the anharmonicity of C–H vs. C–D bonds, manifested in a reduced C–D bond length. This results in increased electron density at a carbon bearing D relative to H, which is also revealed by the increased shielding observed for 13C NMR resonances.’’7 Yet it has long been accepted that a simple inductive effect cannot be operative, whereby deuterium is more electron-donating than protium, because the Born–Oppenheimer approximation guarantees the electronic wave function to be independent of nuclear mass.8 Kinetic IEs are conventionally defined as kheavier/klighter, even though the effect of a change ought to be expressed as kchanged/kunchanged. This convention is chosen for convenience, because the IE is then usually >1. The same
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convention, Kheavier/Klighter, is chosen for equilibrium IEs even though the IE can be >1 or <1 depending on how K is defined. For definiteness K will here refer to the IE on acidity, so K > 1 corresponds to an Hacid stronger than the Dacid.
2
Theory
The theory of IEs was formulated by Bigeleisen and Mayer.9 The IE on the acid–base reaction of Equation (1) is defined as the ratio of its acidity constant Ka to the acidity constant of the isotopic reaction, Equation (2). The ratio Ka/ K*a is then the equilibrium constant KEIE for the exchange reaction of Equation (3). That equilibrium constant may be expressed in terms of the partition function Q of each of the species, as given in Equation (4), which ignores symmetry numbers. HAÐHþ þ A
ð1Þ
HA ÐHþ þ A
ð2Þ
HA þ A ÐA þ HA
ð3Þ
KEIE ¼
QðA ÞQðHA Þ QðHAÞQðA Þ
ð4Þ
The IE and the partition functions can be separated into three factors, MMI, EXC, and ZPE, as in Equation (5). The MMI factor comes from the ratios of molecular masses and moments of inertia, but has been simplified to Equation (6) by using the Redlich–Teller product rule, which assumes harmonic potentials. The products are over all the vibrational frequencies i of each species. This factor is usually negligible (i.e., 1) for secondary IEs, except for very small molecules, and it is often omitted in calculations because it is sensitive to errors in calculating low frequencies. The second factor, EXC, is given by Equation (7), where ui = h i/kT and the products are over all the vibrational frequencies. This factor arises from contributions from thermally excited vibrational states. It too is usually very close to 1, because only isotopes of hydrogen show large differences in vibrational frequency, but those frequencies are so high that their excited vibrational states are not thermally populated to any significant extent. It is easy to calculate the EXC factor, but it is usually so close to 1 that it cannot be measured unambiguously, and the only experimental example that we know of is the kinetic IE for C–N rotation in HCONH2,10 where the frequency of the pyramidalization mode of the NH2 is unusually low.
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KEIE ¼ MMI EXC ZPE
ð5Þ
MMI ¼
i ðA Þ i ðHA Þ i ðHAÞ i ðA Þ
ð6Þ
EXC ¼
ð1 exp ½ui ðA ÞÞ ð1 exp ½ui ðHA Þ ð1 exp ½ui ðHAÞÞ ð1 exp ½ui ðA ÞÞ
ð7Þ
The third factor, ZPE, given in Equation (8), where the sums are over all the vibrational frequencies, is the dominant contributor to the IE. It arises from the zero-point energies. Often terms cancel, so that only a single isotopesensitive vibrational mode dominates. If so, each of the sums in Equation (8) reduces to a singlepterm due to the zero-point energy of that mode. Then, because i = (1/2p) (ki/), ZPE simplifies to the expression in Equation (9). Often the force constant k for that mode is lower in the base A and the reduced mass is higher with the heavier isotope. Then the acid HA with the lighter isotope has the highest zero-point energy, so that the IE is >1. exp½ui ðA Þ=2 exp ½ui ðHA Þ=2 Þ=2 exp½u i ðHAÞ=2 exp ½ui ðA X 1 ¼ exp ½ui ðA Þ þ ui ðHA Þ ui ðHAÞ ui ðA Þ 2
ZPE ¼
p 1X p 1 1 ½ kðA Þ kðHAÞ p p ZPE exp 2
ð8Þ
ð9Þ
An alternative that focuses on molecular structure rather than vibrational frequencies is the nuclear–electronic orbital approach, which calculates equilibrium IEs by treating some or all nuclei quantum mechanically on the same basis as the electrons.11 Because the Born–Oppenheimer approximation is only an approximation, light atoms, especially hydrogen, are quantum mechanical, and the electronic wave function is not independent of nuclear mass. This method provides bond lengths and atomic charges that vary with isotopic substitution. For example, in formate anion-h, -d, and -t, the (Mulliken) charges at oxygen are –0.729, –0.731, and –0.732, respectively, and the C–H, C–D, and C–T bond lengths are 1.1554, 1.1475, and 1.1441 A˚. The increasing negative charge is consistent with a greater basicity. Similarly, D and T substitution in methylamine, dimethylamine, and trimethylamine is calculated to lead to shorter C–D and C–T bonds and greater electron density at nitrogen, consistent with a greater basicity.
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127
Methodology
pH TITRATION
Potentiometric titration and measurement of conductivity are the classic methods for determining pKa experimentally. With a differential method that involves comparison of meter readings for two substances under carefully controlled conditions, it is possible to obtain accurate differences in pKa.
NMR pH TITRATION
NMR pH titration is another method. It depends on the fact that proton transfer among acid and base forms is very fast, so that the observed chemical shift is the average of the chemical shifts A and B of acid and base forms, but weighted by their respective concentrations, as in Equation (10). Solving Equation (10) for [B]/[A] and substituting into the Henderson–Hasselbalch equation [Equation (11)] leads to Equation (12). Finally, solving Equation (12) for leads to Equation (13), expressing the pH dependence of the chemical shift as a familiar titration curve. By fitting the observed variation of chemical shift, or simply by finding the inflection point, where the change in chemical shift is maximum, it is possible to measure pKa. ¼
B ½B þ A ½A ½B þ ½A
ð10Þ
pH ¼ pKa þ log
½B ½A
ð11Þ
pH ¼ pKa þ log
A B
ð12Þ
¼
A 10 pH þ B 10 pKa 10 pH þ 10 pKa
ð13Þ
What is required is that the chemical shift change appreciably between acid and base forms. Because 13C, 15N, 19F, and 31P chemical shifts are dispersed over a large range, there is usually at least one suitable reporter nucleus near enough to the site of protonation, and even 1H chemical shifts show sufficient variation. Thus the pKa of glycine could be measured from the inflection points in the pD dependence of its 1H or 13C chemical shifts.12 Similarly, from the variation with pH of the 13C chemical shifts of acetic, propionic, and butyric acids the pKa of each acid could be measured.13 The separate pKas of four lysines in a pentadecapeptide could be measured from the pH
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dependence of their "-CH2 chemical shifts, whose cross peaks with a-CH are well resolved in a 2D TOCSY spectrum.14 Moreover, because of the sensitivity of NMR chemical shifts to environment, the NMR titration can be applied to a mixture of substances, each with its own NMR spectrum, to determine differences in pKa. It is applicable even to IEs because isotope shifts (isotope effects on NMR chemical shifts)15–18 often lead to separate, resolvable, and assignable signals for isotopologues. The chemical shift of each of the substances then follows its own Equation (13), from which each pKa can be determined. It should be recognized though that chemical shifts do not always respond in the way expected from changes in electron density. For example, the 13C signal of a carboxylic acid shifts downfield on deprotonation,19 and the 15N signal of pyridine shifts upfield on protonation. A further advantage of NMR titration is that all measurements are made in a common solution, so that impurities do not interfere.
NMR TITRATION
It is desirable to avoid errors in pH measurement, which limit the accuracy of the above NMR pH titration. If an NMR titration is applied to a mixture of two acids, HA and HA0 , each of whose chemical shifts, and 0 , follows Equation (13), it is possible to eliminate pH from the two equations and replace it with n, the number of equivalents of titrant added. Thus Ellison and Robinson obtained Equation (14), where D = – 0 , D = – 0 , D = – 0 , and R = Ka/K0 a.20 Moreover, it is not necessary to prepare solutions of exact molarity, because n can be evaluated more readily as ( – )/( – ), from the variation of the chemical shift of HA during the titration. When R is near 1, this is approximately a parabolic dependence of D on n. The titration of a mixture of formic acid and 18O2–formic acid permitted the evaluation of the 18 O IE on acidity from the 13C NMR chemical shifts and 0 of the carboxyl carbons. In practice, this involved fitting to the three parameters D, D, and R. This same equation was used with 31P chemical shifts to evaluate the 18O IE on the acidity of phosphoric acid and alkyl phosphates.21 D ¼ D þ
Rnð þDD Þ nð Þ Rn n þ 1
ð14Þ
Rabenstein and Mariappan applied a very similar procedure to measure the 15N IE on the acidity of glycine from the 13C NMR chemical shifts of the carboxyl carbons during titration of a mixture of glycine-14N and glycine-15N.22 The IE could be evaluated by fitting to Equation (15), where þ 14 15 D = 14 – 15, D ¼ 14 15 , D15 ¼ 15 þ 15 , D14 ¼ 14 14 , R ¼ Ka =Ka , þ and n ¼ ð14 14 Þ=ð14 14 Þ. This is the same as Equation (14), but with a simplification of the numerator. For glycine the carboxyl carbon is sufficiently
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distant from the nitrogen that there is no 13C isotope shift due to 14N versus 15 N in the fully protonated or fully deprotonated material, so D = 0 and D15 = D14, which reduces Equation (15) to a two-parameter fit [Equation (16)]. D ¼ D þ
D¼
RnD 15 nD 14 Rn n þ 1
ð15Þ
RnD 14 nD 14 Rn n þ 1
ð16Þ
Similarly, Lippmaa and coworkers evaluated the relative acidities of linear and branched carboxylic acids from the variation with degree of protonation of the measured 13C NMR shifts.23 The method was then extended to secondary deuterium IEs, evaluated from the variation with degree of protonation of the measured 13C NMR shifts of a mixture of isotopologues.24 The data were fit by nonlinear least squares to Equation (17), where H and D are the observed chemical shifts of undeuterated and deuterated isotopologues, H þ and D are those chemical shifts in the deprotonated form, þ H and D are H D those chemical shifts in the protonated form, R ¼ Ka =Ka , and n is the degree of protonation of the undeuterated material. This is the same equation as Equation (15), but adapted to deuteration, and again n is evaluated from chemical shifts as ðH H Þ=ðH þ H Þ.
H D ¼ H D nðH þ HÞ þ
Rn ð þ DÞ 1 þ ðR 1Þn D
ð17Þ
A further improvement in the NMR titration comes from eliminating both pH and n entirely and expressing the comparison in terms of chemical shifts only.25,26 This is applicable to any pair of acids, AHþ and BHþ, with a ratio of þ þ =KBH . It is readily shown that the chemical acidity constants K equal to KAH a a shifts are related to each other by Equation (18), where a and b are the observed chemical shifts during the titration and A, AHþ , B, and BHþ are limiting chemical shifts of unprotonated and protonated A and B. This is a nonlinear equation in the one parameter K, and it can be fit by nonlinear least squares. a ¼ A þ
ðAHþ A Þðb B Þ ð1 KÞðb B Þ þ KðBHþ B Þ
ð18Þ
A further simplification comes from linearizing this equation, to produce Equation (19). Therefore, a plot of ðb B ÞðAHþ a Þ versus ða A ÞðBHþ b Þ ought to be a straight line, with slope K and zero intercept. This too is a one-parameter equation, which can be analyzed by linear least squares. Error analysis, to obtain the standard deviation of slope and intercept, is especially easy.
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ðb B ÞðAHþ a Þ ¼ Kða A ÞðBHþ b Þ
ð19Þ
The first applications of this method were to conformational analysis of mixtures of cis- and trans-4-phenylcyclohexylimidazole (1) and of the a and b anomers of glucosylimidazole (2, R = H) and its tetraacetate (2, R = COCH3), using 1H NMR. Its generality was demonstrated for other mixtures, including cis- and trans-4-tert-butylcyclohexylamine (3), cis- and trans-4-tert-butylcyclohexanecarboxylic acid (4), and the four stereoisomers of 2-decalylamine (5), using both 1H and 13C NMR.27 These examples demonstrate the power of the method for measuring relative acidities of closely related materials, without the necessity of separating them. Moreover, the method could be applied in a wide variety of solvents, including aqueous methanol, dimethyl sulfoxide (DMSO), and dichloromethane, some of which would never permit the use of a pH electrode. Still another example is the pairwise titration of PhCRR0 N(CH3)2 (R,R0 = H,CH3), showing the same relative basicity with either BF3 or CF3COOH in CDCl3.28
N Ph
N
RO RO RO
COOH t-Bu
N RO
1
4
NH2
O N t-Bu
2
3 H
H
NH2
5
It should be noted that the method depends on accurate determination of the limiting chemical shifts A, AHþ , B, and BHþ , obtained at beginning and end of the titration. Consequently, it is not very suitable for diprotic acids, unless the two pKas are very widely separated.29 This NMR titration method was subsequently applied to equilibrium IEs on acidity.30–33 Like the previous methods, it too benefits from the high sensitivity of 13C and 19F chemical shifts, and even 1H chemical shifts, to both isotopic substitution and state of protonation. Figure 1 shows the NMR titration of a mixture of tri(methyl-d)amine and tri(methyl-d2)amine in D2O, plotted according to Equation (19). The slope is 1.1618 0.0004. The intercept is –0.0061 0.0046, properly zero. The correlation coefficient is an impressive 0.999999, which is an indication of the accuracy achievable. Another remarkable result was the measurement of the relative basicity of the two exceedingly similar isotopomers of 1-benzyl-4-methylpiperidine-2,2,6-d3 (6). These are truly isotopomers (here stereoisomers), which bear the same number of isotopic substitutions and differ only in the position of the isotope, which is either axial or equatorial.
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25
10–3 (δH+ – δH)(δD – δD°)
20
15
10
5
0
0
5
10 10–3 (δH – δH°)(δD– – δD)
15
20
Fig. 1 NMR titration [Equation (19)] of a mixture of (CH2D)3NHþ and (CHD2)3NHþ.33 Reprinted with permission from J Am Chem Soc 2008;130:11143–8. Copyright 2008 American Chemical Society. D H3C
N CH Ph 2 H D D
6
A variant that combines this NMR titration method with NMR pH titration was developed much earlier by Forsyth and Yang.34 The 19F isotope shift between N-methyl or N,N-dimethyl-4-fluoroaniline and its CD3 or (CD3)2 isotopologue shows a maximum at a pH near the pKa of the anilinium ion. Rearranging Equation (19) and ignoring intrinsic isotope shifts leads to Equation (20), where A and AHþ are chemical shifts of the aniline and the anilinium ion, respectively, assumed the same for both isotopologues. From this equation the IE on acidity could be evaluated at any pH, or preferably by averaging over all the pH values near the pKa. KaH ðh AHþ Þðd A Þ ¼ D Ka ðh A Þðd AHþ Þ
ð20Þ
The benefits of this method for measuring IEs on acidity, with its variants, are apparent. It is highly accurate, because it depends only on measurement of NMR chemical shifts, not pH or molarity or solution volume. Numerous reporter nuclei can be used, including 1H, 13C, 19F, and 31P. It is
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applicable to mixtures of isotopologues or isotopomers, without separating them. It is insensitive to the presence of impurities that could lead to systematic errors in comparisons of acidities between separate solutions. A wide variety of solvents can be used. It can be extended beyond IEs to measuring relative acidities of closely related substances, without the necessity of separating them.
EQUILIBRIUM PERTURBATION
A very different method, the equilibrium perturbation method, is applicable to measure equilibrium IEs when the reaction is slow enough that its rate can be measured.35,36 Let the reaction be A ! B [Equation (21)] and its isotopic variant A* ! B* [Equation (22)]. The kinetic IEs in the forward and reverse directions are kf =kf and kr =kr , respectively, and the equilibrium IE KEIE is ðkf =kf Þ=ðkr =kr Þ, or ðBinf =Ainf Þ=ðBinf =Ainf Þ in terms of equilibrium concentrations at infinite time. kf
AÐB kr
kf
B A Ð kr
ð21Þ
ð22Þ
If a mixture is prepared with only A and B*, in an initial ratio r0 equal to A0 =B0 , the reactions of Equations (21) and (22) will occur, to establish the equilibrium. From stoichiometry, it can be shown that at equilibrium the ratio R = kr/kf = Ainf/Binf of unlabeled materials must satisfy Equation (23). This is a quadratic that could be solved to evaluate R if KEIE were known. R2 þ ð1 r0 ÞR r0 ¼0 KEIE
ð23Þ
Because of the kinetic IE, one reaction [Equation (21) for definiteness, as is likely if the heavier isotope reacts more slowly] is faster than the other, so that the total concentration of A þ A* is temporarily depleted (or augmented) until the slower reaction restores the equilibrium. The solution to the kinetic equations is Equation (24), which will simplify because A0 ¼ 0 and Ainf þ Ainf ¼ A0 . The expression in Equation (24) reaches an maximum [or a minimum if Equation (21) corresponds to the faster reaction] given by Equation (25), where ¼ ðkf þ kr Þ=ðkf þ kr Þ. Rearrangement of Equation (25) gives Equation (26), where A0 – Ainf is equal to A0/(1þR) and where R could be obtained from Equation (23) but is adequately approximated by r0.
SECONDARY EQUILIBRIUM ISOTOPE EFFECTS ON ACIDITY
A þ A ¼ Ainf þ Ainf þ ðA0 AinfÞexp ½ðkf þ kr Þt þ A0 Ainf exp kf þ kr t h i ðA þ A Þ max= min ¼ A0 þ ðA0 AinfÞ = ð 1 Þ 1 = ð 1 Þ ðA þ A Þ max = min A0 ¼ = ð 1 Þ 1 = ð 1 Þ ðA0 AinfÞ
133
ð24Þ
ð25Þ
ð26Þ
If A and A* have a characteristic spectrum, usually a UV absorbance, the time course of A þ A* can be followed, and its maximum or minimum, as in Equation (25), can be measured. The experimentally obtained quantity on the right-hand side of Equation (26) can then be solved numerically to evaluate . In practice, there are coreactants X and Y such that the reaction is A þ X Ð B þ Y. The concentrations of X and Y can be varied so as to shift the position of the equilibrium. At high [X] and low [Y] the equilibrium lies toward B, so that kf > kr and kf > kr . Under these conditions the measured kf =kf . At low [X] and high [Y] the equilibrium lies toward A, so that kf < kr and kf < kr . Under these conditions the measured kr =kr . Because R or Ainf/Binf, the solution to Equation (23), expresses the position of the equilibrium, the general expression is given by Equation (27). Therefore, a plot of (1þR)/ versus R is a straight line with slope kr =kr and intercept kf =kf . The ratio of slope to intercept is ðkf =kf Þ=ðkr =kr Þ, which is the desired equilibrium IE KEIE. 1þR R 1 ¼ þ kr =kr kf =kf
ð27Þ
Usually, this method is applied to enzymatic reactions, and the equilibrium IEs are obtained along with kinetic IEs that are of greater interest. An example is the deuterium IE on the reaction of acetone-d6 with NADH, to form 2-propanol-d6 þ NADþ. A mixture of acetone-d6 and 2-propanol is prepared along with coreactants NADH and NADþ at concentrations such that the reaction is at chemical equilibrium. Isotopic equilibration is initiated by adding enzyme. In this case the spectral signature lies in the NADH, but the measured maximum or minimum of absorbance provides the right-hand side of Equation (25) or (26) and thus for each mixture. An estimate of KEIE is needed to solve for each R in Equation (23) in order to fit the data to Equation (27), but after successive iterations the values of R and KEIE converge.
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Secondary deuterium isotope effects on acidities in solution
OH ACIDS
In early studies of secondary deuterium IEs on acidity, benzoic-d5 acid and phenol-d5 were found to be 2.4 0.6 and 12 2% weaker acids, respectively, than their h5 isotopologues.37 Phenol shows the larger IE because its oxyanion is better conjugated with the ring. The IE was attributed to the electrondonating ability of the deuterium, arising through anharmonicity. Streitwieser and Klein used conductivity measurements to determine the secondary deuterium IEs on acidity of some carboxylic acids.38 The data are H listed in Table 1. In all cases pKD a pKa is > 0, meaning that the deuterated acid is the weaker. According to another study, by Bell and Miller, also in Table 1, DCOOH is a weaker acid than HCOOH, by 0.035 0.002 pK units,39 which agrees with the 0.030 0.004 of Streitwieser and Klein. Halevi, Nussim, and Ron obtained further IEs on acidity of carboxylic acids by pH titration, and they are included in Table 1.40 Their DpKa for CD3CO2H is twice that of Streitwieser and Klein, which agrees with the results of yet another study, which also fitted the temperature dependence of DpKa as –91.11/T þ 0.6449 – 0.001086T.41 These results were attributed to an inductive effect, for which the evidence adduced was the strong damping of the IE through a saturated
Table 1 Secondary deuterium IEs on acidity of carboxylic acids AcidD DCO2H DCO2H CD3CO2H CD3COOH CD3COOH CH3CD2COOH CD3CH2COOH (CD3)3CCO2H ClCD2COOH PhOCD2COOH PhSCD2COOH 2,6-C6H3D2CO2H C6D5CO2H PhCD2COOH PhCD2COOH PhCD2COOH PhCD2COOH 4-O2NC6H4CD2COOH 4-CH3OC6H4CD2COOH
H pKD a pKa
0.030 0.004 0.035 0.002 0.014 0.001 0.026 0.002 0.015 0.034 0.002 0.007 0.001 0.018 0.001 0.0052 0.0003 0.0048 0.0003 0.0090 0.0002 0.003 0.001 0.010 0.002 0.048 0.001 0.005 0.003 0.0047 0.006 0.0031 0.0002 –0.0013 0.0009 0.0019 0.0003
Method Conductivity Conductivity Conductivity pH titration pH titration pH titration pH titration Conductivity Conductivity Conductivity Conductivity Conductivity Conductivity pH titration Differential potentiometry NMR pH titration Conductivity Conductivity Conductivity
References 38 39 38 40 41 40 40 38 43 43 43 38 38 40 42 42 44 44 44
SECONDARY EQUILIBRIUM ISOTOPE EFFECTS ON ACIDITY
135
carbon from CD3COOH to CD3CH2COOH. Likewise, the IE of 0.002 per D in pivalic-d9 acid is consistent with a 2.8-fold falloff factor for inductive effects. The deuterium IE on the acidity of phenylacetic acid was reinvestigated by Bary, Gilboa, and Halevi, using both the differential potentiometric method and NMR pH titration.42 The two methods give the same DpKa of 0.005. The differential potentiometric method was judged sound, but the earlier results from pH titration could not be reproduced. Substituent effects on secondary IEs on the acidity of carboxylic acids are H D included in Table 1. For 4-X-C6H4CD2COOH Ka 2 Ka 2 is 1.0072 0.0004, 0.997 0.002, and 1.0045 0.0007 for X = H, NO2, and OCH3, respectively.44 The first value is considerably smaller than that of Halevi, Nussim, and Ron, H D which was later found to be irreproducible. For XCD2COOH Ka 2 Ka 2 is larger than for the arylacetic acids, 1.012 0.0007, 1.011 0.0007, and 1.021 0.0005 for X = Cl, PhO, and PhS, respectively.43 Because the IEs vary with X, it was concluded that a simple inductive effect cannot account for them. Lippmaa and coworkers used 13C NMR titration to measure secondary deuterium IEs on acidities of carboxylic acids.24 The results are listed in Table 2. It is remarkable that the IEs show only a small attenuation with distance, so that the IE from three g-deuteriums in alanine is greater than that from two b-deuteriums in glycine. As a consequence the IEs can be detected and measured from deuteriums as far as seven bonds away from the carboxyl, as in caproic-6,6,6-d3 acid. Moreover, in benzoic acids the IE is practically independent of the site of deuteration. Table 2 Secondary deuterium IEs on acidity of carboxylic acids, by titration24 13
Acid
Reporter
Acetic-d3
COOH CH3/CD3 COOH CH2 CH3/CD3 COOH a-CH2 b-CH2 b-CH2 C1 C4 C4 C1 C1 CH2/CD2 CH
Propionic-3,3,3-d3 Butyric-4,4,4-d3 Caproic-6,6,6-d3 Benzoic-2-d Benzoic-3-d Benzoic-4-d Benzoic-2,3,5-d3 Benzoic-d5 H3NþCD2COOH H3NþCHCD3COOH
C
13
C NMR
D KH a =Ka
DpKa
1.0326 0.0008 1.0298 0.0008 1.0191 0.0006 1.0188 0.0005 1.0172 0.0009 1.0114 0.0003 1.0107 0.0003 1.0098 0.0004 1.0012 0.0003 1.0046 0.0002 1.0045 0.0002 1.0042 0.0005 1.0137 0.0002 1.0230 0.0002 1.0056 0.0002 1.0142 0.0003
0.0139 0.0128 0.0082 0.0081 0.0074 0.0049 0.0046 0.0042 0.0005 0.0020 0.0019 0.0018 0.0059 0.0099 0.0024 0.006
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C.L. PERRIN
Recently, Perrin and Dong measured secondary deuterium IEs on acidities of carboxylic acids (7–10, 14, 15) and phenols (11–13), using 1H, 13C, and 19F NMR titration and reporter nuclei indicated in boldface in the structures.32 H Data are presented in Table 3, where DpK ¼ pKD a pKa . For aliphatic acids the IEs decrease as the site of deuteration becomes more distant from the OH, as expected. In contrast, IEs in both phenol and benzoic acid do not decrease as the site of deuteration moves from ortho to meta to para (as was observed by Lippmaa and coworkers).24 A notable feature in Table 3 is that the IE per deuterium is lower for hydroxyacetic acid (9) than for acetic (8). O
O
D C
CD3C OH
OH
7-d
OH D
F
11-d2
D
F
F D
12-d3
OH
9-d
10-d8
OH
D
O CHD2(CD3)2C
OH
8-d3
OH D
O HOCHD
CD3
D D
D F
COOH
COOH
13-d3
F
14-d2
D
F
F D
15-d3
IEs on acidity of alcohols have been little studied, primarily because they are not sufficiently acidic to be titratable in water, and no studies have been reported in DMSO. One exception is aqueous trifluoroethanol-d2, which is less acidic than trifluoroethanol, according to NMR pH titration, with a DpKa of 0.056.45 In an early study by UV spectroscopy, the acidity constant (pKa) in H2SO4 of protonated acetophenone-d3, PhC(=OHþ)CD3, is –6.30 0.006 (on the Ho scale), lower (more acidic) than protonated acetophenone, PhC(=OHþ)CH3, 46 H whose pKa is –6.19 0.01, corresponding to KD a =Ka ¼ 1:29, or 1.09 per D. 1 Based on H NMR chemical-shift changes in H2SO4 solution, the pKa of O-protonated acetone is –3.09, whereas for O-protonated acetone-d5 it is h d –3.14, corresponding to an equilibrium IE Ka 6 =Ka 5 of 0.87 0.04, or 0.97 47 per D. The NMR data also required inclusion of a hydrogen-bonded complex between acetone and H3Oþ, with a pKa of –1.59 for acetone and –1.68 for acetone-d5. In both these ketones the deuterated acid is more acidic, and the IE is inverse (<1), which is opposite to the behavior of the carboxylic acids. NH ACIDS
An early study of deuterium IEs on amine basicity found that the pKa of morphine-N-CD3 is 8.17, compared to 8.05 for morphine.48 Similarly, codeineN-CD3 has a pKa of 8.19, higher than the 8.06 of codeine itself, and the pKa of PhCH2CD2NH2 is 9.18, whereas that of PhCH2CH2NH2 is 9.08.
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137
Table 3 Secondary deuterium IEs on acidities of carboxylic acids and phenols32 Acid Formic (7-d)b Formic (7-d)b Formic (7-d)b Acetic (8-d2)c Acetic (8-d3)b Acetic (8-d3)b Hydroxyacetic (9-d)c 4-Fluorophenol (11-2,6-d2)d 4-Fluorophenol (11-2,6-d2)d 3,5-Difluorophenol (12-d3)d Pivalic (10-d8)c Pivalic (10-d8)c 4-Fluoro-o-cresol (13-d3)d 4-Fluorobenzoic (14-d4)d 4-Fluorobenzoic (14-d4)d 4-Fluorobenzoic (14-3,5-d2)d 3,5-Difluorobenzoic (15-d3)d
DpK per D
Solvent
KH/KD
D2O DMSO-d6 CD3CN D2O D2O THF-d8 D2O D2O CD3CN D2O D2O CD3CN D2O D2O THF-d8 D2O D2O
1.0743 0.0014 1.0530 0.0016 1.0086 0.0011 1.025 0.003 1.0304 0.0016 1.025 0.006 1.008 0.0014 1.0259 0.0011 1.0188 0.0020 1.0442 0.0005 1.0530 0.0015 1.039 0.005 1.0195 0.0012 1.0159 0.0016 1.0209 0.0016 1.0088 0.0016 1.0133 0.0019
0.031 0.022 0.0037 0.0053 0.0043 0.0036 0.0035 0.0055 0.0041 0.0062 0.003 0.002 0.0028 0.0017 0.0022 0.0019 0.0019
na 2 2 2 3 3 3 3 3 3 3,5 4 4 4 4,5 4,5 5 4,6
a
Number of bonds between D and O. By 13C NMR. c By 1H NMR. d By 19F NMR. b
Bernasconi, Koch, and Zollinger measured the IEs on acidity due to ring deuteration in some anilinium ions.49 The results are listed in Table 4. Deuterium definitely decreases acidity, but it was not possible to distinguish whether the IE decreases with increasing distance of the isotope or whether meta deuterium is ineffective compared to ortho (and perhaps para). A tentative answer to this question comes from phenols (Table 3),32 where the IEs are large enough and the NMR titration method accurate enough to show that there is no decrease as the site of deuteration moves from ortho to meta to para.
Table 4 Deuterium IEs on acidity of anilinium ions ArNH3+49 Ar
D substitution
D log( KH a =Ka )
Phenyl Phenyl Phenyl 4-Methylphenyl 2,6-Dimethylphenyl
2,3,4,5,6 2,4,6 3,5 2,6 4
0.023 0.006 0.017 0.006 –0.005 0.006 0.013 0.005 –0.006 0.005
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The secondary IE of five ring deuteriums on the acidity constant of pyridinium ion corresponds to a DpKa of 0.11, with the deuterated pyridine more basic.50 The temperature dependence is small but detectable, corresponding to an IE arising from an enthalpy difference and no detectable contribution from entropy. For the 4-amino, 4-methoxy, unsubstituted, D 4-chloro, and 4-nitro pyridines, the IE, KH a =Ka , is 1.028 0.016, 1.027 0.019, 1.048 0.028, 1.013 0.013, and 0.966 0.025, respectively.51 The value for pyridine itself corresponds to a DpKa of 0.02, which disagrees markedly with the above 0.11. Also, the inverse IE (KEIE < 1) with 4-nitro is puzzling. Therefore, the authors considered that an origin in zero-point energies is unlikely and that instead the IEs are inductive, but with a C–D bond less able to donate electrons in response to such a strong electron demand as that of a 4-nitro. It was further claimed as a general principle that a strongly electron-demanding environment reduces the normal IE and enhances the inverse one, based on the comparison of anilines with phenols and of methyl or dimethyl amine with formic acid. IEs of aliphatic deuterium on acidity are more certain. Along with the IEs on acidity of carboxylic acids, by pH titration, Halevi, Nussim, and Ron found that PhCD2NH2 is a weaker base than PhCH2NH2 with a DpKa of 0.054 0.001.40 The complementary effects of PhCD2, to increase the acidity of PhCH2COOH and decrease the basicity of PhCH2NH2, were taken as evidence for an inductive origin. By a spectrophotometric method they also found DpKa in H2SO4 for ArNHCD3 is 0.056 0.003 for Ar = 2,4dinitrophenyl and 0.047 0.004 for Ar = 2,4,6-trinitrophenyl. That steric inhibition of resonance does not lead to a difference in these two IEs was taken as further evidence for an inductive origin. Bary, Gilboa, and Halevi reinvestigated the IE in PhCD2NH2 by using both the differential potentiometric method and NMR pH titration,42 and each method gave a DpKa of 0.032, which supersedes the previous 0.054 (with the same reported precision of 0.001). Van der Linde and Robertson measured the secondary deuterium IEs for þ 52 They found the acid dissociation constants of CD3NHþ 3 and (CD3)2NH2 . DpKa = 0.056 for the former and 0.12 for the latter, with the deuterated more basic. Surprisingly, these are temperature-independent between 5 and 45 C. Temperature independence requires that the IE lie in the entropy, not the enthalpy, so the zero enthalpy change was attributed to a fortuitous compensation of force constants. A large IE, easily measured, is seen with (CD3)3NHþ, which is a stronger base than (CH3)3NHþ, with a substantial DpKa, 0.206 at 0C.53 The DpKa per D increases from 0.017 in methylamine to 0.019 in dimethylamine to 0.021 in trimethylamine. This increase was attributed to a lower IE in a strongly electron-demanding environment. Secondary IEs on amine basicity were key to the feasibility of a study of the symmetry of hydrogen bonds in tetramethylnaphthalenediamines.54,55 Because the presence of impurities could explain both the need to revise the DpKa of
SECONDARY EQUILIBRIUM ISOTOPE EFFECTS ON ACIDITY
139
PhCD2NH2,40,42 as well as the temperature independence of the DpKa for þ 52 Perrin and coworkers reinvestigated these and CD3NHþ 3 and (CD3)2NH2 , 30,31 The amines studied were methylamine (16-d0,1,2,3), other secondary IEs. benzylamine (18-d), N,N-dimethylaniline (19-d3), 1-benzyl-4-methylpiperidine (20-d3), pyrrolizidine (21-d), N-methylnorbornylamine (22-d2), and N-benzylnorbornylamine (23-d). The 1H NMR titration method [Equation (19)], which gives highly accurate results, was applied to the reporter H depicted in boldface on the molecular structures. The results are presented in Table 5. According to those data the DpKa for methylamine (16) is proportional to the number of deuteriums, and for 16–18, 22, and 23 the DpKa per D or the DDG per D is nearly constant, 24 cal mol1. CH3-nDn NH2 16-dn D N CH Ph H 2 D D 20-d3
CH3
N H
CD3
CH3 18-d
17-d3 D
19-d3 D
ND CH3 22-d2
N H
Ph N
PhCHD NH2
21-d
CD3
D NH CH2Ph 23-d
The data in Table 5 confirm that there are indeed secondary deuterium IEs on amine basicity, as had also been confirmed by data on glycine, alanine, N-methyl-4-fluoroaniline, and N,N-dimethyl-4-fluoroaniline obtained by Table 5 b-deuterium isotope effects on amine basicities31 Amine
Methylamine (16) Methylamine (16)a Dimethylamine (17) Dimethylamine (17)b Benzylamine (18) N,N-dimethylaniline (19) 1-benzyl-4-methylpiperidine (20) Pyrrolizidine (21) N-methylnorbornylamine (22)a N-benzylnorbornylamine (23) N-benzylnorbornylamine (23)a N-benzylnorbornylamine (23) a
-d2. In DMSO-d6. c Keq/Kax. d Kexo/Kendo. b
KH/KD
DpKa
DDG (cal mol1) per D
1.040 0.006 1.081 0.004 1.144 0.005 1.174 0.007 1.0419 0.0009 1.1051 0.0018 1.060 0.006c 1.037 0.002 1.092 0.004 1.045 0.004 1.086 0.007 1.003 0.007d
0.017 0.003 0.034 0.002 0.058 0.002 0.070 0.002 0.0178 0.0004 0.0434 0.0007 0.0253 0.0025 0.016 0.001 0.038 0.002 0.019 0.002 0.038 0.003 0.001 0.003
23.2 3.4 23.1 1.1 26.6 0.9 31.6 1.1 24.3 0.5 19.8 0.3 34 3 21.5 1.1 26.1 1.1 26.1 2.3 24.4 1.9 1.8 4.1
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C.L. PERRIN
Table 6 Secondary deuterium IEs on acidity of anilines and amino acids AcidD
O2CCD2NHþ 3 O2CCD2NHþ 3 O2CCHCD3NHþ 3 4-FC6H4NH2CDþ 3 4-FC6H4NH(CD3)þ 2
D KH a =Ka
Reporter 13
CO2 CH2/13CD2 13 CH3/13CD3 19 F 19 F 13
1.054 0.001 1.051 0.002 1.0377 0.0004 1.117 0.011 1.252 0.011
DpKa
References
0.023 0.022 0.016 0.048 0.098
24 24 24 34 34
NMR pH titration and summarized in Table 6.24 The DpKa of 0.048 or 0.049 per CD3 for the two anilines agrees with the 0.0434 for N,N-dimethylaniline (19) in Table 5, but these values are slightly lower than the 0.056 reported for 2,4-dinitro-N-methylaniline.40 The IEs in Table 5 can be seen to depend on the dihedral angle between the C–D bond and the nitrogen lone pair. The key evidence comes from 1-benzyl4-methylpiperidine-2,2,6-d3 (20-d3), whose cis and trans isotopomers show a DpKa of 0.0253, with the one with deuterium trans to the methyl group the more basic. This DpKa is then the difference between IEs at = 180 and 60, while the IE in 16 or 17 is the 2:1 sum of contributions at 60 and 180. These data were fit to a cos2 dependence, given in Equation (28). The maximum IE, at = 180, is 46 cal mol1, representing the IE of an antiperiplanar deuterium. Moreover, there is no angle-independent term. Within an exceedingly small experimental error, <3 cal mol1, this is not significantly different from zero.
D DG ðcal mol 1 Þ ¼ ð45:7 4:5Þcos 2 þ ð1:8 2:6Þ
ð28Þ
The assumed cos2 dependence of Equation (28) is based on an angular dependence of orbital overlap that is more appropriate for carbocations.56 It is imperfect here, because it does not distinguish an antiperiplanar relationship between the lone pair and the C–D bond (24, = 180) from a synperiplanar one (25, = 0) and implies the same IEs for both. For 21, 22, and 23 the data in Table 5 do attest to an increased basicity due to synperiplanar D, relative to H. However, the average IE due to synperiplanar deuterium is 24 cal mol1, only half as large as the 46 cal mol1 of an antiperiplanar deuterium. It should be noted that the intramolecular IE Kexo/Kendo for the isotopomers of 23 is an average over two stereoisomers, one with the N-benzyl group exo and the other with it endo, in nearly equal proportions. Each is subject to an IE from a syn deuterium, so that the IE is 1. D N
N D 24
25
SECONDARY EQUILIBRIUM ISOTOPE EFFECTS ON ACIDITY
141
It was also found that the IE on the basicity of dimethylamine is definitely temperature dependent, contrary to the previous report.52 Therefore there is no need to propose a fortuitous compensation of force constants. Moreover, this temperature dependence, along with a zero DDS0, shows that the IE lies entirely in the enthalpy. Secondary deuterium IEs on basicities of the isotopologues (CHnD3 – n)3N of trimethylamine in D2O were also measured.33 As with other amines, deuteration definitely increases pKa, by 0.021 per D. Figure 2 shows DpKa per D, as pairwise comparisons of CH3, CH2D, and CHD2 from left to right, against CH3, CH2D, CHD2, and CD3 from front to back. To exaggerate the variations, 0.021 has been subtracted from every value, so there are very tall columns below the ‘‘floor.’’ The columns are not all of the same height. Instead the IEs of successive deuteriums are not additive, and the increase in basicity, per deuterium, increases with the number of deuteriums. This arises because the IE depends on the dihedral angle between the lone pair and the C–D, and because there is a preference for conformations with H antiperiplanar to the lone pair and D gauche. This nonlinearity of IEs is a violation of the widely
ΔpKa per D – 0.021 0.0012
0.001
0.0008
0.0006
0.0004 0.0002 3 CD
0
CH3
D2
CH2 D
D
CHD 2
CH
H2
3 CH
C
Fig. 2 Nonlinearity of IEs on trimethylamine basicities, comparing (CHnD3 – n)3 (n = 3,2,1) to (CHnD3 – n)3 (n = 2,1,0), displayed as DpKa per D – 0.021.33 Reprinted with permission from J Am Chem Soc 2008;130:11143–8. Copyright 2008 American Chemical Society.
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C.L. PERRIN
assumed Rule of the Geometric Mean.57 The ability to demonstrate this is a tribute to the accuracy of the NMR titration method.
CH ACIDS
The a-secondary IE of two deuteriums on the rate of base-catalyzed C–D exchange of toluene, 3k(PhCH2D)/k(PhCD3), is 1.31, and the b-secondary D IE on the rate of base-catalyzed a-C–D exchange of ethylbenzene, k(PhCHDCH3)/k(PhCHDCD3), is 1.11 0.03.58 Similarly, from the rates of base-catalyzed a-C–D exchange of toluene-a,4-d2, -a,2,4,6-d4, and -a,2,3,4,5,6-d6 and with an assumption of linearity of IEs, the contributions of ortho, meta, and para deuteration lead to rate retardations of 2.4, 0.4, and 1.8%, respectively.59 These are all kinetic IEs, but to the extent that the transition state resembles closely the carbanion, or to the extent that the reverse reprotonation is encounter-controlled and independent of isotopic substitution, these kinetic IEs represent equilibrium IEs on acidity. The IEs were interpreted in terms of an electron-donating inductive effect of D relative to H. By UV spectroscopy in aqueous buffers, the secondary IE of six deuteriums on the acidity of 2-nitropropane, Ka((CH3)2CHNO2)/Ka((CD3)2CHNO2) was found to be 1.233 0.033, or 1.04 per D.60 The IE was attributed to a hyperconjugative interaction, whereby CH3 stabilizes the C=Nþ double bond of the conjugate base, despite the anionic character. The secondary kinetic IEs of four deuteriums on the acid-catalyzed enolization (measured from the rate of bromination, but one that should parallel the equilibrium IE on acidity) of cyclopentyl-2,2,5,5-d4 and cyclohexyl-2,2,6,6-d4 phenyl ketones are 1.21 and 1.41, respectively.61 Secondary deuterium IEs on acidity of carbocations or on proton affinities of alkenes and arenes have not been measured as equilibrium quantities.62 However, they can be predicted on the basis of kinetic IEs in SN1 solvolyses.63 Hyperconjugation stabilizes a CH3–Cþ fragment more than CH2D–Cþ (or CHD2Cþ), so that the CH3-containing cation ought to be a weaker acid. It may be though that the experimental techniques, either in solution or in the gas phase, are not accurate enough to measure these equilibrium IEs for carbocations. There have been few other examples of secondary deuterium IEs on CH acidity. One reason is their low acidity (carbocations excepted), so that their conjugate bases are not so readily accessible. Another reason is that the titration methods are less applicable, because proton-transfer equilibrium is not established ‘‘instantaneously’’. Nevertheless, measurement of IEs in acetylacetone, malononitrile, and related acids ought to be feasible, and they might be larger than the secondary IEs reported here because the deprotonation of these acids can involve rehybridization.
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143
A neglected topic is secondary deuterium IEs on the acidity of metal hydrides. These are related to IEs on CH acids only in that equlibration can be slow. There are many metal hydrides, including polyhydrides, whose acidities have been measured, but not with D.64–67 It is often possible to exchange deuterium into the hydrides, and the hydrides and mixed hydrides have unusual properties and kinetic IEs,68,69 as well as possibilities for hydrogen bonding that might show IEs.70
5
Heavy-atom isotope effects on acidities
Most of the heavy-atom IEs on acidity that have been measured are primary, simply because secondary IEs involving heavy atoms are so small as to be difficult to measure. Examples of secondary IEs are in Table 7. The data for the 13C IE on benzoic acid acidity were obtained by emf measurements with paired hydrogen electrodes, but the large apparent DDH of –82 10 J mol1 derived from the temperature dependence could not be reproduced computationally.71 Moreover, extrapolation 13 suggests that the IE becomes inverse ðK12 a =Ka < 1Þ above 38C. Therefore the strong temperature dependence of the IE was attributed to solvation. It is noteworthy that the IE of the distant 15N in p-nitrophenol could be measured. The 18O IEs on the acidities of carboxylic and phosphoric acids are a combination of primary and secondary. They are primary to the extent that it is an 18O–H bond that is broken, but they are secondary to the extent that an 18O remains in the carbonyl or phosphoryl bond. Despite this ambiguity, such IEs are included in Table 8, where each carboxyl has two 18 Os and each phosphate has four. This experimentally observed 1% IE per 18 O in carboxylic acids found application in studies of the symmetry of hydrogen bonds in monoanions of dicarboxylic acids.73–78 The relative contributions of primary and secondary IEs to the observed IE are considered below.
Table 7 Secondary 13
C or
15
N Acid
CH13 3 COOH H3NþCH13 2 COOH Ph13COOH Ph13COOH p-O15 2 NC6H4OH
13
C and 15N IEs on OH acidity Klight =Kheavy a a 1.0021 1.0012 1.003 (–10C) 1.001 (30C) 1.0023 0.0001
References 24 24 71 71 72
144
C.L. PERRIN Table 8 18
18
O IEs on acidity of carboxylic and phosphoric acids
O Acid
HC18O2H HC18O2D CH3C18O2H H3NþCH2C18O2H PhC18O2H HP18 O4 H2 P18 O4 D2 P18 O4 ROP18O3H a ROP18O3D a ROP18O3D b a b
6
16 K18 a =Ka
1.0222 0.0002 1.0291 0.0001 1.0172 0.0004 1.0168 0.0002 1.020 0.002 1.019 0.001 1.019 0.001 1.0248 0.0007 1.0154 0.0009 1.022 0.001 1.0147 0.0006
References 20 20 24 24 79 21 21 21 21 21 21
R = HOCH2CH(OH)CH2. R = 6-Glucosyl.
Secondary isotope effects on Lewis acid–Lewis base interactions
Just as there can be secondary IEs on acidity and basicity, namely, on protontransfer equilibria, so also can there be secondary IEs on Lewis acidity and basicity. All the examples though have been deuterium IEs, perhaps because heavy-atom effects are too small to measure reliably except when they are primary. Deuteration can affect not only basicity toward protonation but also basicity toward a Lewis acid. Less closely analogous but also possible is the effect of deuteration on the electrophilicity of a Lewis acid. A simple example is the ionization of Ph3CCl to Ph3Cþ and Cl, where the ionization constant of C6D5CPh2Cl is lower by a factor of 1.19 0.01.80 This example of an equilibrium IE is rare, and there are far more examples of secondary deuterium kinetic IEs in solvolysis reactions.81 They arise because hyperconjugation stabilizes CH3–Cþ more than CH2D–Cþ, so that the CH3containing substrate solvolyzes more rapidly. To the extent that the transition state closely resembles the carbocation product, the kinetic and equilibrium IEs will be very similar. Moreover, kinetic IEs in solvolysis of (CH3)2CCl (CHnD3 – n) (n = 0,1,2,3) show a nonlinearity, owing to a conformational preference such that the first C–H bond is aligned trans to the leaving chloride, which allows maximum hyperconjugation, and subsequent C–H bonds provide a reduced acceleration.82 This is similar to the secondary deuterium IEs on basicities of the isotopologues of trimethylamine, as shown in Fig. 2, but the conformational preference in amines is weaker than that for hyperconjugation in carbocations. An early example is the interaction between HCl as Lewis acid and aromatic hydrocarbons as Lewis bases. An aromatic hydrocarbon increases the
SECONDARY EQUILIBRIUM ISOTOPE EFFECTS ON ACIDITY
145
solubility of HCl in methylcyclohexane as solvent. From that increase the equilibrium constant for complex formation between aromatic hydrocarbon and HCl could be measured.83 The equilibrium constant for toluene, 2.6 103 M1, is larger than that for benzene, 1.9 103 M1, showing that electron donation increases the Lewis basicity. The formation constants for deuterated aromatics are larger, by factors of 1.057, 1.079, 1.023, and 1.047, respectively, for benzene-d6, toluene-d8, toluene-CD3, and toluene-d5, suggesting that deuterium is electron donating. Another early example is the report of 1H NMR shifts seen at several signals of cis and trans verbenol-4-d (26) in the presence of various EuL3, where L is the enolate of a b-diketone.84 The greater shifts of the deuterated alcohols means that these are the stronger Lewis bases. OH D 26
Secondary deuterium IEs on the Lewis basicity of CH3CH2CD(CH3)OH, CH3CH2C(CD3)2OH, (CH3)2CHC(CD3)2OH, and (CD3)2CHC(CH3)2OH toward forming 1:1 complexes with the paramagnetic shift reagent Eu(dpm)3 (dpm = [(CH3)3CCO]2CH, dipivaloylmethanato) were measured by 1H NMR.85 The deuterated alcohols are stronger Lewis bases. From the isotope shift at half complexation, the DDG per D was evaluated as –14, –3.5, and –0.75 cal mol1 for a, b, and g deuteration, respectively, corresponding to a fourfold attenuation per intervening bond. Similar secondary deuterium IEs were seen in the chemical shifts of allenic esters, R2C=C=CRCOOR (R = various combinations of H, CH3, or C2H5, or deuterated derivatives) in the presence of shift reagents Eu(fod)3 and Eu(hfc)3, the latter of which distinguishes enantiomers of a chiral allene.86 The largest shifts are with (CH3)2C=C=CDCOOCH3 and CH3CH=C=C(CH3) COOCD3. Formation of the 1:1 complex of (CH3)3N with (CD3)3B is favored in the gas phase to the extent of 1.25 0.03 over the complex with (CH3)3B.87 This is opposite to the general results presented above, where the deuterated base is stronger, but here the deuterated borane is the stronger Lewis acid. The difference is attributed to better hyperconjugation by H into the vacant p orbital on boron, which is lost on complexation. The binding of alkenes to transition metals, to form p complexes or Z2 complexes or metallacyclopropanes, is a Lewis acid–Lewis base interaction that is made more elaborate by back bonding from the metal to the alkene. There are many examples of deuterium IEs on complexation. One that was studied extensively is the binding of ethylene, propylene, and 2-butene to Agþ, where the deuterated alkene binds more strongly.88 For example, KCD2=CD2/KCH2=CH2 is 1.129 at 25C. The IE is greater when deuterium is on
146
C.L. PERRIN
the double bond, but it can be detected for CD3 groups too. The IE was attributed to an increase of bending frequencies when the carbon hybridization changes from sp2 in the alkene toward sp3 in the complex. Another example is the diosmacyclobutane complex (m-Z1,Z1-C2D4)Os2(CO)8 (27), for which KCD2=CD2/KCH2=CH2 is 1.29.89 In this case the IE was attributed to the change of a twisting vibration on formation of the complex. Further study found KCD2=CD2/KCH2=CH2 of 1.16, 1.20, and 1.35, respectively, for binding to gasphase Cuþ, Agþ, and Auþ.90 These values are in excellent agreement with calculations, although it was not possible to attribute the variation with metal to a specific vibrational mode. D
D Os(CO)4
D D
Os(CO)4 27
In the presence of the paramagnetic shift reagent Eu(dpm)3 (dpm = [(CH3)3CCO]2CH) the b-protons (H3,5) of 2,4,6-trimethylpyridine are shifted downfield.91 When the 2- and 6-methyls are replaced by CD3, the shift is greater, although there is no effect of a 4-CD3. Similar results were obtained with selectively deuterated 2,6-diethyl-4-methylpyridines. This represents a secondary deuterium IE on the strength of the Lewis acid–Lewis base complexation. For comparison the pKa of 2,4,6-trimethylpyridinium ion is 7.45 and increases to 7.53 in 2,4,6-trimethylpyridinium-d9, with nearly equal IEs due to each CD3, including a 4-CD3. The contrast is attributed to electron donation by CD3, to increase basicity, but a steric origin for the IE on complexation. The importance of steric interactions is supported by the observation that no complexes are formed with 2,6-diisopropyl- or 2,6-di-tert-butyl-pyridine. One elementary study that does not seem to have been carried out is the 18O IE on the acidity of boric acid. This is a combination of primary and secondary that might be easily measured by 11B NMR in alkali.92,93
7
Secondary isotope effects on gas-phase acidity and basicity
In recent years proton transfers in the gas phase have been extensively studied. The gas phase allows measurements on strong acids and strong bases that are not available in solution. The methodology is rather specialized, involving mass spectrometry and its variants such as ion cyclotron resonance (ICR), so the reader is referred to a review.94 Pulsed ICR spectroscopy was used to measure the IEs due to CD3 substitution on the proton-transfer equilibria of some methylbenzenes.95 Toluene-d3 is 0.33 kcal mol1 less basic than toluene itself, consistent with the lower ability
SECONDARY EQUILIBRIUM ISOTOPE EFFECTS ON ACIDITY
147
of a CD3 to stabilize the positive charge in 28 by hyperconjugation. The IE on protonation of o-xylene-d6 is the same as that for toluene, suggesting that a second, unconjugated CD3 as in 29, does not contribute. For m-xylene and mesitylene, DG is only 0.24 and 0.175 kcal mol1. Therefore a second conjugated CD3, as in 30, diminishes the IE, which is puzzling. The measured equilibrium IE for p-xylene-d6 is only 0.185 kcal mol1, and was interpreted as a consequence of ipso protonation, to form 31. In contradiction to these results, no IE (0.01 or 0.02 0.05 kcal mol1) could be detected in the proton affinity of toluene-d3, also measured by ICR but by comparison of the proton affinities of the two isotopologues with methyl formate.96 Nor was any IE found (0.00 0.03 kcal mol1) for p-xylene-d6, measured by direct equilibration. CD3 CD3 + 28
+
+ CD3
+
CD3
CD3 29
H CD3
30
CD3 31
According to ICR measurements, the basicities of gas-phase CD3NH, CD3O, and CD3S are greater than those of their CH3 isotopologues.97 The DDG is –0.37 0.08, –0.50 0.10, and –0.30 0.08 kcal mol1, respectively, corresponding to KEIE of 1.9, 2.3, and 1.7 on the acidities. In another study, where forward and reverse rate constants for proton transfer were measured, CD3O was found to be a stronger base than CH3O, by 0.5 kcal mol1.98 By comparing the fragmentation of the cluster ions between isopropoxide and deuterated or undeuterated alcohols, CD3OH and C2D5OH are weaker acids than their protium isotopologues, by 0.6 kcal mol1 each.99 All these IEs are in agreement with each other. According to additional ICR measurements, the secondary IE on the acidity of CD3CNHþ is inverse, corresponding to a greater basicity of CH3CN, by 0.05 0.03 kcal mol1.100 The basicities of CD3NH2, (CD3)2NH, and (CD3)3N are greater than those of their CH3 isotopologues by 0.09 0.02, 0.24 0.04, and 0.33 0.06 kcal mol1, respectively, or 0.10 kcal mol1 per CD3 group. An increasing IE per D for the series of three methylated amines, which was seen in solution and attributed to the effect of an electron-demanding environment,53 could not be detected by ICR. From the temperature dependence of the equilibrium constant for proton exchange between some deuterated and undeuterated primary and secondary amines, monitored by high-pressure mass spectrometry, the reaction enthalpy, or difference in proton affinity, could be measured.101 Protonation of the deuterated amine is favored by 0.2 kcal mol1, varying with structure by 0.1 kcal mol1 but with no obvious pattern. However, the equilibrium, at least for CH3CD2NHCH3, appears to be entropy driven, not enthalpy.
148
C.L. PERRIN
By Fourier-transform ICR spectroscopy the equilibrium constant for the proton transfer from pyridinium-d5þ to pyridine was found to be 0.809 0.0270 at 331 K (KEIE = 1.24).102 This corresponds to a DpKa of 0.09 and is in good agreement with the DpKa of 0.11 measured in aqueous solution,50 but not with the alternative 0.02.51 By generating proton-bound dimers and measuring their mode of dissociation, it was claimed possible to measure secondary deuterium IEs on proton affinity.103 Thus protonated 2-pentanone is favored 2.1-fold over protonated 2-pentanone-3,3-d2, corresponding to an 0.16 kcal mol1 greater proton affinity for the undeuterated isotopologue. This can be attributed to hyperconjugative stabilization of the cation, which is more effective with CH2. In contrast, for acetophenone, dissociation of the proton-bound dimer produces a 1.4:1 mixture of PhC(=OHþ)CD3 and PhC(=OHþ) CH3. The opposite (inverse) IE was attributed to delocalization of the positive charge into the phenyl ring, so that hyperconjugation is operative also in the neutral ketone, and (incredibly) to at least as great an extent. A normal IE was found for CD3OC(=O)CH2NH2, which is more basic than the undeuterated glycine methyl ester by 0.05 kcal mol1.104 In another study the proton affinity of pyridine-d5 was again found to be higher than that of pyridine, and KEIE is 1.09 at Teff = 615 K,105 which agrees with the KEIE of 1.24 from ICR at 331 K.102 In that same study the proton affinities of acetone-d6 and acetonitrile-d3 are lower, by factors of 1.19 and 1.32, respectively (KEIE = 0.84, 0.76),105 although the latter disagrees with the above –0.05 0.03 kcal mol1 measured by ICR.100 However, Schro¨der, Semialjac, and Schwarz recently applied this method to the dimer of acetone and acetone-d6.106 They found that the ratio of dissociation products varied with the experimental method, over a range from 0.79 to 1.17. They concluded that systematic errors are too large to permit reliable measurement of secondary IEs by this method.
8
Secondary isotope effects on conformational equilibrium
Many secondary IEs on conformational equilibrium have been measured, usually by NMR. Their relevance here is that they can often be converted, at least in principle, to a secondary IE on acidity or basicity. Only a few examples are given here, but the possibilities are much wider. A simple example is trans-1,3-cyclohexanediol,107 which is a 1:1 mixture of two conformers. If one of the OH groups is converted to OD, as in 32, the equilibrium constant in DMSO-d6 becomes 1.025, favoring the conformation 33 with the remaining OH equatorial. To the extent that axial and equatorial OH have different acidities, the deuterium exerts a secondary IE on the acidity of the OH group.
SECONDARY EQUILIBRIUM ISOTOPE EFFECTS ON ACIDITY
149
OH
K = 1.025
DO
OH OD 33
32
The deuterium-induced isotope shift of the 19F NMR signal in the isotopologues of p-fluorophenylethyl cation are nonlinear in the number of deuteriums.108 The isotope shifts are 0.092, 0.112, and 0.126 ppm for the first, second, and third deuterium, respectively. This nonlinearity is due to a preference for a C–H bond aligned parallel with the vacant p orbital of the carbocation, as in conformer 34 of ArCHCH2Dþ (Ar = 4-FC6H4), because C–H hyperconjugates better than C–D does in 35. Likewise, conformer 36 of ArCHCHDþ 2 is more stable than 37. Because conformer 37 is less stable, it is a stronger acid than 36 with respect to forming their common conjugate base, ArCH=CHD. This is a secondary IE on acidity, where two isotopomers (not isotopologues) differ in acidity. It is an IE that could not be obtained by measuring the relative acidity of the two isotopomers (which strictly are conformers that differ in the position of the isotope). H Ar H
D H D
Ar H
H H H
Ar D
35
34
D H D
36
Ar H
H D 37
A similar situation occurs in acetyl fluoride, where the nonlinearity of deuterium-induced isotope shifts on the 19F NMR signal implies a fractional population >1/3 for the conformer of CH2DCOF with C–D anti to F (38) and a fractional population <1/3 for the conformer of CHD2COF with C–H anti to F (39).109 These populations arise because of the greater zero-point energy of a C–H bond anti to F. They can be translated into deuterium IEs on the acidities of the conformers of acetyl or acetyl-d fluoride. D
H O D
F H
38
O H
F D
39
The conformational equilibrium of N-methylpiperidine-cis-2,6-d2 favors conformer 40 with both deuteriums equatorial, with an equilibrium constant of 1.23.110 To the extent that the conformational preference in the protonated amine is much smaller and can be neglected, this IE also corresponds to a greater basicity of the conformer 41 with the deuteriums axial. Similarly, the preferences of 3-azabicyclo[3.2.2]nonanes and (PhCHD)3N for conformers with H anti to the nitrogen lone pair implies a lower basicity for those conformers.111,112
150
C.L. PERRIN
H D 41
N CH 3 H
D
K = 1.23 H
D
40
N CH 3 D
H
Another example is 1,3,5-cycloheptatriene-7-d, where the equilibrium constant [equatorial]/[axial] is 1.25 favoring the conformer 42 with deuterium equatorial.113 Since deprotonation of either conformer would produce the same cycloheptatrienyl-d anion, the axial conformer must be more acidic, with a DpKa = –log10 1.25. This is a case where the separate acidity constants would not be measurable, because the barrier to conformational equilibration is only 6 kcal mol1 and because the anion is antiaromatic and very unstable. D H D 42 H
9
Secondary isotope effects on tautomeric equilibria
As with conformational equilibria many secondary IEs on tautomeric equilibria have been measured, usually by NMR. They too can be converted to a secondary IE on acidity or basicity. Only a few examples are given here, but the possibilities are much wider. The 2,3-dimethyl-2-butyl cation with a single deuterium in one of the methyls is an equilibrium mixture of two tautomers (43, 44), interconverted by rapid hydride shift.114 The 1H NMR chemical shifts of the CH3 and CH2D groups are averaged over environments a and b to the carbocation. However, hyperconjugation favors CH3 a to the carbocation and CH2D b, leading to methyls that are more downfield than CH2D. The magnitude of the downfield shift corresponds to an equilibrium constant [44]/[43] of 1.132 0.007 at –56C. Because both tautomers have the same conjugate base, 2,3-dimethyl-2-butene-1-d, the greater stability of 44 means that this tautomer must be less acidic, with a DpK of log 1.132, or 0.054. This DpK corresponds to the difference between b and g IEs on acidity, or to the b IE alone if the g IE can be assumed to be negligible. Likewise, the 13 C NMR spectrum of doubly 13C-labeled 2,3-dimethyl-2-butyl cation provided the secondary 13C IE on the tautomeric equilibrium (and on the acidity).115 Note that these IEs could not have been obtained by measuring the individual acidities of the two tautomers, because they equilibrate much too rapidly.
SECONDARY EQUILIBRIUM ISOTOPE EFFECTS ON ACIDITY H3C
+
H H3C
CH2D
H3 C
CH3
H3C
43 Stronger acid
151
CH2D
+
H CH3 44
Similar behavior is seen in (2-propyl)cycloalkyl cations, which are a mixture of two tautomers, 45 and 46, interconverted by rapid hydride shift.116 For n = 5, the equilibrium constant K is 16.56 at –112C. Replacing the two CH3 groups by CD3 increases K by a factor of 2.1, whereas replacing the two aCH2 groups by CD2 decreases K by a factor of 4.54. For n = 6 K is 0.031 at –122C, and replacing the two CH3 groups by CD3 increases K by a factor of 2.1, whereas replacing the two aCH2 groups by CD2 decreases K by a factor of 9. Again these can be converted to the relative acidities of the two tautomers, and a CD3 or CD2 decreases the acidity of an adjacent CH. +
( )n – 4 45
K
+
( )n – 4 46
According to computations on the separate isotopic-exchange equilibria, the deuterium IE on the tautomeric equilibrium between the dihydride H2W (CO)3(PCy3)2 and the dihydrogen complex (Z2-H2)W(CO)3(PCy3)2 is 0.485 at 300 K (or 0.534 if anharmonicity is included).117 This corresponds to a preference of deuterium for the dihydrogen site. Thioacetylacetone is a 66:34 mixture of CH3C(OH)=CHC(=S)CH3 and CH3C(=O)CH=C(SH)CH3 tautomers.118 If the CH3 attached to CS is replaced by CD3, the proportion of SH tautomer increases, whereas if the CH3 attached to CO is replaced by CD3, the proportion of SH tautomer decreases. Because both tautomers have the same conjugate base, these changes of tautomeric ratio mean that the relative acidity of the tautomers is changed by the isotopic substitution. Similar behavior is seen with C6D5C (OH)=CHC(=S)C6H5. The deuterium IE on the equilibrium among the tautomeric forms of the aldohexose D-talose-1-13C was studied by quantitative 13C NMR.119 The percentages of a-pyranose, b-pyranose, a-furanose, and b-furanose are 41.33 0.19, 29.28 0.28, 17.956 0.034, and 11.361 0.049, respectively. The effect of deuteration at C1 is to increase the percentages of a-pyranose and a-furanose to 42.44 0.07 and 18.43 0.027, respectively, and to decrease the percentage of b-furanose to 27.69 0.033. Other changes, such as to the percentages of a-furanose, hydrate, and aldehyde, or among the tautomers of galactose, were not significant. Again, because all tautomers have the same conjugate base, these changes in the equilibrium distribution correspond to deuterium IEs on the relative acidities of the tautomers.
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C.L. PERRIN
IEs were used to verify a tautomeric equilibrium in 2-phenylpropenal-d (47 þ 48) and to distinguish this mixture from a symmetric structure with a hydrogen centered within the hydrogen bond.120 According to 13C and 1H chemical shifts, the equilibrium favors 48. From the temperature dependence DH was estimated as –27 cm1, or –0.08 kcal mol1. Because both tautomers have the same conjugate base, 47, which is less stable, must be the stronger acid, owing to a secondary deuterium IE. O
HO
D
OH H
D
H
Ph 47
O
Ph 48
10 Secondary isotope effects on hydrogen bonding A hydrogen bond AH. . .B between a donor AH and an acceptor B is strengthened by increasing either the acidity of AH and the basicity of B. Therefore IEs on acidity or basicity, including secondary ones, must also affect the strength of hydrogen bonding, and IEs on hydrogen bonding reflect IEs on acidity or basicity. According to deuterium-induced upfield 1H NMR isotope shifts in partially deuterated rigid cyclohexane-1,3-diols dissolved in CDCl3 or benzene-d6, the OH is preferentially solvent-exposed, while deuterium prefers to reside in the intramolecular hydrogen bond (49).121 In acetone-d6 and DMSO-d6 downfield isotope shifts indicate that the OH preferentially resides in the intramolecular hydrogen bond, while OD forms an external hydrogen bond to the acceptor solvent, S (50). S H O D
D O H O
O
TBDMSO
TBDMSO O O
O 49
O O
O 50
In contrast, a partially deuterated rigid 1,4 diol shows upfield isotope shifts not only in CDCl3 but also in acetone-d6 and DMSO-d6.122 Again the OH is preferentially solvent-exposed in CDCl3, while deuterium prefers to reside in the intramolecular hydrogen bond. Again the OD is preferentially solvent exposed in acetone-d6 and DMSO-d6, while OH prefers to reside in the intramolecular hydrogen bond. The paradoxical commonality of upfield isotope shifts is due to a reversal of the chemical shifts of interior and exterior sites of 1,4 diols in acceptor solvents. The equilibrium constant in DMSO-d6 is
SECONDARY EQUILIBRIUM ISOTOPE EFFECTS ON ACIDITY
153
1.018 0.008, which is a secondary deuterium IE on the hydrogen-bonding of the OH. According to ab initio Hartree–Fock calculations, (CH3)2CDOH hydrogenbonds less strongly to methoxide than does (CH3)2CHOH, with a KEIE = 1.095 for the conformer with the C–D bond anti to the OH and 1.051 for it gauche.45 The IE can be traced to a decrease in the C–D and C–H stretching frequencies upon hydrogen-bond formation. This is a stereoelectronic effect whereby the oxygen lone pair in the hydrogen-bonded complex is delocalized by negative hyperconjugation into the C–H or C–D bond. Further B3LYP6-31þG(d,p) calculations on the hydrogen bonding of CH2DOH to NH3 show a KEIE of 1.0233, averaged over all conformers of reactant and product.123
11 Secondary isotope effects in chromatography Chromatography is a powerful method for separations, and IEs often permit separation of isotopologues.124 They are clearly important for isotopic enrichment,125 especially of metals, where they depend on primary IEs associated with the binding of the metal ion itself. There are many different experimental techniques, including reverse-phase liquid chromatography, ion-exchange chromatography, capillary electrophoresis, and gas chromatography, which will all be aggregated here as simply chromatography. A recent review describes the equipment used and also some results with deuterated solvents.126 Many isotopic separations are not related to IEs on acidity, such as separations of biomolecules based on noncovalent interactions,127 or of hydrocarbons and other nonpolar substances, where the IE arises from hydrophobic interactions that include a reduction of the C–H or C–D vibrational frequency on complexing with the p-face of an aromatic.128,129 A notable example is the separation of the enantiomers of C6D5CHPhOH on a (chiral) cellulose tribenzoate column that preferentially binds the (R)-C6D5 group.130 Another example, in solution [but monitored by ESI–MS (electrospray ionization mass spectrometry)], is the preferential binding of 3,5-dinitrobenzoylleucine over 3,5-dinitrobenzoyl-d9-leucine to a quinine or quinidine derivative that distinguishes (R) from (S).131 In many cases the separation of isotopologues is based on differences in acidity or basicity. It is effective not only for deuterium and tritium but also for heavier atoms. An early example was the lower mobility of 14C-labeled amino acids on a column eluted with a gradient of increasing pH.132 The effect is operative only when the isotope is at C1 or C2 or at the carboxyl carbon of aspartic acid. It was attributed to an inductive effect, whereby the 14C decreases the acidity of the amino acid and thus increases its binding to the cation-exchange resin. Other heavy-atom IEs, as with Ph15NH2, Ph15NMe2, 17 18 p-O2NC6H18 4 OH (also p-O2NC6H4 OH), and PhC O2H, do depend on IEs on
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C.L. PERRIN
basicity or acidity,79,133,134 but these are primary IEs (although the last also has a secondary component). A more extensive study of mobilities of 3H- and 14C-labeled amino acids again found that amino acids labeled with 14C at C1 or C2 are retained on the column, relative to the unlabeled forms.135 Lysine is an exception. Tritiation at C3 also increases the retention time, but tritiation at C2 of glycine or at C4, C5, or C6 of lysine decreases it, and large decreases are seen with methionine tritium-labeled in the methyl and with tyrosine tritium-labeled at C30 ,50 . The 14 C IEs can be attributed to a decrease of acidity, but the IEs of distant 3H may be due to hydrophobic interactions with the resin. A remarkable result is that intramolecular isotopic isomers (isotopomers) can be distinguished on the basis of their chromatographic mobilities. Another example of the separation of isotopomers was observed with deuterated benzoic acid, eluted with acidified 30% aqueous methanol. Deuteration, especially at meta and para positions, decreases retention.136 Ratios of retention times are presented in Table 9, where the IEs of monodeuterated benzoic acid or of benzoic-2,6-d2 acid are omitted because they are too small to produce resolvable peaks although they do lead to detectable peak broadening. Because the IEs are strongest at positions more distant from the carboxyl group, and because the elution conditions were sufficiently acidic that the benzoic acid was not ionized, an IE on the pKa was rejected as responsible. Instead some sort of lipophilic interaction was suggested, and deuteration at the ortho positions is less effective because the carboxyl group hinders those positions. However, it should be noted that the data in Tables 2 and 3 indicate that the IE on acidity does not fall off at meta and para positions.24,32 Many chromatographic separations of isotopologues of various amines that are biologically active or have drug properties have been achieved. Among these are perdeuteronucleosides;137 a tetracyclic 3,3,4,4-d4-piperazine with antimigraine activity;138 the tetracyclic antidepressant mianserin with 2H or 3H in the N-methyl;139 N-CH3-tritiated chlorpromazine Table 9 Chromatographic retention times of benzoic acid isotopomers and isotopologues136 PhCOOH-dn
tH/tD
2,3,4,5,6 2,3,5 3,4,5 3,4 3,5 2,4 2,5
1.038 1.029 1.023 1.019 1.019 1.013 1.010
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155
Ar2NCH2CH2CH2N(CH3)2;140 N-methyl-labeled benzazepines;141 deuterated dopamine;142 tritiated imipramine Ar2NCH2CH2CH2N(CH3)2 and desmethylimipramine Ar2NCH2CH2CH2NHCH3;143 Bepridil (N-benzyl-3-isobutoxyN-phenyI-2-(pyrrolidin-1-yI)propylamine) with 3H in the pyrrolidine ring;144 and various isotopomers of caffeine and of its metabolites theophylline, theobromine, paraxanthine, and trimethyluric acid.145 In general, deuteration or tritiation extends the retention time, and in some cases the IE was attributed to an IE on the basicity of the amine. The ability to separate isotopomers raises a caution regarding using chromatography to establish the identity and purity of radiochemicals. On an anion-exchange column glucose-1-d but not glucose-2-d is retarded relative to glucose (51).146 Therefore, the retardation is not due simply to the greater mass of a deuterated molecule but is due to a deuterium IE that decreases the acidity. From a correlation between retention time and pKa for a series of monosaccharides the pKa of glucose-1-d is 12.31, slightly higher than the 12.28 of glucose. C6 HO C4 O HO C5 C2 HO C1 C3 OH 51
OH
On an anion-exchange column with a pH 11.7 eluent [3H]glucose elutes ahead of glucose (51) (actually [14C]glucose for ease of comparative analysis).147 The ratios of retention times, tglucose/t3H-glucose, are 1.057 0.0007, 1.012 1.0005, 1.014 0.0004, 1.024 0.0003, 1.014 0.0004, and 1.015 0.0014 for [1-3H]-, [2-3H]-, [3-3H]-, [4-3H]-, [5-3H]-, and [6,6-3H2]glucose, respectively. These arise from secondary tritium IEs on the pKa of glucose OH groups. By an NMR pH titration, in which all but two 13C signals move downfield on deprotonation, the pKa of glucose was found to be 12.1. The second pKa is not reached until pH 13.85, beyond the range of these experiments, so only a single OH can be ionized. In most molecules this is OH1 but in others it is OH4 or perhaps another, all in equilibrium. Two of these observations, the increased retention time even for [5-3H]glucose and the deprotonation-induced shift of the NMR signal of C5 (which has no OH), are strong evidence that the anionic charge is shared among all the oxygens, perhaps through a bridge of water molecules.
12 Secondary isotope effects on molecular structure According to the Born–Oppenheimer approximation, the electronic wave function and the potential energy governing nuclear motion are independent of nuclear mass. What does depend on nuclear mass is the zero-point energy,
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p equal to (1/2)h, or (h/4p) (k/), where is the reduced mass, which is approximately the mass of the lighter atom on a bond. This is what causes the zero-point energy to decrease from H to D to T. Of course, the Born–Oppenheimer approximation is only an approximation, and it is most likely to break down for bonds to hydrogen. Owing to the anharmonicity of the potential-energy function, the vibrational wave function is not symmetric about its minimum. The distortion increases the probability of longer bond lengths, especially for H. When averaged over the vibrational wave function, the distances are in the order C–H > C–D > C–T. Various estimates of dCH–dCD all give 0.005A˚ (0.5 pm), based on a C–H frequency of 3000 cm1 and a Morse potential with dissociation energy of 100 kcal mol1, or on the spectroscopic data for HCl,148 or as the experimental Dd in C2D6.149 This is a primary IE on the bond length. It is responsible for ‘‘steric’’ kinetic IEs arising because CHn groups are effectively larger than CDn and possibly for various IEs dependent on intermolecular forces, such as those on vapor pressure, adsorption, and chromatographic separations. Secondary IEs on molecular structure arising from the anharmonicity of C–H bonds are more subtle. An example is the C–C bond in C2D6, which is calculated to be shorter by 0.0015 A˚ than that in C2H6, owing to the anharmonicity of bending modes, which also make CHn groups effectively larger than CDn.150 A prominent example is the Ubbelohde effect, where the OO distance in an ODO hydrogen bond is shorter than in an OHO hydrogen bond.151 The relevant question regarding secondary IEs on acidity is the extent to which IEs affect the electronic distribution. How can an inductive effect be reconciled with the Born–Oppenheimer approximation? Although the potential-energy function and the electronic wave function are independent of nuclear mass, an anharmonic potential leads to different vibrational wave functions for different masses. Averaging over the ground-state wave function leads to different positions for the nuclei and thus averaged electron densities that vary with isotope. This certainly leads to NMR isotope shifts (IEs on chemical shifts), because nuclear shielding is sensitive to electron density.16 A more pertinent question is the extent to which IEs affect dipole moments, which can exert an inductive effect on acidities. A benchmark is the difference between the dipole moments of HCl and DCl, which is 0.005 0.002 D, or only 0.5% of the total 1.08-D dipole moment of their very polar bond.148 The dipole moment of ND3 is 0.0135 0.001 D greater than the 1.475 D of NH3, a 1% effect, but this may be due to the anharmonicity of the bending modes.152,153 The key role of bending modes is demonstrated by the comparison of CD3F and CDF3.154 The dipole moment of the former is larger than that of CH3F by 0.0112 D, whereas the difference for CDF3 is only 0.0007 D. If the IE on dipole moment were due to electron donation from H or D to F, these two differences ought to have been similar. Another estimate of the IE on dipole moments comes from experimental measurements on (CH3)3CD and
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(CH3)3CH (although it was acknowledged that bending modes may contribute).155 Their dipole moments differ by 0.0086 D, or 6.5%, which is high for such a nonpolar bond. This estimate was used to support an inductive contribution to deuterium IEs on acidity of carboxylic acids.38 An alternative estimate,32 based on the stretching mode alone, can be derived from the above dCH–dCD = 0.5 pm and a @/@d of 0.004e from infrared intensities of methane,156 leading to D = 0.0001 D, two orders of magnitude lower than the 0.0086 D reported.
13 Origin of secondary isotope effects on acidity Above are presented the experimental observations regarding secondary IEs on acidity and basicity, with little discussion or speculation on the causes. The final question, addressed here, is the origin of those IEs. The interpretations proposed below are often reinforced with calculations or with other types of experimental data.
EVIDENCE FROM VIBRATIONAL SPECTROSCOPY
According to Equation (8), the dominant contributor to the IE arises from zero-point energies. There is plenty evidence to support this. An early example was the use of the observed vibrational frequencies of gas-phase HCOOH and DCOOH and of aqueous HCO 2 and DCO2 to calculate the deuterium IE on the acid dissociation constant of formic acid.157 The zero-point energy contribution was found to be the most important, especially from the isotope-sensitive C–H stretch, whose frequency decreases from 2943 cm1 in HCOOH to 2825 cm1 in HCO 2, although this is not the only contributor, and there is considerable mixing of the various vibrations. The calculated IE of 0.037 is in good agreement with the average of two contemporary experimental values, and it was concluded that there is no need to assume any electronic differences between C–H and C–D bonds. Similarly, the IEs on the acidities of CD3COOH and CT3COOH could be calculated from a force field based on observed vibra158 The IE tional frequencies of CH3COOH and adjustments for CH3CO 2. 41 for CD3COOH agrees well with the experimental value, although the agreement is very sensitive to the choice of adjustments. In support of a vibrational origin for the decreased acidity of CF3CD2OH, the Raman spectrum of aqueous CF3CHDOH shows two C–D stretches at 2217 and 2172 cm1 (assigned to two conformers), whereas the corresponding stretch in CF3CHDO is lower than either, at 2117 cm1.45 The 18O IE on acidity of carboxylic acids was estimated from known vibrational frequencies of carboxylic acids and carboxylate anions.159 The
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Table 10 Vibrational frequencies159 of RCOOH(D), RC18O18OH(D), RCO-2, and RC18O2 Mode
(16O) (cm1)
(18O) (cm1)
D (cm1)
C=O C–OH O–H C€ Od Sumb Sumc
1760 1300 3000 1500a 3060 2228
1718 1271 2990 1464a 3051 2218
42 29 10 36 9 10
a
Average of symmetric and asymmetric stretches. C=O þ C–OH þ O–H – 2 CO € : C=O þ C–OD þ O–D – 2 CO € :
b c
frequencies of the labeled species were calculated by correcting for the changes in reduced mass. The values are listed in Table 10. They can be converted to the equilibrium constant for proton transfer between unlabeled and doubly 18 O-labeled acids [Equation (29)]. The net difference of 9 cm1 corresponds to a zero-point energy difference of 4.5 cm1 for the two sides of Equation (29), or to a KEIE of 1.022 at 26C, with the di-18O acid weaker. It was recognized that this calculation assumes 12C acids and doubly labeled oxygens, but these simplifications do not matter. Even for 13C-substituted acids the net D is still calculated to be 9 cm1. Also, in a mono-18O-labeled carboxylic acid the proton can be on either of its oxygens, and a calculation for the mixture of two tautomers gives a KEIE of 1.011, or simply half the effect due to double labeling. A similar calculation for RC18O18OD leads to a higher D, also included in Table 10 and corresponding to KEIE = 1.024 for Equation (30). Indeed, it is observed experimentally that the doubly 18O-labeled acids show twice the isotope shifts of the corresponding singly labeled ones, and also that KT increases in D2O.159 These calculations agree with the experimental values 16 for K18 a =Ka of carboxylic acids in Table 8. 18 18 RCCOH þ RC18 O 2 ÐRC O OH þ RCO2
ð29Þ
18 18 RCOOD þ RC18 O 2 ÐRC O OD þ RCO2
ð30Þ
The values in Table 10 allow the 18O IEs on acidity of carboxylic acids to be apportioned between primary and secondary IEs. The largest D is the 42 cm1 between C=16O and C=18O, which represents a contribution to the secondary IE. The total D of 39 cm1 from C–OH and O–H represents a contribution to the primary IE. Although these differences are nearly equal, they imply the surprising result that the secondary IE is slightly larger than the primary.
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COMPUTATIONS
According to calculations at the STO-3G level, the C–H bonds are longer in the anions CH3NH, CH3O, and CH3S than in their protonated forms.97 To the extent that the lengthening corresponds to a weaker bond, with a lower stretching force constant, this can account for the greater acidities of gas-phase CD3NH2, CD3OH, and CD3SH, relative to their CH3 isotopologues. Calculations at the 4-31G level give KEIE = 2.4, 2.9, and 1.25 for CD3NH2, CD3OH, 160 in good agreement with the experimental values of 1.9, 2.3, and CD3NHþ 3, and 1.25, which further supports a vibrational origin for the IE. Also, according to 4-31G calculations, the basicity of CD3NH2 is 0.11 kcal mol1 greater than that of CH3NH2, which agrees with the experimental 0.10 kcal mol1 per CD3 group.100 According to further 4-31G calculations, KEIE for the acidity of þ CD3OH, CD3OHþ 2 , HOCD2OH, or CD3NH3 is 2.620, 1.149, 1.682, or 1.214, 161 respectively. The IEs are due to changes in the C–H stretching frequencies upon deprotonation. Moreover, for CD3OH the D anti to the OH contributes 1.430 to KEIE, while each gauche D contributes only 1.357. Molecularmechanics calculations provide further support for a decrease of vibrational frequency for a C–H bond antiperiplanar to a lone pair.162 However, according to MNDO calculations, KEIE for the acidity of CD3NH2, CD3OH, CD3SH, or 163 The first three are in CD3NHþ 3 is 1.71, 2.08, 1.21, or 0.97, respectively. reasonable agreement with the experimental gas-phase values, but the last is inverse and contradictory. Calculations of vibrational zero-point energies at the MP2/6-31G(d,p) level favor protonation of RNHCD3, RNHCD2CH3 and RNHCH2CD3 over their undeuterated isotopologues by 0.12, 0.09, and 0.03 kcal mol1, respectively, independently of whether R is methyl, ethyl, propyl, or butyl.101 These values are about half of the experimental enthalpies. MP2 calculations on acetaldehyde and its enolate anion show that the equilibrium IE on the C–H acidity depends on the orientation of the retained H or D with respect to the carbonyl group.47 In particular, when D is in the molecular D plane (52), KH a =Ka is 1.32, owing to reduction of the C–H out-of-plane bending D frequency as the sp3-hybridized carbon is converted to sp2, but KH a =Ka is only 1.23 for the conformer with D out of plane (53), owing to hyperconjugation, which weakens the C–H (or C–D) bond and decreases the IE. If these gas-phase IEs are recalculated for the enolate complexed with water, the IE that retains the in-plane D is lower by 30%, but the one that moves the out-of-plane D into the plane of the enolate is lower by 50%, because hyperconjugation is reduced by hydrogen bonding of the enolate lone pair. H
HH
H
HD
O
D
O
H
52
53
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C.L. PERRIN
The KEIE of 1.24 expressing the greater gas-phase basicity of pyridine-d5 is in good agreement with a value of 1.21 (DG = 0.52 kJ mol1) calculated at the B3LYP/cc-pVTZ level.102 The IE is associated with a weakening and lengthening of the C–N bonds upon protonation and a strengthening and shortening of the Ca–Cb, Ca–H, and Cb–H bonds. These changes in bond lengths are paralleled by changes in electron density in the bonds. There is a net difference in zero-point energies of 46 cm1, favoring Py þ (Py-d5)Hþ, although it is difficult to assign all the vibrational frequencies that are tabulated. The IE must be due to the increased strength of the C–H bonds on protonation, which increases their zero-point energies, and of the C–D to a lesser extent. Another calculation, at the B3LYP/6-311þþG(2df,2p) level, obtained a net zero-point energy difference of 0.120 kcal mol1 favoring (Py-d5)Hþ,105 which is in excellent agreement with the above 0.52 kJ mol1. This corresponds to a KEIE of 1.10 at Teff = 615 K, which is also in good agreement with the experimental KEIE of 1.09. Additional calculations at the B3LYP/6-311þþG(2df,2p) level obtained net zero-point energy differences of 0.042 kcal mol1 favoring (CH3)2COHþ over (CD3)2COHþ and 0.081 kcal mol1 favoring CH3CNHþ over CD3CNHþ.105 These do not agree with the same authors’ experimental differences in proton affinities of 0.19 and 0.34 kcal mol1 (KEIE = 0.84, 0.76). However, the calculations do reproduce qualitatively the inverse IEs here and the normal IE for pyridine-d5. The experimental IEs on the acidities of carboxylic acids and phenols in Table 3 are corroborated by B3LYP computations.32 The IEs originate in isotope-sensitive vibrations whose frequencies and zero-point energies are lowered on deprotonation. For formic acid this is the C–H vibration, in agreement with the spectroscopy. For acetic acid the three C–H distances increase. The increase is greater for the C–H that is in the molecular plane. This is consistent with the result in Table 3 that the IE per deuterium is lower for hydroxyacetic acid than for acetic, because the OH of the former lies in the molecular plane,164 relegating deuterium to a position where it affects the IE to a lesser extent. The computations reproduce the decrease of IE in aliphatic acids as the site of deuteration becomes more distant from the OH, as expected. They also reproduce the constancy of IEs in both phenol and benzoic acid as the site of deuteration moves from ortho to meta to para. However, the calculations substantially overestimate the IEs. The average ratio of calculated IE to experimental is 9. Figure 3 shows a graph of DpKa per D versus the number of bonds between D and O (or the average if there are two distances), along with the calculated DpK per D but scaled down by a factor of 6. A discrepancy is also seen between the calculated and experimental 18O IEs on the acidities of (H18O)2P18O2 and CH3OP18O218OH, although it is only approximately twofold.165 Again the IEs were attributed to changes in
161
0.032
0.032
0.028
0.028
0.024
0.024
0.020
0.020
0.016
0.016
0.012
0.012
0.008
0.008
0.004
0.004
0
2
3
4 n
5
6
ΔpKcalc/6
ΔpKexptl
SECONDARY EQUILIBRIUM ISOTOPE EFFECTS ON ACIDITY
0
Fig. 3 Deuterium IE on acidity of carboxylic acids and phenols versus number of bonds between D and O: ( ) Observed DpK per deuterium. (o) Calculated DpK per deuterium, scaled down sixfold.32 For clarity, the dashed lines connect the averages for each integer n. Reprinted with permission from J Am Chem Soc 2007;129: 4490–7. Copyright 2007 American Chemical Society.
zero-point energies. Of course, the calculations are of gas-phase IEs, whereas solvation affects the experimental IEs that are measured in aqueous solution. Indeed, calculations that included solvent molecules clustered around the phosphate ion substantially improved the agreement with experimental IEs. Nevertheless, the IEs in Table 3 in the less polar aprotic solvents DMSO-d6 and CD3CN, which better resemble the gas phase, are neither larger nor closer to the calculated values.32 The IEs on amine basicity in Table 5 depend on the dihedral angle between the C–D bond and the nitrogen lone pair, including IEs due to synperiplanar deuterium in 21, 22, and 23. To probe such IEs, beyond the oversimplified cos2 dependence of Equation (28), calculations were performed on methylamine at the B3LYP/6-31G(d,p) level.31 It was found that the C–H bond length is maximum and the stretching frequency is minimum when the dihedral angle between the bond and the nitrogen lone pair is 180, but there is a secondary maximum of bond length and minimum of vibrational frequency at 0. This is consistent with an average IE due to synperiplanar deuterium that is approximately half as large as that of an antiperiplanar deuterium and also with an IE due to gauche deuterium that is weaker than predicted from a cos2 dependence.
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These results are consistent with 4-31G calculations of the IE on the 2 basicity of DCH2CH 2 , for which DE could be fit to 0.070 þ 0.086 cos – 2 0.058 cos /2, where is the dihedral angle between the lone pair and the C–D.166 This shows a maximum IE of 0.156 kcal mol1 when the lone pair is antiperiplanar to the C–D ( = 180), a minimum near 90, and a subsidiary maximum of 0.98 kcal mol1 when it is synperiplanar. Surprisingly, the maximum IE and the variation with conformation are larger for DCH2CH 2 than for DCH2CHþ 2. In summary, calculations of vibrational frequencies confirm a crucial role for zero-point energies in secondary IEs on acidity. They are especially important when the C–H bond or C–D bond is antiperiplanar or (to a lesser extent) synperiplanar to a lone pair.
CAUSE OF FREQUENCY CHANGES
With few exceptions, secondary IEs on acidity can be attributed to reductions of vibrational frequencies on deprotonation, as expressed by Equation (9). Because the zero-point energy of a C–H bond is greater than that of C–D (or more generally, the bond to a heavier element than that of a lighter one), reducing the vibrational frequency decreases the zero-point energy and stabilizes the conjugate base for the lighter isotope. This leads to an IE =Kheavier > 1. Klighter a a The remaining question is the cause of the changes in vibrational frequencies on deprotonation. This question is much easier for solvolysis, where hyperconjugation stabilizes a carbocation.166 Hyperconjugation is a stabilizing interaction between a filled C–H bonding orbital and a vacant nonbonding p orbital, as in 54. In resonance theory it corresponds to ! Hþ CH2=CR2. It is much stronger than the interaction H–CH2–CRþ 2 between a lone pair and a vacant antibonding *C–H orbital, as in 55 or 56. This is often called negative hyperconjugation, even if the species is not an anion. It corresponds to H–CH2–X: ! H CH2=Xþ. There are two possibilities for the lone pair on X, an sp3 lone pair on a nitrogen, as in 55, and a pure p lone pair on an oxygen (not an sp3 lone pair), as in 56, where the hybridized lone pair does not contribute.167,168 Because hyperconjugation removes electron density from a bonding orbital, the C–H force constant and vibrational frequency decrease. Similarly, negative hyperconjugation adds electron density into a C–H antibonding orbital, and again the force constant and the vibrational frequency decrease. The few exceptions above, namely the inverse IEs with CD3CNHþ, PhC(=OHþ)CD3, protonated 2-pentanone-3,3-d2, and acetone-d6, are due to hyperconjugation in the cationic conjugate acids, which are stabilized by H more than by D.
SECONDARY EQUILIBRIUM ISOTOPE EFFECTS ON ACIDITY
163
H + N
O H
H 55
54
56
Calculations on ethyl anion support the role of n–* delocalization, or negative hyperconjugation.166 In support of the lower acidity of tritiated glucose, which was responsible for its faster chromatographic elution at pH 11.7, density-functional-theory calculations obtain a tritium IE on the Ka of (CH3)2CTOH of 1.36.147 For glucose, the calculations indicate that tritiation at any carbon exerts a secondary IE on the pKa of every OH group, which further supports the conclusion that the anionic charge in the conjugate base is shared among all the oxygens. The experimental IEs on the acidities of carboxylic acids and phenols in Table 3 are corroborated by B3LYP computations.32 The IEs originate in isotope-sensitive vibrations whose frequencies and zero-point energies are lowered on deprotonation. In the simplest case, formate, the key vibration can be recognized as the C–H stretch, which is weakened by n–* delocalization of the oxygen lone pairs (57). For other acids the key isotopesensitive vibrations are less readily identifiable. Prime candidates are the C–H stretching modes, but bending modes also contribute. For acetic and pivalic acids, the average of the three or nine C–H stretching frequencies decreases from 3085 to 3007 cm1 in acetate anion or from 3105 to 3056 cm1 in pivalate anion. It is difficult to associate these changes with delocalization or negative hyperconjugation, especially in view of the overestimates in Fig. 3. For the aromatic acids delocalization cannot account for the near constancy of IEs from ortho, meta, and para deuteriums, but the observed IEs are consistent with calculated vibrational frequencies, which respond to electron densities in ways that do not lend themselves to simple pictures of delocalization. δ –O
H 57
δ –O
The IEs on amine basicity are also due to changes in vibrational frequencies, not only computationally but also experimentally. Gas-phase IEs of 0.10 kcal mol1 per CD3 group on basicities of methylamine, dimethylamine, and trimethylamine can be reproduced by ab initio force constants for C–H stretching, which increase on N-protonation.100 Infrared spectra of amines show characteristic bands (called ‘‘Bohlmann bands’’) in the 2700–2800 cm1 region, lower than the 2900 cm1 of a typical C–H stretch.169,170 Upon N-protonation these bands revert to a typical, higher frequency. Therefore the zero-point energy of the C–H increases on
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C.L. PERRIN
protonation, but the increase is less for C–D. Indeed, a D of 100 cm1 would produce a DpKa of 0.03, comparable to the IEs in Table 5. This good agreement supports the involvement of stretching modes, rather than the bending modes proposed for the kinetic IE in methylation of N,N-dimethylaniline-d6.171 The Bohlmann bands are associated with a C–H bond antiperiplanar to the nitrogen lone pair.172 The B3LYP/6-31G(d,p) calculations yield a minimum stretching frequency and maximum C–H bond length when the dihedral angle between the bond and the nitrogen lone pair is 180, along with a secondary minimum of vibrational frequency at 0.31 The bond lengthening and the frequency reduction are due to delocalization of the lone pair into the C–H antibonding orbital, as in 55. The maximum delocalization is when is 180, and the minimum is near 90, when the lone pair is orthogonal to the C–H. The variation of the experimental IEs with dihedral angle also shows that there is a stereochemical dependence of the IE, which is maximum when the C–D bond is antiperiplanar to the nitrogen lone pair and about half as large when synperiplanar. This behavior thus supports the interpretation of IEs in terms of zero-point energies that are reduced by negative hyperconjugation when the C–H or C–D is antiperiplanar to the nitrogen lone pair. This also agrees qualitatively with the absence of distinctive Bohlmann bands in those amines where the nitrogen lone pair is syn to the C–H.173,174 Also, the lower IE of 0.0434 for PhN(CH3)2, as compared to 0.058 for (CH3)2NH, is consistent with negative hyperconjugation, which is less stabilizing when the lone pair is also delocalized into the aromatic ring.
NECESSITY FOR AN INDUCTIVE EFFECT?
Calculations of vibrational frequencies are never accurate enough to verify that the secondary IE arises entirely from zero-point energies. Therefore although they do confirm a role for zero-point energies, which was never at issue, they cannot exclude the possibility of an additional inductive effect arising from changes of the average electron distribution in an anharmonic potential. The question then is whether it is necessary to invoke anharmonicity to account for a part of these secondary IEs. The calculated IEs ignore anharmonicity. Therefore, the ability of these calculations to reflect IEs discredits an inductive origin that requires anharmonicity. The calculations on carboxylic acids and phenols do overestimate the IEs, as shown in Fig. 3, but only an underestimate would be support for an inductive effect. The overestimation is likely to be due, at least in part, to the neglect of solvation, which stabilizes the anion and reduces the n–* delocalization that is responsible for the changes of vibrational frequencies. A simple inductive effect, wherein deuterium is more electron-donating than protium, cannot be responsible. If that were the case, deuterium would not only increase basicity but also accelerate solvolysis. Instead the inductive effect
SECONDARY EQUILIBRIUM ISOTOPE EFFECTS ON ACIDITY
165
is described as one that arises as an increased electron density at a carbon bearing D, owing to anharmonicity and a shorter average C–D bond length. In solvolysis that inductive effect is overwhelmed by the greater ability for hyperconjugation with C–H. Negative hyperconjugation is weaker, so that perhaps the inductive effect can contribute to the IE on basicity. The dilemma is that negative hyperconjugation and inductive effect both increase the IE on basicity, so that it is difficult to separate their relative importance. Intriguing evidence for an inductive effect comes from computations that treat nuclei quantum mechanically.11 This takes account of anharmonicity and leads to bond lengths and atomic charges that vary with isotopic substitution. Whether those charge variations are large enough to account for the IEs on acidity, independently of changes of vibrational frequencies, is not yet clear. Evidence against an inductive contribution comes from experimental IEs on amine basicity. According to Equation (28), there is no angle-independent term. This is the term that would arise from an electrostatic interaction between a positive charge on the N and a C–H or C–D bond dipole.3 Although Equation (28) is imperfect, and there are smaller IEs from synperiplanar C–D, we conclude that an inductive effect is too small to contribute to the observed IE. Moreover, the inductive contribution of a b deuterium to the IE on amine basicity was estimated.31 The inductive effect on pK due to an sp2–sp3 C–C bond, with a dipole moment of 0.35 D, as in propene, can be assigned as 0.95, the DpK between allylamine and methylamine. Above, in connection with the structural question of the extent to which IEs affect dipole moments, dCH–dCD is 0.5 pm and @/@d is 0.004e. These combine to a DpK on deuteration of 0.001, which is much smaller than the measured IEs in Table 5. An inductive contribution does exist, but it is negligible. Another estimate seemed to support an inductive contribution to deuterium IEs on the acidity of carboxylic acids.37 This IE on acidity of some carboxylic acids was attributed to an inductive effect arising from the electrostatic interaction of the C–H or C–D dipole with the negative charge of the carboxylate, as expressed in Equation (31). The derivative @pK/@ was estimated from the effect of a C–Cl dipole on acidity, using the difference in pKas of trichloroacetic acid (0.63) and acetic acid (4.75) and the difference between the dipole moments of t-butyl chloride (2.13 D) and isobutane (–0.13 D). Next D was estimated as 0.0086 D, the difference between the dipole moments of (CH3)3CD and (CH3)3CH. Thus DpK was estimated as 0.005 per D, in excellent agreement with the observed 0.014 for acetic-d3 acid. Moreover, the IE of 0.002 per D in pivalic-d9 acid is consistent with a 2.8-fold falloff factor for inductive effects. Yet those estimates depend crucially on the difference between the dipole moments of isobutane and isobutane-d, which is unusually large, amounting to 6.5% of either’s total dipole moment.
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C.L. PERRIN
The alternative estimate of this D above, based on a dCH–dCD of 0.5 pm and a @/@d of 0.004e, is 0.0001 D.32 Application to Equation (31) then leads to a revised DpK per deuterium of only 0.00006, which is two orders of magnitude lower than either the earlier estimate or the observed IE. Therefore the contribution to the IE from an inductive effect dependent upon anharmonicity is again found to be negligible.
DpK ¼
DpK DpK=DnCl D D ¼ D=DnCl D
ð31Þ
Finally, an inductive effect arising from the difference between the dipole moments of C–H and C–D bonds ought to be proportional to the number of C–D bonds. Instead, with trimethylamines the increase in basicity, per deuterium, increases with the number of deuteriums.33 This nonlinearity in the basicities is strong evidence against an IE of inductive origin. It arises from zero-point energies because the IE depends on the dihedral angle between the lone pair and the C–D bond, and because there is a preference for conformations with C–H antiperiplanar to the lone pair and C–D gauche. One remaining puzzle is the decreasing DpKa per D from methylamine to dimethylamine to trimethylamine in solution. Such behavior was ascribed to an inductive effect,51,53 but inductive effects ought to be linear in the number of deuteriums. It may be that conformational restraints due to additional methyls increase the negative hyperconjugation. Computations might be informative. Nearly all the evidence adduced for an inductive origin for all the secondary IEs on acidity is equally consistent with an origin in zero-point energies, analyzed according to Equation (9). The damping of the IE falloff factor in through a CH2, as in CD3CH2COOH, or p the 2.8-fold p pivalic-d9 acid would be due to a smaller k(A) – k(HA) when there is an additional carbon. The complementary effects of CD2 on the acidity of 40 PhCH2COOH p and the p *basicity of PhCH2NH2 arise because both IEs have the same 1/ – 1/ . The principal evidence that a strongly electrondemanding environment decreases KEIE comes from comparison of anilines with phenols and of methylamine or dimethylamine with formic acid,51 but the larger IEs in the latter of each comparison are simply due to the greater electron delocalization from an oxyanion than from an amino group, so that p p k(A) – k(HA) is larger. In summary, Equation (9) can account for secondary IEs on acidity, in terms of changes of vibrational frequencies and zero-point energies. There is no need to invoke anharmonicity or inductive effects.
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Acknowledgments This article is dedicated to Jerry Kresge, one of the pioneers in isotope effects and a leader in the field of physical organic chemistry. The writing of this chapter was supported by NSF Grant CHE07-42801.
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Molecular dynamics simulations and mechanism of organic reactions: non-TST behaviors HIROSHI YAMATAKA Department of Chemistry, College of Science and Research Center for Future Molecules, Rikkyo University, Tokyo, Japan 1 Introduction 174 2 Nonstatistical product distribution 176 MD analyses by using model PES 176 [1,3] sigmatropic migration of bicyclo[3.2.0]hept-2-ene 177 Reaction of diaza-[2.2.1]bicycloheptane to [2.1.0]bicyclopentane Degenerate rearrangement of bicyclo[3.1.0]hex-2-ene 180 Chemistry of trimethylene 181 Vinylcyclopropane to cyclopentene rearrangement 184 Dissociation of acetone radical cation 186 The wolff rearrangement 187 3 Avoided intermediate on IRC 189 SN2 reaction 189 [3,3]Sigmatropy 189 4 Non-IRC reaction pathway 190 Photoisomerization of cis-stilbene 191 Ionic fragmentation reaction 191 Cyclopropyl radical ring-opening 192 Ionic molecular rearrangement 193 Ene reaction 196 Thermal denitrogenation 198 Unimolecular dissociation 199 SN2 reaction 200 5 Path bifurcation 200 Bifurcation on symmetrical PES 201 Dynamic bifurcation 204 Cycloaddition 206 Beckmann rearrangement/fragmentation 207 6 Reaction time course and product and energy distributions 209 SN2 reactions 209 SN2 reactions in water 210 Other reactions 211 7 Nonstatistical barrier recrossing 211 SN2 reactions 212 Vinilydene to acetylene rearrangement 213 Cycloaddition of cyclopentadiene and ketenes 214
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173 ADVANCES IN PHYSICAL ORGANIC CHEMISTRY VOLUME 44 ISSN: 0065-3160 DOI: 10.1016/S0065-3160(08)44004-2
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8 QM/MM-MD 214 9 Full quantum MD simulation in water SN2 reaction in water 215 10 Summary and outlook 218 Acknowledgments 218 References 218
1
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Introduction
History of physical organic chemistry is essentially the history of new ideas, philosophies, and concepts in organic chemistry. New instrumentations have played an essential role in the mechanistic study. Organic reaction theory and concept of structure–reactivity relationship were obtained through kinetic measurements, whose precision depended on the development of instrument. Development of NMR technique resulted in evolution of carbocation chemistry. Picosecond and femtosecond spectroscopy allowed us to elucidate kinetic behavior of unstable intermediates and even of transition states (TSs) of chemical reactions. Back in the mid-1900s, mechanistic organic chemistry, strengthened by Robinson–Ingold’s electronic theory and frontier orbital theory, enjoyed its golden age and clarified mechanisms of many organic reactions. Appreciation of organic reaction theories and reaction mechanisms allowed organic chemists to develop new synthetic reactions. It is no exaggeration to say that recent progress in many fields of chemistry such as synthetic chemistry, supramolecular chemistry, biochemistry, and nanochemistry has been realized on the basis of the knowledge and the way of thinking that arose from mechanistic study in the last century. On the other hand, mechanistic study itself has reached a stationary stage because of the maturity of experimental methodology. This brought about a recent situation that provocative and controversial issues were seldom discussed and that novel concept ceased to emerge. In these 10 years, however, development of novel and reliable simulation methods and comprehension of the importance of reaction dynamics gained from simulation studies started to produce novel results, which likely bring about a new stage or paradigm in the field of mechanistic organic reactions. The computational and experimental studies of reaction mechanisms are complementary to each other. Experiment provides a picture of the real world but hardly the whole picture even for a simple reaction. Computation gives us detailed information about reaction mechanisms, but the results ought to rely on the assumptions involved. Interplay of the two is important; reliability of the calculated results is assured by comparing with experiment, and interpretation of experimentally observed facts is strengthened by computations.
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Further, computation provides insights into reaction mechanisms that can never be reached by experiment. Huge amount of studies by means of molecular orbital (MO) calculations have been reported in the literature, which calculate the structures of reactants, products, reactive intermediates, and TSs of possible reaction pathways, as well as minimum energy paths from the TSs to both the reactant and product sides on the potential energy surface (PES). The information thus obtained, together with experimental findings, has been used to deduce reaction mechanisms. The combined use of experiment and MO calculations has become a common method for physical organic chemists. However, it should be noted that the calculated structures and energies are at 0 K and that therefore the information obtained from MO calculations may not directly be related to experimental observation at a finite temperature. Ultimate goal of mechanistic studies of chemical reactions is to see how atoms in reacting molecules behave at the molecular level and to understand why they do so. Computational study toward this goal should take the effect of temperature into account, since chemical reactions only proceed at a finite temperature. Molecular dynamics (MD) simulations can give information on the dynamic nature of a chemical event and the results are, in principle, comparable with the experiments. In a pioneer study reported in 1985, Carpenter has demonstrated a possible role of dynamics in chemical reactions.1 He showed by using a model PES that when two symmetrical products were formed from a common intermediate through isoenergetic barriers, the two products were obtained in unequal amounts depending on how the common intermediate was formed. This was a new interpretation of an old idea, a memory effect. Investigation of how chemical reaction takes place at the molecular level needs methods that describe bond-breaking/formation processes properly. It thus requires an ab initio MD method, in which the forces are derived from quantum mechanics while the nuclei are propagated via classical mechanics subject to quantum-derived forces. The methodology of the ab initio MD simulation is still in the stage of development and its application has become active only in these 10 years. Nevertheless, already during the last decade, studies by means of this new computational method have produced important findings, which require serious modification of traditional ideas regarding chemical reactivity and stimulate experimental study aiming at confirming and establishing new concepts. The ‘‘dynamics effect’’ emerged from trajectory calculations has many phases and can be argued from many points of view. Although these phases and viewpoints are not independent but strongly overlapped to each other, I will categorize them in this chapter as listed in the index and show the current status of the work in these categories.
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Nonstatistical product distribution
MD ANALYSES BY USING MODEL PES
When an organic chemist tries to elucidate the mechanism of a reaction, what is to be done first is to analyze the products of the reaction. If more than one product is formed, the product ratio is determined. The effects of substituent on the product ratio and on the rate of the reaction are the most basic information for a physical organic chemist to discuss the reaction mechanism. Suppose that there is a reaction as shown in Chart 1, in which enantiomeric reactants A and A0 yield enantiomeric products B and B0 through a common intermediate I. Regardless of whether the reaction starts from A or A0 or from a mixture of A and A0 , the product ratio B versus B0 should be unity, since they are enantiomeric. Such ordinary convention was challenged by Carpenter, inspired by critical inspection of experimental results on some unimolecular diradical-type rearrangement reactions.1 Carpenter constructed a model mathematical surface to simulate the reaction in Chart 1 and carried out dynamics simulations starting from reactant A. Initial direction of the trajectories and initial kinetic energy were varied by small increments. The product ratio was quite different from what is expected from transition state theory (TST): 89% B0 and 11% B rather than 50% B and 50% B0 . The results were interpreted that trajectories need to approach I on paths close to the diagonal line connecting A and B0 in order to climb up the barrier effectively, and that those trajectories that successfully reach the intermediate region keep going on to B0 because of conservation of momentum. It was thus suggested that for a reaction, whose reactive intermediates are connected to more than two product regions of similar energies, dynamics effect may control the product ratio that is unable to explain on the basis of a statistical TST. It was commented that ‘‘In most reactions of complex molecules the intermediate has many more degrees of freedom and so the tendency will be to spend more time near the intermediate potential minimum and, thereby, to lose the directional information in the trajectory’’, but the model simulation certainly displays a possible role of dynamics effect on chemical reaction.
′
Chart 1
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[1,3] SIGMATROPIC MIGRATION OF BICYCLO[3.2.0]HEPT-2-ENE
In the mechanistic study of borderline reactions, situation happens, in which stereochemical outcome is the key to decide concerted versus stepwise mechanistic possibilities. Concerted mechanism leads to a product of single stereochemistry, whereas stepwise mechanism would give a mixture of products of different stereochemistry. If the possible intermediate is symmetric with respect to the bond(s) to be formed or broken on going to the products, equal amount of two products are expected to form. One such example is the [1,3] sigmatropic migration of bicyclo[3.2.0]hept-2-ene (1) to norbornene (2) shown in Equation (1). Mechanistic argument whether the reaction proceeds through biradical intermediate has been made on the basis of product stereochemistry. It was determined experimentally that the reaction of mono-deuterated substrate 1a at 307C gave 2a and 3a in the ratio of >95% and <5%. Thus, the inversion of configuration at the migrating CHD group was preferred. Dideuterated substrate 1b gave 2b and 3b in the ratio of 76:24 at 276C and 89:11 at 312C. Again, the inversion was preferred, but not exclusive as expected from the Woodward–Hoffmann rule for [1,3] sigmatropic migration, which predicts the inversion of configuration.2,3 Apparently, the observed stereochemistry does not support the concerted mechanism. At the same time, the product ratio was far from 50:50, as expected for the stepwise mechanism if secondary deuterium isotope effect was neglected. Another important finding was unusual temperature dependence with larger stereoselectivity at higher temperature. Calculations at the PM3 semi-empirical MO method indicated that a 5 kcal mol1 local minimum corresponding to the biradical intermediate existed on the PES and that the TS leading to norbornene (2 and 3) was about 4 kcal mol1 higher in energy than the TS to 1. Thus, trajectories from the intermediate region on the PM3 PES would give 1 more than 2 and 3.
(1)
Direct dynamics calculations using the PM3 method were carried out for reaction 1.4 The trajectories starting from the TS between the biradical intermediate and norbornene (2, 3) with 2 kcal mol1 kinetic energy on the imaginary frequency mode together with zero-point energy (ZPE) on other real
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frequency modes gave 1 with the counterclockwise rotation at the CXY–CHD bond to give preferentially 1 with the inversion of configuration. Another set of simulations were carried out, in which low-lying vibrational modes were mode-selectively energized to their ZPE levels. It was found that trajectories with the torsion at the CXY–CHD bond energized in the counterclockwise fashion led quickly to 1 in a little over 250 fs with the inversion of configuration without staying in the biradical intermediate region, whereas those with initial clockwise CXY–CHD rotation gave a long-lived (>1 ps) biradical. The fate of these long trajectories was not followed, but it is likely that product formation would occur with equal probability of the inversion and retention stereochemistry, since the long lifetime of the intermediate would allow a redistribution of internal energy and hence intrinsic ‘‘memory’’ of the stereochemistry would be lost. It was claimed that, due to the principle of microscopic reversibility, the trajectory results would allow one to draw conclusions about the real reaction. The calculations showed an apparent preference for the inversion of configuration in the reaction, for which the PES had a very distinct local minimum corresponding to a biradical. It was suggested that an experimental observation of a preference for inversion of configuration at the migrating carbon should not be taken as definitive evidence against a biradical mechanism. The dynamics effect may make mechanistic discussion by means of product analyses less straightforward. Direct trajectory calculations for the isomerization of bicyclo[3.2.0]hept-2ene (1) and bicyclo[2.2.1]hept-2-ene (2 and 3) were further carried out more extensively at AM1 and PM3.5 Simulations were started for a quasiclassical canonical ensemble at T = 300C in the vicinity of TSs between the biradical intermediate and 2 (3). The calculated trajectories could be grouped into two types: short trajectory, which gave 1 in a single pass within 250–350 fs, and long trajectory, which stayed in the biradical region for some time before giving the stable species 1. The inversion/retention ratio in the ring closure to 1 should be statistical for long trajectory (slow closure with more lifetime as biradical), whereas it is unequal and thus nonstatistical for short trajectory (rapid closure). In other words, the inversion exit channel is much more strongly coupled to the entrance than is the retention exit channel in the biradical intermediate, despite the degeneracy that ensures identical geometries and potential energies for the two transition structures leading from biradical to compound 1. As a result, the overall preferred stereochemical outcome was inversion, which is consistent with the experimental observations.2,3 In a language of statistical kinetics, the dynamics behavior observed in this study appears to imply concurrent concerted and stepwise pathways, which in fact arises from a dynamics effect on a stepwise PES. It was claimed that bimodal lifetime distributions as was observed in this system could be common for other reactions with reactive intermediates.
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REACTION OF DIAZA-[2.2.1]BICYCLOHEPTANE TO [2.1.0]BICYCLOPENTANE
The sigmatropic isomerization of 1 and 2 þ 3 was considered to proceed through biradical intermediate [Equation (1)], whose lifetime had bimodal distribution.5 The short-lived component of such a distribution arises from direct reactive trajectories that do not randomize the internal energy of the intermediate prior to product formation. These trajectories lead to product with inversion of configuration preferentially. The longer-lived component arises from trajectories that does not form products on the first pass through the intermediate region and then become trapped in that region for some time, before exiting to products. These trajectories are expected to be energetically randomized before going on to the products. The phenomenon of such bimodal lifetime distribution proposed for reaction 1 on the basis of direct quasiclassical trajectory calculations were tested experimentally with the reaction of diaza-[2.2.1]bicycloheptane to [2.1.0]bicyclopentane [Equation (2)].6–8 Experimental study on reaction 2 showed that the exo isomer 5x is formed favorably over the endo isomer 5n by about 3:1 in the gas phase. One explanation for the preferential formation of 5x invokes a competitive concerted and stepwise mechanism; the concerted pathway directly from 4 to 5 gives 5x with the inversion of configuration at the carbon from which N2 is departing, whereas the stepwise pathway goes through the radical intermediate and leads to both 5x and 5n in equal amount. Alternatively, the product stereochemistry can be rationalized by dynamic matching between the entrance channel to the cyclopentane-1,3-diyl radical intermediate and the exit channel to bicyclo[2.1.0]pentane as was assumed for reaction 2.
(2)
Pressure effect on the product distribution in supercritical media would resolve the problem. If the reaction proceeds via the competitive concerted/ stepwise mechanism, the reaction under a higher pressure is expected to give more exo isomer because the activation volume is considered to be smaller for concerted process than the stepwise one and hence more concerted reaction is expected under a higher pressure. If, on the other hand, bimodal lifetime distribution of trajectories is the origin of the stereoselection, the product ratio is expected to approach to unity under high-pressure conditions, since energy randomization is more effective under a high pressure. The experimental results were clear-cut. The reaction under supercritical propane gave the exo/endo ratio decreasing from 5 to 2 with increasing
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pressure from 1 to 200 bar. Thus, the experimentally observed product stereoselectivity in reaction 2 was best explained by dynamics effect.
DEGENERATE REARRANGEMENT OF BICYCLO[3.1.0]HEX-2-ENE
Degenerate rearrangement of bicyclo[3.1.0]hex-2-ene (Chart 2) has a PES, in which four degenerate products are separated through four degenerate TSs with the common energy plateau on the surface.9 Here, four compounds are identical except for the position of deuterium. The rearrangement from 4-exo isomer (6x) is expected to afford 4-endo (6n), 6-exo (7x), and 6-endo (7n) isomers in equal amount if the reaction follows statistical reaction theory (TST). Thus, this reaction provides a situation previously presented by Carpenter to predict nonstatistical product distribution due to dynamics effect.1 The CASPT2(4,4)/6-31G*//CASSCF(4,4)/6-31G* calculations revealed that there are four degenerated TSs, which is 43.0 kcal mol1 higher than 6 and 7 in electronic energy. The biradical intermediate is only 0.2 kcal mol1 lower in energy than the TSs. Trajectory simulations were carried out on an AM1-SRP (specific reaction parameters) surface. The AM1-SRP has some fitted parameters that differ from the AM1 parameter set in order to reproduce the results at the above level of theory. Quasiclassical trajectory calculations were started at the TS that connects 6x and the intermediate at 498 and 528 K. Initial conditions were determined by using the TS normal-mode sampling procedure, which generates a set of initial coordinates and momenta that approximate a quantum mechanical Boltzmann distribution on the TS.
Chart 2
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The trajectories yielded 6n, 7x, and 7n as products. The product ratio determined for 4000 trajectories was not equal as expected from statistical theories but was 47:38:15 for 6n, 7x, and 7n at both temperatures of 498 and 528 K. The ratio was in excellent agreement with experimental value, 48:36:16. The relative yields were, however, time-dependent, in that 7x started to form quickly after 50 fs, the formation of 6n caught up soon in 100 fs, and 7n was formed much slowly. It appeared that many trajectories could be understood in terms of straight paths from the entrance to the various exit channels. These trajectories traversed the biradical intermediate region much faster than energy could be redistributed to other vibrational modes. Some trajectories entering the plateau from the TS moved toward the high-energy region between 7x and 6n and then led to exit channels for 7x and 6n. In contrast, trajectories that moved toward the high-energy region between 6n and 7n tended to lose initial momentum and led to one of the exit channels. It was interesting to find that the branching ratio depends on the elapsed time; trajectories were more selective when they reached product region faster. Thus, the fate of the trajectories is primarily determined by dynamics effect, or momentum, and the branching ratio depends on the shape of the surface.
CHEMISTRY OF TRIMETHYLENE
Trimethylene is an extremely reactive intermediate for isomerization of cyclopropane to propene [Equation (3)]. The lifetime of trimethylene was measured by Zewail and coworkers by molecular beam experiment as 120 20 fs,10 which was reproduced by variational Rice–Rampsperger–Kassel–Marcus (RRKM) theory,11 and by direct dynamics simulations.12 The dynamics simulations carried out on the AM1-SRP surface with the efficient microcanonical sampling or quasiclassical normal-mode sampling method revealed that the decay process exhibited double exponential decay and thus nonstatistical for low-energy simulations, which arose from incomplete intramolecular vibrational energy redistribution (IVR). The product ratio (cyclopropane/propene) was reported to decrease with increasing energy from 90/10 to 50/50 for 54.6 and 164 kcal mol1. (3) Ab initio MRCI calculations showed that the barrier from trimethylene to propene is 7.9 kcal mol1 higher than that from trimethylene to cyclopropane.11 Thus, cyclopropane stereomutation may occur through trimethylene as an intermediate (Chart 3). Trimethylene biradical may cyclize by double rotation of the two C–C bonds in conrotatory or disrotatory fashion or successive single rotation. The calculations showed that the PES at the
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Chart 3
trimethylene intermediate region is nearly flat with conrotatory double rotation being favored over single rotation and disrotation by about 1.5 and 1.0 kcal mol1, respectively. Trajectory calculations were carried out on the AM1-SRP surface, which is similar to the MRCI surface, with barriers of 0.4, 2.8, and 2.0 kcal mol1 for conrotation, disrotation, and single rotation TSs, respectively.13,14 Trajectories for fixed energy ensembles starting at the conrotatory barrier with quasiclassical normal-mode sampling revealed strong mode selectivity, in that the stereochemical outcome of the product strongly depends on the initial conditions. Thus, when all excess energy above the ZPE was given in the conrotatory reaction coordinate, product via conrotation was formed exclusively. On the other hand, when most of the excess energy was injected to the lowest orthogonal mode (disrotation), both single rotation and disrotation trajectories increased and the conrotatory trajectories became minor ones. Furthermore, the stereochemical outcome varied strongly with the ratio of kinetic to potential energy in the initial excess energy injected to the disrotational mode. The overall double/single rotation ratio from Boltzmann sampling was computed as 2.9–3.5, which is well above the value of 1.5 predicted from TST. The lifetime distribution was calculated from the ratio of the number of trajectories that had not formed product (N(t)) and the total number of trajectories (N0). Counting (N(t))/(N0) at a series of time intervals gave timedependent decay plots. The plots of (N(t))/(N0) versus time gave two separated decay plots, one for double rotation and the other for single rotation, showing the existence of short-lived and long-lived trajectories. The decay time constants were derived from straight-line part of the decay plots for the double and single rotation trajectories: = 130 and 430 fs for double and single rotation, respectively. The calculated time constant ratio, 3.3, was essentially the same as the number calculated from the product ratio. The most double rotation trajectories underwent a set of 180 rotations and cyclized
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immediately. In contrast, the common feature of the long-lived trajectories was a mismatch of torsional phases, which appeared to prolong the trajectory. The trajectory calculations reported here were nonstatistical, indicating that both concerted (short-lived) and nonconcerted (long-lived) behavior could occur on the PES for the concerted/stepwise mechanistic borderline reaction. Trajectory calculations for cyclopropane stereomutation were further carried out on analytical PES built up by fitting parameters for three important internal coordinates, C–C–C angle and two terminal torsions, to reproduce CASPT2N/6-31G* energy.15 The MD analysis for trimethylene-1,2-d2 and trimethylene-1,3-d2 began by generation of quasiclassical canonical ensembles at 400C in the vicinities of conrotation, disrotation, and monorotation stationary points. A total of 12,000 trajectories were examined. The ratio of double to single rotations for stereomutation of cyclopropane-1,2-d2 at 400C was calculated to be 4.73 0.11. This ratio was clearly different from that deduced by TST analysis as mentioned above. It was claimed that this high value was due to dynamic matching phenomenon,4 in which trimethylene formed by distortion tends to follow direct trajectories across the surface and to exit (reclose) by distortion, despite the fact that distortion barrier is higher in energy. The lifetime distribution was found to be around 140 fs, which was in agreement with the value derived from direct dynamics on a semi-empirical surface.13,14 The reaction of trimethylene biradical was successfully treated by means of dynamics simulations by two groups with different PESs as described above.11–15 The success led one of the groups to extend the study to analyze the collisional and frictional effects in the trimethylene decomposition in an argon bath.16 A mixed QM/MM direct dynamics trajectory method was used with argon as buffer medium. Trimethylene intramolecular potential was treated by AM1-SRP fitted to CASSCF as before, and intermolecular forces were determined from Lennard-Jones 12-6 potential energy functions. Trajectories were initiated by generating initial conditions with the efficient microcanonical sampling or quasiclassical normal-mode sampling procedures at 54.6 or 146.0 kcal mol1 of vibrational energy for trimethylene. Trimethylene was then placed in the center of a box, with periodic boundary conditions, and surrounded by an argon bath with an equilibrium temperature and density. Initially, trimethylene was in a nonequilibrium state with respect to the bath, since its coordinates and momenta were held fixed while the bath was equilibrated, and the trajectories were propagated until either cyclopropane or propene was formed. Cyclopropane versus propene branching ratio was analyzed under isolate conditions in the gas phase and under the argon environment with different reduced densities (*). At a low density (* = 0.5), the branching ratio was nearly constant at 0.8–0.85, for the two initial sampling methods, with various bath temperature regions (100–1000 K) for the lower energy trajectories (54.6 kcal mol1). These numbers were similar to those (0.85–0.90) obtained
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by trajectories under isolated conditions in the gas phase. The barrier recrossing, estimated from the comparison of the cyclopropane:propene branching ratio in the first barrier crossing and in the final products, was not observed in these trajectories. Thus, the low-density trajectories showed basically similar features to those in the gas phase. The branching ratio, however, was found to strongly depend on the density. It decreased from 0.82 to 0.90 at * = 0.26 to 0.01–0.02 at * = 3.06 with the initial energy of 54.6 kcal mol1. With the higher initial energy of 146.4 kcal mol1, it changed from 0.50–0.56 at * = 0.26 to 0.01–0.03 at * = 3.06. Thus, the ring-closure channel was nearly closed under high-density conditions. The origin of the dramatic effect of the argon density on the product ratio was not very clear, but might be due to a frictional effect that retards cyclization more than H-transfer that leads to the formation of propene. With the language of physical organic chemistry, a molecule with a larger internal energy at a higher temperature may overcome a high-energy barrier. The barrier to propene is higher than that to cyclopropane, and therefore more propene formation at higher temperature is acceptable, but the observed nearly exclusive formation violates the reactivity–selectivity principle, which requires less selective product distribution at a higher temperature.
VINYLCYCLOPROPANE TO CYCLOPENTENE REARRANGEMENT
Stereochemical product distributions of [1,3] sigmatropic rearrangement of vinylcyclopropane (VCP) to cyclopentene (CP) [Equation (4)] were calculated with quasiclassical trajectory simulations on AM1-SRP PES parameterized to fit ab initio (MRCI) calculations.17–19 In Equation (4), the reaction of deuterium-labeled compound is illustrated to show the reaction stereochemistry. In the [1,3] sigmatropic rearrangement, four products can be formed from the combination of stereochemistry at the migrating methylene group (inversion (i) vs. retention (r)) and at the allyl group (suprafacial (s) vs. antarafacial (a)). Experimentally, the reaction was shown to give product distribution of si-9:sr-9:ar-9:ai-9 = 40:23:13:24.20 The ratio of Woodward–Hoffmann allows (si-9 þ ar-9) to forbidden (sr-9 þ ai-9) products was nearly 1:1. Argument had been whether the reaction proceeds via a biradical intermediate or a set of competing direct reactions.
(4)
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Chart 4
Potential energy calculations at B3LYP/6-31G* and CASSCF(4,4)/6-31G* indicated that there was no well-defined local minimum in the biradical region, and a broad flat region had a TS (TS1, Chart 4), whose IRC led to si-9. The TS was the only TS of [1,3] sigmatropy, and there were two other local TSs (TS2 and TS3) within a narrow range of energy of less than 2 kcal mol1, which were not connected to products.21–23 If the TS1 connected to si-9 gives other three products, TST cannot be used to predict product ratio. The stereochemical product distribution of the VCP rearrangement to CP was calculated based on quasiclassical trajectories (VENUS-MOPAC) run on a modified AM1 PES parameterized to reproduce ab inito energies (AM1SRP). Trajectories were initialized at TS1, TS2, and TS3 with quasiclassical TS sampling, in which initial coordinates and momenta that approximated a quantum mechanical Boltzmann distribution were generated by the TS normal-mode sampling procedure. The results showed that trajectories starting from each TS gave all four products. Furthermore, total average of the product distribution agreed with experimental observations. Thus, the TS region of the PES is shared by all four reactions, as suggested by previous PES calculations.21–23 However, trajectories initialized at the three TS structures did not give identical product distributions under any circumstances. For example, trajectories starting from TS1 gave si as a major product, and the ratio of suprafacial products (si-9 þ sr-9) amounts to 80%. Trajectories initiated at another TS2 yielded ai-9 as a major product and the products with insertion of configuration (si-9 þ ai-9) were nearly 70%. Trajectories initiated at TS3 were much less selective. These data demonstrated nonstatistical dynamics, which were inconsistent with a mechanism involving a statistical intermediate. Counting the number of products at a series of time intervals gave time-dependent product distribution. Such analysis revealed that trajectories could be classified into short-lived and long-lived ones. The short-lived trajectories were stereoselective, and the product ratio was strongly time dependent. For example, the suprafacial/ antarafacial (s/a) product ratio for the trajectories initiated at TS1 was 463 for the 100–200 fs range, while it was 2.3 for the 300–400 fs range. Likewise, inversion/retention (i/r) product ratio for the trajectories initiated at TS3 was
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88 for the 100–200 fs range, while it was 9.8 for the 300–400 fs range. For the long-lived trajectories, these ratios were similar and more or less near unity, regardless of the time range and initial conditions. Thus, short-lived trajectories were nonstatistical and mode specific, whereas long-lived trajectories showed considerable stereorandomness. The observed nonstatistical dynamics is likely due to the torsional motions that are approximately decoupled from other modes and thus do not participate in IVR before the reaction is over.
DISSOCIATION OF ACETONE RADICAL CATION
Acetone radical cation, generated in a mass spectrometer by 1,3 H migration of its enol isomer, dissociates to give acetyl cation þ methyl radical [Equation (5)]. Although the two methyl groups are symmetrical in acetone radical cation, the methyl newly formed by the hydrogen transfer is known to be lost preferentially.24 It was interesting to clarify the origin of this preference by simulations. Direct dynamics trajectory calculations were carried out on an AM1-SRP surface parameterized to fit energies and geometries of key stationary points, as determined at the B3LYP/cc-pVTZ level of theory. Trajectories were initiated at the TS for keto/enol isomerization and at the acetone radical cation minimum. The number of trajectories was 1807 for the former and 1816 for the latter set of calculations. Initial states were generated by quasiclassical normal-mode sampling, and a microcanonical ensemble of initial states was selected so that each trajectory had a total energy of 10 kcal mol1 in excess of the ZPE.
(5)
Trajectories initiated from the vicinity of acetone radical cation showed essentially equal loss of either methyl (branching ratio 1.01 0.01). In contrast, the branching ratio observed for methyl loss in trajectories originating the TS was 1.13 0.01, which is in qualitative agreement with the experimental values of 1–1.4.24 When the trajectories were divided into time courses, with a resolution of 5 fs, a unique phenomenon appeared that the newly created methyl dissociated predominantly at very short reaction time intervals. It was found that the trajectories that would lose the newly formed methyl at very short times never entered the PES minimum of the acetone radical cation. The shortest duration trajectories simply took the exit without ever attaining the equilibrium geometry of the radical cation.
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An exponential fit to a plot of undissociated ions versus time yielded a halflife of the reaction as 238 fs, which was in reasonable agreement with an experimental estimate of 500 fs. It should be noted that the reaction initiated from the TS was significantly faster than that from the acetone radical cation. This phenomenon appeared to be due to nonstatistical coupling of the kinetic energy acquired during the TS to the radical cation transformation into modes of importance for the subsequent dissociation of the radical cation. It was suggested that the observed chemically significant nonstatistical dynamics for an intermediate that sits in a potential energy well some 20 kcal mol1 deep might have potential relevance to other organic reactions. The reaction was further studied by ab initio classical trajectories at the MP2/6-31G(d) level of theory using a Hessian-based predictor-corrector method25,26 implemented in the Gaussian suite of programs.27 Here, a microcanonical ensemble using quasiclassical normal-mode sampling was constructed by distributing 10 kcal mol1 of excess energy above the barrier. Trajectory started at the keto/enol tautomerization TS showed that the dissociation was again favored for the loss of the newly formed methyl group in agreement with experiments and previous simulations.24,28 The branching ratio of the methyl loss was calculated to be 1.53 0.20, which is in agreement with the experimental ratio. It was also found that the translational energy distribution of the methyl radicals was bimodal, in that the radical derived from the newly formed methyl had higher average translational energy than that from the other methyl.
THE WOLFF REARRANGEMENT
Flash vacuum thermolysis of the formal Diels–Alder adduct (10) of acetylmethyloxirene to tetramethyl-1,2,4,5-benzenetetracarboxylate to give acetylmethylketene (15, in Scheme 1) was examined in an attempt to find an example of nonstatistical dynamics effect on product distribution.29 With two carbon13-labeled starting materials (# and * show the labeled carbon in separated experiments), the reaction yielded 15 with different 13C locations. It was originally expected that 10 would give 12, which then via carbene formation would yield 15a and 15b. The ratio of the two products was anticipated to show the occurrence of nonstatistical product distributions. Compound 15c might be formed via 12 and 13, but this route was considered to be minor since 13 was much unstable than 14. The experimental finding was surprising. The product ratio of 15a, 15b, and 15c, which was determined as relative yields of diols after MeOH addition and DIBAL reduction, was 1.9–2.6:1.0:12–14.3. The predominant formation of 15c required reconsideration of the reaction pathways. Electronic-structure calculations at CCDS(T)/cc-pVTZ//CCSD/cc-pVDZ showed that carbene 13 was 8.7 kcal mol1 unstable than carbene 14 in
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Scheme 1
enthalpy, although the energy difference became much smaller (0.5 kcal mol1) in free energy. Thus, there was no reason to conclude that 12 gave 13 predominantly over 14. Thoughtful reinvestigation of the reaction energies revealed that the favorable route from 10 to 13 was through 11; 11 was 47.9 kcal mol1 more stable than 12 in enthalpy at the DFT method (MPWB1K6-31þ G(d,p)), and TSs from 10 to 11 and from 11 to 13 were more stable than the TS from 10 to 12 by 19.0 and 11 kcal mol1, respectively. The barrier from 13 to 15c was 3.4 kcal mol1 while the step from 13 to 14 required 6.4 kcal mol1, both in free energy. Thus, the formation of 15c was the primary process of the reaction of 13. The three isotopically labeled 150 s were concluded to be formed from 10 via the pathways shown in solid arrows in Scheme 1. Despite that 15a and 15b were minor products for the reaction of 10, it should be noted here that the reaction mechanism in the scheme requires that the product ratio 15a/15b to be very close to unity, if 13C kinetic isotope effect (KIE) is neglected, since they are symmetric. Thus, the observed ratio as large as 2.5 could be an indication of dynamics effect. Direct dynamics calculations were carried out with quasiclassical normalmode sampling from a canonical ensemble at 923 K (the experimental reaction temperature). Simulations initiated at the vicinity of TS for rearrangement of carbene 13 to 14 via oxirene 12, and 300 trajectories were obtained at DFT methods. The preliminary results reported in the manuscript showed that preferred formation of 15a over 15b by the ratio of 1.8–7.6 depends on the method used. The results were qualitatively consistent with the value of 2.5 deduced from the experiment. The non-unity ratio likely arises from the situation that two methyl groups in 14 are dynamically unequal on the carbene formation process.
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3
189
Avoided intermediate on IRC
SN2 REACTION
In the previous section, examples were shown in that product distribution does not follow what is expected from statistical TST. In many cases, reactions that were formally assigned, on the basis of the analysis of PES, to proceed via a stepwise mechanism with a distinct radical intermediate actually behaved dynamically as concerted reactions. This is one way of appearance of dynamics effect. In this section further examples of the discrepancy between reaction pathways on the PESs and dynamics pathways are discussed. One of the earlier examples was reported on SN2 reactions. Basilevsky reported more than two decades ago quantum-dynamical evidence that SN2 reactions of CH3F with nucleophiles X were direct without trapping in the X CH3F pre-reaction complex.30 Trajectory calculations were carried out in another SN2 of CH3Cl þ F.31 In this study, trajectories were initiated at the reactant state, in which the initial geometrical configurations at time zero were randomly generated in the range 180 3 for the collision angle and of RF–Cl = 6.0–6.5 A˚. The vibrational phase of CH3Cl was generated to take a temperature of 10 K. The quantum part was calculated at HF/3-21 þ G(d). The calculations showed that almost all available energy is partitioned into the relative translational mode between the products (43%) and the C–F stretching mode (57%) at zero collision energy. It was found that the lifetime of the post-reaction complexes was short enough to dissociate directly to products, while the energy was not completely distributed within the lifetime. It was concluded that the SN2 reaction proceeds nonstatistically via a direct mechanism in the case of near-collinear collision. Hase and coworkers carried out extensive trajectory calculations for the reaction of CH3F þ OH.32 The direct dynamics calculations were initiated at the central barrier at MP2/6-31þG*. Quasiclassical sampling, which includes ZPE, was used with a 300 K Boltzmann distribution for all vibrational degrees of freedom and rotations. Out of 31 trajectories, only 4 were trapped in the postreaction complex, whereas 27 gave directly the dissociated products with F approximately along the O-C F collinear axis. Thus, only a small fraction followed the IRC pathway. It is worth noticing that the post-reaction complex has an O-H F interaction and therefore the departing F has to be turned back to CH3OH to form the complex, which is dynamically unfavorable unless efficient IVR is realized. It was noted that the central barrier recrossing was unimportant for this reaction, consistent with the direct dissociation mechanism.
[3,3]SIGMATROPY
Experimental study on the [3,3] sigmatropic rearrangement of 1,2,6-heptatriene [Equation (6)] suggested that the reaction proceeds via a stepwise mechanism
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with a biradical intermediate (17) on the basis of the trapping experiment with O2.33 At the same time, by extrapolation of the product ratio to infinite O2 pressure, it was also deduced that roughly half of the reaction proceeds concertedly without formation of intermediate 17. Since the potential energy calculations at the CASSCF(8,8) or B3LYP level of theory did not give TS corresponding to the direct concerted rearrangement from 16 to 18, it was assumed that the diradical intermediate 17 and final product 18 are formed from TS4 by bifurcation. Bifurcation here does not mean that the path bifurcates on the way to two products, but means that trajectories may stay in the intermediate region for long enough time for statistical energy distribution or may go over the intermediate or stay in the region for only a short period of time to reach product region as if it is concerted process.34
(6)
CASSCF(8,8) as well as AM1-SRP direct dynamics calculations revealed that when a few key normal modes were energized trajectories did not stay in the biradical region and led directly to the product, 18. AM1-SRP MD calculations using quasiclassical normal-mode sampling of the initial states from a canonical ensemble at 438 K showed that 17% of 400 trajectories run from the vicinity of TS4 bypassed biradical 17 and directly gave 18. These trajectories should be counted in as the ‘‘concerted’’ component of the reaction. The results that trajectories starting at TS4 led both to the biradical intermediate and product regions suggested that a reaction whose steepestdescent path from a TS leads only to one product may give additional products by dynamically favored non-steepest-descent paths.35
4
Non-IRC reaction pathway
Dynamics effect discussed so far deals with reaction systems, in which an unstable intermediate exists in a shallow well on the PES connecting the reactant and product states. These putative intermediates have been biradicals, radical ions, carbenes, or post-TS complexes. Trajectory calculations showed examples where reacting molecules stride over a shallow well to give product directly or cases where the lifetime of the species trapped in a well is short enough to avoid thermal equilibration and quickly escape to the product. In these cases, reactions occurred effectively in a concerted manner, although the PES dictates a stepwise mechanism.
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Another manifestation of a dynamics effect on reaction pathways is a socalled ‘‘dynamics-driven’’ reaction pathway, in which trajectories go through a nonminimum energy pathway due to a dynamics effect.
PHOTOISOMERIZATION OF CIS-STILBENE
One example of non-IRC trajectory was reported for the photoisomerization of cis-stilbene.36,37 In this study trajectory calculations were started at stilbene in its first excited state. The initial stilbene structure was obtained at CIS/631G, and 2744 argon atoms were used as a model solvent with periodic boundary conditions. In order to save computational time, ‘‘finite element interpolation’’ method was used, in which all degrees of freedom were frozen except the central ethylenic torsional angle and the two adjacent phenyl torsional angles. The solvent was equilibrated around a fully rigid cis-stilbene for 20 ps, and initial configurations were taken every 1 ps intervals from subsequent equilibration. The results of 800 trajectories revealed that, because of the excessive internal potential energy, the trajectories did not cross the barrier at the saddle point. Thus, the prerequisites for common concepts of reaction dynamics such TST or RRKM theory were not satisfied.
IONIC FRAGMENTATION REACTION
The reaction of base-mediated decomposition of peroxide had previously been studied experimentally and it was shown that the reaction of CH3OOH with F gave HF þ CH2O þ OH as major products.38 This process is an elimination reaction of H and OH from CH3OOH (ECO2). The result was surprising since the observed products were much higher in energy than HF þ CH2(OH)O, products of a sort of migration of OH from O to CH2 upon H abstraction. Scheme 2 shows the electronic energies (in kcal mol1) calculated at B3LYP/6-311þG(d,p) for the reactant complex, TS, and the two product states. Thus, HF þ CH2(OH)O are 36.5 kcal mol1 more stable than HF þ CH2O þ OH. Furthermore, IRC calculations from the TS led to HF þ CH2(OH)O rather than HF þ CH2O þ OH. Direct
Scheme 2
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trajectory calculations were carried out to examine the apparent discrepancy between the experimental observation and the expectation from PE calculations. Ab initio direct dynamics trajectory calculations were performed at the B3LYP/6-311þG(d,p) level of theory.39 The trajectories were initiated at the separated reactants, TS (HOOCH3 F), and the CH2(OH)O–H F region on IRC, with quasiclassical sampling including ZPE. The trajectories from the reactants were started at 15 A˚ separation of the two species with small attractive potentials of –0.21 or –0.13 kcal mol1. The collision impact parameter was chosen randomly between zero and maximum. The initial CH3OOH vibrational and rotational degrees of freedom were selected from their 300 K Boltzmann distributions. Out of the 200 trajectories started at the separated reactants, 145 gave productive trajectories and 55 stayed in the reactant state. Among the 145 trajectories, 97 were trapped in the CH3OOH F potential energy well as reactant complex and stayed up to 4 ps. Forty-five trajectories led to HF þ CH2O þ OH, which were the major products observed in the experiment, and three gave HF þ CH3OO. The path along IRC leading to a deep potential energy minimum for the CH2(OH)2 F complex followed by dissociation to HF þ CH2(OH)O was not observed by dynamics simulations, despite the fact that this path has an energy release of –63.4 kcal mol1 and is considerably more exothermic than the ECO2 path whose energy release is –27 kcal mol1. Analyses at the molecular level showed that the major products, HF þ CH2O þ OH, were formed via initial C-H F interaction, followed by concerted OH and HF elimination to give CH2O. Trajectories started at other initial structures; TS and HOCH2O–H F also gave HF þ CH2O þ OH, again along paths different from the IRC path. This is an example that two-bond fission is favored over one-bond fission þ intramolecular migration; the situation is similar to the Beckmann rearrangement versus fragmentation reactions that will be discussed in section ‘‘Path Bifurcation’’.
CYCLOPROPYL RADICAL RING-OPENING
The ring-opening reaction of cyclopropyl radical [Equation (7)] was shown to occur at 174C to give ally radical, but the product stereochemistry was unclear. Ab initio direct dynamics study was carried out to clarify the stereochemical course of the reaction.40 Trajectories were initiated at the ringopening TS obtained at CASSCF(3,3)/6-31G(d), with quasiclassical normal sampling at the experimental temperature of 174C. ZPE was included, and thermal vibrational energy was sampled from the normal-mode Boltzmann distribution. A rotational energy of RT/2 was added toward the allyl radical product.
MOLECULAR SIMULATIONS OF ORGANIC REACTIONS
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(7)
For 21 out of the total 141 trajectories examined, barrier recrossing was observed leading back to cyclopropyl radical after up to 21 fs of dynamics, which is a violation of TST. The ring-opening step from the TS to allyl radical requires rotation of the two C–C bonds. In all reactive trajectories observed, the two bond rotations were found to occur in a nonconcerted fashion in agreement with the IRC calculations. Further, 68 out of the 120 reactive trajectories followed the asynchronous disrotatory motion on the minimum energy path. However, the remaining 52 trajectories also had an asynchronous motion, but with the two terminal methylene groups rotated in the conrotatory manner. Thus, the trajectories as a whole did not follow the IRC path. The significance of small preference (57%) for disrotatory ringopening over conrotatory opening was not clear, because the number of trajectories performed in the study was limited, and it is possible that a larger ensemble of trajectories may predict no stereochemical preference for ringopening.
IONIC MOLECULAR REARRANGEMENT
Direct MD studies described above have demonstrated that reacting molecules do not necessarily follow the reaction intermediates along the IRC when kinetic energy is incorporated. A paper published in 2003 further showed that chemical reactions may in fact proceed through a reaction route totally different than the IRC path.41 The intramolecular rearrangement of protonated pinacolyl (3,3-dimethyl-2-butyl) alcohol (Me3C-CHMe-OH2þ, 19), which, upon heterolysis, gives a rearranged tertiary carbocation (20) via either a concerted or a stepwise mechanism (Scheme 3). KIE studies on the reactions of pinacolyl sulfonates in hydroxylic solvents suggested the concerted pathway, but the mechanism was still not clear.42 Ab initio calculations at the HF, MP2, and B3LYP theories with the 6-31G* and 6-311G** basis sets gave only one TS that corresponds to the saddle point of the concerted pathway, and no other TSs could be characterized as indicated in the potential energy contour map at HF/ 6-31G* (Fig. 1). The TS was 9.3 kcal mol1 above the reactant state and the reaction was exothermic by 6.3 kcal mol1 at HF, which was in semiquantitative agreement with the B3LYP/6-311G** and MP2/6-311G** results. Direct ab initio molecular dynamic simulations starting at the reactant with total Maxwell-Boltzmann equipartitioned thermal kinetic energy of 26 kcal mol1, however, demonstrated that the reaction pathway did not follow the IRC (dotted line in Fig. 1) on the PES, but that it was rather
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Scheme 3
2
reactant region
100
sec-cationic region
CH3-C-C angle/degree
6
80 TS 30
10
12
16
60
8
10
130
4 0
50 –4
4
40
2
1.5
2.0
–4
2.5
–6
3.0
product region 3.5
4.0
RC-O/Å
Fig. 1 3D map for heterolysis of 19.
controlled by the dynamics of the reaction. In most cases, trajectories were first initiated by the C–O bond cleavage to lead to a secondary carbocation intermediate (21) region, despite that there is no energy minimum at this region. The intermediate cation could have a lifetime up to 4 ps, and then yielded rearranged products, via an overall stepwise mechanism. A typical example of trajectories is illustrated in Fig. 2. The variations of three Me-C–C angles in Fig. 2c and the charges on the leaving group (H2O) and Ca in Fig. 2d showed
Potential energy (hartree)
MOLECULAR SIMULATIONS OF ORGANIC REACTIONS –310.48
195
(a)
–310.49 –310.50 –310.51 –310.52 –310.53 –310.54 6.0
(b)
RC-O (Å)
5.0 4.0 3.0 2.0 1.0 0
1000
2000
3000
2000
3000
Mulliken group change
Me-C–C angle (degree)
time (fs) 140.0
(c)
120.0 100.0 80.0 60.0 40.0 20.0 0.5
(d) Cα
0.2 0.0
H2O
–0.2
Cβ
–0.5 0
1000 time (fs)
Fig. 2 The variation of (a) potential energy, (b) C–O distance, (c) Me–Cb–Ca angles of the three Me groups, and (d) the Mulliken charge in one of the trajectories.
that none of the methyl groups started to migrate at 2700 fs, despite that the C–O bond was cleaved at a very early stage of the reaction at 100 fs. Thus, the reaction dynamics preferred the stepwise rather than the concerted pathway.
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This occurred probably because the initial motion of the reacting species was to the cationic region due to the shape of the energy surface and thus one bond cleavage was preferred over the concerted migration. These results clearly indicated that a TS of a given character may have only limited significance with respect to the actual mechanism.
ENE REACTION
Singleton and coworkers took up the ene cyclization reaction of ene-allene (Scheme 4) and carried out combined experimental-computational investigation.43 The ene reaction had been known to show mechanistic uncertainty, in particular whether it proceeds via a concerted or stepwise route, and therefore provided a challenge for dynamics study. KIE measurement for the reaction of 22 (R1 = R2 = TMS) in toluene at 50C gave kCH3/kCD3 of 1.43, which was smaller than what was normally observed in concerted ene reactions. However, the isotope effect was too large to support a stepwise ene reaction. Thus, this was in line with the idea that the mechanism is near the concerted-stepwise borderline. Computational study at B3LYP/6-31G** showed three possible pathways. The first one was the concerted process that directly gives the ene product, 25. The TS, 23, is 23.8 kcal mol1 higher in energy than 22. Biradical intermediate, 24, for a stepwise process, which is formed with an inward Me rotation optimized. However, the TS leading to 24 could not be obtained, and all attempts to locate the TS converged on 23. Alternative stepwise process with outward Me rotation gave a TS which is 8.8 kcal mol1 less stable than 23.
Scheme 4
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The absence of the TS leading to 24 suggested the authors to assume that the concerted and stepwise merge in the single TS, 23. KIE was calculated for the two optimized TSs. The stepwise TS with outward Me rotation gave the kCH3/kCD3 value of 1.06, which was much smaller than the observed isotope effect. The kCH3/kCD3 value for the concerted process was predicted to be 1.54. This is slightly larger than the experimental observation, and it was suggested that the observed isotope effect represents a mixture of concerted and stepwise mechanisms. Quasiclassical direct dynamics trajectory calculations at UB3LYP/6-31G** for the concerted TS of model compound (TS6) was carried out. Simulations were started either at the TS geometry or with atomic positions near the TS randomized by using linear sampling of each normal mode. The two types of simulations gave similar results. Although the minimum energy path from the concerted TS goes directly to the product, 29 out of 101 trajectories afforded diradical intermediate in the stepwise route. The result implied that the TS for the concerted process would give the ene product through the stepwise intermediate. Another interesting observation was that in another 29 trajectories the hydrogen transfer occurred ahead of the C–C bond formation, giving rise to another diradical intermediate. It should be stressed that this intermediate is not associated with a potential energy minimum; the situation is similar to the case described above for the ionic molecular rearrangement.41
It was found that this reaction is not well described by either a concerted or two-step mechanism and that the consideration of dynamic effects is necessary to understand the nature of the intriguing reaction. When a reaction involves multiple bonding changes, a question may arise whether the bonding changes occur by a stepwise or concerted pathway. An answer to such a question based on the classical reaction theory is that the reaction proceeds by a concerted pathway, by a stepwise pathway, or by a mixture of the two separate pathways. However, if one takes into account dynamic effects, the answer to the question of concerted versus stepwise may be much more complex. It is interesting to point out here that the case reported by Singleton for the ene reaction affords a case, where stepwise mechanism can dynamically operate on a concerted PES. This contrasts with the reactions described in section ‘‘Nonstatistical Product Distribution’’, in which the
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trajectories showed effectively a concerted character on the stepwise PES. Thus, a possible role of dynamics appears in different ways in mechanistic organic chemistry.
THERMAL DENITROGENATION
Concerted versus stepwise issue was studied for another radical reaction. The thermal denitrogenation of 4-spirocyclopropane-1-pyrazolines (27) gives alkylidenecyclobutanone (28) and spiropentane (29) in three possible pathways (Scheme 5), via (a) diazenyl diradical intermediate (30), (b) 1,3-diradical intermediate (31), or (c) concerted cycloreversion TS. Computational study at (U)B3LYP/6-31G* for the reaction of 27 (R = Z = H) showed that the activation barrier (DE þ ZPE correction) for the diradical (31) formation (path b) is 40.2 kcal mol1, which is 2.1 kcal mol1 lower than that for the diazenyl diradical (30) formation step (path a).44 The barrier from 31 to 29 is very small (0.6 kcal mol1), whereas the barrier from 31 to 28 is 7.0 kcal mol1. Direct formation of 28 from 27 via a [2 þ 2 þ 2] reaction did not give TS. Thus, the calculations suggested that the reaction of 27 (R = Z = H) would give 29 as a major product via path b. This is consistent with experimental report, which showed that the denitrogenation of the parent 27 nearly exclusively gave spiropentane.45
Scheme 5
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Calculations for 27 (R = Me, Z = CO2Me) at B3LYP/6-31G* and MP2/ 6-31G* gave qualitatively the same results as for 27 (R = Z = H). However, experimental study for 27 (R = Me, Z = CO2Me) revealed that the major product was 28 (R = Me, Z = CO2Me) rather than 29. Thus, calculations and experiment did not match for the reaction of this species. It is important to note that the experimental activation energy for the formation of 28 was determined as 26.8 0.5 kcal mol1, which is close to the value (DE6¼ þ ZPE = 26.9 kcal mol1) for the formation of 31 from 27, despite that 31 gives 29 on the PES. In order to reconcile this discrepancy, dynamics effect was examined by means of ab initio MD simulations at (U)B3LYP/6-31G*.44 Trajectories were initiated at the TS for the denitrogenation from 27 (R = Z = H) to 31 with 353 K Boltzmann distribution for the reaction coordinate translation. Out of 10 trajectories, 1 went back to the reactant, 8 gave 31, and 1 led directly to 29. Thus, the trajectory calculations reproduced experimental trend reported in the literature,45 namely spiropentane is the major product for the reaction of the parent 4-spirocyclopropane-1-pyrazoline. Analogous trajectory calculations for 27 (R = Me, Z = CO2Me) gave quite different results. Out of 31 trajectories, 25 went back to the reactant, 5 gave 28, and only 1 led to 31. In order to examine the effect of substituents, simulations were also carried out for 27 (R = H, Z = CO2Me), which showed that 11 out of 36 trajectories gave 31, and 25 led to 28. Thus, it appears that an electronwithdrawing substituent (CO2Me) plays a crucial role in the dynamics effect, which facilitates the selective production of 28 despite that the minimum energy path affords 31 and eventually 29. The effect of the electronwithdrawing substituent was considered to arise from more effective hyperconjugative interaction between the radical orbitals and the -orbitals of the cyclopropane ring in 31 (Z = CO2Me) than in 31 (Z = H), which makes the cyclopropane ring prone to ring-opening.
UNIMOLECULAR DISSOCIATION
A combined experimental and theoretical investigation of unimolecular dissociation of laser-excited formaldehyde (H2CO) to H2 and CO revealed that there exist two dissociation channels: the one proceeding through a wellestablished TS to produce rotationally excited CO and vibrationally cold H2, and the other yielding rotationally cold CO in conjunction with highly vibrationally excited H2 [Equation (8)].46 Quasiclassical trajectory calculations on a global PES constructed from least-squares fits to ab initio results suggested that this second channel represents an intramolecular hydrogen abstraction mechanism, in which one hydrogen atom is first dissociated and roams around the HCO fragment and abstracts the second H atom to give H2. Thus, this channel entirely goes off the saddle point on the PES.
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(8)
SN2 REACTION
Recent experimental advances allow one to obtain insight into the gas-phase reaction dynamics, such as the probabilities for energy redistribution within the ion-dipole complexes, their dependences on initial quantum states, the branching into different product quantum states, and the role of tunneling through the central barrier from measurements of correlated angle- and energy-differential cross sections. Such experimental study provides complementary information to dynamics calculations. For the SN2 reaction of Cl þ CH3I, MP2(fc)/EPC/aug-cc-pVDZ trajectory calculations initiated at the reactant state with 1.9-eV collision energy revealed that the reaction occurred by two mechanisms: direct and indirect ones.47 As the atomic level, the direct mechanism proceeded by the classical SN2 pathway with Cl attacking the backside of CH3I. On the other hand, the indirect mechanism occurred via a roundabout mechanism, in which Cl first stroke the side of the CH3 group, causing it to rotate around the I atom. This rotation occurred since I is a heavy atom compared to the other part of the molecule. When proper orientation was attained, then Cl attacked the backside of CH3I. The ratio of the two mechanisms depended on the collision impact factor; the ratio was 0.4, 0.8, 0.8, and 1.0 for impact factors of 0.0, 1.0, 2.0, and 3.0 A˚, respectively. The product energy partitioning for the direct mechanism was 0.04, 0.23, and 0.73 for rotation, vibration, and translation, respectively, whereas it was 0.28, 0.56, and 0.16 for indirect mechanism. The overall fraction partitioned to translation was calculated as 0.6–0.7, which was in agreement with the experimental value. Thus, the combined study of gas-phase experiment and high-level MD simulations revealed that the detailed mechanism of the SN2 reaction at the molecular level varies depending on how two reacting groups collide. Similar situation, in which trajectory largely deviates from the minimum energy path, has been reported for H þ HBr -> H2 þ Br.48
5
Path bifurcation
As is described in previous sections, dynamics effect often plays important role in determining reaction mechanisms. This is because such a reaction proceeds via a region mechanistically intermediate between two extremes, and thus the mechanism is sensitive to a subtle perturbation. In those cases, the minimum
MOLECULAR SIMULATIONS OF ORGANIC REACTIONS (a)
201
(b)
Fig. 3 Path bifurcation on (a) symmetrical PES and (b) asymmetrical PES.
energy path and the shape of PES are less relevant than ordinary thought. In this section, different types of examples of dynamics effect are presented, in which single TS gives two products through path bifurcation. There are cases where a minimum energy path from a TS leads to another TS that separates two product states.49–55 If PES is symmetrical, the minimum energy path goes to a valley-ridge inflection (VRI) point and bifurcates before reaching the product region. The situation is schematically shown in Fig. 3a. Mechanisms of reactions with such symmetrical PES are reported for ene reaction,56–59 isomerizations,60,61 Berry pseudorotation,62,63 and deazetization.64 There may be cases, where a minimum energy path from TS leads to one of the two different types of products located close to each other on the PES, and due to dynamics effect the path may bifurcate leading to two products (Fig. 3b). Examples of this kind of reactions include ET-SN2 borderline reaction,65–75 pseudorotation,76–78 isomerization,50,79–84 cycloaddition,85–87 Beckmann rearrangement,88 and sigmatropic isomerization via biradical intermediate.89 For some of the reactions dynamics simulations were carried out to study how the bifurcation occurs and the product ratio is determined.58,60,62,63,70– 75,83,84,87,90 Dynamics effect of some of these reactions are discussed below.
BIFURCATION ON SYMMETRICAL PES
Ene reaction Ene reactions of simple alkenes with singlet oxygen have been studied by both computational and experimental methods.56,57,59 The reactions may proceed via a concerted or a stepwise mechanism [Equation (9)]. For a stepwise mechanism, four types of intermediates, biradical, zwitterion, perepoxide,
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H. YAMATAKA
and p-complex, were proposed. Deuterium KIE study of CD3-labeled 2,3dimethyl-butenes revealed that the reaction gave only small intermolecular KIEs (kH/kD = 1.04–1.09) whereas intramolecular KIEs were of significant magnitude (1.38–1.41). The results had been interpreted to show that the reaction proceeds via rate-determining formation of symmetrical perepoxide. Intermolecular 13C KIE for Me2C=C(i-Pr)2 showed that the two olefinic carbons have small KIEs of the same magnitude, which clearly indicated that the rate-determining TS is symmetrical with respect to the two carbons. Intramolecular 13C KIE study supported the mechanism that the reaction proceeds via symmetrical TS, followed by intramolecular product-determining selection between methyl groups.
′
″
″ ′
′
″
(9) ″
″
′
′
″
″
′
′
Computational study at UHF or UB3LYP level of theory disagreed the intermediacy of perepoxide and showed that the reaction proceeds via biradical intermediate. However, calculations at CCSD(T)/6-31G*//RB3LYP/631G*, which includes substantial dynamic configuration interaction, revealed that the reaction of cis-2-butene with 1O2 proceeds through an early ratedetermining TS, and then the reaction path appears to lead toward a perepoxide-like structure (Scheme 6, R = R1 = H). The first TS (TS6) is of Cs symmetry, and the hydrogen abstraction has not yet started. The perepoxidelike structure is also of Cs symmetry and is the TS (TS7) for interconversion of the two symmetrical products. There exists VRI between TS6 and TS7. Since the minimum energy path is on a valley before VRI but it is on the ridge after
MOLECULAR SIMULATIONS OF ORGANIC REACTIONS
203
Scheme 6
VRI, the actual reaction path bifurcates into two products before reaching TS7. The rate is determined by TS6, whereas the product ratio is controlled by the shape of the PES near the VRI point and TS7. Thus, a question arises: how the product selection occurs when a subtle perturbation, such as isotopic substitution, is introduced and two symmetrical products become asymmetric? Singleton et al. have carried out quasiclassical direct dynamics calculations on the B3LYP/6- 31G* PES for the ene reaction of 32.58 The trajectories were started at the point in a region between TS6 and VRI, centered on the minimum energy path with both O–C distances of 1.95 A˚. The trajectories were initialized either at 0 K, giving each mode in total only its ZPE with a random sign for its initial velocity, or at 263 K, using a Boltzmann sampling of vibrational levels. Trajectories for 32 with one of the methyl groups deuterated (CH3CH=CHCD3) gave two products, CH2=CH-CH(OOH)CD3 and CH3CH(OOD)-CH=CD2, in the ratio of 122/61 at 0 K, which corresponds to the intramolecular kH/kD of 2.1. Similarly, simulations at 263 K gave the ratio of 257/149, corresponding to kH/kD of 1.38. Thus, KIE was calculated to be smaller at a higher temperature. The magnitude of KIE at 263 K agreed with the experimental observation. The product selection obtained by these trajectory calculations is not due to any enthalpic or entropic origin. It was concluded that this selectivity is a new form of KIE, dynamical in origin, unrelated to the usual effect of ZPEs on the barriers.
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Another set of trajectory calculations for the reaction of 2-pentene (C2H5CH=CHCH3) is worth mentioning. Experimentally, the ene reaction of 2-pentene gave nearly equal amount of the two possible alkenes. However, since the two alkyl groups on the double bond are different, the PES is asymmetric and the minimum energy path does not bifurcate on the surface but leads only to the terminal alkene (C2H5CH(OOH)-CH=CH2). Trajectory calculations on such PES gave two products in 13/7 ratio, consistent with experimental observation qualitatively. This is an example of dynamic bifurcation in that the reaction path bifurcates dynamically, despite that the minimum energy path on the PES does not bifurcate. The dynamic bifurcation will be discussed in detail in section ‘‘Dynamic Bifurcation’’. The dynamics effect on path bifurcation and nonstatistical product distribution on a slightly perturbed symmetrical PES have also been reported for the C=N isomerization of benzylideneanilines.60
DYNAMIC BIFURCATION
As described above, path bifurcation is classified into two types: statistical bifurcation and dynamical bifurcation. In the statistical bifurcation, a minimum energy path down from a TS reaches another TS through a VRI point, and the actual reaction path ought to bifurcate near the VRI region. This is observed for reactions with symmetrical PESs. On the other hand, there are cases in which a minimum energy path does not bifurcate on the PES and leads to one product as in a normal reaction, but when two product regions are located close to each other on the PES and a barrier (a ridge) separating the two region is low, dynamics trajectories can give both products. This is the dynamical bifurcation. This may occur for reactions of a borderline mechanism. ET/SN2 bifurcation An early example of dynamical bifurcation is seen for SN2/ET borderline reaction shown in Scheme 7.65–68,70–75 Computational studies by Shaik, Schlegel, and coworkers on the reactions of formaldehyde anion radicals with methyl chloride demonstrated that the reaction gave two distinct TSs: SUB(O) TS that gives substitution product at O of the carbonyl function (CH2-OCH3) and ET TS that yields neutral aldehyde þ methyl radical.65–68 SUB(C) product (OCH2CH3) is formed in a stepwise manner through the ET step. Bertran et al., on the other hand, suggested that the ET TS could be viewed as an SN2 (SUB(C)) TS involving the carbon atom of CH2=O radical anion as a nucleophilic center.69 The origin of the different mechanistic assignment for the TS was analyzed by Shaik et al. on the basis of the PES calculated at the UHF/6-31G* level of theory.65–68 These
MOLECULAR SIMULATIONS OF ORGANIC REACTIONS
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Scheme 7 Numbers are calculated enthalpy in kcal mol1 at UHF/6-31G* (G3) relative to reactant complex.
authors showed that the reaction path descends from a broad saddle point to a flat ridge that separates the ET and SN2 products. After entering the flat ridge region the path bifurcates to the two product states. Different reaction-path methods give different mechanistic assignments as follows: the steepest-descent path in Z-matrix internal coordinates leads directly to the ET product; and the path in mass-weighted internal coordinates leads to a ridge and descends to the SN2 product. The surface calculated at the UQCISD(T)/6-31G* level resembles the UHF one, indicating that the branching of the potential surface into two mechanisms is also expected at this level. However, these discussions based on the MO calculations are only relevant for the reaction at 0 K, and the interpretation of the reaction mechanism ought to rely on reaction dynamics at finite temperature. Ab initio direct MD calculations are a means to obtain the desired dynamical characterization. Yamataka and collaborators carried out ab initio MD simulations for the reaction of CH3Cl and a H2C=O radical anion using the program packages of HONDO.70–72 Simulations were started from the ET TS. The initial atomic velocities were assigned from a random distribution with the total kinetic energy being consistent with the simulation temperatures (100, 298, and 400 K). A velocity re-scaling algorithm similar to the constant-temperature algorithm of Berendsen et al. was used. Hundred fifty-three MD simulations were performed at the UHF/6-31þG* level of theory. In the MD simulations starting from the ET TS, four types of trajectories were observed: those leading back to the reactants (36 trajectories), those leading to the SN2 product (99), those passing through the SN2 valley and crossing over to the ET valley (9),
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and those going to the ET valley directly (9). Thus, the dynamics calculations clearly confirm that the TS leads directly to both the ET and SN2 products. It was also found that the trajectories at the lower temperature (100 K) follow the IRC path, whereas at higher temperatures the kinetic energy affects the reaction route. Shaik, Schlegel, and coworkers later carried out extensive direct MD simulations on the reaction using higher levels of theory and determined the branching ratio more precisely.73–75 It was found that more ET product was obtained with more energy available, consistent with the previous observation, confirming that the kinetic energy of reacting species plays an important role in controlling the pathway of the reaction. These direct MD simulations revealed that the TS yields intrinsically the SN2 product. At finite temperature, however, a route opens up in which the system may evolve either directly or indirectly toward the ET product after passing over the barrier. It was thus demonstrated that the TS characteristics themselves do not always dictate the reaction mechanism and that the formation of two different products does not necessarily mean the presence of two independent pathways with different TSs. A possible occurrence of branching from single TS to several products introduces additional complexities in mechanistic assignment for borderline reactions. Furthermore, an observation that more ET product is formed at a higher temperature would often be taken as an indication that the reaction would follow two competitive routes with a higher activation energy for the ET route than for the SN2 route. The present analysis offers an alternative interpretation that a similar temperature effect on the product distribution can also arise from traversing single TS and undergoing temperaturemediated mechanisms to different products for a borderline reaction.
CYCLOADDITION
The cycloaddition reactions of ketenes with cyclopentadiene have been known to give formal [2 þ 2] cycloadduct (35) instead of [4 þ 2] Diels–Alder products (34) (Scheme 8). A combined computational and experimental study suggested that the reaction initially gives [4 þ 2] cycloadduct, which subsequently rearranges to 35 via [3,3] sigmatropy.91,92 The MP2/6-31G*//HF/3-21G calculations
Scheme 8 Numbers in parentheses are electronic energies in kcal mol1 relative to the separated reactants calculated at mPW1K/6-31þG**.
MOLECULAR SIMULATIONS OF ORGANIC REACTIONS
207
for 33 showed that the [4 þ 2] cycloaddition TS is 14.6 kcal mol1 (in DG) more stable than the [2 þ 2] TS, and the TS of the [3,3] sigmatropic rearrangement from 34 to 35 is 0.6 kcal mol1 more stable than the first TS. The NMR study was consistent with the mechanism, in which 34 is formed rapidly at the early stage of the reaction and converted to the final product, 35. Recently, Singleton claimed on the basis of close examination of lowtemperature NMR results that the product composition–time dependence was most nicely fit for the mechanism, in which 35 is formed not only by the 33 ! 34 ! 35 route but also directly from 33.87 Computational study with DFT methods (mPW1K and B3LYP), however, did not support the mechanism with concurrent pathways. As is shown in Scheme 8, the mPW1K/6-31þG** PES was consistent with the consecutive mechanism. The B3LYP calculations, on the other hand, suggested slightly different picture, in which the [4 þ 2]-like TS did not give 34 but instead led to an unstable biradicaloid intermediate located in a very shallow well, and this intermediate gives 34 and 35 directly. Thus, the experimental suggestion and PES calculations disagreed to each other. In order to understand the origin of the discrepancy, quasiclassical direct trajectory calculations were carried out.87 The initial TS for each computational theory was used as the starting point, and the atomic positions were randomized using linear sampling for each normal mode. The trajectories were initiated by giving each mode a random sign for its initial velocity, along with an initial energy based on a random Boltzmann sampling of vibrational levels for 273.15 K. The imaginary frequency mode was treated as a translation and given a Boltzmann sampling of translational energy in the forward direction. The results were striking that out of 130 trajectories at mPW1K/6-31G*, 67 gave 35, 4 gave 34, and 56 recrossed the TS. Trajectories at mPW1K/631þG** and B3LYP/6-31G* gave qualitatively the same results. The trajectory calculations revealed that the two products may be formed directly from a single TS. The results were different from the expectation from either mPW1K or B3LYP PES calculations, but were consistent with experimental observations. BECKMANN REARRANGEMENT/FRAGMENTATION
The Beckmann rearrangement is a textbook reaction, in which oximes under acidic conditions give amide via an intramolecular rearrangement. Oximes may give fragmentation products when the R1 group, which is located anti to the leaving group, is stabilized as a cation by an adjacent group [Equation (10)].93
(10)
208 3.0
H. YAMATAKA 6.0
(a)
5.0
R(N-C) /Å
2.5 p-NH2 p-OMe p-Me m,m'-Me2 m-Me H p-Cl p-CHO p-CN p-NO2
2.0
1.5
1.0 0.0
(b)
1.0
2.0
3.0
4.0 RC/amu½ Bohr
5.0
6.0
4.0 3.0
IRC
RT TS 2.0 1.0 1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
RN-C /Å
Fig. 4 (a) IRC pathways for 36-X and (b) two-dimensional plots of MD trajectories for 36-H at HF/6-31G*.
MO calculations for the gas-phase reactions of 36-X at HF/6-31G* and MP2/6-31G* revealed that the TS structure varied smoothly from a more product-like to a more reactant-like one when the substituent varied from electron-withdrawing NO2 to electron-donating NH2, in a manner consistent with the Leffler–Hammond principle.94,95 The smooth TS variation itself was suggestive of the same reaction mechanism for all substituted substrates. The Hammett plots derived from relative activation enthalpies gave a linear correlation, which also suggested that the mechanism does not change as a function of substituent. On the other hand, IRC calculations showed that each TS led either to the fragmentation or the rearrangement product region, depending on the electronic nature of the substituent (Fig. 4a). It was clear that the IRC pathway varied with the substituent, from clear rearrangement (p-CHO, p-CN, and p-NO2) to fragmentation (X = p-NH2, p-MeO, p-Me, m,m0 -Me2, m-Me, H, and p-Cl). As a result, despite the fact that the nature of the TS in terms of energy and structure varied smoothly with substituent, the reaction product and hence the reaction mechanism on the PES exhibited a sharp change as a function of the substituent. These findings in turn mean that mechanistic variation is not necessarily accompanied by a sharp difference in reactivity and TS structure, and hence experimentally observable quantities, such as relative reactivities (Hammett equation) and KIEs, which are commonly considered to be useful means to detect a change in reaction mechanism, may not always be useful. Direct MD calculations starting at the TS of each substituted substrate were carried out in order to see how the mechanism changes with substituent.90 Three methods, HONDO, PEACH, and Gaussian (G03), were used, and total 810 trajectories were obtained at the HF/6-31G* level. Three types of productive trajectories were observed: type R leading directly to the rearrangement region, type F leading directly to the fragmentation region, and type R ! F, which initially goes to the rearrangement region and then leads to the fragmentation product.
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It was found that the three MD methods gave qualitatively the same results. Substrates with electron-donating substituents (p-MeO, p-NH2) led to fragmentation region exclusively, whereas those with an electron-withdrawing substituent (p-NO2) gave predominantly rearranged products. For the borderline substrates, however, trajectories from their respective TS gave both fragmentation and rearrangement products directly in such a manner that more F-type trajectories were obtained for a substrate with a more electron-donating substituent. Representative trajectories for 36-H are illustrated in Fig. 4b, in which the abscissa is the N–O atomic distance and the ordinate is the atomic distance between the benzylic carbon and the nitrogen. The observation that the trajectories starting from a TS led to two products indicated that the reaction path bifurcates on the way from the TS to the products, despite that IRC path on the PES is connected to either one of the two products for each borderline substrate. The path bifurcation violates of the TS-based reaction theory. The fact that more F-type trajectories were obtained for 36-X with a more electron-donating substituent was explained by the existence of the barrier separating the two product regions and the shift of the barrier with substituent. Since an electron-donating substituent makes the fragmentation product more stable, the barrier moves toward the rearrangement side, and then more trajectories go to the fragmentation side. The shift of the barrier is consistent with the Thornton rule.96 The product ratio is, thus, governed by the electronic nature of substituents in a manner consistent with traditional electronic theory. As a result, the dynamically controlled substituent effects on the product distribution are readily reconciled with traditional reaction theory, which implies that such path bifurcation phenomenon would not easily be detected by experiment, unless critical examinations of those results are made.
6
Reaction time course and product and energy distributions
SN2 REACTIONS
SN2 reactions of methyl halides with anionic nucleophiles are one of the reactions most frequently studied with computational methods, since they are typical group-transfer reactions whose reaction profiles are simple. Back in 1986, Basilevski and Ryaboy have carried out quantum dynamical calculations for SN2 reactions of X þ CH3Y (X = H, F, OH) with the collinear collision approximation, in which only a pair of vibrations of the three-center system X-CH3-Y were considered as dynamical degrees of freedom and the CH3 fragment was treated as a structureless particle [Equation (11)].30 They observed low efficiency of the gas-phase reactions. The results indicated that the decay rate constants of the reactant complex in the product direction and in the reactant direction did not represent statistical values. This constitutes a
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good early example of dynamically derived selectivity that is much different from what one would expect from statistical theory.
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In 1996, Hase and coworkers reported direct dynamics simulations of the reaction, Cl þ CH3Br, using semi-empirical AM1 theory with two different sets of specific reaction parameters (SRP1 and SRP2).97 The simulations were started at the Cl CH3Br complex with different initial nonrandom energy distributions and the total energy of 2.7 kcal mol1 plus harmonic ZPE of the complex. Excitation of different internal modes of the complex led to different results. The mode-specific dissociation trajectories were compared with previous results using analytical potential functions.98 The study showed that different PES gave quantitatively different dynamics. Hase and coworkers later carried out a full ab initio MD simulations at HF/3-21 þ G* for SN2 of CH3Cl þ Cl.99 The two reactant species were separated 10 A˚ in the initial state, and relative translational energy of 100 kcal mol1 was added. Trajectories with random initial conditions were generated and the initial Cl CH3 Cl angle was scanned. Reaction took place by the backside attack, and the Cl–C–Cl angle at the TS increased to 180. It was suggested that extensive CH3Cl vibrational excitation should be needed to access the frontside reaction pathway. The product energy partitioning was also analyzed from the trajectories initiated at the barrier top. Quasiclassical direct dynamics trajectories at the various levels of theory were later calculated to study the central barrier dynamics for the C1 þ CH3Cl, Cl þ C2H5Cl, Cl þ CH3I, F þ CH3Cl, OH þ CH3Cl, and other SN2 reactions.31,32,47,97–108 The effect of initial reaction conditions, such as energy injection, substrate orientations, and the mode of collision, on the fate of the reaction, product, and energy distribution, was analyzed. Some of these trajectory calculations required serious modification in RRKM and TST for SN2 reactions.32,103–105
SN2 REACTIONS IN WATER
SN2 reactions are classified into two types. Type I is the reaction of neutral substrate with charged nucleophile and type II is the reaction of neutral substrate with neutral nucleophile.109,110 In contrast to the cases of type I reactions, the number of computational studies for type II SN2 is limited because the reaction generates an ion pair in the product state and hence it necessarily experiences a strong solvent effect. Therefore, it is a challenge to perform MO as well as MD studies on this type of reactions.
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The methyl chloride hydrolysis [Equation (12)] is a type II SN2 reaction. The attacking species is a water molecule, which loses a proton to a solvent water molecule with the hydroxide ion formally substituting the chloride ion in methyl chloride. Thus, during hydrolysis, bond breaking and bond formation involving both solute and solvent molecules take place. It is essential, therefore, to consider the solvent molecules explicitly in modeling the methyl chloride hydrolysis. This is in contrast to type I SN2 reactions, such as the reaction in Equation (11), in which bond breaking and bond formation occur only in the solute molecules and the solvent molecules do not participate actively in the reaction except as a medium. nH2 O þ CH3 Cl ! HOCH3 þ ðn 1ÞH2 O þ HCl
ð12Þ
Hydrolysis reactions of methyl chloride have been analyzed by with a water cluster model for CH3Cl.100,101 The CH3Cl hydrolysis does not have the TS in the gas phase, and a certain number of water molecules ought to be included in the system. The effect of the number (n) of water molecules on the activation barrier was examined with a cluster model, and it was found that a cluster model with 13 water molecules reproduced nicely the experimental activation energy. The trajectory calculations were carried out from the TS with n = 3. It was demonstrated that nucleophilic H2O attacks CH3 displacing Cl to from CH3OH2þ and proton transfer occurs afterwards to give CH3OH þ H3Oþ þ Cl. Similar trajectory calculations with a cluster model were reported for the SN2 reaction of CH3Cl with Cl.111
OTHER REACTIONS
Trajectory calculations for proton transfer and ionization in water cluster,112–116 isomerization,117 and various types of unimolecular reactions6,118–128 have been carried out, and the analyses on time course of the reaction, product ratio, and product energy distribution were reported.
7
Nonstatistical barrier recrossing
Since an early stage of the history of ab initio MD study, many cases have been observed in which the calculated trajectories do not support expectation derived from traditional reaction theories, such as RRKM and TST, and thus the applicability or suitability of these theories has been a matter of argument. In this section examples of one of those dynamics-derived phenomena are shown, namely nonstatistical barrier recrossing.
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SN2 REACTIONS
For SN2 nucleophilic substitution reactions, TST predicts that crossing the central barrier region of a PES is the rate-controlling step. Previous classical trajectory calculations on analytical PES fitted to HF/6-31G* for SN2 reaction of CH3Cl þ Cl have indicated that a significant amount of central barrier recrossing was observed in the trajectories initialized at the central barrier, which suggested that TST is an incomplete model for calculating the Cl þ CH3Cl SN2 rate constant.129 The authors found two types of recrossings in the trajectories: one was intermediate recrossings in which trajectories stayed near the central barrier and the other was complex recrossings in which trajectories was trapped in the Cl CH3Cl complex and then returned to the central barrier region. Although RRKM theory predicted extensive dissociation of the Cl CH3Cl complex to Cl þ CH3Cl and negligible complex recrossings, the trajectory calculations indicated that negligible Cl þ CH3Cl formation and continual complex recrossings occurred on a time scale longer than the complex’s lifetime predicted by RRKM. The disagreement between trajectory calculations and the prediction from the RRKM theory arose from decoupling between the C–Cl stretch mode of CH3Cl and other Cl CH3Cl intermolecular modes; the former is excited for barrier crossing and the latter is important for complex association/dissociation mode. Quasiclassical direct dynamics trajectories at the MP2/6-31G* level of theory were later calculated by sampling 300 K Boltzmann energy distributions either at the central barrier on the reaction coordinate or at the reactant state.103,105 Again extensive recrossing of the central barrier was observed in the trajectories initiated at the barrier. The dynamics of the Cl CH3Cl complex was non-RRKM and TST was indicated to be an inaccurate model for calculating the Cl þ CH3Cl SN2 rate constant. The MP2 direct dynamics trajectories further showed that trajectories from the reactant state did not form the Cl CH3Cl complex. This confirmed the previous trajectory study based on a HF/6-31G* analytic potential energy function,129 in that weak coupling between the Cl CH3Cl intermolecular and CH3Cl intramolecular modes prevents translation-to-vibration energy transfer. Overall, occurrence of recrossing of the barrier suggested that crossing the central barrier may not be a rate-controlling step, as assumed by statistical theories for many reactions. The MP2/6-31G* direct dynamics simulation study was later extended to cover the dynamics from the central barrier for the SN2 reaction of Cl þ C2H5Cl.104 The majority of the trajectories starting from the saddle point moved off the central barrier to form the Cl C2H5Cl complex. The results were different from those obtained previously for the CH3Cl reaction, in which extensive recrossing was observed. The reaction of C2H5Cl was, in this sense, consistent with the prediction by the RRKM theory. However, some of the
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trajectories moved directly to products without forming the complex, which is clearly a non-RRKM result. The results for C2H5Cl were strikingly different from for CH3Cl. The origin of the remarkable difference for the two systems was not clear. A possible explanation given by the authors is that the CH3 substituent in the [Cl CH3CH2 Cl] system enhances IVR through coupling between the CH3 rotation and low-frequency vibrations of the molecules. These interactions suppress central barrier recrossing and promote the formation of a complex after the barrier crossing. The clear different outcome for closely related systems is by itself very interesting, and further study to understand such newly discovered results is strongly desired to deepen and expand our knowledge in mechanistic organic chemistry.
VINILYDENE TO ACETYLENE REARRANGEMENT
The reaction that shows non-RRKM and non-TST reactivity is not limited to SN2, but other types of reactions have been also reported to exhibit nonstatistical behavior. CASSCF(10/10)/6-31þþG** calculations for vinylidene-acetylene rearrangement [Equation (13)] gave the activation barrier of 5.6 kcal mol1 and the reaction energy of –47.9 kcal mol1 in terms of electronic energy. Ab initio MD simulations for this unimolecular rearrangement were carried out at the CASSCF level of theory without ZPE.130 The MD simulations were first carried out for vinylidene anion, and the vinylidene-acetylene rearrangement trajectory calculations were performed for a series of coordinates taken at different times along the anion trajectory. Thus, the starting point was vibrationally excited singlet state of vinylidene, which was formally generated through electron detachment from vinylidene anion. The Born–Oppenheimer trajectories were followed for 1 ps, which was long enough compared to the estimated lifetime of vinylidene of subpicosecond range. It was found, however, that none of the vinylidenes equilibrated at 600 K (slightly below the isomerization barrier) and only 20% of the vinylidenes equilibrated at 1440 K (just above the isomerization barrier) isomerized, suggesting average lifetimes >1 ps for the vibrationally excited vinylidene. Since the anion and neutral vinylidene are structurally similar, and yet vinylidene generated by electron detachment is extremely different geometrically from the isomerization TS, it could live until it has sufficient kinetic energy in the correct vibrational modes. Thus, insufficient orbital rearrangement and IVR would be responsible to the results. Another important point observed from the simulations was that every trajectory that did isomerize violated conventional TST by recrossing back to vinylidene multiple times, even though the isomerization is highly exothermic (47.9 kcal mol1) and hence expected to be irreversible.
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CYCLOADDITION OF CYCLOPENTADIENE AND KETENES
In the course of the study of cycloaddition reaction of cyclopentadiene and ketenes [Equation (14)], Singleton and coworkers carried out ab initio dynamics simulations and observed nonstatistical recrossing of the barrier leading to the adducts.87 The authors argued that, for reactions that involve two bond-forming events in a single barrier-passing step as in reaction 14, one bond might form ahead of the other and a formally concerted reaction might dynamically fail to complete in a single barrier crossing process. It was suggested that such nonstatistical recrossing would become more common in complex reactions than simple reactions. Therefore, the consideration of trajectories would be essential to understanding the mechanism of mechanistically borderline reactions. Further analysis of dynamics effect in this reaction is presented in detail in section ‘‘Path Bifurcation’’.
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8
QM/MM-MD
I would like to summarize this chapter by briefly introducing recent advances in QM/MM methodology. QM/MM-MD is one of the promising methods to examine chemical reactions in solution. It has been used to analyze solvation structure of ions,131–133 solvation dynamics,134,135 and chemical reaction in solution.136,137 The potential mean force (PMF) calculations by using the QM/MM-MD method has been used to obtain free energy change along the reaction coordinate in solution.138–141 TS optimization and minimum energy path calculations on the PES were carried out for a methyl-transfer reaction in water, and PMF calculations along the path were used to obtain the free energy of activation of
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the reaction.139 Recent development further allows one to locate TS on the free energy surface by using free energy gradient methods.142,143 Dynamics effects, which were described in previous sections, on reaction pathways, concerted-stepwise mechanistic switching, and path bifurcation have in most cases been examined for isolate systems without medium effects. Since energy distribution among vibrational and rotational modes and moment of inertia of reacting subfragment are likely to be modified by environment, it is intriguing to carry out simulations in solution. The difference or similarity in the effect of dynamics in the gas phase and in solution may be clarified in the near future by using QM/MM-MD method. Such study would provide information that is comparable with solution experiment and help us to understand reaction mechanisms in solution.
9
Full quantum MD simulation in water
SN2 REACTION IN WATER
The traditional reaction mechanism in organic chemistry considers that the hydrolyses of CH3 substrates (CH3-X, X = leaving group) proceed via a concerted pathway, in which the CH3-X bond cleavage is facilitated by the H2O– CH3 bond formation. Such a mechanism is intuitively reasonable, since solvent reorganization is believed to be faster than bonding changes in reacting substrates and hence there is enough time for a solvent molecule to react as a nucleophile. However, as is discussed in this chapter, dynamic effects may cause a behavior that differs from what is predicted by the TST and, in particular, a seemingly concerted reaction actually may take place via stepwise processes with bond-cleavage and bond-formation steps occurring successively. Reactions in solution have been analyzed computationally using the QM/ MM method. Although the QM/MM method can treat chemical events in solution at a reasonable computational expense, it has the inherent limitation that nucleophilic participation by solvent molecules cannot be treated by the classical MM scheme. Thus, a full QM method is required to describe the hydrolysis mechanism of CH3 substrates. The fragment molecular orbital (FMO)-MD scheme,144–146 which treats the whole system in a full QM fashion, makes it possible to deal with solution reaction dynamics with a reasonable number of solvent molecules explicitly with the accuracy of the given QM level. FMO-MD simulations at HF/6-31G for reaction 15 were carried out by using a water droplet model, in which CH3-N2þ was located at the center of gravity of a sphere consisting of 156 water molecules.102 The initial structure of CH3-N2þ was taken from the gas-phase optimized structure at HF/6-31G, which was equilibrated in the water droplet with the substrate structure fixed
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for 0.5 ps at 300 K and then for 5.0 ps at 1000 K. Fifteen seeds from these 5-ps initial equilibrations were taken, and out of 15 runs at 700 K, 10 trajectories led to the substituted products, CH3-OH2þ þ N2. Although the number of productive trajectories was small, the results showed reasonable diversity together with some common features. The trajectories were classified into three groups: tight SN2, loose SN2, and intermediate types.
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In Fig. 5 the initial water droplet, the time course of the O–C and C–N bond lengths, and the O–C–N angle are shown for two representative trajectories: (a) tight SN2 and (b) loose SN2. Trajectory (a) provided a molecular level picture of how the tight SN2 reaction takes place. The C–N bond cleavage and the C–O bond formation occured concertedly within 100 fs around t = 5.91 ps. The transition point where the two atomic distances became equal occured with a tight structure with the distances of 2.15 A˚ at t = 5.90 ps. The O–C–N angle, which was small and less than 140 before the reaction, rapidly increased when the reaction started to occur, and became 166 at t = 5.91 ps. Thus, the results clearly indicated the synchronicity of the bond-formation–bond-cleavage processes, consistent with the qualitative picture of the enforced SN2 mechanism. Finally, one of the hydrogens (a) 12.0
150.0
8.0
120.0
6.0
2.0
90.0
RC-O
4.0 RC-N
60.0
O-C-N angle (degree)
Distance (A)
180.0
αO-C-N
10.0
αO-C-N
Distance (A)
6.0
150.0
5.0
120.0 RC-O
4.0
90.0
3.0 2.0 1.0 1.8
RC-N 1.9
60.0 2.0
2.1
2.2
2.3
2.4
2.5
2.6
O-C-N angle (degree)
30.0 0.0 1.8 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 180.0 (b) 7.0
30.0 2.7
Ttime (ps)
Fig. 5 Structure of the initial droplet, and time course of bond lengths and angles of two representative trajectories.
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originally on the attacking H2O molecule started to move to a neighboring H2O when the O–C bond was formed. Trajectory (b) gave basically similar results and shared common features characteristic of concerted SN2 processes as described above. The C–N bond cleavage and the O–C bond formation occurred concertedly within the 150 fs time scale. However, trajectory (b) was different from (a) in that the transition point, where the two atomic distances became equal, was associated with a much looser structure with the distances of 2.68 A˚. It was noticeable that the C–N bond cleavage started to occur without the attacking H2O molecule coming close to the backside of CH3-N2þ. The trajectory indicated that the reaction proceeded via a two-stage concerted process, and the product CH3OH stayed in the protonated form for a longer time. Charge-transfer (CT) interaction energies between the two fragments were plotted against the C–N distance in Fig. 6. The CT interaction increased rapidly when the C–N distance increased to 1.6 A˚ for trajectory (a), whereas for trajectory (b) the CT became large only when RC–N was 2.4 A˚ or longer. Clearly the C–N bond-cleavage and O–C bond-formation events took place in a two-stage fashion in the latter case. Most of other trajectories obtained in this study exhibited intermediate characters between trajectories (a) and (b). An important message was that the chemical reaction does not always proceed through the lowest energy pathway with optimal solvation. In conclusion, the simulations for the first time illustrated how the atoms in reacting molecules behave in solution at the molecular level, which was made possible by using full QM simulations with the recently developed FMO-MD methodology.
CT Energy (kcal/mol)
0.0 –2.0 –4.0 –6.0 –8.0 –10.0 –12.0 1.2
1.4
1.6
1.8
2.0 2.2 RC-N (Å)
2.4
2.6
2.8
3.0
Fig. 6 Charge-transfer interaction energies between attacking H2O and CH3N2þ versus C–N. Open circle is for trajectory (a), and filled triangle for trajectory (b).
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10 Summary and outlook According to traditional interpretation of chemical reactivity, the reaction rate and hence the product selectivity are governed by the energy of the TS and its variation. However, ab initio direct MD simulation studies described in this chapter revealed that this is not universally true and that the organic reactivity theory must consider the effect of dynamics explicitly. In reactions of mechanistic borderline, the reaction pathway may not follow the minimum energy path, but the reaction proceeds via unstable species on the PES. In other cases, the reacting system remains on the IRC but does not become trapped in the potential energy minimum. In some cases, intermediates are formed in reactions that should be concerted, whereas in other reactions a concerted TS gives an intermediate. Thus, the question of concerted versus stepwise appears too simple and the definition of concerted and stepwise reactions becomes unclear. In some reactions, the post-TS dynamics do not follow IRCs, and path bifurcation gives two types of products through a common TS. In all these reactions, dynamics effect can govern the reaction mechanism outside of the realm of TS theory. It is hoped that computational methods outlined in this chapter would serve as a means to facilitate development of a new reaction theory in the next decade.
Acknowledgments The author gratefully acknowledges the financial support from the SFR project of Rikkyo University. The author thanks Prof. Jerry Kresge, to whom this chapter is dedicated, for his pioneering work in the field of physical organic chemistry.
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The principle of nonperfect synchronization: recent developments CLAUDE F. BERNASCONI Department of Chemistry and Biochemistry, University of California, Santa Cruz, CA 95064, USA 1 Introduction 223 Intrinsic barriers 224 Transition state imbalance and the PNS 224 Scope of this chapter 225 2 Proton transfers in solution 226 The effect of resonance on intrinsic barriers and transition state imbalances 226 Why does delocalization lag behind proton transfer? 237 Other factors that affect intrinsic barriers and transition state imbalances 238 3 Proton transfers in the gas phase: ab initio calculations 261 The CH3Y/CH2=Y Systems 261 The NCCH2Y/NCCH=Y Systems 280 Aromatic and anti-aromatic systems 282 4 Other reactions 293 Nucleophilic additions to alkenes 293 Nucleophilic vinylic substitution (SNV) Reactions 298 Nucleophilic substitution of Fischer carbene complexes 303 Reactions involving carbocations 309 Miscellaneous reactions 312 5 Summary and concluding remarks 316 Acknowledgments 319 References 319
1
Introduction
This year marks the 25th anniversary of the principle of nonperfect synchronization (PNS); it was introduced in 19851 as the principle of imperfect synchronization (PIS) but in later papers and reviews2–4 the name was changed due to the awkwardness of the acronym PIS. The foundations of the PNS rest mainly on a marriage between two fundamental concepts of physical organic chemistry, i.e., the concept of intrinsic barriers and that of transition state imbalances.
223 ADVANCES IN PHYSICAL ORGANIC CHEMISTRY VOLUME 44 ISSN: 0065-3160 DOI: 10.1016/S0065-3160(08)44005-4
2010 Elsevier Ltd. All rights reserved
224
C.F. BERNASCONI
INTRINSIC BARRIERS
Marcus5–8 taught us that the most appropriateand useful kinetic measure of chemical reactivity is the intrinsic barrier DG‡o rather than the actual barrier (DG‡), or the intrinsic rate constant (ko) rather than the actual rate constant (k) of a reaction. These terms refer to the barrier (rate constant) in the absence of a thermodynamic driving force (DGo = 0) and can either be determined by interpolation or extrapolation of kinetic data or by applying the Marcus equation.5–8 For example, for solution phase proton transfers from a carbon acid activated by a p-acceptor (Y) to a buffer base, Equation (1), ko may be determined from Br½nsted-type plots of log k1 or Bν + H
C
Y
k1
C
Y– + Bν+1
k–1
(1)
log k–1 versus log K1 (K1 = k1/k–1) by interpolation or extrapolation to K1 = 1,9 while DG‡o can be calculated from ko via the Eyring equation. Or, using the Marcus equation which, in its abbreviated form, is given by Equation (2), allows one to solve for DG‡o for a given set of DG‡ and DGo values.
DG ¼ ‡
DG‡o
DGo 2 1þ 4DG‡o
ð2Þ
The benefit of determining intrinsic barriers or intrinsic rate constants as measures of chemical reactivity is that they can be used to describe the reactivity of an entire reaction family, irrespective of the thermodynamic driving force of a particular member of that family and to make comparisons between different families. For example, DG‡o or ko determined for the deprotonation of acetylacetone by a series of secondary alicylic amines may be compared with DG‡o or ko for the deprotonation of nitroacetone by the same series of secondary amines. This comparison would provide insights into how the change of one of the pacceptor groups from acetyl to nitro may affect the intrinsic proton-transfer reactivity without regard to how this change may affect the pKa value of the carbon acid. Furthermore, DG‡o or ko for the reaction of acetylacetone with secondary alicyclic amines may be compared to DG‡o or ko for the deprotonation of the same carbon acid by a series of primary amines, leading to insights as to how differences in the solvation characteristics between primary and secondary amines may affect their intrinsic kinetic reactivity. TRANSITION STATE IMBALANCE AND THE PNS
The PNS derives from the realization that the majority of elementary reactions involve more than one concurrent event such as bond formation, bond
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION Product stabilizing factor
Reactant stabilizing factor
Develops late: ko ↓; ΔGo‡ ↑
Lost early: ko ↓; ΔGo‡ ↑
Develops early: ko ↑; ΔGo‡ ↓
Lost late: ko ↑; ΔGo‡ ↓
Product destabilizing factor
Reactant destabilizing factor
Develops late: ko ↑; ΔGo‡ ↓
Lost early: ko ↑; ΔGo‡ ↓
Develops early: ko ↓; ΔGo‡ ↑
Lost late: ko ↓; ΔGo‡ ↑
225
Chart 1
cleavage, solvation/desolvation, transfer and delocalization/localization of charge, etc., and often these processes have made unequal progress at the transition state. When this is the case, the reaction is said to have an imbalanced transition state, a term introduced and popularized by Jencks,10,11 although others before him had recognized this phenomenon in various reactions, especially in E2-eliminations.12–14 The virtue of the PNS is that it establishes a connection between transition state imbalances and intrinsic barriers of reactions. Its original formulation is still valid today; it states that any product stabilizing factor whose development lags behind the main bond changes at the transition state, or any reactant stabilizing factor whose loss at the transition state is ahead of these bond changes, increases the intrinsic barrier or decreases the intrinsic rate constant. For product stabilizing factors that develop ahead of the main bond changes, or reactant stabilizing factors whose loss lags behind the bond changes, the effects are reversed, i.e., there is a decrease in DG‡o or an increase in ko. For product or reactant destabilizing factors the opposite relationships hold. Chart 1 provides a summary of these various manifestations of the PNS. Product or reactant stabilizing factors that have been studied thus far include resonance/charge delocalization, solvation, hyperconjugation, intramolecular hydrogen bonding, aromaticity, inductive, p-donor, polarizability, steric, anomeric, and electrostatic effects, as well as ring strain and soft–soft interactions. Product or reactant destabilization factors are mainly represented by anti-aromaticity, steric effects in some types of reactions, and, occasionally, electrostatic effects. What makes the PNS particularly useful is that it is completely general, mathematically provable,4 and knows no exception.
SCOPE OF THIS CHAPTER
Regarding the scope of this chapter, the main focus is on work published after my detailed 1992 review.4 Older material will only be presented when necessary
226
C.F. BERNASCONI
to put new results into perspective to emphasize important points neglected in earlier reviews or to correlate new data with old results in the form of summary tables or graphs. Proton transfers from carbon acids have continued to play a particularly prominent role in illustrating the multiple manifestations of the PNS and hence their studies constitute a major part of this chapter. This is especially true for ab initio calculations of proton transfers in the gas phase that have been performed after 1992 and have added novel insights into the workings of the PNS. Also new is an important expansion of the list of product stabilizing factors to include aromaticity and, for product destabilizing factors, anti-aromaticity. Other reactions for which a discussion of their structure-reactivity behavior in terms of the PNS has provided valuable insights include nucleophilic addition and substitution reactions on electrophilic alkenes, vinylic compounds, and Fischer carbene complexes; reactions involving carbocations; and some radical reactions. The number of reports on reactions that have been discussed in the context of the PNS or that would benefit from being treated within this framework far exceeds the space available in this chapter. Hence the purpose of this review is not to give a comprehensive account of all such reactions but rather to be selective and focus on those cases that provide genuine insights into the workings of the PNS.
2
Proton transfers in solution
THE EFFECT OF RESONANCE ON INTRINSIC BARRIERS AND TRANSITION STATE IMBALANCES
In contrast to proton transfers between normal acids and bases, which typically have very high intrinsic rate constants that are close to the diffusion-controlled limit15,16 and depend little on the nature of the acid, proton transfers from carbon acids have intrinsic rate constants that vary strongly with structure and are mostly much lower than the diffusion-controlled limit.15,17,18 Table 1 summarizes DG‡o and log ko values for a number of representative examples.4,18–28 The data show a dramatic decrease in ko (increase in DG‡o ) as the p-acceptor strength of the activating groups increases from the top to the bottom of the table. The main reason for the observed trend is that the transition state is imbalanced in the sense that the degree of charge delocalization into the p-acceptor lags behind the proton transfer. This is shown, in exaggerated form, in Equation (3) (for a more nuanced representation of the transition state see below) for a ‡
Bν + H
C
Y
k1
ν+δ B H
δ– C Y
k–1
C
Y– + BHν + 1
(3)
Entry 1
Solvent, Ta
C–H acid CH2(CN)2
H2O, 25C
50% DMSO, 20C
2 H
3
pKCH a
log kob
11.2
7.5
DG‡o kcal mol1
References
7.2
18
9.53
4.58
10.9
19
11.54
4.03
11.7
20
50% DMSO, 20C
4.70
3.90
11.9
4
50% DMSO, 20C
12.62
3.70
12.1
21
50% MeCN, 25C
12.50
3.70
12.1
22
50% DMSO, 20C
6.35
3.13
12.9
22
50% DMSO, 20C
9.12
2.75
13.4
24
H2O, 20C
7.72
2.29
14.0
20
CN
CH3
PhSO2CH2 CH3
OOC
CH3
OOC
CH2
4
5
O2N
6
(CO)5Cr
CH2CN
H2O, 20C
OMe CH3 CO CH2 CO
7 O
8
C
O
CH3CCH2CCH3
PhCCH2
+ N CH3
227
O
9
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
Table 1 Representative intrinsic rate constants (ko) and intrinsic barriers ( DG‡o ) for the deprotonation of carbon acids by secondary alicyclic amines
228
Table 1 (continued ) Entry
C–H acid
10
(CO)5Cr
11
CH3NO2
12
+ Cp*Ru
13
PhCH2NO2
Solvent, Ta
pKCH a
log kob
DG‡o kcal mol1
50% MeCN, 25C
10.40
1.86
14.6
50% DMSO, 20C
11.32
0.73
16.1
25
50% DMSO, 25C
5.90
0.10c
17.2
26
50% DMSO, 25C
7.93
–0.25
17.7
25
22
OMe C CH2Ph
CH2NO2
References
2,4-(NO)2C6H4 CH2
14
50% DMSO, 25C
10.9
–0.55
18.1
27
2,4-(NO)2C6H4
15
CH3NO2
H2O, 20C
10.28
–0.59
17.9
25
16
PhCH2NO2
H2O, 20C
6.77
–1.22
18.7
25
H2O, 25C
2.50
–2.15
20.3
28
CH3
N+ O N
17 NO2 a
50% DMSO = 50% DMSO–50% water (v/v); 50% MeCN = 50% MeCN–50% water (v/v). In units of M1 s1. c Reaction with primary aliphatic amines. b
C.F. BERNASCONI
O 2N
O–
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
229
generalized carbon acid with the p-acceptor Y. Because of the imbalance, the transition state derives only a minimal benefit from the stabilizing effect of charge delocalization into the p-acceptor, and this is the reason why the intrinsic barrier is high. It is as if at the transition state the carbon acid were less acidic than indicated by its pKa. The increase in DG‡o is perhaps even more easily understood when the reaction in the reverse direction (k–1) is considered. Here the reason for the high intrinsic barrier is that most of the resonance stabilization of the carbanion is lost at the transition state, i.e., it costs extra energy to localize the charge on the carbon in reaching the transition state. The increase in DG‡o with increasing acceptor strength thus reflects the increasing cost of localizing the charge and goes hand in hand with an increase in the imbalance. In cases where there is strong solvation of the carbanion, as for example hydrogen bonding solvation of enolate or nitronate ions in hydroxylic solvents, the intrinsic barrier is increased further because the transition state cannot benefit significantly from this solvation. This is the reason why DG‡o for the deprotonation of nitroalkanes in water is particularly high, i.e., much higher than in dipolar aprotic solvents, see, e.g., entry 11 versus 15 and entry 13 versus 16 in Table 1. These solvation effects will be discussed in more detail below. Evidence of imbalance based on Br½nsted coefficients. A. aCH > bB Since the observed trends in the intrinsic barriers can plausibly be explained by assuming that charge delocalization lags behind proton transfer (or charge localization is ahead of proton transfer in the reverse direction), this may be taken as evidence for the existence of imbalance. Nevertheless, independent evidence for the presence of transition state imbalances would be desirable. Such evidence exists in the form of structure-reactivity coefficients such as Br½nsted a and b values and has in fact been known before the connection between imbalance and intrinsic barriers was recognized. For example, assume that one of the groups attached to the carbon is an aryl group with various substituents Z [Equation (4)] and that the transition state is imbalanced in the same way as shown in Equation (3). One may, for a given B , determine a Br½nsted a value designated
‡
Bν
k1 + H
C
Z
Y
ν+δ B H
δ– Y C
C
k–1
(4) Z
Z
Y– + BHν + 1
230
C.F. BERNASCONI
as aCH (CH for carbon acid) by measuring k1 as a function of the acidity constant of the carbon acid as varied by changing Z, and, for a given Z, determine a Br½nsted b value designated as bB by measuring k1 as a function of the basicity of B . As long as B is not a carbanion with its own resonance stabilization, it has generally been assumed that bB is an approximate measure of the degree of proton transfer at the transition state.11,29,30 However, with aCH the situation is different when there is an imbalance, i.e., aCH is not a good measure of proton transfer. Rather, aCH is typically larger than bB. This is because, due to the closer proximity of the charge to the Z-substituent at the transition state compared to that in the product ion, the substituent effect on the transition state is disproportionately large relative to that on the carbanion. This means that the sensitivity of k1 to the substituent Z is disproportionately strong compared to that of is exalted, the acidity of the carbon acid and hence aCH ¼ d log k1 =d log kCH a i.e., aCH > bB. Note that for the Br½nsted coefficients determined in the reverse direction, bC ¼ d log k1 =dpKCH and aBH ¼ d log k 1 =d log KBH a a , the relationship bC < aBH holds. This is a consequence of the equalities aCH þ bC ¼ 1 and bB þ aBH = 1. Table 2 summarizes aCH and bB values for some representative proton transfers where the imbalance leads to aCH > bB;31–39 below we will discuss cases where the imbalance leads to aCH < bB. The best-known and one of the most dramatic examples of an imbalance is provided by the deprotonation of arylnitromethanes by secondary alicyclic amines in aqueous solution (entry 9 in Table 2) where aCH = 1.29 and bB = 0.56.31 In this case the imbalance is so large that aCH is greater than the boundary value of 1.0. This implies that in the reverse direction bC is negative (–0.29) which means that electronwithdrawing substituents enhance not only the rate of deprotonation (k1) but also the rate (k–1) of the protonation of the carbanion. The large magnitude of the imbalance as reflected in the large difference between aCH and bB (aCH – bB = 0.73) is the result of the exceptionally strong p-acceptor strength of the nitro group, coupled with the strong hydrogen bonding solvation of the nitronate ion in aqueous solution. This solvation reduces the need for stabilization of the nitronate ion by the Z-substituent and hence decreases the dependence of the acidity constant on Z. But since the transition state does not significantly benefit from the solvation, the dependence of the rate constant on Z changes little with the solvent and hence aCH becomes larger. We see again the direct connection between imbalance and DG‡o at work, i.e., the exceptionally large imbalance for the nitroalkanes goes hand in hand with the exceptionally high intrinsic barrier (see Table 1). A very large imbalance is also seen for the reaction of ArCH2NO2 with HO (entry 11); even though no bB value could be determined for this reaction to provide an approximate measure of proton transfer at the transition state, the mere fact that aCH > 1 demonstrates the presence of a strong imbalance. The same is true in even more dramatic fashion for the HO-promoted
Entry 1 2
C–H acid
Base
ArCH2CN ArCH2CH(CN)2 O
Solvent, T
aCH
bB
aCH – bB
References
Ar0 CH2NH2 RCOO
DMSO, 25C H2O, 25C
0.74 0.98
0.61 0.83
0.13 0.15
32 33
3
Z
RCOO
H2O, 25C
0.78
0.54
0.24
34
4 5 6 7
ArCH2NO2 ArCH2CH(COMe)COOEt ArCH2NO2 ArCH(CH3)NO2
Ar0 COO RCOO Ar0 COO R2NH
MeCN, 25C H2O, 25C DMSO, 25C H2O, 25C
0.82 0.76 0.92 0.94
0.56 0.44 0.55 0.55
0.26 0.32 0.37 0.39
35 33 36 31
R2NH
50% DMSOa, 25C
0.87
0.45
0.42
37
R2NH Ar0 COO HO
H2O, 25C MeOH, 25C H2O, 25C
1.29 1.31 1.54
0.56 0.50 –
0.73 0.81 large
31 38 31
HO
H2O, 25C
>>1
–
v. large
39
Z
8
CH2
O2N
NO2
NO2
9 10 11
ArCH2NO2 ArCH2NO2 ArCH2NO2 MeO
12
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
Table 2 Br½nsted coefficients and imbalances aCH – bB for the deprotonation of C–H acids by amines and carboxylate ions. Cases where aCH > bB
CH3
H
N+
C
CH3 S
50% DMSO–50% water (v/v).
231
a
232
C.F. BERNASCONI
deprotonation of the 2-benzylthiazolium ion shown as the last entry in Table 2. The authors39 report that with Z = (CH3)3Nþ the rate constant is about 1100values of the two compounds fold higher than with Z = H while the pKCH a differ by less than one half of a log unit, implying an aCH value 4. The reason why aCH is so large in this case must be related to the fact that the negative charge that builds up at the transition state [Equation (5)] is not only delocalized away from the substituent Z but completely disappears in the product, very insensitive to Z. rendering the pKCH a ‡ δ– HO H
OCH3 C
H
δ– OCH3 CH3 C N+
CH3
N+
HO– + Z
S
CH3
CH3
S
Z
(5)
OCH3 CH3
C N Z
S
+ H2O CH3
Coming back to the nitro compounds we note that in several cases the imbalances are not nearly as large as for the reactions of ArCH2NO2 with amines or HO in water. For example, for the reactions of ArCH2NO2 with benzoate ions in DMSO (entry 6) and MeCN (entry 4), the imbalances are much less dramatic than in water and are the result of smaller aCH values. This reduction is due to the strongly reduced solvation of the nitronate ion in dipolar aprotic solvents. There is also a reduction in the imbalance of the reaction of ArCH(CH3)NO2 (entry 7) with amines in water relative to the corresponding reaction of ArCH2NO2 (entry 9). This is again the result of a decrease in aCH and can be explained in terms of reduced charge delocalization into the nitro group of the nitronate ion due to steric hindrance of coplanarity by the methyl group. Evidence of imbalance based on Br½nsted coefficients. B. aCH < bB In all examples listed in Table 2 the lag in the charge delocalization behind proton transfer leads to aCH being greater than bB. There are, however, cases where the opposite is true, i.e., aCH < bB. Representative examples40–43 are reported in Table 3. Does this mean that the imbalance is reversed in these
Entry
C–H acid
B
Solvent, Ta
aCH
bB
aCH – bB
References
R2NH
90% DMSO, 20C
0.46
0.64
–0.18
40
R2NH
50% DMSO, 20C
0.29
0.49
–0.20
41
RND2
5% DMSO, 25C
0.46
0.70
–0.24
42
RNH2
H2O, 25C
0.27
0.55
–0.28
43
NO2
1
Z
CH2CN
2
+ PPh3
H
+ Z S(CH3)2
3
O
4 a
Z
H
PhCCH2
+ N CH2Ar
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
Table 3 Br½nsted coefficients and imbalances aCH – bB for the deprotonation of C–H acids by amines. Cases where aCH < bB
90% DMSO = 90% DMSO–10% water (v/v); 50% DMSO = 50% DMSO–50% water (v/v); 5% DMSO = 5% DMSO–95% D2O (v/v).
233
234
C.F. BERNASCONI
reactions; in other words, is charge delocalization ahead of proton transfer? Closer inspection of the situation illustrated with the example of Equation (6) demonstrates that this is ν +δ B H
CH2CN
δ– CH
NO2
‡ CHCN
CN
NO2
NO2
Bν +
Z
+ BHν + 1
(6)
Z
Z
not the case. The reason why aCH < bB is that here the lag in the charge delocalization creates a situation where it is the charge in the product ion that is closer to the substituent than the developing charge at the transition state; this is opposite to the situation in Equation (4) or all examples of Table 2. This makes aCH disproportionately small and leads to aCH < bB. The last entry in Table 3 is of particular interest because there is potential competition between two p-acceptors stabilizing the product. There is evidence indicating that resonance
O– Ph
C
O + N CH2Ar
CH
Ph
C CH
a
N
CH2Ar
b
structure b is dominant. Hence the reaction can be represented by Equation (7) which shows that at the ‡ O
Ph C
CH2
O
Ph ν +δ B
C H
δ– CH
Ph
O C CH
(7) Bν +
+ BHν + 1 N+
N+
N
CH2Ar
CH2Ar
CH2Ar
transition state the negative charge is far away from the aryl group but moves closer to it in the product, thereby neutralizing the positive charge.
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
235
The above interpretation of the imbalance is supported by a comparison of 44 For the aCH values for the deprotonation of 1 and 2 by HO and CO2 3 . reactions with HO , aCH(1) = 0.59
+ N
ArSO2CH2
+ N
PhSO2CH2
CH3
CH2Ar
2
1
and aCH(2) = 0.33, while for the reactions with CO2 3 , aCH(1) = 0.45 and aCH(2) = 0.29. The aCH(2) values are seen to be quite small for the same reason as in the reaction of Equation (7), i.e., because the product is dominated by a resonance structure that is analogous to that in Equation (7). On the other hand, aCH(1) is larger than aCH(2) because in this case the aryl group is on the other side of the molecule and hence closer to the developing negative charge at the transition state. Other examples of imbalances The determination of Br½nsted coefficients provides the most transparent tool for the evaluation of imbalances, but there are other ways to probe transition structure in search for evidence of transition state imbalances. Terrier et al.45 reported that the change to a more electron-withdrawing Zsubstituent in 3
δ– OMe X
X H
H O2N
C
NO2
Z
O2 N
C
NO2
Z Y
3
δ–
Y 4
increases the rate of deprotonation by MeO more than making X or Y more electron withdrawing, but the change in X or Y enhances the thermodynamic acidity of 3 more than the change in Z. This finding is consistent with the imbalanced transition state 4. Pollack’s group46 has studied the deprotonation of substituent 2-tetralone by HO. Based on a combination of kinetic data and 13C NMR spectra they
236
C.F. BERNASCONI
estimated the charge distributions in the transition state and anion as shown in 5 and 6, respectively. These charges imply a highly imbalanced transition state with a strong lag in the delocalization of the charge into the carbonyl group. –0.45 OH –0.33
H –0.26 –0.29 O –0.03
O
–0.68
–0.08
–0.03
0.09
5
6
Based on secondary kinetic deuterium isotope effects and some ab initio calculations, Alston et al.47 calculated that the transition state in the deprotonation of acetaldehyde by HO is imbalanced in the sense shown in Equation (3). Anslyn’s48 group examined the effect of the phenolic OD group on the deprotonation of 7 by imidazole to form the enolate ion 9. This OD group leads to a significant stabilization of the ‡
D OD
O C
B +
O
O
C
CH3
D O
δ– CH2
O– C
CH2
+ BH+
(8)
H Z 7
Z
B 8
δ+
Z 9
enolate ion 9 due to intramolecular hydrogen bonding, but its effect on the rate of deprotonation is quite small. The authors concluded that intramolecular hydrogen bonding at the transition state (8) is only minimally developed because there is only a small amount of charge on the carbonyl oxygen while most of the charge resides on the carbon. Amyes and Richard49 deduced the presence of a transition state imbalance in the deprotonation of methyl and benzylic mono carbonyl compounds by HO from the linearity of the Br½nsted plot of the rate constants versus the pKa of these carbonyl compounds. They argued that because of the large reactivity range the Br½nsted plot should have shown ‘‘Marcus curvature’’5– 8 if the intrinsic barriers for these reactions were all the same and hence the absence of such curvature indicates changes in the intrinsic barriers. They
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
237
attributed the variations in the intrinsic barriers mainly to the lag in enolate ion resonance development. However, Angelini et al.50 reached somewhat different conclusions regarding the linearity of a similar linear Br½nsted plot which were based on an examination of inductive and steric effects competing with resonance effects. According to their analysis, resonance effects play a minor role while the inductive and steric effects are dominant, a conclusion supported by additional analysis based on kinetic data for the deprotonation of 2-nitrocyclohexanone.
WHY DOES DELOCALIZATION LAG BEHIND PROTON TRANSFER?
In view of the fact that nature always chooses the lowest energy pathway, one may wonder why these reactions do not proceed via a more balanced transition state with more advanced delocalization, which would presumably lower its energy. This question has been discussed at considerable length in our 1992 review4 and hence only an abbreviated version is presented here. The reason why delocalization is not more advanced is that there are constraints imposed on the transition state that prevent extensive delocalization. This was first pointed out by Kresge51 in the context of the deprotonation of nitroalkanes, but it applies to any proton transfer from carbon. The situation is represented in Equation (9) which is a more nuanced version of Equation (3) and allows for a certain degree of charge delocalization into the p-acceptor (d Y) at the transition ‡ ν + δB
Bν + H
C
Y
B
H
–δC
–δ Y
C
Y
C
Y– + BHν + 1
(9)
state. Kresge’s argument is that d Y depends on the C–Y p-bond order as well as on the charge that has been transferred from B (d B) [Equation (10)], while the p-bond order is related to d B [Equation (11)] d Y pb:o: d B
ð10Þ
pb:o: d B
ð11Þ
d Y ðd B Þ2
ð12Þ
238
C.F. BERNASCONI
since the p-bond is created from the electron pair transferred from the base. Hence d Y is given by Equation (12); it is a small number because it represents only a fraction of a fraction. A more refined picture which takes the charge on the proton-in-flight into consideration will be presented later. However, the basic features and conclusions will remain the same. In other words, because of the constraints embodied by Equations (10–12), delocalization must always lag behind proton transfer or other bond changes in other types of reactions, i.e., there cannot be exceptions. It should be noted that the origins of the imbalance have also been discussed in the context of the valance bond configuration-mixing model proposed by Shaik and Pross.52,53 This model describes the reaction energy profile in terms of the conversion of a reactant configuration (c) into a product configuration (d) and the mixing of a third configuration (e); this latter plays a
Bν: H
C c
Y
Bν + 1 H
C d
Y–
Bν: H+ – :C
Y
e
dominant role in the transition state region. The mixing in of e confers to the transition state its carbanionic character. We prefer the Kresge model because it shows that the imbalanced character of the transition state is enforced by the constraints described by Equations (10–12) whereas the Shaik–Pross model is more a post facto explanation of the imbalance. We shall return to the question of the origin of imbalances in the section on ab initio calculations.
OTHER FACTORS THAT AFFECT INTRINSIC BARRIERS AND TRANSITION STATE IMBALANCES
There are a number of factors that affect intrinsic barriers and/or transition state imbalances. Many of these may be viewed as ‘‘derived’’ effects because they are a consequence of the imbalance caused by the presence of p-receptors, i.e., in the absence of this imbalance they would not affect the intrinsic barriers even if they affect actual barriers and equilibria. Solvation Solvation can have a large effect on intrinsic barriers or intrinsic rate constants, especially hydrogen bonding solvation of nitronate or enolate ions in hydroxylic solvents. Table 4 reports intrinsic rate constants in water and aqueous DMSO for a number of representative examples.19,20,23–25,40,54–56 Entries 1–4 which refer to nitroalkanes show large increases in log ko when
Entry
1 2 3 4 5
CH3NO2 PhCH2CH2NO2 PhSCH2NO2 PhCH2NO2 CH2(COCH3)2
log ko(RCOO)a
log ko(R2NH)a
C–H Acid H2O
50% DMSO– 50% H2O
90% DMSO– 10% H2O
H2O
–0.59 –1.16 1.02 –0.86 2.60
0.73
–0.25 2.75
3.06 2.51 4.08 1.75 3.64
2.97b
3.13
3.85
1.57
1.87
2.75
55
2.51
20
2.29
2.50
4.03
3.95
3.85
20
2.85
2.76
2.54
40
–2.10 2.89
50% DMSO– 50% H2O
90% DMSO– 10% H2O
References
–0.59 3.80
1.88 5.3
25 54 54 25 24
3.18
4.53
23
CO
6
CH2
2.64b
CO
7
PhCOCH2NO2
8
PhCOCH2
9
PhSO2CH2
+ N CH3 + N CH3
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
Table 4 Solvent effects on intrinsic rate constants for the deprotonation of C–H acids by secondary alicyclic amines and carboxylate ions at 20C
NO2 O2N
CH2CN
239
10
240
Table 4 (continued ) Entry
H2O
4.44b
11 H
log ko(RCOO)a
log ko(R2NH)a
C–H Acid
50% DMSO– 50% H2O
90% DMSO– 10% H2O
H2O
50% DMSO– 50% H2O
4.58
4.39
19
3.30
2.98
56
90% DMSO– 10% H2O
References
CN
Cr(CO)3
12 (CO)3Cr a
In units of M1 s1. 10% DMSO–90% H2O (v/v).
C.F. BERNASCONI
b
CH2
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
241
the water content of the solvent is reduced. This implies that hydrogen bonding solvation of the anion leads to particularly large increases in the intrinsic barrier. The reason for the large intrinsic barrier is that solvation of the incipient charge lags behind proton transfer, just as delocalization of the charge into the p-acceptor group lags behind proton transfer. Hence the scheme of Equation (3) may be extended to include solvation as shown in Equation (13). Again, the easiest way ‡ Bν +
H
C
Y
ν+δ B H
δ– C Y
C
Y–
H2O + BHν + 1
(13)
to understand the barrier-enhancing effect is to consider the reaction in the reverse direction. To reach the transition state, energy is required not only to localize the charge on the carbon but also to desolvate the carbanion. In other words, there is a solvational PNS effect that is superimposed on the resonance/ delocalization PNS effect. Entries 5 and 6 refer to diketones. The delocalization of the anionic charge into two carbonyl oxygens in the respective enolate ions reduces the strength of hydrogen bonding solvation relative to that of nitronate ions. This reduces the solvational PNS effect as seen in the less dramatic solvent effect on the log ko values. The same is true for nitroacetophenone (entry 7) where the negative charge is shared between the nitro and the carbonyl group. Entries 8 and 9 involve cationic acids with the main resonance structure of the conjugate base being neutral, e.g., 10b. Hence hydrogen bonding solvation plays a minimal role and there
O– PhC
O CH
N 10a
+
CH3
PhC CH
N
CH3
10b
is no significant solvent dependence of ko. Entries 10–12 also show negligible solvent effects even though the conjugate bases of the respective carbon acids are anionic. In these cases the anionic charge is so highly dispersed that, once again, hydrogen bonding solvation is insignificant. More detailed analysis of the solvent effects on intrinsic rate constants which takes into consideration potential contributions from nonsynchronous solvation/desolvation of the carbon acid itself as well as of the proton acceptors and
242
C.F. BERNASCONI
their conjugate acids have been discussed in our previous review4 and elaborated upon in some subsequent studies.20,55 They involve the determination of solvent transfer activity coefficients and an estimate of the degree of solvational imbalance at the transition state.20,56,57 Even though a somewhat more refined picture emerges from such analysis, the broad qualitative conclusions stated above which focus on the solvation of the carbanions remains the same, at least with amines as the proton acceptor. For reactions involving carboxylate ion proton acceptors, the PNS effect of early desolvation of the carboxylate58 ion can make a significant contribution to the solvent effect on ko. This is illustrated by entries 4–6 of Table 4, which show a significantly larger change in log ko(RCOO) compared to log ko(R2NH). A complementary aspect of solvation is that it affects the magnitude of the transition state imbalance. This can be seen for the reactions of ArCH2NO2 in DMSO and MeCN where the imbalances are much smaller than in water (Table 2, entries 4 and 6). Again we see the connection between imbalance and intrinsic barriers: the greater imbalance induced by solvation leads to an enhanced intrinsic barrier. Polar effect of remote substituents One of the consequences of the imbalanced nature of the transition state is that the polar effect of a remote substituent may either increase or decrease the intrinsic barrier; whether there is an increase or decrease depends on the location of the substituent with respect to the site of charge development. Let us consider a reaction of the type shown in Equation (4). In this situation an electron-withdrawing substituent Z will decrease DG‡o or increase ko. This is because there is a disproportionately strong stabilization of the transition state compared to that of the product anion due to the closer proximity of Z to the charge at the transition state than in the anion. As discussed earlier, this also leads to an exalted Br½nsted aCH value and is the reason why aCH > bB for the deprotonation of carbon acids such as 11–13 and others (Table 2).
CH2NO2
CH2CH(COMe)CO2Et O Z
Z
Z 11
12
13
A different situation exists when the substituent is attached to the Y-group as schematically shown in Equation (14). In this case Z is closer to the negative charge in the anion than at
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
243
(14)
the transition state. Hence it is the carbanion rather than the transition state that receives a disproportionately strong stabilization by an electronwithdrawing substituent. The result is an increase in DG‡o or decrease in ko which translates into a depressed aCH value and is the reason why aCH < bB for the deprotonation of carbon acids such as 14–16 and others (Table 3). Note
that for 16, upon delocalization of the initially formed negative charge, there is neutralization of the positive charge on the pyridinium nitrogen to form a neutral conjugate base, as discussed earlier [Equation (7)]. Polar effect of adjacent substituents In principle, polar substituents directly attached to the carbon, Equation (15), should have a similar effect
(15)
on DG‡o or ko as in the situation described by Equation (4) for remote substituents, i.e., an electron-withdrawing substituent should reduce DG‡o or increase ko. In practice, it is difficult to quantify such effects because in most known examples factors other than the polar effect of Z contribute to changes in ko such as steric crowding, polarizability, hyperconjugation, and charge delocalization into Z. Nevertheless, there are several cases where changes in ko could definitely be attributed to the polar effect of Z. They are summarized in Table 519,20,25,42,43,54,55,66–70 which includes log ko values as well as Taft sF and sR values71 as measures of the polar and resonance effects, respectively, of Z.
244
Table 5 Effect of adjacent polar substituents on intrinsic rate constants Entry
C–H acid
1 H
sR
0.19
0.16
0.54
0.18
4.58b
log ko(RNH2)a
log ko(RCOO)a
References
2.84b
19
3.76b
19
CO2Me
2 H
log ko(R2NH)a
sF
CN
PhCOCH2
+ N CH3
0.29
0.16
2.29c
20
4
PhSO2CH2
+ N CH3
0.59
0.12
4.03c
20
5 6 7 8 9 10 11
CH3NO2 MeO2CCH2NO2 PhCOCH2NO2 CH3CH(NO2)2 HOCH2CH2NO2 PhCH2CH2NO2 PhSCH2NO2
0 0.19 0.29 0.64 0.13 0.04 0.29
0 0.16 0.16 0.16 –0.05 –0.08 –0.05
–0.5c 1.22d 1.57c
25 66 55 67 68 54 54
1.00c
d
–0.59 –1.16d 1.02d
–2.06d –0.13d
C.F. BERNASCONI
3
H
+ SMe2
13
F3CSO2CH2
14
F3CSO2CH2
SO2CF3
In units of M1 s1. In 50% DMSO–50% water (v/v) at 20C. c In water at 20C. d In water at 25C. e In 50% DMSO–50% water (v/v) at 25C. a
b
4.1d
1.01
0.13
42
0.83
0.26
5.0e
0.83
0.26
4.2e
69
70
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
12
245
246
C.F. BERNASCONI
Comparison of entry 2 with entry 1 shows a significant increase in ko that is caused by the greater electron-withdrawing strength of the CN (sF = 0.54) relative to that of the COOMe group (sF = 0.19). The CN group is also a somewhat stronger p-acceptor (sR = 0.18) than the COOMe (sR = 0.16) group which should slightly reduce ko and hence offset some of the increase resulting from the polar effect, i.e., the increase in ko due to the larger polar effect is probably somewhat greater than the observed increase in ko. On the other hand, the large size of the COOMe group could, in principle, lead to a steric reduction of ko for the COOMe derivative relative to the CN derivative. However, it was shown that this is not the case for these reactions which involve primary aliphatic amines as the proton acceptors.41 The change from PhCO (sF = 0.20) to the much more electron-withdrawing PhSO2 group (sF = 0.59) leads to a large increase in ko as seen from entries 3 and 4, respectively. In this case there may be a small contribution to the large difference in the ko value that arises from the stronger p-acceptor effect of the PhCO group (sR = 0.16) relative to that of the PhSO2 group (sR = 0.12) which reduces ko for the PhCO derivative relative to the PhSO2 derivative. In comparing entries 6 and 7 to entry 5 we note a substantial increase in ko when replacing a hydrogen with a COOMe or PhCO group. This implies that the main resonance structures of the corresponding anions are 17a and 18a, respectively, i.e., the COOMe and
CH3O
CH3O C
NO2–
CH
O
17a
O
CH
NO2
17b
O–
O PhC
C –
CH 18a
NO2–
PhC
CH
NO2
18b
PhCO groups act mainly through their polar effects. The somewhat larger ko for the PhCO derivative is consistent with the larger sF value of the PhCO group; the difference in the log ko values of 0.35 actually underestimates the true difference because ko for the PhCO derivative was determined at 20C rather than 25C. The higher intrinsic rate constant for 1,1-dinitroethane (entry 8) compared to that for CH3NO2 is open to two interpretations but both are related to the steric hindrance of the coplanarity of the two nitro groups in the anion. According to the first interpretation one nitro group in the anion is planar
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
247
and exerts its full p-acceptor effect while the second one is largely twisted out of the plane and enhances ko by its polar effect. The second, more likely, possibility is that both nitro groups are somewhat twisted out of plane so that neither exerts its full p-acceptor effect, while both exert their polar effect. For the entries 9–14 the potential polar effects of the respective substituents are either offset or enhanced by other factors such as hyperconjugation or polarizability as discussed in the next sections. Hyperconjugation Despite the fact that the HOCH2 group is mildly electron withdrawing (sF = 0.13), the log ko(R2NH) value for HOCH2CH2NO2 (Table 5, entry 9) does not show the expected increase relative to the respective log ko value for nitromethane (entry 5). This implies the presence of a ko-reducing factor that offsets the expected increase from the polar effect. In view of the higher temperature used for the reaction of HOCH2CH2NO2 (25C) compared to that with CH3NO2 (20C), the presence of a ko-reducing factor is even more compelling. A similar reduction in ko is seen in the deprotonation of PhCH2CH2NO2: even though the PhCH2 group exerts hardly any polar effect, log ko(R2NH) is measurably lower than for CH3NO2 (Table 5, entry 10). The reason for these reductions in ko has been identified as hyperconjugation in the anion (19b, R = OH or Ph).54,68
RCH2CH 19a
+ N
O– O–
H+ RCH
O– CH 19b
N O–
This hyperconjugation contributes to the stability of the respective nitronate ions as reflected in the reduction of the pKa values for HOCH2CH2NO2 (pKa = 9.40) and PhCH2CH2NO2 (pKa = 8.55) relative to CH3NO2 (pKa = 10.29). Inasmuch as hyperconjugation is expected to follow the same pattern as resonance/delocalization, i.e., being poorly developed at the transition state, its PNS effect should lower the intrinsic rate constant, as observed. Perhaps the best-known case of such hyperconjugation at work is seen when comparing pKa values and rate constants of the deprotonation of nitromethane, nitroethane, and 2-nitropropane by HO (Table 6). The pKa values show the increased hyperconjugative stabilization of the nitronate ion by one and two methyl groups, respectively (e.g., 19b, R = H). Since the transition state hardly benefits from hyperconjugation, the rate constants remain essentially unaffected by this factor and are mainly governed by the electron donating effect of the methyl groups which leads to a reduction in kOH.
248
C.F. BERNASCONI
Table 6 Deprotonation of nitroalkanes by HO in water at 25Ca C–H acid
pKCH a
kOH, M1 s1
CH3NO2 CH3CH2NO2 (CH3)2CHNO2
10.22 8.60 7.74
27.6 5.19 0.136
a
From Reference 51.
Interestingly, the fact that the trend in the rate constants is the opposite of that in the acidity constants translates into a negative aCH value of about –0.5 which has been called ‘‘nitroalkane anomaly.’’51 A somewhat similar situation has been observed in the deprotonation of the Fischer carbene complexes 20–24 summarized in Table 7.72,73 There is an increase in acidity in the order 20 < 21 < 22 and 23 < 24 which has been Table 7 Deprotonation of Fischer carbene complexes by HO in 50% MeCN–50% water (v/v) at 25C Entry
pKCH a
Carbene complex OMe
1
(CO)5Cr
C
2
(CO)5Cr
C
3
(CO)5Cr
C
4
(CO)5Cr
CH3 OMe CH2CH3 OMe CH(CH3)2
kaOH (M1 s1)
log ka,b o
1.07
(20)c
12.78
(21)c
12.62
23.4
0.09
(22)c
12.27
10.8
–0.99
(23)d
14.77
37.0
1.36
(24)d
13.41
39.5
0.70
152
O
O
5
(CO)5Cr CH3
a
Statistically corrected for the number of acidic protons.
Estimated based on the simplified Marcus equation log ko 0.5 log KOH with KOH = KCH a /Kw, Kw = 6.46 1016 M2.
b
c
From Reference 72.
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
249
attributed to an increasing stabilization of the anions in the order 20 < 21 < 2272 and 23 < 2473 by the methyl groups. This effect reflects the wellOMe (CO)5Cr
OMe
OMe C
(CO)5Cr
C
(CO)5Cr
CH2
C C(CH3)2
CHCH3
20–
21–
22–
O
O
(CO)5Cr
(CO)5Cr 23–
24– CH3
known stabilization of alkenes by methyl or alkyl groups74 and is commonly attributed to hyperconjugation as shown for the example of 21. The rate constants do not show the expected
OMe
OMe (CO)5Cr
C
(CO)5Cr CH
C CH
CH3
21–
CH2H+
21a–
increase with increasing acidity. This translates into a reduction of the intrinsic rate constants which is mainly due to the lag in charge delocalization into the (CO)5Cr group at the transition state (25). This lag not only prevents significant development of the hyperconjugative stabilization, there is also a destabilization of the transition state by the unfavorable interaction between the methyl group and the negative charge on the carbon. OMe (CO)5Cr
C
25
δ– CH
H
δ– OH
CH3
Polarizability The log ko(R2NH) value for PhSCH2NO2 of 1.02 (Table 5, entry 11) is about of 1.6 log units greater than that for CH3NO2 (–0.59) and the pKCH a
250
C.F. BERNASCONI
PhSCH2NO2 (6.67) is about 3.6 units lower than that of CH3NO2 (10.28). It was established that even though most of the increased acidity may be accounted for by the polar effect of the PhS group (sF = 0.29), at best one third or one half of the increase in log ko(R2NH) may be attributed to the polar effect.54 The rest was shown to be the result of a transition state stabilization of the negative charge on carbon by the polarizability effect of sulfur.54 The high intrinsic rate constant for the deprotonation of dimethyl-9fluorenylsulfonium ion (entry 12) has also been attributed to the polarizability of the sulfur atom.42 The same is true for the effect of the trifluoromethylsulfonyl group on the benzyltriflones in entries 13 and 14. The latter group has a very high sF value (0.83) and hence its electron-withdrawing inductive effect certainly contributes significantly to the very high ko values. However, its sR value is also very high (0.26) which implies that the resonance effect may offset a significant fraction of the ko-enhancing inductive effect. Hence, the high ko values strongly suggest a major contribution by the polarizability effect. This conclusion is strongly supported by 1H, 13C, and 19F NMR data as well as solvent effect studies on the kinetic and thermodynamic acidities of various trifluoromethylsulfonyl derivatives from Terrier’s laboratory.69,70,75,76 There is a broader significance to the conclusion regarding the importance of polarizability effects on intrinsic barriers because it also addresses the question whether d–p p bonding or negative hyperconjugation in the anion may play a significant role. The notion that d–p bonding between the carbanion lone pair and the sulfur 3d orbital (e.g., 26) may account for the stabilization of carbanions was promoted by numerous authors,77–82 although
CH3
S
CH –2
CH3
26a
S
CH2
26b
theoretical work later challenged this idea, suggesting the polarizability of sulfur as the main source of stabilization.83–86 A third potential interaction mechanism, negative hyperconjugation (e.g., 27), has also been invoked by several authors,84,86–88 and Wiberg et al.89 as well as Cuevas and Juaristi90 have concluded that this may be the main factor in the stabilization of the dimethylsulfide ion by sulfur.
CH3
S 27a
CH –2
CH3
S
CH 2
27b
If d–p bonding or negative hyperconjugation were to play an important role in the stabilization of the conjugate bases of the dimethyl-9flurorenylsulfonium ion, the benzyltriflones, or thiophenylnitromethane, one
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
251
would expect a reduction in the intrinsic rate constant. This is because these interaction mechanisms belong to the broad category of resonance effects and hence their development at the transition state is expected to lag behind proton transfer and lower the intrinsic rate constant. The large increase in log ko(R2NH) for the deprotonation of PhSCH2NO2 relative to that for CH3NO2 and the unusually high ko values in entries 12–14 indicate that the influence of these factors on ko is negligible compared to the polarizability effect. A further comment regarding the nature of the ko-enhancing effect by a polarizable substituent is in order. It is quite similar to that exerted by the polar effect of an electron-withdrawing group in that it leads to a disproportionately strong stabilization of the transition state due to the closer proximity of the substituent to the site of the incipient negative charge. However, there are some important differences between the two effects that result from the fact that polarizability effects are proportional to the square of the charge91 and drop off very steeply with the 4th power of distance,91 whereas polar effects are simply proportional to the charge and drop off only with the square of the distance.91 The steep drop off with distance may potentially render polarizability effects on intrinsic rate constants more dramatic than polar effects but only when the imbalance is large and proton transfer has made significant progress at the transition state. A more detailed discussion of these points has been presented elsewhere.3,41 Electrostatic effects Electrostatic effects may significantly affect intrinsic barriers or intrinsic rate constants, especially when there is a positive charge directly adjacent to the carbon that gets deprotonated, as exemplified by Equation (16). Keeffe and Kresge92 have shown that a large body of data on the ‡ + N
CH2 28
C
O–
O
O Ph
+ N
δ– CH
C
Ph
+ N
CH
C
Ph + H2O
(16)
H δ– OH
deprotonation of simple aldehydes and ketones by HO in water obey a linear correlation between log(kOH/p) and log ðKCH a =qÞ over a range of 11 pKa units. The points on the correlation may be understood to refer to reactions with equal or at least comparable intrinsic rate constants, while deviating points indicate higher or lower intrinsic rate constants. The point for the reaction of Equation (16)93 shows a positive deviation of almost 3 log units92 which suggests a strongly enhanced intrinsic rate constant. This increase in ko can
252
C.F. BERNASCONI
be attributed to a combination of the PNS effect by the polar effect of the pyridinio group and the electrostatic stabilization of the negative charge at the transition state which is disproportionately strong compared to that of the enolate ion due to its closer proximity to the positive charge. The deprotonation of 29 by HO93 also shows a positive deviation from the Keeffe/Kresge plot but it amounts to only about 1 log unit, as
CH2
Ph C O
N + CH3 29
expected due to the greater distance of the positive charge from the reaction site. In fact, it is not clear whether in this case the entire acceleration might be due to a polar rather than an electrostatic effect. An interesting case is the deprotonation of 30 by HO94 with a rate constant, if placed on the Keeffe/Kresge plot, would deviate positively by about 0.34 log units. The following
‡
HO– +
O
N + CH3
C CH3
N + CH3
O C δ– CH2
N
+ CH3
C
CH2 + H2O
O–
H
30
31
δ– OH
32
interpretation was given. The likely conformation of the transition state is one with the closest distance between the charges as shown in 31, while the same is true for the product 32 except that at the transition state the negative charge mainly resides on the carbon while in the product ion (32) it mainly resides on the oxygen. Hence, even though the distances between the charges are about the same in 31 and 32, to the extent that carbon is much less able to support a negative charge than oxygen, the transition state derives a disproportionately large degree of stabilization from the electrostatic effect of the positive charge compared to the product; the stabilization of the latter by the positive charge is further attenuated by the strong solvation of the anionic oxygen.
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
253
The above interpretation is supported by data on the deprotonation of 33 by HO.95 In this situation, it is only the product 35 that benefits from electrostatic stabilization while the ‡ HO– +
+ H2O
δ–
N + CH3
O
N + CH3
H O
33
N + CH3
δ– OH
34
O–
35
negative charge at the transition state 34 is too far for a significant interaction with the positive nitrogen. In the terminology of the PNS this is a case where the product stabilization factor lags behind proton transfer and hence ko should be reduced. This is borne out by the fact that when the rate constant of this reaction is included on the Keeffe/Kresge correlation it shows a negative deviation of 0.85 log units. Whether the entire 0.85 log units deviation should be attributed to this PNS effect is not clear because cyclohexanone also shows a slight negative deviation from the Br½nsted line. p-Donor effects Carbon acids activated by strong p-acceptors that also contain a p-donor capable of interacting with the p-acceptor in a push–pull fashion pose an interesting problem. Fischer carbene complexes such as 20,94 23,97 36,96 37,96 38,98 and 3998 fall into this category. Thermodynamic
OCH3 (CO)5Cr
C CH3 20
OCH3 (CO)5W
C CH3
C
37
SCH3 (CO)5Cr
C CH3
23
C CH3
36
O (CO)5Cr
OCH2CH3 (CO)5Cr
38
SCH3 (CO)5W
C CH3 39
and kinetic data for these carbene complexes are reported in Table 8.96–98 There is a strong correlation between the strength of the p-donor and the pKa
254
Table 8 Acidities of Fischer carbene complexes and intrinsic rate constants for their deprotonation by secondary alicyclic amines, primary aliphatic amines and hydroxide ion in 50% MeCN–50% water (v/v) at 25C pKa
log ko(R2NH)
log ko(RNH2)
log ko(HO)
References
(36)
12.36
3.18
2.72
1.09
96
(20)
12.50
3.70
3.04
1.31
96
(37)
12.98
1.38
96
(23)
14.47
1.51
97
(39)
8.37
2.51
2.50
98
(38)
9.05
2.61
2.09
98
Entry
C
1
(CO)5W
2
(CO)5Cr
C
3
(CO)5Cr
C
4
(CO)5Cr
5
(CO)5W
6
(CO)5Cr
OCH3 CH3 OMe CH3 OCH2CH3 CH3 O
C
SCH3
C
SCH3 CH3
C.F. BERNASCONI
CH3
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
255
values, i.e., the stronger the p-donor, the lower the acidity of the carbene complex. For example, the pKa of 36 is about 4.0 units higher than that of 39 while that of 20 is about 3.5 units higher than that of 38. This reflects the fact that the MeO group is a stronger p-donor (sR = –0.43)71 than the MeS group (sR = –0.15)71 and leads to stronger resonance stabilization (40, 40) of the carbene complex which reduces its
+ XCH3
XCH3 (CO)5M
C 40
(CO)5M CH3
40±
M = Cr or W X = O or S
C CH3
acidity. The cyclic complex 23 is of particular interest with a pKa that is 2 units higher than that of 20. In this case the resonance stabilization of the carbene complex is enhanced by virtue of its cyclic structure in which the oxygen atom is locked into a position for better p-overlap with the carbene carbon.97 53Cr NMR data are in agreement with this interpretation.99 An even greater reduction in acidity is observed for the Me2N derivative, 41 (sR = –0.56)71
NMe2 (CO)5Cr
C CH3 41
which makes it impossible to determine its pKCH in an aqueous environment. a 32.5 was estimated in acetonitrile which is more than 10 However, a pKCH a 22.2 of 20 in the same solvent.100 pKa units higher than the pKCH a The p-donor effect on intrinsic rate constants is more difficult to interpret. For the alkoxy carbene complexes the log ko(HO) values are all about the same within the experimental uncertainty, suggesting that changing p-donor strength has no significant effect on the intrinsic barriers. This seems surprising because one might have expected that the push–pull resonance would follow the same PNS rules as resonance delocalization, i.e., it should lower the intrinsic rate constants due to early loss of the resonance effect at the transition state. The most plausible explanation for the results is that there is another factor that offsets the ko-lowering PNS effect. It has been suggested that this other factor comes from an attenuation of the lag in the carbanionic resonance development by the p-acceptor because the contribution of 40 to the structure of the carbene complex leads to a preorganization of the (CO)5M-moiety
256
C.F. BERNASCONI
toward its electronic configuration in the anion. This preorganization is likely to stabilize the transition state by facilitating the delocalization of the negative charge into the (CO)5M-moiety, i.e., by reducing the degree of imbalance.96–98 Additionally or alternatively, the electrostatic interaction between the partial positive charge on X and the partial negative charge at the carbon of the transition state (42) is expected to stabilize the latter and lower the intrinsic barrier. δ+ XCH3
δ– (CO)5Cr
C
42
δ– CH2
H
Bν + δ
The reduction in the imbalance by preorganizing the carbene complex structure in the manner described above also manifests itself in the Br½nsted aCH and bB values for the deprotonation of phenyl-substituted (benzylmethoxycarbene) pentacarbonyl chromium (43-Z) by amines.101
OCH3 (CO)5Cr
C
δ+ OCH3
δ– Z
(CO)5Cr
C
CH2
δ– Z
(CO)5Cr
CH2
43-Z
43-Z′
C
δ+ OCH3 δ– CH
Z
44-Z H B
δ+
The results are summarized in Table 9. They show that, within experimental error, aCH bB rather than the expected aCH > bB. It appears, then, that the p-donor effect of the methoxy group masks the true extent of the imbalance by reducing aCH. One way to understand this reduction is to assume that the partial positive charge on the MeO group of the resonance hybrid 43-Z0 is largely maintained at the transition state 44-Z. This means that the stabilizing effect of an electron-withdrawing Z-substituent on the negatively charged carbon at the
Table 9 Reactions of 43-Z with amines in 50% MeCN–50% water (v/v) at 25Ca Reaction 43-H þ R2NH 43-H þ RNH2 a
From Reference 101.
bB
Reaction
aCH
0.48 0.07 0.54 0.04
43-Z þ piperidine 43-Z þ n-BuNH2
0.530.02 0.560.03
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
257
Table 10 Average aCH and bB values for the deprotonation of 45-Z and 46-Z by amines in 50% MeCN–50% water (v/v) at 25Ca Parameter
R2NH 45-Z 0.41 0.55 –0.15 46-Z 0.33 0.45 –0.12
aCH bB aCH – bB aCH bB aCH – bB a
RNH2 0.37 0.73 –0.36 0.33 0.47 –0.14
From Reference 102.
transition state is partially offset by its destabilizing effect on the positively charged oxygen and hence aCH is reduced.102 Supporting evidence for the above explanation comes from the study of the deprotonation of 45-Z and 46-Z by a series of amines.102 Average aCH and bB values are summarized in Table 10.
Z (CO)5Cr
Z
OCH2
S
C
(CO)5Cr
CH3
C CH3
45-Z
46-Z
Taking 45-Z as an example, the reaction can be described by Equation (17). The observation ‡ δ+ OCH2
δ– B + (CO)5W
C CH3
Z
δ– (CO)5W
C
δ+ OCH2 δ– CH2
Z
H
B δ+
45-Z′
(17) Z OCH2 (CO)5W
C
+ BH+
CH2
that aCH < bB is reminiscent of the situation described in Equation (6) and other cases summarized in Table 3. In both situations there is creation of partial negative charge on the carbon at the transition state and in both cases the Z-substituent is located far away from that carbon. In the
258
C.F. BERNASCONI
deprotonation of 2-nitro-4-Z-phenylacetonitrile [Equation (6)], the negative charge moves closer to Z and becomes a full charge in the product ion; in the deprotonation of 45-Z the negative charge also moves closer to Z but here the effect is the neutralization of positive charge on the oxygen. In terms of substituent effects, i.e., aCH versus bB, the outcome is the same in both situations. A further example of an imbalance reduction is seen in the reaction 1benzyl-1-methoxy-2-nitroethylenes (47-Z) with secondary alicyclic amines in 50% DMSO–50% water (v/v).103
OMe
H C
C
O2N
Z CH2
47-Z
47-Z is analogous to 43-Z. The reported Br½nsted coefficients are aCH = 0.84 and bB = 0.47. These values still show a large imbalance (aCH – bB = 0.37) but it is much smaller than that for the deprotonation of phenylnitromethanes (aCH = 1.29, bB = 0.56, aCH – bB = 0.73). Turning to the effect of the heteroatom, the change from MeX = MeO to MeS (36 vs. 39 and 20 vs. 38 in Table 8) leads to a decrease in log ko(R2NH) of 0.67 (M = W) and of 1.09 (M = Cr) log units, respectively, and a decrease in log ko(RNH2) of 0.22 (M = W) and of 0.95 (M = Cr) log units, respectively. Even though weaker, due to the reduced p-donor strength of the MeS group, the two compensating factors discussed for the alkoxy derivatives may still essentially offset each other. This means that the decreases in ko for the sulfur derivatives must be due to other factors. One such factor is early developing steric crowding at the transition state due to the larger size of the sulfur atom. Another is the weaker polar effect of the MeS compared to that of the MeO group which favors the methoxy derivative. Aromaticity The question how aromaticity in a reactant or product might affect intrinsic barriers has only recently received serious attention. Inasmuch as aromaticity is related to resonance one might expect that its development at the transition state should also lag behind proton transfer (or its loss from a reactant would be ahead of proton transfer) and hence lead to an increase in DG‡o , as is the case for resonance/delocalized systems. However, recent studies from our laboratory suggest the opposite behavior. The first such study involved the deprotonation of the cationic rhenium Fischer carbene complexes 48Hþ-X by primary aliphatic amines, secondary
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
259
alicyclic amines, and carboxylate ions in aqueous acetonitrile.104 The conjugate bases, 48-X, represent heterocyclic aromatic X Bν
+ + Cp(NO)(PPh3)Re
X
k1 k–1
Cp(NO)(PPh3)Re
+-O
+ BHν + 1
48-O (X = O) 48-Se (X = Se) 48-S (X = S)
(X = O) 48H 48H+-Se (X = Se) 48H+-S (X = S)
(18) derivatives of furan, selenophene, and thiophene, respectively. The increase in aromaticity along the order 48-O < 48-Se < 48-S105 is reflected in the decreasing pKa values of the respective 48Hþ-X (Table 11). The intrinsic rate constants for proton transfer follow the order ko(X = O) < ko(X = Se) < ko(X = S) for each buffer family (Table 11), i.e., they increase with increasing aromaticity of 48-X. According to the PNS, these results imply that development of the aromatic stabilization of 48-X has made more progress at the transition state than proton transfer. A second system showing similar results is that of Equation (19).108 Table 12 values and intrinsic rate constants for the reactions with summarizes pKCH a primary aliphatic and secondary O–
O k1
Bν + X
+ BHν + 1
k–1
(19)
X 49–-O (X = O) 49–-S (X = S)
49H-O (X = O) 49H-S (X = S)
alicyclic amines in aqueous solution. Again, the stronger aromatic stabilization of the sulfur heterocyclic system is reflected in the greater acidity of 49H-S Table 11 Acidities of rhenium Fischer carbene complexes and intrinsic rate constants for their deprotonation by amines and carboxylate ions in 50% MeCN–50% water (v/v) at 25Ca,b Carbene complex
pKCH a
log ko(R2NH)
log ko(RNH2)
log ko(RCOO)
48Hþ-O 48Hþ-Se 48Hþ-S
5.78 4.18 2.50
–0.46 0.92 1.05
–0.88 0.14 0.27
–0.01 0.72 1.21
a b
ko in units of M1 s1. From Reference 104.
260
C.F. BERNASCONI
Table 12 Acidities of benzofuranone and banzothiophenone and intrinsic rate constants for their deprotonation by amines in water at 25Ca,b C–H Acid
pKCH a
log ko(R2NH)
log ko(RNH2)
49H-O 49H-S
11.72 9.45
1.64 2.64
1.16 1.72
a b
ko in units of M1 s1. From Reference 108.
(pKa = 9.45) compared to that of 49H-O (pKa = 11.72) and again the intrinsic rate constants are greater for the more aromatic system. A third reaction, Equation (20), yielded somewhat ambiguous results stemming from k1
Bν +
O– + BHν + 1
O k–1
X
(20)
X 50–-O
50H-O (X = O) 50H-S (X = S)
(X = O) 50–-S (X = S)
complications due to the p-donor effects of the ring heteroatom (50H-X).109 However, a
O X 50H-X
O–
+ X ± 50H-X
detailed analysis108 revealed that here again the greater aromaticity of the sulfur derivative increases ko relative to that for the oxygen derivative. An interesting situation exists in the deprotonation of the pentacarbonyl(cyclobutenylidene)chromium complexes 51 and 52.110 These complexes are characterized by a strong Me
Ph
(CO)5Cr
NEt2 Me
H 51
(CO)5Cr
NEt2 Me
H 52
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
261
push–pull interaction represented by 53a/53b but their most interesting feature is that their R
R
(CO)5Cr Me
H
+ NEt2
(CO)5Cr
NEt2
Me
R = Me or Ph
53a
H 53b
conjugate bases are derivatives of cyclobutadiene (54) which makes them antiaromatic. This anti-aromaticity is reflected in the very high pKa values determined in acetonitrile and the R Me2N (CO)5Cr
NEt2 Me
54 (R = Me or Ph)
Me2N
P
N
NMe2 + NEt P NMe2
Me2N P2-Et
extremely low calculated gas phase acidities.110 The intrinsic rate constants for the reaction of 51 with the phosphazene base P2-Et111 in acetonitrile suggests that the anti-aromaticity of the anion has an intrinsic barrier-lowering effect, although this conclusion was tentative because ko for this reaction is affected by several other factors. The implication of this result is that the development of anti-aromaticity at the transition state may lag behind proton transfer. Possible reasons why transition state aromaticity is able to develop early while resonance development lags behind proton transfer at the transition state, and why anti-aromaticity lags behind proton transfer, will be discussed in the section on ab initio calculations. These calculations have provided important additional insights because they allow a direct probe of transition state aromaticity or anti-aromaticity.
3
Proton transfers in the gas phase: ab initio calculations
THE CH3Y/CH2=Y SYSTEMS
The computational investigation of identity proton transfers such as Equation (21) in the gas phase has been particularly useful because the barriers of such reactions are the intrinsic barriers and the
262 Y
C.F. BERNASCONI CH3 + CH2
Y–
–Y
CH2 + CH3
(21)
Y
transition state is symmetrical with respect to the proton transfer (50%) which makes it easy to recognize the presence of imbalances. These studies have provided further insights into the PNS that complement those gained from solution phase reactions. The p-acceptor groups Y examined include CH=O,112–116,118 NO2,117,118 NO,118 CH=CH2,114,115,118,119 C N,114,118 þ
þ
CH=NH,118 CH=S,118 CH=OH ,120 and NO2 H.117 The most comprehensive study which also incorporates results form earlier work is that by Bernasconi and Wenzel118; the present discussion is largely based on this paper and on references 113, 117, and 120. A major conclusion is that even though the intrinsic barriers of these gas phase reactions depend on the same factors as solution phase proton transfers such as resonance, polar, and polarizability effects, the relative importance of these factors is quite different in the gas phase, and electrostatic effects involving the proton-in-flight constitute an important additional factor. Evidence of imbalance One of the first questions we113,117,118 and others112,114,117 asked is whether the Y-group induces similar transition state imbalances as observed in solution. Calculation of geometric parameters such as bond lengths and angles as well as group charges indicate that the transition states of these reactions are indeed imbalanced in the sense that charge delocalization into the Y-group lags behind proton transfer. In order to quantify the degree of charge imbalance for a given reaction we developed a formalism based on Equation (22)113; note that in Equation (22) B stands for
–1 + χ – χ C Y
and the full representation of the
transition state is given by 55. Equation (22) represents a further ‡ –1 + δB δH
B– + H
C
Y
B
H
–δC –δY
C
–1 + χ –χ Y + BH C
Y
(22)
refinement of Equation (9) which was a more nuanced version of Equation (3); it not only allows for a certain
–δY –δC
δH
Y
H
C
55
–δC –δY
C
Y
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
263
Table 13 Relative contraction of C–Y bond in the anion and negative charge on Y-group of aniona in the CH3Y/CH2=Y and NCCH2Y/NCCH=Y systems CH3Y/CH2=Yb Y
100 DroCY =rC Y d
CN C CH CH=CH2 CH=NH(syn) CH=NH(anti) CH=O CH=S NO2 NO þ CH=OHf,g þ NO2 Hf,h
4.10 6.69 6.86 7.11 7.14 7.64 8.94 9.18 10.8 8.26 11.3
Charge on Ye –0.356 –0.587 –0.539 –0.507 –0.548 –0.531 –0.756 –0.854 –0.866 0.086 –0.171
NCCH2Y/NCCH=Yc 100 DroCY =rC Y d
Charge on Ye
4.63
–0.232
6.16
–0.312
8.64 8.78 10.4 11.9
–0.343 –0.544 –0.654 –0.683
a
MP2/6-311þG(d,p). From Reference 118. c From Reference 140. d % reduction of C–Y bond length upon conversion of CH3Y into CH2=Y. e NPA at MP2/MP2. f Here the conjugate base is neutral. g From Reference 117. h From Reference 114. b
amount of charge delocalization at the transition state (–d Y, Equation (9)) but also takes into account that the negative charge in the anion is not necessarily completely delocalized into the Y-group (–w) and that some positive charge may develop on the proton-in-flight at the transition state (dH). The results summarized in Table 13 indicate that even for the strongest pacceptors, NO2 and NO, the charge on Y in the anion, –w, is somewhat less than –1.0 and substantially less than –1.0 for the weaker p-acceptors. Furthermore, the results reported in Table 14 show that there is in fact a substantial positive charge on the proton-in-flight in the range of 0.3 in all cases. The refinements introduced into Equation (22) require corresponding modifications to Equations (10–12), i.e., Equation (10) becomes Equation (23), Equation (11) becomes Equation (24), and Equation (12) becomes Equation (25). The negative charge d Y pb:o: ðd B þ dY Þu
ð23Þ
264
Table 14 NPA group charges in the CH3Y/CH2=Y systemsa,b CH3
CH2=Y
Differencec
CH3C N CH3(CH2) C N H (transferred)
0.041 –0.041
–0.644 –0.358
–0.685 –0.315
–0.446 –0.208 0.303
–0.487 –0.165
CH3C CH CH3(CH2) C CH H (transferred)
0.028 –0.028
–0.463 –0.537
–0.491 –0.509
–0.429 –0.219 0.296
–0.457 –0.191
CH3CH=CH2 CH3(CH2) CH=CH2 H (transferred)
0.003 –0.003
–0.461 –0.539
–0.464 –0.536
–0.376 –0.266 0.285
–0.379 –0.263
CH3CH=NH (syn) CH3(CH2) CH=NH H (transferred)
–0.013 0.013
–0.493 –0.507
–0.480 –0.520
–0.398 –0.246 0.293
–0.386 –0.261
CH3CH=NH (anti) CH3(CH2) CH=NH H (transferred)
0.004 –0.004
–0.452 –0.548
–0.456 –0.544
–0.366 –0.281 0.293
–0.370 –0.277
CH3CH=O CH3(CH2) CH=O H (transferred)
–0.021 0.021
–0.469 –0.531
–0.448 –0.522
–0.384 –0.266 0.301
–0.363 –0.287
Group
TS
Differenced
C.F. BERNASCONI
0.021 –0.021
–0.244 –0.756
–0.265 –0.785
–0.233 –0.413 0.291
–0.254 –0.392
CH3NO2 CH3(CH2) NO2 H (transferred)
0.244 –0.244
–0.146 –0.854
–0.390 –0.610
–0.093 (–0.060)g –0.535 (–0.582)g 0.253 (0.286)g
–0.337 (–0.304)g –0.291 (–0.388)g
CH3NO CH3(CH2) NO H (transferred)
0.155 –0.155
–0.134 –0.866
–0.289 –0.711
–0.082 –0.548 0.260
–0.237 –0.393
CH3CH=OHþe CH3(CH2) CH=OHþ H (transferred)
0.149 0.851
–0.086 0.086
–0.235 –0.765
–0.132 0.472 0.320
–0.281 –0.379
CH3NO2Hþf CH3(CH2) NO2Hþ H (transferred)
0.403 0.597
0.171 –0.171
–0.232 –0.768
0.172 0.207 0.240
–0.231 –0.390
a
MP2/6-311þG(d,p).
b
From Reference 118.
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
CH3CH=S CH3(CH2) CH=S H (transferred)
Difference between anion and neutral. On the Y-group this difference corresponds to w in Equations (12–14). d Difference between TS and neutral; it corresponds to –d C and –d Y in Equations (12–14), respectively. c
From Reference 120.
f
From Reference 117.
g
CH3 NOþ 2 H/CH2=NO2H system, from Reference 117.
265
e
266
C.F. BERNASCONI
pb:o: wðd C þ dY Þ
ð24Þ
d Y wðd C þ d B Þn
ð25Þ
transferred from the base to the CH2Y fragment of the transition state is now d B þ dH which is equal to d C þ dY, while the p-bond order is not only related to the transferred charge but also to the degree of charge delocalization in the anion (w). Furthermore, there is no requirement that the exponents u and v be exactly 1.0 or that n be exactly 2.0; as pointed out by Kresge,51 there may not be a strict proportionality between dY and (dC þ d Y) and hence n = u þ v may be £2 or 2. Note, however, that imbalance in the sense of delayed charge delocalization requires n > 1; this is because such an imbalance implies that the ratio of the charge on Y to the charge on C is smaller at the transition state than in the anion, i.e., dC/dY < w/1– w and this is only possible for n > 1. By the same token, n = 1 would mean that delocalization is synchronous with proton transfer. Note also that Equations (23–25) are not only valid at the transition state but at any point along the reaction coordinate, including the final products where d C þ dY = 1 and hence dY = w. Table 15 summarizes the imbalance parameters n calculated from Equation (26) which is the logarithmic version of Equation (25) solved for n. The n values range from 1.28 to 1.61 in most cases
n¼
log ðdY =wÞ log ðd C þ d Y Þ
ð26Þ
except for CH3C CH where n = 2.26.121 These numbers suggest that in the gas phase the imbalances are relatively small and substantially smaller than those estimated for proton transfers in hydroxylic solvents.3,4 Calculations by Yamataka et al. of the deprotonation of several nitroalkanes by CN122 and 123 also indicate sharply reduced imbalances. For example, the HOðH2 OÞ 2 Br½nsted aCH value for the deprotonation of substituted phenylnitromethanes is ‘‘normal,’’ i.e., < 1; this contrasts with aCH = 1.54 or 1.29 for the deprotonation of substituted phenylnitromethanes in water by HO or piperidine, respectively (Table 2). Furthermore, aCH based on a comparison between CH3NO2 and CH3CH2NO2 is also normal, i.e., aCH > 0122 rather than < 0 (‘‘nitroalkane anomaly,’’ Table 6). These results are not all that surprising in view of the absence of the strong solvational contribution to the imbalance in hydroxylic solvents discussed earlier. Table 15 includes two geometric parameters that provide complementary information about transition state imbalances. They are the % progress of the
CH3Y/CH2=Ya
Y
CN C CH CH=CH2 CH=NH(syn) CH=NH(anti) CH=O CH=O(constr)f CH=S NO2 NO2 (constr)f NO CH=OHþg h NOþ 2H a
NCCH2Y/NCCH=Yb
nc
100 ðDr‡CY =DroCY Þd
100 (Da‡/Dao)e
nc
100 (Dr‡CY =DroCY )d
100 (Da‡/Dao)e
1.51 2.26 1.61 1.58 1.55 1.52 1.10 1.42 1.59 1.33 1.28 1.69 1.42
53.3 34.7 56.3 57.0 61.7 65.2 73.8 64.2 57.7 71.5 70.0 62.8 64.9
21.2 9.0 22.6 25.8 27.6 34.1 100 41.0 26.8 100 44.0 27.6 27.2
1.94
44.1
11.1
2.14
48.4
20.0
1.99
60.2
33.0
1.85 2.06
60.9 56.9
37.7 23.1
1.67
66.1
29.4
From Reference 118. From Reference 140. c From Equation (26). d % Progress of C–Y bond contraction. e % Change in pyramidal angle. f Transition state geometry constrained to be planar with a = 0. g From Reference 120. h From Reference 117.
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
Table 15 Imbalance parameter n, progress in C–Y bond contraction and planarization of the a-carbon at the transition state in the CH3Y/CH2=Y and NCCH2Y/NCCH=Y systems
b
267
268
C.F. BERNASCONI
C–Y bond contractions and of the planarization of the a-carbon as measured by the % progress in the change of the pyramidal angle a. The pyramidal angle is defined as shown in 56 where the dashed lines are the projection
C
Y
H H
α
56
of the C–Y bond and the bisector of the HCH group, respectively; note that for a planar molecule or ion (sp2-carbon) a is zero. There is a strong inverse correlation between n and the progress in the planarization as well as the progress in the C–Y bond contraction. The relatively small Da‡/Dao values indicate substantial retention of the sp3 character of the a-carbon that is particularly pronounced for CH3C CH which has the largest n value, but still appreciable for CH3NO and CH3CH=S which have the smallest n values. þ Tables 13–15 include results for the CH3CH=OH/CH2=CHOH and þ
CH3 NO2 H/CH2=NO2H systems; the patterns relating to the C–Y bond contraction, planarization, and charge changes are quite similar to those observed for the respective neutral/anion systems. Regarding the imbalance parameter n, it is still given by Equation (26) because, even though the absolute charges on the various sites are different as shown in the reaction scheme of Equation (27), it is the charge changes during the reaction that determine the imbalance. ‡
B+H
C
+ YH
δB
δH
B
H
–δC 1–δY C
YH
–1 + χ 1 – χ YH + BH+ C
(27)
Additional insights into the reasons for the presence of transition state imbalances have come from the study of the CH3CH=O/CH2=CH–O113 117 and CH3NO2/CH2=NO systems for which the geometries of the transition 2 states were constrained to be planar, i.e., a = 0. The results are included in Table 15. The consequence of these constraints is a reduced n value and greater progress in the C–Y bond contraction. However, as will be discussed later, this greater charge delocalization does not result in a lower barrier but rather in a higher barrier. Similar conclusions were reached by Lee et al.116 and by the Saunders–Shaik group115,119 as discussed in more detail below.
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
269
More O’Ferrall–Jencks diagrams Reactions with imbalanced transition states are conveniently described by More O’Ferrall124–Jencks125 diagrams. Such a diagram is shown in Fig. 1 for the deprotonation of a nitroalkane by the general base B which, e.g., could be an amine or HO. In reactions where both the proton donor and acceptor contain the p-acceptor group Y as in Equation (21), there is a two-fold imbalance, one for the lag in the charge delocalization into the p-acceptor of the incipient product ion and one for the advanced localization of the charge from the reactant anion. This two-fold imbalance can be represented by a sixcorner diagram; such a diagram is shown in Fig. 2 for the CH3NO2/CH2= 117 Corners 1 and 4 are the reactants and products, respectively. NO 2 system. Corners 2 and 3 are hypothetical states where the respective nitromethide ions have their charge localized on the a-carbon (57), while corners 5 and 6 are hypothetical states where the nitromethane is polarized in the manner shown in 58.
– CH2
NO2
+ HCH2
57
RCH
H+-transfer
NO–2 + BHν + 1
Delocalization
NO–2
58
Delocalization
H+ Bν + RCH
– NO2
‡
Bν + RCH2NO2
H+-transfer
–
RCHNO2 + BHν + 1
Fig. 1 More O’Ferrall–Jencks diagram for the deprotonation of a nitroalkane. The curved line shows the reaction coordinate with charge delocalization lagging behind proton transfer.
270
C.F. BERNASCONI NO– 2
CH2 CH3
NO2 4C ) t ha c rg du
ne
pro
es
hif
a eth
t (n
m itro
+ HCH2 CH2
ion
6 – NO2 C ha rge NO –
sh
ift
pro
du
g
ar – NO2 Ch 5
2
te
(ni
ate
tro
me
tha
ne
cta
nt)
CH3 CH2
s rge
NO2
2 3 nt) CH – a t c CH2 rea
NO2 NO2
n itro
t (n
hif
rea
ion
NO2
3
TS (optim)
• •
– ct) CH 2 3 CH
Proton transfer
es
TS (constr)
2
na
hi
Proton transfer
CH2 + HCH2
NO–
itro
n ft (
a
1
Ch
NO2
NO2–
Fig. 2 Modified More O’Ferrall–Jencks diagram for the CH3NO2/CH2=NO 2 system. The curved lines represent the reaction coordinates through the optimized and constrained transition state, respectively. The constrained transition state is less imbalanced as indicated by its location to the left of the optimized transition state.
Calculations suggest that corners 5 and 6 are 34.3 kcal mol1 above the level of the reactant/product corners while corners 2 and 3 are about 9.4 kcal mol1 above the reactant/product corners.117 This indicates that the energy surface defined by the diagram exhibits a strong downward tilt from left to right, suggesting that the reaction coordinate and transition state should be located in the right half of the diagram. This is consistent with the observed imbalance according to which charge shift from the nitro group toward the carbon of the reactant nitromethide anion is ahead of proton transfer and the charge shift from the carbon to the nitro group in the incipient product nitromethide anion
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
271
lags behind proton transfer. We also note that the smaller imbalance observed for the reaction through the geometrically constrained (a = 0) transition state (Table 15) requires placement of this transition state to the left of the optimized transition state, but still in the right half of the diagram; this move to the left is also in the direction of increased energy, consistent with the higher energy calculated for the constrained transition state (see below). The features and conclusions from Fig. 2 are very similar to those obtained from a similar diagram for the CH3–CH=O/CH2=CHO system,113 including the left-to-right downward tilt of the surface and the relative placement of TS(optim) and TS(constr) within the right half of the diagram. Valence bond analysis of the imbalance The Shaik–Pross valence bond (VB) configuration-mixing model mentioned earlier has been further developed and applied to Equation (21) with Y = CH=CH2115,119 and CH=O.115 Specifically, the relative importance of the various contributing VB structures to the optimized transition state structure was determined by the self-consistent field valence bond (VBSCF) method and the effect on the energy evaluated. The calculated VB structures are shown in Chart 2. The numbers in parentheses are the relative weights contributed to the transition state structure by each VB structure: the first numbers refer to X = CH2, the second to X = O. These weights were calculated by the ‘‘localized valence bond method’’ (LVB)115; the authors also calculated weights by the
X
CH
CH2
– H :CH2
CH
X
X
– CH CH2: H
φ1 (0.187, 0.151)
X
CH
CH2
H CH2
CH2
CH
X
φ3 (0.187, 0.151)
CH
X:–
–:X
CH
CH2 H
CH2
CH
X
CH
X
φ4 (0.049, 0.118)
φ2 (0.049, 0.118)
X
CH
+ – – CH2: H :CH2
CH
X
φ5 (0.402, 0.540) X
CH
+ – CH2: H CH2
CH
X:–
–:X
CH
φ7 (0.059, 0.102)
φ6 (0.059, 0.102) –:X
CH
+ CH2 H CH2
CH
φ8 (0.006, 0.029)
Chart 2
+ – CH2 H :CH2
X:–
272
C.F. BERNASCONI
‘‘delocalized valence bond method’’ (DVB).115 The main conclusion, irrespective of which method was used, is that the triple ion structure f5 is dominant which is in full agreement with the computational results summarized in Table 14. Why are carbon-to-carbon proton transfers slow? Costentin/Sav eant analysis Applying DFT and QCISD methodology, Costentin and SavO˜ant126 have analyzed Equation (21) with Y=H, CH=CH2, NO2, and CH2=CH–NO2 using a different theoretical framework in order to answer the question: why are carbon-to-carbon proton transfers slow? A major difference in their approach is that their description of the reaction coordinate only requires consideration of the distance, Q, between the two fragments CH2Y and the intramolecular reorganization (i.e., delocalization)127 that occurs during the proton transfer, but not the distance, q, that defines the location of the proton as it moves along the reaction coordinate (Scheme 1). In other words, the dynamics of the reaction is entirely governed by the heavy atom reorganization although tunneling needs to be considered as well. The major conclusions emerging from this analysis are as follows. For the carbon-to-carbon proton transfer, the rate of the reaction depends on the intramolecular reorganization127 and the characteristics of the barrier through which the proton tunnels. The relative slowness of the proton transfer in a non-activated carbon system such as CH4/CH 3 is the result of a larger distance (Q) between the carbon centers compared to that between nitrogen or oxygen in the H2O/HO or NHþ 4 /NH3 systems. In the presence of an electronwithdrawing substituent such as a nitro group, there is an increase in the C– H bond polarity which leads to a decrease in barriers but this decrease is attenuated by the imbalance in the internal reorganization (charge localization-delocalization) which occurs during the proton transfer. The conclusions reached by Costentin and SavO˜ant are in fact quite consistent with our own. The main difference is that, according to these authors, ‘‘the notion of an imbalanced transition state should be placed within the context of charge localization-delocalization heavy-atom intramolecular reorganization rather than of synchronization (or lack thereof) between charge delocalization and proton transfer.’’
Q YCH2
H q
Scheme 1
CH2Y
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
273
Gas phase acidities and reaction barriers Table 16 provides a summary of the enthalpic gas phase acidities (DHo) and enthalpic reaction barriers (DH‡) for the reactions of Equation (21).117,118,120 The table includes data for the CH4/CH 3 reference system. Broadly speaking, the acidities mainly reflect the resonance stabilization of the anion, although the field effect of the Y-group adds significantly to the stabilization of the anion and, for Y = CN, it is the dominant factor. An attempt to quantify the relative contributions of the resonance and field effects as well as the potential role played by the polarizability of the Y-group was made by correlating DDHo = DHo(CH3Y) – DHo(CH4) with the gas phase substituent constants71 sF (field effect), sR (resonance effect), and sa (polarizability effect) according to the Taft128 Equation (28). DDH o ¼ roF sF þ roR sR þ roa sa
ð28Þ
The least squares correlation is shown in Fig. 3 for those systems for which sF, sR, and sa were available; the correlation was excellent (r2 = 0.992) and yielded roF = –43.0, roR = –192.5, and roa = –4.64 (Table 17). The ro values confirm the dominance of the resonance effect for most cases as well as the significant contribution of the field effect. They also suggest that the Table 16 Gas phase acidities of CH3Y and NCCH2Y (DHo) and reaction barriers (DH‡)a Y
H CH=CH2 C CH CH=NH (anti) CH=NH (syn) CN CH=O NO2 NO CH=S CH= OHþ NOþ 2H
CH3Y/CH2=Yb DHo
DH‡
DHo
DH‡
418.1 390.2 385.9 379.8 376.1 375.4 367.2 359.0 351.9 348.7 195.0 192.6
8.1 4.7 1.8 2.9 0.3 –8.5 –0.3 (1.5)d,e –6.2 (9.8)d,f –1.1 0.3 –5.1 –1.0
375.4 354.9
–8.5 –10.6
336.3 335.5 328.3 322.5 322.1
–14.3 –8.4 –16.3 –4.7 –7.0
In kcal mol1. From Reference 118. c From Reference 140. d Geometrically constrained transition state. e From Reference 113. f From Reference 117. a
b
NCCH2Y/ NCCH=Yc
274
C.F. BERNASCONI 430 420
CH4
410
ΔHo, kcal mol–1
400 390
CH3CH = CH2
380 CH3CN
370
CH3CH = O
360
CH3NO2 CH3NO
350 340 0
10
20 30 40 50 60 –43.0σF – 192.5σR – 4.64σα
70
80
Fig. 3 Plot of DHo according to Equation (28) for the acidities of CH3Y. Table 17 Analysis of acidities and barriers by means of Taft equations CH3Y/CH2=Ya
NCCH2Y/NCCH=Yb
DDHo roF roR roa
–43.0 –192.5 –4.64
–41.1 –135 0.54
DDH‡ r‡F r‡R r‡a
–22.6 9.81 7.59
–7.01 36.6 11.9
r
a b
From Reference 118. From Reference 140.
polarizability effect is almost negligible which is perhaps surprising in view of its potential importance for certain gas phase anions.129,130 The small role played by polarizability in the present systems suggests that its effect is greatly diminished when the ionic charge mainly resides on the Y-group rather than the neighboring CH2 group, as is the case for all present anions except for CH2CN. In fact, because the sa values are defined as negative numbers,128
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
275
the slightly negative roa value suggests a small anion destabilizing effect; however, in view of the smallness of the effect, not much significance should be attached to this finding. A possible interpretation of the negative roa value is that it could result from a slight stabilization of the neutral CH3Y. A clearer indication of the absolute and relative contributions of field, resonance, and polarizability effects to the acidity of the various compounds can be obtained by calculating the individual roF sF, roR sR, and roa sa terms for each acid rather than just focusing on the roF , roR , and roa values, respectively. These terms are summarized in Table 18; for the compounds with Y-groups with unknown substituent constants (Y = C CH, CH=NH, and CH=S), these terms were calculated based on approximate substituent constants estimated as described in reference 118. The information in Table 18 is quite revealing. For example, the resonance contribution amounts to about –63 kcal mol1 for CH3CH=S, –50 kcal mol1 for CH3NO, is in the range of –26 to –36 kcal mol1 for CH3CH=CH2, CH3C CH, CH3CH=NH, CH3CH=O, and CH3NO2, and a mere –19 kcal mol1 for CH3CN. On the other hand, the field effect contribution for CH3CN (–26 kcal mol1) is larger than for any of the other compounds except for CH3NO2 (–27 kcal mol1), and for CH3C CH (–6 kcal mol1) and CH3CH=CH2 (–2.6 kcal mol1) it is very small to almost negligible. The polarizability effect, if there is any significance to it at all, is seen to lower the acidities by a mere 2.1–3.4 kcal mol1 for CH3CH=CH2, CH3CN, and CH3CH=O, and even less (1.2 kcal mol1) for CH3NO2 and CH3NO. Turning to the barriers we note that they are defined as the difference in enthalpy between the transition state and the separated reactants. This is important because in gas-phase ion-molecule reactions the transition state is typically preceded by an ion–dipole complex131–133 formed between the reactants, and the term ‘‘barrier’’ is sometimes used for the enthalpy difference between the transition state and the ion–dipole complex. However, these ion– dipole complexes have little relevance to the main topic discussed in this chapter and hence the chosen definition of DH‡ is more appropriate. For reasons explained elsewhere,118 the barriers reported in Table 16 have not been corrected for the basis set superposition error (BSSE),134 although such corrected values are available.118 The barriers for all CH3Y/CH2=Y systems are lower than for the CH4/ CH 3 system. This means that the stabilization of the transition states by the Ygroup is greater than that of the respective anions. The situation is illustrated in Fig. 4 for the case of CH3NO2; it shows that the transition state for the CH3NO2 reaction is more stable than the transition state for the methane reaction by 73.3 kcal mol1 while CH2=NO 2 is more stable than CH3 by only 1 59.1 kcal mol . The greater stabilization of the transition state compared to that of the anion may be attributed to the fact that, because the proton in flight is positively charged, each CH2Y fragment carries more than half a negative
276 Table 18 Dissection of the contribution of field, resonance, and polarizability effects to DHo and DH‡ in the CH3Y/CH2=Y systemsa CH3Y
sF
sR
sa
DDHo [Equation (28)] roF sF
roR sR
DHo
b
DDH‡ [Equation (29)] r‡F sF,
roa sa
r‡R sR
DH‡
b
r‡a sa
CH4 CH3CH=CH2 CH3CN CH3CH=O CH3NO2 CH3NO
Y-groups with 0 0 0.06 0.16 0.60 0.10 0.31 0.19 0.65 0.18 0.41 0.26
known sF, sR, and sa values 0 0 0 0 –0.50 –2.6 –30.8 2.3 –0.46 –25.8 –19.2 2.1 –0.46 –13.3 –36.6 2.1 –0.26 –27.9 –34.6 1.2 –0.25 –17.6 –50.0 1.2
418.1 390.2 375.4 367.2 359.0 351.9
(418.6) (387.5) (375.7) (370.8) (357.2) (352.1)
0 –1.4 –13.6 –7.0 –14.7 –9.3
0 1.6 1.0 1.9 1.8 2.6
0 –3.8 –3.5 –3.5 –2.0 –1.9
8.05 (8.08) 4.65 (4.50) –8.46 (–7.98) –0.31 (–0.55) –6.15 (–6.81) –1.06 (–0.53)
CH3C CH CH3CH=NH(syn) CH3CH=NH(anti) CH3CH=S
Y-groups with 0.14 0.15 0.27 0.17 0.20 0.17 0.22 0.33
estimated sF, sR, –0.40 –6.0 –0.45 –11.6 –0.40 –8.6 –0.75 –9.5
and sa valuesc –28.9 1.8 –32.7 2.1 –32.7 1.8 –63.5 3.4
385.9 376.1 379.8 347.7
(385.5) (376.4) (379.1) (349.0)
–3.2 –6.1 –4.5 –5.0
1.5 1.7 1.7 3.2
–3.0 –3.4 –3.0 –5.7
1.75 0.30 2.90 0.32
(3.36) (0.28) (2.28) (0.58)
From Reference 118, in kcal mol1. Number in parentheses from correlation according to Equation (28) (DHo) with DDHo = –43.0sF – 192.5sR – 4.60sa or Equation (29) (DH‡) with DDH‡ = –22.6sF – 9.81sR þ 7.59sa, respectively. c sF, sR, and sa estimated as described in Reference 118. a
C.F. BERNASCONI
b
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
(H3C
277
CH3)–
H
8.0 CH4 + CH3–
–59.1
CH2NO2 + CH2
–73.3
–
NO2
–6.2 (O2NCH2
H
CH2NO2)–
Fig. 4 Stabilization of CH2=NO 2 relative to CH3 and stabilization of the transition reaction relative to the transition state of the CH4/ state of the CH3NO2/CH2=NO 2 CH 3 reaction.
charge (Table 14). This leads to a stronger substituent effect on the transition state than on the anion that results from the interaction of the Y-group with the negative charges. It also provides additional stabilization by electrostatic/ hydrogen bonding effects between the proton in flight and the negative CH2Y fragments.135 This latter effect is consistent with Gronert’s139 findings of an inverse correlation between transition state energy and charge on the transferred proton in identity proton transfers of nonmetal hydrides. The importance of electrostatic/hydrogen bonding effects can also be seen by comparing the barrier of the reactions going through the geometrically constrained transition state with that going through the optimized transition state for the CH3NO2/CH2=NO 2 and CH3CH=O/CH2=CH–O systems. In the former system the barrier going through TS(constr) is 16.8 kcal mol1 higher than going through TS(optim), while for the CH3CH=O/CH2=CH– O system the difference is 10.5 kcal mol1 (Table 16). Using the VB approach mentioned earlier, Harris et al.119 calculated a 8.2 kcal mol1 higher energy for the delocalized transition state relative to that of the optimized structure in the
278
C.F. BERNASCONI
CH3CH=O/CH2=CH–O system. The higher energy of TS(constr), despite the larger resonance effect, probably results mainly from the fact that the product of the positive charge on the proton-in-flight and the negative charge on the CH2Y fragments is smaller for TS(constr) than for TS(optim) (Table 14) which greatly reduces the electrostatic/hydrogen bonding stabilization. Furthermore, to the extent that more resonance delocalization into the Ygroup occurs, the field effect of Y is reduced. The barriers for the CH3CH=OHþ /CH2=CHOH and CH3 NOþ 2 H/ CH2=NO2H systems fall within the same general range as for the other systems. This seems surprising since the much higher carbon acidities of CH3CH=OHþ and CH3 NOþ 2 H might have been expected to lead to much lower barriers. The most important reason for the higher than expected barriers is likely to be the absence of the stabilizing electrostatic and hydrogen bonding effects found in the CH3Y/CH2=Y systems that arise from the interaction of the positively charged proton-in-flight with the negative CH2 groups and/or the entire CH3Y fragments at the transition state. In the CH3 YHþ /CH2=YH systems, the electrostatic stabilization is not only lost but even replaced by a destabilization since the CH2YH fragments in the transition state are positively charged and this is expected to lead to a substantial increase in the barrier. Further insights were obtained by analyzing the relative contributions of field, resonance, and polarizability effects to the barriers in a similar way as for the acidities, i.e., by correlating DDH‡ = DH‡(CH3Y) – DH‡(CH4) with the respective Taft substituent constants according to Equation (29). The correlation is shown in Fig. 5; it yielded r‡F = –22.6, r‡R = 9.81 and r‡a = 7.59 with DDH ‡ ¼ r‡F sF þ r‡R sR þ r‡a sa
ð29Þ
r2 = 0.995 (Table 17). The r‡ values indicate that the field and polarizability effects lower the barriers while the resonance effect increases the barriers. The individual r‡F sF, r‡R sR, and r‡a sa terms which allow a detailed assessment of the relative contribution of the various effects to the barriers for each system are included in Table 18. The following conclusions emerge. 1. For all systems except CH3CH=CH2 and CH3CH=S, the field effect is dominant and lowers the barrier by substantial amounts (–7.0 to –14.7 kcal mol1). The barrier-lowering effect results from the fact that the transition state stabilization corresponds to roF sF þ r‡F sF, i.e., the field effect on the transition state is (roF þ r‡F )/roF = (–43.0 – 22.6)/ (–43.0) = 1.52-fold stronger than on the anion. 2. The polarizability effect contributes –1.9 to –5.7 kcal mol1 to the lowering of the barrier. For most cases this is a minor contribution compared to that of the field effect; for CH3C CH and CH3CH=S it is comparable to the
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
279
10 CH4
8 6
CH3CH = CH2
ΔH ‡ , kcal mol–1
4 2 0 CH3NO
CH3CH = O
–2 –4 –6
CH3NO2
–8
CH3CN
–10 –5
0
5 10 –22.6σF + 9.81σR + 7.59σα
15
20
Fig. 5 Plot of DH‡ according to Equation (29) for the CH3Y/CH2=Y systems.
field effect while for CH3CH=CH2 it is the dominant factor. The lowering of the barrier by the polarizability effect comes about because the stabilization of the transition state, which is given by roa sa þ r‡a sa, more than offsets the destabilization of the anion ( roa = –4.6, r‡a = 7.59). The fact that the transition states, which have less charge on the Y-group than the anions, are stabilized but that the anions are destabilized (or hardly affected) supports our conclusion mentioned above that the polarizability effect is greatly reduced when the Y-group carries a large negative charge. Because even for the transition states there is a significant charge on the Ygroup, the polarizability effect on their stability is still rather modest. This contrasts with the reactions of the type ZCH3 þ ZCH 2 ! ZCH2 þ ZCH3 with Z = F, Cl, Br, OH, SH where the polarizability of Z has a strong barrier-reducing effect.130 3. The resonance effect increases the barriers by 1.0 to 3.2 kcal mol1. The reason for this small increase is that the resonance stabilization of the transition state which is given by roR sR þ r‡R sR is only ( roR þ r‡R )/ roR = (–192.5 þ 9.81)/(–192.5) = 0.95 as strong as that of the anion. Note that the rather modest barrier-enhancing effect of resonance is consistent with the rather small transition state imbalances (Table 15).
280
C.F. BERNASCONI
THE NCCH2Y/NCCH=Y SYSTEMS
The reactions of Equation (30) show many similarities with those of Equation (21) but there are also important Y CH2 CNþNCCH ¼ Y Ð Y ¼ CHCNþNCCH2 Y
ð30Þ
differences resulting from the strong electron-withdrawing effect of the cyano group. The specific systems studied include Y = CN, CH=CH2, CH=O, NO2, NO, and CH=S.140 The changes in the C–Y bond lengths that result from the ionization of NCCH2Y are summarized in Table 13. They are very similar to those for the ionization of CH3Y. On the other hand, the anionic charges on the Y-groups of NCCH=Y are significantly smaller than for CH2=Y (Table 13). This is because part of the charge is delocalized into the cyano group; this latter charge varies from –0.175 to –0.267 depending on Y. The transition states for the NCCH2Y/NCCH=Y systems are more imbalanced than those of the respective CH3Y/CH2=Y systems. This is seen both in the geometric parameters and the n values summarized in Table 15. In each case the C–Y contraction and planarization of the a-carbon at the transition state is less advanced than for the respective CH3Y/CH2=Y systems while n is larger, indicating a greater lag in charge delocalization in the NCCH2Y/ NCCH=Y systems. The larger imbalance has been attributed to the strong field effect of the cyano group which, because of its proximity to the a-carbon, strongly stabilizes the negative charge on that carbon. This allows for a greater accumulation of the negative charge on the a-carbon of the transition state in the NCCH2Y/NCCH=Y systems than in the CH3Y/CH2=Y systems. As was observed for the CH3Y/CH2=Y systems, the proton that is being transferred carries a significant positive charge. For the NCCH2Y/ NCCH=Y systems this charge is about 0.30 0.03, slightly larger than the 0.275 0.025 charge for the CH3Y/CH2=Y systems (Table 14). The slightly larger positive charge in the NCCH2Y/NCCH=Y systems may be related to the larger negative charges on the NCCHY fragments and provide greater electrostatic stabilization of the transition state, a point to be elaborated upon when discussing the barriers. The acidities of NCCH2Y and barriers of the NCCH2Y/NCCH=Y systems are summarized in Table 16. As expected, the acidities of NCCH2Y are substantially higher than those of CH3Y since the respective anions are strongly stabilized by the cyano group. The acidifying effect of the cyano group decreases as the p-acceptor strength of the Y-group increases. Analysis of the acidities according to Equation (31) affords roF = –41.1, roR = –135.0, and DDH o ¼ DH o ðNCCH2 YÞ DH o ðNCCH3 Þ ¼ roF sF þ roR sR þ roa sa
ð31Þ
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
281
roa = 0.54 (Table 17). The roF and roa values are very similar to those observed for CH3Y but roR is substantially smaller compared to that for CH3Y. This means that the presence of the cyano group mainly reduces the resonance contribution of Y to the stabilization of the anion but not the contribution by the field and polarizability effects. The reduced roR value is consistent with the reduced charge on the Y-group (Table 13). Regarding the barriers, the cyano group leads to a substantial reduction in all cases, with the largest effect being on those CH3Y/CH2=Y systems with a relatively high barrier. This barrier reduction indicates that the electronwithdrawing effect of the cyano group stabilizes the transition state to a greater extent than the anion which is consistent with the larger transition state imbalance. This effect is reminiscent of the influence of electronwithdrawing substituents on DG‡o in solution phase reactions discussed in the section on ‘‘Polar effect of adjacent substituents.’’ Of particular interest is a comparison of the relative contributions of field, resonance, and polarizability effects to the barriers for the NCCH2Y/ NCCH=Y systems relative to those for the CH3Y/CH2=Y systems. These relative contributions were obtained from the correlation according to Equation (32) which yields r‡F = –7.01, r‡R = 36.6, and r‡a = 11.9 (Table 17). These
DDH ‡ ¼ DH ‡ ðNCCH2 YÞ DH ‡ ðNCCH3 Þ ¼ r‡F sF þ r‡R sR þ r‡a sa
ð32Þ
numbers show the same qualitative pattern as for the CH3Y/CH2=Y systems, i.e., the field and polarizability effects lower the barriers while the resonance effect increases the barriers. But there are major quantitative differences. The field effect is much smaller than for the CH3Y/CH2=Y systems. This is because the cyano group takes over much of the role played by the field effect of the Y-groups. The barrier enhancement by the resonance effect is much greater than in the CH3Y/CH2=Y systems. As stated before, a positive r‡R value does not mean that the transition state is destabilized by the resonance effect; it only means that the resonance stabilization of the transition state is weaker than that of the anion. In quantitative terms, transition state resonance stabilization is given by roR sR þ r‡R sR which yields (roR sR þ r‡R sR)/roR sR = (roR þ r‡R )/ roR = (–135 þ 36.6)/(–135) = 0.73 as the fraction of transition state stabilization relative to resonance stabilization of the anion. This compares with (roR þ r‡R )/ roR = 0.95 for the CH3Y/CH2=Y systems. The smaller resonance stabilization of the transition state in the NCCH2Y/NCCH=Y systems is a direct consequence of the larger imbalance.
282
C.F. BERNASCONI
AROMATIC AND ANTI-AROMATIC SYSTEMS
In keeping with the advantages of examining identity reactions, a number of identity proton transfers involving aromatic systems were subjected to ab initio calculations. The first study involved the highly aromatic benzene and cyclopentadienyl systems, Equations (33a) and (34a).141
H
H
H
+
+
+
+
H
(33a)
+
+
+
+
(33b)
+
–
–
+
(34a) H
H
H
+
–
–
+
H
(34b)
Calculations at the MP2/6-311þG(d,p) level showed a significantly lower ‡ DH‡ for the more aromatic C6 Hþ 7 /C6H6 system (Equation (33a), DH = –7.6 1 kcal mol ) compared to the less aromatic C5H6/C5 H5 system (Equation (34a), DH‡ = 2.2 kcal mol1). A substantial lowering of the intrinsic barrier due to aromaticity was also deduced from a comparison between the DH‡ values for the aromatic systems and those for the corresponding noncyclic reference systems, i.e., 33a versus 33b, and 34a versus 34b. The numerical results of these calculations are summarized in Table 19. These results imply a disproportionately large aromaticity development at the transition state,
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
283
Table 19 Barriers (DH‡) of reactions 34a, 34b, 35a, 35b, 36a, and 36b and aromatic stabilization energies (ASE) in the gas phasea System
Equations
C6 Hþ 7 =C6 H6 +
C5 H6 =C5 H 5 –
C4 Hþ 5 =C4 H4 +
ASE (kcal mol1)
DH‡b (kcal mol1)
DDH‡c,d (kcal mol1)
33a 33b
–36.3
–7.6 3.5
–11.1
34a 34b
–29.4
2.2 9.8
–7.6
35a 35b
38.9
3.6 –2.4
6.0
a
At MP2/6-311þG**, Reference 141. Corrected for BSSE. c DDH‡ = DH‡(cyclic) – DH‡(noncyclic). b
i.e., the sum of the aromatic stabilization energies (ASEs) of the two halves of the transition state is greater than the ASEs of the respective aromatic reactant/product. This is illustrated by the schematic energy profiles shown in Fig. 6 for reactions 33a/33b (a) and 34a/34b (b), respectively. The arrows pointing down represent the aromatic stabilization energies of the reactants (ASER), products (ASEP), and the transition state (ASETS), respectively. The greater than 50% aromaticity in both halves of the transition state is reflected in the fact that |ASETS| > |ASER| = |ASEP|. The conclusions based on energy calculations are supported by the calculation of aromaticity indices such as HOMA142,143 and NICS(1)144,145 values as well as the pyramidal angle of the transition state. The pyramidal angle, a, is defined as illustrated for the benzenium ion (59) and the transition state (60) for reaction 33a (B = benzene); this angle is 0 in the aromatic species.
B H
H α α
α H
H 59
60
The various indices are summarized in Table 20; they show that the change in these indices in going from reactants to the transition state is significantly greater than 50%.
284
C.F. BERNASCONI
(A)
+
+
+
+
ASEP
ASER HH
HH
ASETS +
+
+
+
(B) –
+
–
+
HH
HH +
–
ASER
ASETS
ASEP
–
+
(C) HH +
ASER +
+
HH
STRAIN
+
+
+
ASEP ASETS
+
+
Fig. 6 Reaction energy profile for reactions 34a/34b (A), 35a/35b (B), and 36a/36b (C). (A) and (B): Aromatic stabilization of the transition state is greater than that of benzene or cyclopentadienyl anion, respectively. (C): Anti-aromatic destabilization (positive ASE) of the transition state is less than that of cyclobutadiene; the high barrier results from the additional contribution by angular and torsional strain at the transition state.
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
285
Table 20 Aromaticity indices for the reactions of Equations (34a), (35a), and (36a)a HOMA C6 Hþ 7 TS C6H6 % Progress at TSb C5H6 TS C5 H 5 % Progress at TSb C4 Hþ 5 TS C4H4 % Progress at TSb a b
NICS(1)
Equation (34a) 0.415 0.874 0.963 83.8 Equation (35a) –0.791 0.560 0.739 88.3 Equation (36a) –0.99 –0.156 –3.55 22.3
–6.05 –9.26 –10.20 77.3 –0.517 –8.33 –9.36 75.4 –13.69 –12.64 18.11 3.30
a 50.1 11.5 0.0 71.0 53.5 21.9 0.0 59.0 60.5 52.2 0.0 13.7
At MP2/6-311þG**, Reference 141. [Index(TS) – Index(Reactant)]/[Index(Product) – Index(Reactant)] 100.
A reaction of particular interest is that of Equation (35a) because it involves an anti-aromatic system. The barriers for Equation (35a) and its noncyclic reference system [Equation (35b)] are included in H
H
+
+
H +
+
H +
(35a)
+
+
+
(35b)
Table 19 while the corresponding aromaticity indices are included in Table 20. The HOMA, NICS(1), and a values all indicate a very small degree of antiaromaticity development at the transition state.146 Since the transition states for Equations (33a) and (34a) are able to benefit from the stabilization conferred by the strong development of aromaticity it seems reasonable that in Equation (35a) the transition state should be able to avoid much of the destabilization that arises from anti-aromaticity, i.e., keeping the development of anti-aromaticity lagging behind proton transfer. Hence, according to the PNS, the barrier should be lowered by this effect. However, DH‡ for Equation
286
C.F. BERNASCONI
(35a) was calculated to be higher than for Equation (35b) (Table 19) which seems inconsistent with the above conclusions unless the barrier-lowering PNS effect is masked and overshadowed by other factors. As discussed in more detail elsewhere,141 angle and torsional strains at the transition state are in fact believed to be responsible for the higher than expected barrier, i.e., in the absence of these strains the barrier would indeed be lower than for Equation (35b). This is illustrated in Fig. 6, part (C). Another study involved the identity reactions shown in Equation (36).147 Calculations at the O–
O
O–
+
O
+
(36) X
X
X
X
61H-O (X = O)
61–-O (X = O)
61–-O (X = O)
61H-O (X = O)
61H-S (X = S)
61–-S
61–-S
61H-S (X = S)
(X = S)
(X = S)
MP2/6-31þG** level yielded a DH‡ for X = S that is lower than for X = O. It was also found that DH‡ for the reactions of Equation (36) was lower than for the corresponding noncyclic reference systems of Equation (37). The results are summarized in Table 21. Furthermore, the intrinsic barrier for O–
O CH2
CH
C
CH2XCH3 + CH2
CH
C
62H-O (X = O)
62–-O (X = O)
62H-S (X = S)
62–-S (X = S)
CHXCH3
(37) O– CH2 62–-O
CH
(X = O) 62–-S (X = S)
C
O CHXCH3 + CH2
CH
C
CH2XCH3
62H-O (X = O) 62H-S (X = S)
the deprotonation of 61H-S by CN is lower than for the deprotonation of 61H-O by the same base. All these results indicate that aromaticity lowers the intrinsic barrier and increasingly so with increasing aromaticity. Further evidence showing disproportionately high transition state aromaticity comes form NICS values,144,145 Bird indices,148,149 and HOMA142,143
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
287
Table 21 Barriers of reactions 37 and 38 in the gas phasea System
DH‡ (kcal mol1)
DDH‡b (kcal mol1)
3.6 5.4 2.3 4.3
–1.8
61H-O/61-O 62H-O/62-O 61H-S/61-S 62H-S/62-S a b
–2.0
At MP2/6-31þG**, Reference 147. DDH‡ = DH‡(cyclic) – DH‡(noncyclic).
Table 22 Aromaticity indices for the identity proton transfers of Equation (36)a Species
HOMA
Bird index
NICS(–1)
61H-O TS 61-O % Progress at TSb 61H-S TS 61-S % Progress at TSb
–0.686 0.217 0.544 73.4 –0.854 0.231 0.566 76.4
22.68 36.65 40.28 80.0 31.31 53.19 64.20 66.5
–2.47 –5.46 –6.74 69.9 –2.45 –5.37 –7.33 59.8
a b
At MP2/6-31þG**, Reference 147. [Index(TS) – Index(Reactant)]/[Index(Product) – Index(Reactant)] 100.
values as indicators of aromaticity. These aromaticity indices are summarized in Table 22 for the identity reactions [Equation (36)]. As was the case for reactions 33a and 34a, the progress in the development of aromaticity at the transition state is greater than 50%. NICS, HOMA, and Bird indices were also calculated for the transition states of the reactions of 61H-O and 61H-S with a series of carbanions. The results are reported in Table 23. The trends in these parameters show a clear increase as the transition state becomes more product-like with increasing endothermicity, indicating an increase in transition state aromaticity. Even more revealing is the % progress at the transition state which indicates that this progress is >50% not only for the endothermic reactions (product-like transition states) but even for most of the exothermic reactions (reactant-like transition states) except those with strongly negative DHo values. Additional confirmation of early development of aromaticity as the reaction progresses comes from plots of NICS values and Bird indices versus the reaction coordinate for the reaction of 61H-S with CH2 NO (Figs. 7 and 8), and of 61H-O with CH2 NO2 (figures not shown). These reactions were chosen
288
Table 23 Transition state aromaticity indices for the reactions of 61H-O and 61H-S with carbanions in the gas phasea % progress at TS 1
o
DH (kcal mol )
HOMA
Bird index
NICS(–1)
HOMA
Bird index
61H-Ob CH2CN CH2CO2H CH2COCH3 CH2CHO CH2NO2 CH3 CHNO2 CH(CN)2
–19.8 –14.3 –13.0 –10.4 –1.2 –0.9 19.8
–0.097 0.083 0.105 0.132 0.115 0.126 0.245
28.99 32.58 32.81 34.04 33.34 34.04 33.89
–3.98 –4.70 –4.64 –4.99 –4.92 –4.76 –5.04
47.9 62.6 64.4 66.6 65.2 66.1 75.8
–0.097 0.083 57.6 64.6 60.6 64.6 63.7
33.3 52.1 50.7 59.0 57.3 53.5 60.2
61H-Sc CH2CN CH2CHO CH2NO2 CH2NO CH2CHS CH(CN)2 CH(NO2)2
–26.5 –17.1 –7.9 –0.3 1.3 13.1 24.7
–0.188 0.062 0.082 0.248 0.196 0.l36 0.236
42.66 48.19 48.91 54.17 53.79 51.31 53.08
–3.71 –4.69 –4.92 –5.43 –5.55 –5.03 –5.42
46.3 64.5 65.9 77.6 71.2 73.9 76.7
33.9 51.3 53.5 69.5 68.3 60.8 66.2
25.9 46.0 50.7 61.0 63.6 52.9 60.8
RCHY
At MP2/6-31þG**, Reference 147. 61H-O/61-O: HOMA – 0.686/0.544, Bird index 22.68/40.28, NICS(–1) – 2.47/–6.74. c 61H-S/61-S: HOMA – 0.854/0.566, Bird index 31.31/64.20, NICS(–1) – 2.45/–7.33. b
C.F. BERNASCONI
a
NICS(–1)
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
289
0 NICS(0)
–2
NICS(–1)
NICS value
–4
–6
–8
–10
–12 –2.0
–1.5 –1.0 –0.5
0.0
0.5
1.0
1.5
2.0
2.5
Reaction coordinate (amu½ Bohr)
Fig. 7 Plots of NICS(0) and NICS(–1) versus IRC for the reaction of 61H-S with CH2 NO.
70 65
Bird Index
60 55 40 35 30 25 20 –2.0
–1.5
–1.0
–0.5
0.0
0.5
1.0
1.5
2.0
2.5
Reaction coordinate (amu½ Bohr)
Fig. 8 Plot of the Bird index versus IRC for the reaction of 61H-S with –CH2NO.
290
C.F. BERNASCONI
because they are nearly thermoneutral (see Table 23) and have fairly symmetrical transition states as indicated by the C- --H- --B bond lengths.147 The plots show a steep rise in aromaticity as a function of the reaction coordinate as the transition state is reached and a pronounced leveling off toward the value of the anionic product once the transition state has been traversed. As indicated in Table 23, the % progress in the development of product aromaticity at the transition state of the reaction of 61H-O with CH2 NO2 is 57.3 for NICS(–1) and 60.6 for the Bird index, while for the reaction of 61H-S with CH2 NO these percentages are 61.0 and 69.5, respectively. Decoupling of aromaticity development from charge delocalization In solution phase reactions such as Equation (1) as well as in the gas phase reactions of Equation (21) charge delocalization always lags behind proton transfer at the transition state. For the solution phase reactions this feature not only manifests itself in enhanced intrinsic barriers but also in the Br½nsted coefficients. For the gas phase reactions this lag can be deduced from calculated NPA charges. An interesting question is whether in systems such as Equation (33a), (34a), or (36) the early development of aromaticity would induce charge delocalization to do the same rather than to follow the typical pattern of delayed charge delocalization found in non-aromatic systems. NPA charges for some representative systems are shown in Chart 3. They indicate that negative charge is being created at the reaction site of the transition state which then either disappears (C6 Hþ 7 /C6H6 system) or decreases (C5H6/C5 H5 system) due to delocalization in the product. This implies that, in terms of
H
H
0.095
H
0.905
H
0.001
Chart 3
H –0.001
0.428 H –0.154
0.440
0.000
0.000 0.376 H
–0.200
H –0.275
–0.413
–0.800
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
291
charge delocalization, the transition state is imbalanced in the same way as in non-aromatic systems, i.e., development of aromaticity and charge delocalization are decoupled. Comparisons with aromatic transition states in other reactions Aromaticity in transition states is a well-known phenomenon, especially in pericyclic reactions, as recognized more than half a century ago.150–152 A prototypical example is the Diels–Alder reaction of ethylene þ 1,3-butadiene ! cyclohexene; a computational study by the Schleyer group153 has shown that the absolute value of the diamagnetic susceptibility, which is a measure of aromaticity, goes through a maximum at the transition state. Similar situations have been reported for other Diels–Alder reactions,154 for 1,3-dipolar cycloadditions,155 and enediyne cyclizations,156 where the aromaticity of reactants, products, and transition states was evaluated using NICS values. A recent report regarding transition state aromaticity in double group transfer reactions such as the concerted transfer of two hydrogen atoms from ethane to ethylene is also worth mentioning.157 For many additional examples and references, the review by Chen et al.145 should be consulted. It is important to note, though, that for these reactions the situation is quite different from that in Equations (33a), (34a), and (36). In pericyclic reactions aromaticity is mainly a special characteristic of the transition state whereas the reactants and products are not aromatic or less so than the transition state. This is quite different from the proton-transfer reactions discussed in this chapter where the aromaticity of the transition state is directly related to that of the reactants/products. An analogy with steric effects on reaction barriers may illustrate the point. In a reaction of the type of Equation (38), steric effects at the transition state will definitely increase the intrinsic A þ BÐC þ D
ð38Þ
barrier if the reactants are bulky. However, because there are no steric effects on the reactants or products, the concept of early or late development does not apply here, and the same is true for the aromaticity of the Diels–Alder transition state. In contrast, in a reaction of the type of Equation (39) there is steric crowding both in the product and the transition state. In this case, the intrinsic A þ BÐAB
ð39Þ
barrier will be enhanced if steric crowding has made disproportionately large progress relative to bond formation at the transition state, as is the case for
292
C.F. BERNASCONI
nucleophilic addition to alkenes discussed in a later section; on the other hand, DG‡o will be reduced if development of the steric effect is disproportionately small. This, then, is akin to early or late development of transition state aromaticity or anti-aromaticity in our reactions.
Aromaticity versus resonance Why does aromaticity and resonance affect intrinsic barriers differently? The lowering of the barrier by providing the transition state with excess aromatic stabilization appears to be in keeping with Nature’s principle of always choosing the lowest energy path. The fact that the transition states are able to be so highly aromatic suggests that only relatively minor progress in the creation of appropriate orbitals or the establishment of their optimal alignment and distances from each other may be required for aromatic stabilization to become effective. There are several precedents that support this notion. For example, the NICS value of KekulO˜ benzene (rCC fixed at 1.350 e´ and 1.449 e´) is only 0.8 ppm less than the NICS value for benzene itself or, with rCC = 1.33 e´ (ethylene-like) and 1.54 (ethane-like), the NICS value is only 2.6 ppm less than that for benzene.145,158 Or the NICS value for 63 (–8.1 ppm)159 is quite close to that of benzene (–9.7 ppm)145,158 even though there is strong bending of the benzene ring. Other relevant observations have been discussed elsewhere.141
CN
NC
CN
NC
63
In contrast, in reactions that lead to resonance stabilized/delocalized products such as Equation (1) or (21), the transition state is not able to maximize the potentially stabilizing effect of extensive charge delocalization. As discussed in the section ‘‘Why does delocalization lag behind proton transfer,’’ this is because delocalization can only occur if there is significant C–Y p-bond formation. Hence, the fraction of charge on Y at the transition state depends on the fraction of p-bond formation which in turn depends on the fraction of charge transferred from the base to the carbon acid. This imposes an insurmountable constraint on the transition state because the charge on Y can never be large since it is a fraction of a fraction [Equations (12) and (25)].
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
4
293
Other reactions
NUCLEOPHILIC ADDITIONS TO ALKENES
Reactions of the type of Equation (40) with nucleophiles such as HO, water, aryloxide ions, thiolate
Y Nuν +
C
C
Y–
k1 k–1
C
C
(40)
Nuν + 1
ions, and amines follow similar patterns as proton transfers of the type of Equation (1). This is not surprising since delocalization of the negative charge into the Y-group plays a similar role as in Equation (1). Most of the systematic kinetic studies of these reactions were published before 1992 and thus have been reviewed in detail in our 1992 chapter.4 Hence, only a brief summary, based on Reference 4, of the major features is given here. The main conclusions can be summarized as follows. Correlation with proton transfers There is a strong correlation between the intrinsic rate constants of reactions 40 with those of reactions 1. For example, a plot of log ko for the reactions of piperidine and morpholine with PhCH=C(CN)2, PhCH=C(COO)2C(CH3)2, PhCH=C(CN)C6H4-4-NO2, PhCH=C(CN)C6H3-2,4-(NO2)2, PhCH=CHNO2, PhCH=C(C4Cl4),160 and PhCH=C(Ph)NO2 versus the log ko for the deprotonation of CH2(CN)2, CH2(COO)2C(CH3)2, 4-NO2-C6H4CH2CN, 2,4-(NO2)2C6H3CH2CN, CH3NO2, C5H2Cl4,160 and PhCH2NO2, respectively, gives a good linear correlation. This indicates that the resonance effect of the p-acceptors is qualitatively similar in both reactions. However, there is an attenuation of this effect in Equation (40) as indicated by the slope of 0.46. This attenuation is also reflected in smaller transition state imbalances, as measured by annuc bnnuc ; annuc was obtained from plots of log k1 versus log K1 by varying the aryl substituents and corresponds to aCH in proton transfers, while bnnuc was obtained from plots of log k1 versus log K1 by varying the nucleophile and corresponds to bB in proton transfers. A major reason for the reduced imbalances is the fact that the b-carbon in the alkene is already sp2-hybridized which facilitates p-overlap with the Y-group at the transition state. This is symbolized in 64 by showing a small degree of charge delocalization into the Y-group as indicated by the small ‘‘d–.’’
294
C.F. BERNASCONI
C
Yδ–
δ– C
Nuν + δ 64
There are other factors that contribute to the reduction in the imbalance. This can be seen by comparing intrinsic rate constants of reactions that create the same carbanions as in proton transfer reactions, e.g., comparing reactions 41 and 42. These reactions do involve sp3 ! sp2 rehydrization just as in proton transfers and hence, if hydrization were the only important factor, PhCH O
CH(CN)2
PhCH
– O + CH(CN)2
CH2NO2
PhCH
O + CH2
(41)
–
PhCH
– NO2
(42)
O–
the difference in the log ko values between Equations (41) and (42) should be comparable to that between the log ko values for the deprotonation of malononitrile and nitromethane, respectively. The difference, Dlog ko 3.9, between reactions 41 and 42 is indeed larger than for the corresponding nucleophilic addition reactions to PhCH=C(CN)2 and PhCH=CHNO2, respectively (Dlog ko 2.6), but still smaller than for the corresponding proton transfers (Dlog ko = 6.8). A smaller Dlog ko (5.1) than for proton transfers was also found by the Crampton group161,162 for reactions 43 and 44. H
CH(CN)2 NO2
O2N
NO2
O2N
– + CH(CN2)
–
NO2
NO2
H
CH2NO2 NO2
O2N
NO2
O2N
+
–
NO2
(43)
NO2
CH2
– NO2
(44)
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
295
One potential second reason for the attenuation of the imbalance is steric hindrance to perfect co-planarity of Y in the anionic adducts of Equation (40). An additional factor that may enhance the differences between the imbalances in proton transfers and those in the other carbanion forming reactions is hydrogen bonding in the transition state of proton transfer. This hydrogen bonding stabilizes the transition state by keeping more of the negative charge on the carbon. The gas phase ab initio calculations discussed earlier support this notion.
Effect of intramolecular hydrogen bonding In reactions with amine nucleophiles the reaction leads to a zwitterionic adduct that is in rapid acid–base equilibrium with its anionic form, Equation (45). In some cases, the zwitterion is strongly
Y C
C
+ RR′NH
Y–
k1 C C + RR′NH
k–1
Y–
‡
Ka
H+
C
C
(45)
RR′N
stabilized by an intramolecular hydrogen bond as in the example of the reaction of benzylideneacetylacetone (65) with secondary amines. At the transition state this hydrogen bond
CH3 Ph H
C
C
C
– C
RR′N+
O CH3
O H 65
is only weakly developed because the partial charges on the nitrogen and oxygen atoms are small and the distance between the donor and acceptor atoms is relatively large. Hence the stabilizing effect at the transition state is disproportionately small which leads to a reduction in the intrinsic rate constants of such reactions.
296
C.F. BERNASCONI
Steric effects Steric effects reduce rate and equilibrium constants of nucleophilic additions but the question how the intrinsic barrier is affected does not always have a clear answer. Comparisons of intrinsic rate constants for the addition of secondary alicyclic amines versus primary aliphatic amines suggest that ko is reduced by the F-strain. This implies that the development of the F-strain at the transition state is quite far advanced relative to bond formation. The effects of other types of steric hindrance on ko such as prevention of coplanarity of Y in the adduct or even prevention of p-overlap between Y and the C=C double bond in the alkene have not been thoroughly examined and hence are less well understood. Effect of polar substituents The polar effect of remote substituents on intrinsic rate constants is qualitatively similar to that in proton transfer, irrespective of whether the aryl group is attached to the a-carbon (e.g., 66) or the b-carbon (67); in both cases the partial negative charge in the transition state is closer to the Z
C
δ– Y C
δ– Y C
C
Nuν + δ
Z
Nuν + δ
66
67
substituent Z than in the adduct where the charge is on Y and hence an electron-withdrawing substituent will increase the intrinsic rate constant. This is also reflected in the above-mentioned fact that annuc > bnnuc . p-Donors in the para position of a-aryl groups can lead either to a reduction or an enhancement of the intrinsic rate constant. Examples where a reduction has been observed is the reaction of amines with benzylidene malononitriles, Equation (46), or with benzylidene Meldrum’s Z
Z CN C H
+ R2NH
C CN
CN
k1 k–1
H
C + R2NH
C CN
(46)
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
297
acid. This reduction may be understood in terms of the resonance stabilization of the alkene (68 ! 68). Just as is true for resonance effects in general, the loss of this reactant resonance Z
Z+ CN
CN C
C
C CN
H
H
C
– CN
68±
68
stabilization is expected to be ahead of C–N bond formation at the transition state which should decrease ko. In the reaction of piperidine with b-nitrostyrenes, Equation (47), ko for the reactions of the Z
Z H C H
C
H + R2NH
NO2
H
C + R2NH
(47)
C – NO2
p-OMe derivatives is enhanced, suggesting the above early loss of resonance is overshadowed by another effect. This effect can be understood as arising from a preorganization of the =CHNO2 group in the reactant toward its structure in the adduct (–CH=NO 2 ), thus reducing the transition state imbalance and avoiding some of the detrimental effect of the lag in the charge delocalization. This explanation is similar to that given for the p-donor effect in the deprotonation of Fischer carbenes and of 43-Z. Apparently the two types of p-donor effects operate simultaneously, with the former dominating in reaction 46 and the latter dominating in reaction 47. Polarizable nucleophiles Even though the high carbon basicity of thiolate ion nucleophiles is a major reason why their nucleophilic reactivity is much higher than that of oxyanions or amines of comparable pKa, there is an added effect that comes from a reduced intrinsic barrier. For example, intrinsic rate constants for thiolate ion addition to a-nitrostilbene or b-nitrostyrene are up to 100-fold higher than for amine addition. This has been explained in terms of the soft–soft interaction
298
C.F. BERNASCONI
responsible for the high thermodynamic stability of thiolate ion adducts developing ahead of C–S bond formation.
NUCLEOPHILIC VINYLIC SUBSTITUTION (SNV) REACTIONS
The most common mechanism of nucleophilic vinylic substitution163 is the two-step process of Equation (48) shown for the reaction of an anionic nucleophile with a vinylic substrate activated by one
Y
R Nu–
C
+
C Y′
LG
R k1
LG
C
k–1
Y
k2
C
Y
R C
C
Nu
Y′
+ LG– Y′
(48)
Nu 69
or two electron-withdrawing substituents Y and/or Y0 and a leaving group LG.163–170 The first step is essentially the same as that in nucleophilic additions to alkenes, Equation (40), except that steric and electronic effects of the leaving group affect the reactivity not only of the k2 step but also of the k1 and k–1 steps in important ways. Early mechanistic work on these reactions dealt exclusively with systems where 69 is an undetectable steady-state intermediate,163–167 making it impossible to determine intrinsic rate constants. However, more recent studies focusing on systems with strong nucleophiles such as thiolate or alkoxide ion, poor leaving groups such as alkoxide or thiolate ions, and strongly activated vinylic substrates allowed direct observation of 69 and determination of the individual rate constants k1, k–1, and k2.168,170 The reactions of 70-LG-74-LG with O
O NO2
Ph C
Ph
C
LG
O
CH3
Ph
CH3
LG
C Ph
C
LG
O O
70-H (LG = H) 70-OMe (LG = OMe) 70-Pr (LG = SPr-n) Ph C LG
Ph
NO2
LG
C
CN C
73-SMe (LG = SMe)
O
71-H (LG = H) 71-OMe (LG = OMe) 71-SMe (LG = SMe)
COOMe
C
C CN
74-H (LG = H) 74-OMe (LG = OMe)
72-H (LG = H) 72-SMe (LG = SMe)
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
299
thiolate ions171–176,178 have provided the most insights into how structural factors affect intrinsic rate constants in such systems. Table 24 summarizes RS RS kRS 1 , K1 , and k2 values for the reactions with HOCH0 2CH2S as a repreCH2 YY values of CH2YY0 , sentative thiolate ion. Included in the table are pKa RS log ko for the intrinsic rate constants for RS addition determined from plots PT versus log KRS values for the deprotonation of of log kRS 1 1 , and log ko 0 CH2YY by secondary alicyclic amines. CH2 YY0 Figure 9 shows an excellent correlation of log KRS for 1 with pKa 0 LG = H( ) (slope = 1.11), indicating charge stabilization by YY in the adduct is similar to that for CHYY0 . For LG = OMe ( ) and SMe (D) the correlation is poor due to steric crowding in the adduct which is strongest for YY0 = MA,177 intermediate for YY0 = ID,177 (NO2,CO2Me) and (Ph,NO2), and smallest for YY0 = (CN)2. The leaving group steric effects follow the expected order SPr-n > SMe > OMe >> H. and log KRS are Figure 10 shows that the correlations between log kRS 1 1 RS poor, implying that ko differs substantially from substrate to substrate and not only depends on YY0 but on the leaving group as well. This is best demonstrated in Fig. 11 which shows that, for a given leaving group, there and log kPT just as had been is a linear correlation between log kRS o o observed for the correlation between log ko for the reaction of amines with alkenes [Equation (40)] and log ko for the corresponding proton transfer mentioned earlier. Also as observed for reaction 40, the slopes are less than unity (0.32 for LG = H, 0.40 for LG = OMe, and 0.56 for LG = SMe) due to the sp2 hybridization of the b-carbon which facilitates overlap with the YY0 groups at the transition state and reduces the imbalance. However, as the differences in the slopes imply, the degree by which the imbalance is reduced depends on the leaving group and is largest for LG = H and smallest for LG = SMe. This conclusion is corroborated by the Br½nsted-type coefficients annuc and bnnuc for the reactions of thiolate ions with the phenyl-substituted Meldrum’s acid derivatives of 71-H and 71-SMe: for 71-SMe, annuc – bnnuc = 0.34, for 71-H annuc – bnnuc = 0.13, implying a smaller imbalance for 71-H. We further note that the kRS o values for the reactions with LG = OMe and SMe are much lower than with LG = H, especially for LG = SMe. There are two main factors that contribute to this result. One is the p-donor effect of the OMe and SMe groups (75 $ 75) which reduces kRS o
Y
R C MeX
+ MeX
Y′ 75
Y
R
C
X = O or S
C
C Y′ 75±
300
Table 24 Rate and equilibrium constants for SNV reactions with HOCH2CH2Sin 50% DMSO–50% water at 20C 2 YY pKCH a
Substrate Ph
0
1 1 kRS s ) 1 (M
1 KRS 1 (M )
1 kRS 2 (s )
log kRS o
log kPT o
References
CN C
C
H
(74-H)
10.21
4.40 106
5.18 104
5.7
7.0
171
(70-H)
7.90
5.18 104
8.16 106
3.4
–0.25
172
(72-H)
6.35
4.47 106
1.16 109
4.8
3.13
171
(71-H)
4.70
1.44 107
5.38 1010
5.2
3.90
173
10.21
2.80 105
1.62 102
5.1
70
171
CN
Ph
Ph C
C
H
NO2 O
Ph C
C
H O O O CH3
Ph C
C
O CH3
O Ph
CN C
MeO
(74-OMe)
C CN
0.133
C.F. BERNASCONI
H
C
C
MeO
NO2
(70-OMe)
7.90
3.89 102
7.59 103
9.60 106
2.2
–0.25
174
(71-OMe)
4.70
4.40 104
2.57 104
2.16 104
3.7
3.13
175
(70-SPr)
7.90
4.70
10.4
4.50 102
0.29
2.44
175
(72-SMe)
6.35
5.62 102
2.25 102
0.245
2.5
3.90
171
(73-SMe)
5.95
2.48 102
5 104
5.80 105
£1.1
171
(71-SMe)
4.70
9.22 102
3.32 102
0.115
2.5
176
Ph O O CH3
Ph C
C MeO
O CH3
O Ph
NO2 C
C
n-PrS
Ph O
Ph C
C
MeS O Ph
Ph C
C
MeS
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
Ph
CO2Me O O CH3
Ph C
C
MeS O
O CH3
301
302
C.F. BERNASCONI 12
71-H 10
72-H
log K1RS
8
70-H 6
4
74-H
73-H 71-OME 70-OME
2
72-SMe 71-SMe
74-OME
70-SR 0 –12
–10
–8
–6
–4
–2
0
CH YY′ –pKa 2 0
2 YY Fig. 9 Plots of log KRS (RS = HOCH2CH2S) versus pKCH . a 1 LG = OMe; D, LG = SMe.
,
LG = H;
,
by the PNS effect of the early loss of the resonance stabilization of the substrate; this is similar to the effect of p-donor substituents in the phenyl group of alkenes as, e.g., in 68 $ 68. In view of the stronger p-donor effect of the OMe group,71 this factor should affect the reactions with LG = OMe more strongly than those with LG = SMe. However, since kRS o for the MeS derivatives is lower than for MeO derivatives, there must be one or more additional factors that reduce kRS o for the MeS derivatives relative to that for the MeO derivatives. One such factor appears to be steric hindrance (Fstrain) at the transition state which is quite advanced relative to the C–S bond formation and hence should result in a greater reduction of ko for the MeS derivative due to the larger size of the sulfur atom. This conclusion is in agreement with one reached for the reaction of amines with alkenes discussed earlier. Another factor may be the stronger electron-withdrawing inductive effect of the MeO group which imparts greater stabilization to the imbalanced transition state than the MeS group and hence increases the ko(OMe)/ko(SMe) ratio.
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
303
8
71-H 72-H
74-H 6
log k 1RS
74-OMe 70-H
71-OMe 4
71-SMe 70-OMe
→
72-SMe
73-SMe
2
70-SPr 0
0
2
4
6
8
10
12
RS
log K1
RS Fig. 10 Plots of log KRS 1 versus log K1 (RS = HOCH2CH2S ) generated by varying YY0 . , LG = H; , LG = OMe; D, LG = SMe.
NUCLEOPHILIC SUBSTITUTION OF FISCHER CARBENE COMPLEXES
Intrinsic rate constants The reactions of Fischer carbene complexes with an anionic nucleophile may be represented by Equation (49).179–181 Typical carbene complexes that have been the subject of kinetic studies are 76-M and XR Nu– + (CO)5Cr
C R′
77-M
182–185
XR (CO)5Cr
k –1
k2
R′
(CO)5Cr
+ RX–
C
(49)
R′
as well as others mentioned below.
C
OCH2CH2O–
SMe (CO)5M
Ph
76-Cr (M = Cr) 76-W (M = W)
C Nu
OMe (CO)5M
Nu
–
k1
(CO)5Cr
C Ph
77-Cr (M = Cr) 77-W (M = W)
C
SCH2CH2O– (CO)5Cr
C
Ph 78-Cr
Ph 79-Cr
304
C.F. BERNASCONI 6
74-H
71-H 5
72-H 74-OMe
log k ORS
4
71-OMe 70-H
3
72-SMe
2
71-SMe
70-OMe
73-SMe
1
70-SPr 0 –1
0
1
2
3 log
4
5
6
7
8
k OPT
PT Fig. 11 Plots log kRS o (RS = HOCH2CH2S ) versus log ko . , LG = H; , LG = OMe; D, LG = SMe.
These reactions show many similarities with the SNV reactions of Equation (48) but there are differences as well. Table 25 summarizes approximate log ko values for the addition of various nucleophiles to 76-M and 77-M. The table includes results for the intramolecular reactions of 78-Cr186 and 79-Cr186 that lead to the cyclic intermediates 80-Cr and 81-Cr, respectively. For
– (CO)5Cr
O C Ph 80-Cr
– O
(CO)5Cr
S C
O
Ph 81-Cr
the purpose of comparison, log ko values for the reactions of the vinylic substrate with the highest intrinsic rate constant (74-OMe) and the ones with
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
305
Table 25 Approximate intrinsic rate constants for the reactions of Fischer carbene complexes with nucleophilesa log ko
Nu = MeO
b
Nu = ROc
Nu = RSc
OMe (CO)5Cr
C
(76-Cr)
0.96d
0.74e
2.11f
(76-W)
1.25d
0.96e
2.56f
Ph OMe (CO)5W
C Ph OCH2CH2O–
(CO)5Cr
(78-Cr)
C
1.19g
Ph SMe (CO)5Cr
C
(77-Cr)
–0.3h
(77-W)
0.0h
Ph SMe (CO)5W
C Ph SCH2CH2O–
(CO)5Cr
(79-Cr)
C
–1.53g
Ph OMe
NC C
C
NC C
C
(70-OMe)
2.2i
(70-SPr)
0.29i
Ph
Ph
SPr-n
O 2N C
a
5.1i
OMe
O 2N
Ph
(74-OMe) Ph
C Ph
In most cases log ko was determined using the simplest version of the Marcus equation, log ko = log k1 – 0.5 log K1. b In methanol at 25C. c In 50% MeCN–50% water (v/v) at 25C. d Reference 182. e Reference 183. f Reference 184. g Reference 186. h Reference 185. i From Table 24.
306
C.F. BERNASCONI
the lowest ko values (70-OMe and 70-SMe) are included in the table. The following points are noteworthy. 1. The intrinsic rate constants for thiolate ion addition to the Fischer carbenes are close to those for thiolate addition to the respective a-nitrostilbene derivatives 70-OMe and 70-SMe but much lower than for thiolate ion addition to methoxybenzylidinemalononitrile (74-OMe); for example, log ko = 2.1 for 76-Cr versus log ko = 2.2 for 70-OMe versus log ko = 5.1 for 74-OMe, or, log ko = –0.3 for 77-Cr versus log ko = 0.29 for 70-SPr. This is consistent with the extensive charge delocalization into the (CO)5M moiety that is responsible for the relatively high stability of the addition complexes176,177,183 and the lag of this delocalization behind bond formation at the transition state, see, e.g., 82; note that to show the imbalance the partial negative charge is placed on the metal atom rather than on the entire (CO)5M group. OMe δ– (CO)5M
C
Ph
δ– Nu 82
2. The intrinsic rate constants are much lower for nucleophilic attack on the thia carbene complexes than on the oxa carbene complexes. This is true irrespective of the nucleophile. For example, log ko = –0.3 for RS attack on 77-Cr versus log ko = 2.1 for RS attack on 76-Cr, or log ko = –1.53 for cyclization of 79-Cr versus log ko = 1.19 for cyclization of 78-Cr. These findings are reminiscent of the lower intrinsic rate constants for thiolate ion addition to vinylic substrates with a MeS leaving group compared to those with a MeO leaving group and hence must have similar explanations in terms of inductive, steric and possibly p-donor effects. Specifically, the stronger inductive effect of the MeO(RO) group enhances ko(OR) relative to ko(SR) while the larger steric effect of the MeS(RS) group lowers ko(SR) relative to ko(OR); both factors lower the ko(SR)/ko(OR) ratios. As discussed for the SNV reactions, the p-donor effects may partially offset the inductive and steric effects because early loss of the resonance stabilization of the carbene complex should lower ko(OR) more than ko(SR). However, based on our discussion of the p-donor effects in the deprotonation of Fischer carbene complexes, the ko-increasing preorganization effect may counteract or even override the ko-reducing effect of the early loss of carbene complex resonance and hence contribute to the lower ko(SR)/ko(OR) ratios.
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
307
3. The intrinsic rate constants for thiolate ion addition to 76-Cr and 76-W are substantially larger than those for alkoxide ion addition. This is similar to the previously mentioned higher intrinsic reactivity of thiolate ions compared to amine nucleophiles for the addition to a-nitrostilbene and b-nitrostyrene. It can be understood in terms of the soft–soft interaction of the thiolate ion with the carbene complex which is more advanced than C–S bond formation at the transition state.184 Transition state imbalances The fact that the intrinsic rate constants for nucleophilic addition to Fischer carbene complexes are relatively low, for example, much lower than for most reactions with comparable vinylic substrates or carboxylic esters,188 constitutes strong evidence for the presence of substantial transition state imbalances. However, there have only been a few studies of substituent effects that demonstrate the imbalance directly by showing annuc > bnnuc or by providing an estimate of its magnitude from the difference annuc – bnnuc . One such study is the reactions of 76-Cr-Z and 76-W-Z with HC CCH2O and CF3CH2O.183 It yielded annuc = 0.59 and bnnuc £ 0.46 for 76-Cr-Z, and annuc = 0.56 and bnnuc £ 0.42 for 76-W-Z, i.e., annuc > bnnuc as expected.
OMe (CO)5M
C
Z 76-Cr-Z (M = Cr) 76-W-Z (M = W)
Desolvation of the nucleophile There exists substantial evidence that in reactions that involve oxyanions or amines as bases or as nucleophiles, their partial desolvation, as they enter the transition state, typically has made greater progress than bond formation. In the context of the PNS, this partial loss of solvation represents the early loss of a reactant stabilizing factor and hence reduces the intrinsic rate constant. As discussed at some length in our 1992 chapter,4 for strongly basic oxyanions this desolvation effect often manifests itself in terms of negative deviations from Br½nsted plots and/or in abnormally low b or bnuc values.58,188 In fact, a number of cases have been reported where the bnuc value was close to zero or
308
C.F. BERNASCONI
even negative. Examples of negative bnuc values include the reaction of quinuclidines with aryl phosphates,193 of amines with carbocations,194,195 and of oximate ions with electrophilic phosphorous centers.192,196,197 The reactions of thiolate ions with several carbene complexes are also characterized by substantially negative bnuc values: they are –0.28 for 76-Cr,184 –0.25 for 76-W,184 –0.24 for 77-Cr,186 –0.30 for 77-W,186 –0.18 for 83-Cr,198 and –0.21 for 84-Cr198; for the reaction of 84-Cr with aryloxide ions bnuc = –0.39.199
O (CO)5Cr
C
O (CO)5Cr
Ph 83-Cr
NO2
C Ph 84-Cr
According to Jencks et al.,193 negative bnuc values result from a combination of minimal progress of bond formation at the transition state and the requirement for partial desolvation of the nucleophile before it enters the transition state. In a first approximation bnuc may be expressed by Equation (50) where bd and bnuc are defined by Equations (51) and (52), respectively. Kd represents 0
bnuc ¼ bd þ b nuc
ð50Þ
bd ¼ dlogKd =dpKaNucH
ð51Þ
0
0
b nuc ¼ dlogk1 =dpKaNucH
ð52Þ
the equilibrium constant for partial desolvation of the nucleophile while k0 1 is the rate constant for nucleophilic attack by the partially desolvated nucleophile. Since desolvation becomes more difficult with increasing basicity of the nucleophile, bd < 0 which, along with a small b0 nuc value, can lead to a negative bnuc value. A more elaborate treatment of this problem has been presented elsewhere.184 The fact that b0 nuc is so small as to lead to negative bnuc values implies a very small degree of C–S or C–O bond formation at the transition state. One factor that seems to play a role is the particularly severe steric crowding in the transition state due to the very large size of the (CO)5M group.186,200 The small degree of bond formation would seem to reduce the steric repulsion. The even more negative bnuc value for the aryloxide ion reactions is probably the result of a more negative bd value due to the stronger solvation of oxyanions compared to thiolate ions.
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
309
REACTIONS INVOLVING CARBOCATIONS
Following previous studies of reactions of carbocations with nucleophiles201–204 discussed in our 1992 chapter,4 Richard’s group205,206 reports that electronwithdrawing a-substituents in 4-methoxybenzyl cations, 85, reduce the rate of nucleophilic addition of alcohols and water to
R1
+ C
R2
R1
R2 C
R1, R2 = H, CF3; CF3, CF3; H, CH2F; H, CHF2; H, COOEt; CH3, CF3
OMe 85
+ OMe 85±
these cations. This is contrary to what one would expect since the electronwithdrawing a-substituents destabilize the carbocation and should make it more reactive. The reason for the reduced reactivity is that the electronwithdrawing substituents lead to a stronger resonance effect by the methoxy group. Hence the PNS effect of the early loss of resonance stabilization at the transition state increases the intrinsic barrier sufficiently as to lower the actual rate of the reaction. A similar study by Schepp and Wirz had led to the same conclusion.207 For an interesting example where the small degree of transition state resonance stabilization corresponds to a late development of product resonance is the acid-catalyzed aromatization of benzene cis-1,2-dihydrodiols.208 The reaction is shown in Scheme 2 where the loss of water is rate limiting. The rate constants as a function of 17 Z-substituents gave a good correlation with the regular Hammett s values with r = –8.2. Interestingly, there were no deviations from the Hammett plot for the p-donor substituents MeO and EtO, i.e., there was no need to use sþ constants, implying that resonance stabilization of the transition state is of minor importance despite the strongly developed positive charge indicated by the very large r value. A situation where the late development of a product destabilizing factor lowers the intrinsic barrier is the nucleophilic addition reaction shown in Equation (53).209 Kinetic data for this reaction and the reaction of a series of thiols have led to the following conclusions. The adduct, 87, is strongly stabilized by the polar and polarizability effect of the two methyl groups on the sulfur but strongly destabilized by the electron-withdrawing CF3 groups. There is also a relatively strong stabilization of the incipient positive charge on
310
C.F. BERNASCONI
Z
Z OH
OH
OH
H+ + OH2
OH
Z
Z
OH slow –H2O
+
+
H
H
hydride shift
–H+
Z
Z OH
OH –H+
+ H H
Scheme 2 + SMe2 F3C
CF3
F3C
+ CF3
CF3
F3C
(53)
+ Me2S
O–
O–
O 86
87
the sulfur atom by the methyl groups at the transition state as indicated by bnuc > 0.5 based on the addition of thiols, but only a small destabilization of the transition state by the more distant CF3 groups. The picture that emerges is that of a transition state where bond formation to the nucleophile develops at a relatively large distance so that the interaction between the positive charge and the CF3 groups remains weak until after the transition has passed while the interaction between the positive charge and the methyl groups can be strong. This, then, leads to a lowering of the intrinsic barrier. A case where the late solvation of halogen leaving groups in a carbocation forming solvolysis reaction increases the intrinsic barrier is the one shown in Equation (54). CH2X
+
CH2
+ X–
OMe
OMe
(54)
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
311
Toteva and Richard210 showed that DG‡o for F expulsion is about 3 kcal mol1 higher than for Cl expulsion. Since solvation of the fluoride ion is much stronger than that of the chloride ion, the difference in DG‡o must arise from the PNS effect of late solvation. A PNS effect involving anomeric stabilization of a geminal dialkoxy compound has been observed when comparing kinetic and thermodynamic data of reactions 55 and 56. Reaction 55
H CF3CH2O
C
OCH2CF3
CF3CH2O
+ C
H
H+ +
+ CF3CH2OH OMe
(55)
OMe
88-(OCH3CF3)2
88-OCH2CF3
H CF3CH2S
C
OCH2CF3
CF3CH2S
+ C
H
H+ +
+ CF3CH2OH OMe
88-(OCH2CF3)(SCH2CF3)
(56)
OMe 88-SCH2CF3
was reported to be thermodynamically less favorable than reaction 56 but the rate for reaction 55 is higher than for reaction 56.211 One possible interpretation of these results offered by the authors is that stabilization of 88(OCH2CF3)2 by the geminal interaction of the two oxygens, the anomeric effect,212–216 is responsible for the less favorable thermodynamics of reaction 55 but that the loss of this interaction lags behind C–O bond cleavage at the transition state. This late loss of a reactant stabilizing factor results in a lower intrinsic barrier for reaction 55.
312
C.F. BERNASCONI
MISCELLANEOUS REACTIONS
Gas phase SNV reactions Kon ´ ˘ a et al.217 reported DFT calculations on gas phase SNV reactions such as Equations (57), (58), and other similar processes. Their calculations show the expected strong stabilization of the anionic adduct HO– + CH2
CH
– CH2
OCH3
OCH3 CH
CH2
CH
OH + CH3O–
OH
(57)
HO– + O
CH
CH
CH
– O
OCH3
OCH3 CH
CH
CH
(58)
OH O
CH
CH
CH
OH + CH3O–
in Equation (58) that results from the delocalization of the negative charge onto the carbonyl oxygen. As to the barriers, the one for the first step in Equation (58) is lower than that for the first step in Equation (57) but not by an amount that would imply a strong expression of adduct stabilization in the transition state. In other words, resonance stabilization of the transition state lags behind C–O bond formation. A similar situation exists for the second step in reaction 58, i.e., the barrier is disproportionately high because of early loss of the resonance stabilization of the intermediate. Intramolecular SN2 reactions The intramolecular SN2 reaction shown in Equation (59) is an example where the development of a product destabilizing factor lags behind bond formation which contributes to the lowering of the S
–
S CH2
CH2
CH2
CH2
+ HS–
(59)
SH
CH3S– + CH3
CH2
CH3 SH
CH2 SCH3 + HS–
(60)
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
313
intrinsic barrier. Specifically, an ab initio calculation by Gronert and Lee218 has shown that the enthalpic barrier DH‡ for Equation (59) (19 kcal mol1) is lower than for Equation (60) (24 kcal mol1), even though Equation (60) is thermodynamically much more favored (DHo = –1 kcal mol1) than Equation (59) (DHo = 19 kcal mol1). This means that the intrinsic barrier of Equation (59) is much lower than for Equation (60). The cyclization is thermodynamically unfavorable due to the large ring strain of the threemembered ring. However, at the transition state, the ring strain is small because the developing C–S bond is quite long, and hence this lowers the intrinsic barrier. Another factor that contributes to the lowering of the intrinsic barrier is what the authors call the proximity effect. This effect derives from the fact that in the cyclization reaction the nucleophilic atom is forced to be close to the a-carbon which amounts to a destabilization of the substrate by 1,3-repulsive interactions. Similar results were also reported for the reactions of Equation (61).219 X CH
– XCH CH2
CH2
CH2
(61)
CH2 + Cl–
Cl X CH O, C
CH, CN
Epoxidation of alkenes Based on a kinetic study of the epoxidation of alkenes by m-chloroperbenzoic acid, Equation (62), O
O
OH
C
C
OH
O
C
C
O
+
+ C
R
(62)
C
Cl
Cl
R
R = alkyl or aryl
Perrin’s group220 concluded that, for aromatic alkenes (R = aryl), the transition state, schematically represented as 89, may be imbalanced in that the delocalization of the positive
δ+ C
C
+ •
‡
X δ– δ+
C
Ar
Ar 89
C
90
314
C.F. BERNASCONI
charge into the aromatic ring is delayed. Specifically, they showed that the kinetic data correlated with the ionization potential of the alkenes, implying that the radical cation 90 with a significant fraction of the positive charge delocalized into the aryl group, may serve as a model for the product. There were two separate correlation lines, one for aliphatic (R = alkyl) and the other for aromatic alkenes (R = aryl), and, for a given ionization potential, the reactivity of the aromatic alkenes was lower than that of their aliphatic counterparts. These results were interpreted as being the consequence of the above-mentioned transition state imbalance, which raises the intrinsic barrier of the reaction and explains the lower reactivity of the aromatic alkenes as well as the lower sensitivity of the rate to the ionization potential. Hemiacetal decomposition McClelland et al.221 have suggested that the general acid-catalyzed decomposition of a hemiacetal anion, Equation (63), proceeds through an imbalanced transition state where sp3 to sp2
‡ O–
Ar
+ HA
C CH3
OR
Oδ–
Ar
ArCCH3 + ROH + A–
C CH3
O
OR
(63)
H Aδ–
rehybridization of the central carbon lags behind C–O bond cleavage. This imbalance is in the expected direction since sp2 hybridization allows development of the acetophenone resonance. The authors based their conclusion on a relatively large blg value (large degree of C–O bond cleavage) and a small r value determined from the aryl substituent effect (small degree of charge development in the aryl group). A similar conclusion has been reached by Kandanarachchi and Sinnott222 for the hydrolysis of orthocarbonates such as (ArO)4C, (ArO)2C(OAr0 )2, or (ArO)3COAr0 . The rate-limiting step in these reactions is the spontaneous or general acid-catalyzed cleavage of the bond between the central carbon and the oxygen of the least basic aryloxy group. Again, r and blg values suggest that resonance development in the resulting carbocation lags behind C–O bond cleavage.
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
315
Radical reactions In an attempt to understand the origin of the barrier in the fragmentation of the radical cations of 2-substituted benzothiazoline derivatives, Shukla et al.223 examined the kinetics of reaction 64 as •+ S
R
S
N
Me
+ N
Me
Me + R•
(64)
Me
a function of R (PhCH2, Ph2CH, PhCMe2, 9-MeFl, Ph2CMe) and performed DFT energy calculations. Even though the activation barriers decreased with increasing resonance stabilization of the radical R, it was shown that the lowering of the barriers was rather modest relative to the large increases in the thermodynamic driving force that resulted from the enhanced radical stability. This unusually small effect on the barrier was attributed to an increase in the intrinsic barrier with increasing resonance stabilization of the radical. The increase in the intrinsic barrier was attributed to ‘‘large reorganization energies in the product fragments.’’ The authors did not refer to the transition state as ‘‘imbalanced’’ and apparently were unfamiliar with the PNS, but their results are of course a classic example of the PNS at work. In a theoretical paper, Costentin and SavO˜ant224 examined the dimerization of neutral radicals by constructing potential energy profiles from AMI calculations, subjecting some selected dimerizations to B3LYP/6-31G* calculations and applying VB theory in analyzing the results. The dimerization of conjugated radicals, e.g., Equation (65), is subject to an 2 CH2
CH
CH2
CH2
CH
CH2
CH2 CH
CH2
(65)
activation barrier which contrasts with the barrierless dimerization of nonconjugated radicals; these barriers are higher for more highly delocalized radicals, even when the reactions are more thermodynamically favored. These results are consistent with the notion that loss of the resonance of the radicals is ahead of bond formation, or, in the reverse direction, development of the radical resonance lags behind bond cleavage. However, based on their analysis of the reaction in the reverse direction for which the resonance integral apparently increases at the same pace as bond cleavage, Costentin and SavO˜ant concluded that delocalization is synchronous with bond breaking. It would appear that further study is needed to resolve this apparent inconsistency between their conclusion and the predictions of the PNS.
316
C.F. BERNASCONI
Enzyme-catalyzed hydride transfer A biologically relevant example of a reaction with an imbalanced transition state is the hydride transfer catalyzed by dihydrofolate reductase of Escherichia coli. In a theoretical study by Pu et al.225 the hybridization changes at the donor carbon atom (C4N) and acceptor carbon atom (C6) that occur along the reaction coordinate were examined. It was shown that the changes in hybridization at both carbon centers progress in a nonlinear fashion with respect to the progress of the hydride transfer. Specifically, the change from sp3 to sp2 hybridization of C4N lags behind hydride transfer while the change from sp2 to sp3 hybridization of C6 is ahead of hydride transfer. This is strictly analogous to the findings for the proton transfer reactions of the type of Equation (21) where the change in the pyramidal angle (56) lags behind proton transfer. Additional evidence for the imbalanced nature of the transition state was deduced from an analysis of the changes in the C4–H and C6–H bond orders along the reaction coordinate.
5
Summary and concluding remarks
Most elementary reactions involve several molecular events such as bond formation/cleavage, charge transfer, charge creation/destruction, charge delocalization/localization, creation/destruction of aromaticity or antiaromaticity, increase/decrease in steric strain, etc. It is rare that all these events have made equal progress at the transition state; in other words, in most cases, the transition state is imbalanced in the sense that some process develops ahead of or lags behind others along the reaction coordinate. It has proven useful to regard the main bond changes as the ‘‘primary’’ process and to regard the development of the various product stabilizing/destabilizing factors, or the loss of the various reactant stabilizing/destabilizing factors, as ‘‘secondary’’ processes. This definition then allows us to use the extent of the bond changes as a frame of reference in gauging whether the development of a product stabilizing/destabilizing factor or the loss of a reactant stabilizing/destabilizing factor is early or late. Within this framework the various manifestations of the PNS summarized in Chart 1 are unambiguous and there can be no exceptions. What makes the PNS universal is that it is applicable to all reactions that involve bond changes. It provides a qualitative and sometimes even semiquantitative understanding of chemical reactivity using the language of physical organic chemistry. Its main virtue and usefulness is that, for the most part, a given factor follows a consistent pattern, i.e., it invariably either develops late or early, regardless of the specific reactions, and hence its effect on the intrinsic barrier is predictable. A summary of how the various factors discussed in this chapter affect intrinsic barriers/intrinsic rate constants is provided in Table 26. They include charge delocalization/resonance, solvation, aromaticity, anti-
Factor
1
Effect on molecule
Late development/ early loss
Early development/ late loss
Effect on DG‡o
ko
"
#
Ubiquitous, no exceptions, predicted by theory [Equations (12) and (25)]
" #
# "
Ubiquitous, no exceptions Limited number of known cases [Equations (18–20), (33a), (34a), and (36)] One established case [Equation (35a)], one tentative case (deprotonation of 51 and 52) Numerous cases, e.g., deprotonation of HOCH2CH2NO2, PhCH2CH2NO2, (CH3)2CHNO2, and Fischer carbenes Effect sometimes masked by preorganization (deprotonation of Fischer carbenes, nucleophilic additions) Limited number of cases (nucleophilic additions) Limited number of cases (RS as nucleophile) One tentative case [Equation (55)] Limited number of cases, e.g., 65 [Equation (45)]
Stabilizing
H
2 3
Charge delocalization (resonance) Solvation Aromaticity
Stabilizing Stabilizing
H
4
Anti-aromaticity
Destabilizing
H
#
"
5
Hyperconjugation
Stabilizing
H
"
#
6
p-Donor effect
Stabilizing
H
"
#
7
Steric effect (Fstrain) Soft–soft interactions Anomeric effect Intramolecular hydrogen bonding Ring strain
Destabilizing
H
"
#
Stabilizing
H
#
"
H
8 9 10 11
H
Comments
Stabilizing Stabilizing
H
# "
" #
Destabilizing
H
#
"
317
Limited number of cases, e.g., Equations (59) and (61)
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
Table 26 The effect of product/reactant stabilizing/destabilizing factors on DG‡o and ko
318
C.F. BERNASCONI
aromaticity, hyperconjugation, p-donor effects, F-strain, soft–soft interactions, and anomeric effects. There are other factors that can affect DG‡o and ko; they do so not because they inherently develop nonsynchronously relative to bond changes but because of delayed charge delocalization. They include the effects of remote as well as adjacent polar and polarizable substituents, of remote and adjacent charge, and of substituents that impede charge delocalization by steric crowding. They are summarized in Table 27. What the PNS cannot deal with is the effect on reactivity by factors that only operate at the transition state level but are not present in either reactant or product. Examples mentioned in this chapter include transition state aromaticity in Diels Alder reactions, steric effects on reactions of the type A þ B ! C þ D, or hydrogen bonding/electrostatic effects that stabilize the
Table 27 The effect of substituents and charges on DG‡o and ko for reactions with imbalanced transition states Factor
1 2 3
4
5 6
EW polar substituent close to charge of TS ED polar substituent close to charge of TS EW polar substituent far from charge at TS ED polar substituent far from charge at TS Adjacent polarizable substituent Adjacent positive charge
7
Remote positive charge
8
Steric hindrance of resonance by substituent
Effect on TS versus effect on product
Effect on
Comments
DG‡o
ko
Disproportionately large TS stabilization Disproportionately large TS destabilization Disproportionately small TS stabilization
#
"
"
#
"
#
Disproportionately small TS destabilization
#
"
Equation (14) (leads to aCH < bB); Equation (6)
Disproportionately large TS stabilization Disproportionately large TS stabilization Disproportionately small TS stabilization Disproportionately small TS destabilization
#
"
#
"
Proton transfer progress must be substantial e.g., Equation (16)
"
#
e.g., nucleophilic addition to 85
#
"
e.g., CH3CH(NO)2 versus CH3NO2 deprotonation
Equation (4) (leads to aCH > bB); Equation (15) Equation (4) (leads to to aCH > bB); Equation (15) Equation (14) (leads to aCH < bB); Equation (6)
THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION
319
transition state of proton transfers of the type CH3Y þ CH2=Y ! CH2Y=Y þ CH3Y which are especially strong in the gas phase.
Acknowledgments I gratefully acknowledge the many outstanding contributions of all of my coworkers whose names are cited in the references and the financial support by the National Science Foundation (grant no. CHE-0446622).
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.
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156. Stahl F, Moran D, Schleyer PvR, Prall M, Schreiner PR. J Org Chem 2002;67:1453. 157. Fernandez I, Sierra MA, CossU´o FP. J Org Chem 2007;72:1488. 158. Schleyer PvR, Maerker C, Dransfeld A, Jiao A, van Eikema Hommes WJR. J Am Chem Soc 1996;118:6317. 159. Tsuij T, Okuyama M, Ohkita M, Kawai H, Suzuki T. J Am Chem Soc 2003;125:951. 160. PhCH=C(C4Cl4) = 1,2,3,4-tetrachloro-6-phenylfulvene; C5H2Cl4 = 1,2,3,4-tetrachloro-1,3-cyclopentadiene. 161. Atherton JH, Crampton MR, Duffield GL, Steven JA. J Chem Soc, Perkin Trans 2 1995:443. 162. Cox JP, Crampton MR, Wight P. J Chem Soc, Perkin Trans 2 1988:25. 163. Rappoport Z. Adv Phys Org Chem 1969;7:1. 164. Modana G. Acc Chem Res 1971;4:73. 165. Rappoport Z. Acc Chem Res 1981;14:7. 166. Rappoport Z. Recl Trav Chim Pays-Bas 1988;104:309. 167. Shainyan BA. Russ Chem Rev 1986;55:511. 168. Rappoport Z. Acc Chem Res 1992;25:474. 169. Okyama T, Lodder G. Adv Phys Org Chem 2002;37:1. 170. Bernasconi CF, Rappoport Z. Acc Chem Res 2009:42:993. 171. Bernasconi CF, Ketner RJ, Ragains ML, Chen X, Rappoport Z. J Am Chem Soc 2001;123:2155. 172. Bernasconi CF, Killion RB, Jr. J Am Chem Soc 1988;110:7506. 173. Bernasconi CF, Ketner RJ. J Org Chem 1998;68:6266. 174. Bernasconi CF, Fassberg J, Killion RB, Jr., Rappoport Z. J Am Chem Soc 1990;112:3169. 175. Bernasconi CF, Ketner RJ, Chen X, Rappoport Z. J Am Chem Soc 1998;120:7461. 176. Bernasconi CF, Ketner RJ, Chen X, Rappoport Z. Can J Chem 1999;77:584. 177. MA = Meldrum’s acid, ID = indandione. 178. Bernasconi CF, Ketner RJ, Chen X, Rappoport Z. ARKIVOC 2002 (xii) 2002:161. 179. The physical organic chemistry of Fischer carbene complexes has been reviewed;176,177 only studies relevant to the PNS will be discussed in this chapter. 180. Bernasconi CF. Chem Soc Rev 1997;26:299. 181. Bernasconi CF. Adv Phys Org Chem 2002;37:137. 182. Bernasconi CF, Flores FX, Gandler JR, Leyes AE. Organometallics 1994;13:2186. 183. Bernasconi CF, GarcU´a-RU´o L. J Am Chem Soc 2000;122:3821. 184. Bernasconi CF, Kittredge KW, Flores FX. J Am Chem Soc 1999;121:6630. 185. Bernasconi CF, Ali M, Lu F. J Am Chem Soc 2000;122:1352. 186. Bernasconi CF, Ali M. J Am Chem Soc 1999;121:11384. 187. D—tz KH, Fischer H, Hofmann R, Kreissl FR, Schubert U, Weiss K. Transition metal carbene complexes. Deerfield Beach, FL: Verlag Chemie; 1983. 188. Numerous authors189–191 have compared the reactions of Fischer carbene complexes with nucleophiles to the corresponding reactions of carboxylic esters.183,185– 187 Our view is that there is much more resemblance between the reactions of Fischer carbene complexes and SNV reaction than between the reactions of Fischer carbene complexes and reactions with esters because in the latter reactions there are no strong resonance effects. 189. Schubert U, editor. Advances in metal carbene chemistry. Dordrecht, Holland: Kluwer; 1989. 190. Werner H, Fischer EO, Heckl B, Kreiter CG. J Organomet Chem 1971;28:367.
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191. Aumann R, Hinterding P, Krger C, Goddard R. J Organomet Chem 1993;459:145. 192. Takka RM, Buncel E. J Am Chem Soc 1995;117:1503. 193. Jencks WP, Haber MT, Herschlag D, Nazaretian KL. J Am Chem Soc 1986;108:479. 194. Richard JP. J Chem Soc, Chem Commun 1987:1768. 195. McClelland RA, Kanagasabapthy VH, Banait NS, Steenken S. J Am Chem Soc 1992;114:1816. 196. Terrier F, Le GuO˜vel E, Chatrousse A-P, Moutiers G, Buncel E. Chem Commun 2003:600. 197. Terrier F, Rodriguez-Dafonte P, Le GuO˜vel E, Moutiers G. Org Biomol Chem 2006;4:4352. 198. Bernasconi CF, PO˜rez-Lorenzo M, Codding SJ. J Org Chem 2007;72:9456. 199. Bernasconi CF, Zoloff Michoff ME, deRossi RH, Granados AM. J Org Chem 2007;72:1285. 200. Bernasconi CF, Bhattacharya S. Organometallics 2003;22:426. 201. Richard JP. J Am Chem Soc 1986;108:6819. 202. Richard JP. J Am Chem Soc 1989;111:6795. 203. Richard JP, Amyes TL, Stubblefield V. J Am Chem Soc 1990;112:9513. 204. Richard JP, Amyes TL, Stevens IW. Tetrahedron Lett 1991;32:4255. 205. Amyes TL, Stevens IM, Richard JP. J Org Chem 1993;58:6057. 206. Richard JP. J Org Chem 1994;59:25. 207. Schepp NP, Wirz J. J Am Chem Soc 1994;116:11749. 208. Boyd DR, Blacker J, Byrne B, Dalton H, Hand MV, Kelly SC, et al. J Chem Soc, Chem Commun 1994:313. 209. Toteva MM, Richard JP. J Am Chem Soc 2000;122:11073. 210. Toteva MM, Richard JP. J Am Chem Soc 2002;124:9798. 211. Jagannadham V, Amyes TL, Richard JP. J Am Chem Soc 1993;115:8465. 212. Hine J. Structural effects on equilibria in organic chemistry. New York: WileyInterscience; 1975. pp. 8–10. 213. Kirby AJ. The anomeric effect and related stereoelectronic effects in organic chemistry. Oxford:Pergamon; 1983. 214. More O’Ferrall RA, Murray BA. J Chem Soc, Chem Commun 1988:1098. 215. Schleyer PvR, Jemmis ED, Sptiznagel GW. J Am Chem Soc 1985;107:6393. 216. Reed AE, Schleyer PvR, J Am Chem Soc 1987;109:7362. 217. Kon ´ ˘ a J, Zahradnik P, Fabian WMF. J Org Chem 2001;66:4998. 218. Gronert S, Lee JM. J Org Chem 1995;60:6731. 219. Gronert S, Azizian K, Friedman MA. J Am Chem Soc 1993;120:3220. 220. Kim C, Traylor TG, Perrin CL. J Am Chem Soc 1998;120:9513. 221. McClelland RA, Engelt KM, Larsen TS, S½rensen PE. J Chem Soc, Perkin Trans 2 1994:2199. 222. Kandanarachichi P, Sinnott ML. J Am Chem Soc 1994;116:5592. 223. Shukla D, Liu G, Dinnocenzo JP, Farid S. Can J Chem 2003;81:744. 224. Costentin C, SavO˜ant J-M. J Phys Chem A 2005;109:4125. 225. Pu J, Ma S, Garcia-Viloca M, Gao J, Truhlar DG, Kohen A. J Am Chem Soc 2005;127:14879.
Kinetic studies of keto–enol and other tautomeric equilibria by flash photolysis JAKOB WIRZ Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland 1 Introduction 325 2 Methods 326 Flash photolysis 326 Derivation of the rate law for keto–enol equilibration 327 Halogen titration method 332 pH–Rate profiles 333 General acid and general base catalysis 338 3 Examples 340 4 Rate–equilibrium relationships 345 The Brønsted relation, statistical factors, and the acidity of solvent-derived species (H and H2O) 345 Mechanism of the ‘‘uncatalyzed’’ reaction 348 The Marcus model of proton transfer 350 5 Conclusion and outlook 353 References 354
1
Introduction
Erlenmeyer was first to consider enols as hypothetical primary intermediates in a paper published in 1880 on the dehydration of glycols.1 Ketones are inert towards electrophilic reagents, in contrast to their highly reactive enol tautomers. However, the equilibrium concentrations of simple enols are generally quite low. That of 2propenol, for example, amounts to only a few parts per billion in aqueous solutions of acetone. Nevertheless, many important reactions of ketones proceed via the more reactive enols, and enolization is then generally rate-determining. Such a mechanism was put forth in 1905 by Lapworth,2 who showed that the bromination rate of acetone in aqueous acid was independent of bromine concentration and concluded that the reaction is initiated by acid-catalyzed enolization, followed by fast trapping of the enol by bromine (Scheme 1). This was the first time that a mechanistic hypothesis was put forth on the basis of an observed rate law. More recent work
E-mail: J.
[email protected] 325 ADVANCES IN PHYSICAL ORGANIC CHEMISTRY VOLUME 44 ISSN: 0065-3160 DOI: 10.1016/S0065-3160(08)44006-6
2010 Elsevier Ltd. All rights reserved
326
J. WIRZ O
slow H2O/H
OH
fast Br2
O Br
+ HBr
Scheme 1
has shown that the reaction of bromine with various acetophenone enols in aqueous solution takes place at nearly, but not quite, diffusion-controlled rates.3 In 1978, we observed that flash photolysis of butyrophenone produced acetophenone enol as a transient intermediate, which allowed us to determine the acidity constant KaE of the enol from the pH–rate profile (section ‘‘pH–Rate Profiles’’) of its decay in aqueous base.4 That work was a sideline of studies aimed at the characterization of biradical intermediates in Norrish Type II reactions and we had no intentions to pursue it any further. Enter Jerry Kresge, who had previously determined the ketonization kinetics of several enols using fast thermal methods for their generation. He immediately realized the potential of the photochemical approach to study keto–enol equilibria and quickly convinced us that this technique should be further exploited. We were more than happy to follow suit and to cooperate with this distinguished, inspiring, and enthusing chemist and his cherished wife Yvonne Chiang, who sadly passed away in 2008. Over the years, this collaboration developed into an intimate friendship of our families. This chapter is an account of what has been achieved. Several reviews in this area appeared in the years up to 1998.5–10 The enol tautomers of many ketones and aldehydes, carboxylic acids, esters and amides, ketenes, as well as the keto tautomers of phenols have since all been generated by flash photolysis to determine the pH–rate profiles for keto–enol interconversion. Equilibrium constants of enolization, KE, were determined accurately as the ratio of the rate constants of enolization, kE, and of ketonization, kK, Equation (1). KE ¼ kE =kK
ð1Þ
Strong bases in dry solvents are usually used in organic synthesis to generate reactive enol anions from ketones. Nevertheless, the kinetic studies discussed here were mostly performed on aqueous solutions. Apart from the relevance of this medium for biochemical reactions and green chemistry, it has the advantage of a well-defined pH-scale permitting quantitative studies of acid and base catalysis.
2
Methods
FLASH PHOTOLYSIS
The technique of flash photolysis, introduced in 1949 by Norrish and Porter,11 now covers time scales ranging from a few femtoseconds to seconds and has become a ubiquitous tool to study reactive intermediates. Most commonly,
KINETIC STUDIES OF KETO–ENOL TAUTOMERIC EQUILIBRIA
327
light-induced changes in UV-Vis optical absorption are monitored, either at a single wavelength (kinetic mode) or spectrographically at a given delay with respect to the light pulse used for excitation (spectrographic mode, pump–probe spectroscopy). Instruments of a conventional design,12 which employ an electric discharge to produce a strong light flash of sub-millisecond duration, usually have sufficient time resolution and are then most suitable to study the kinetics of keto–enol tautomerization reactions. Nowadays, instruments using a Q-switched laser as an excitation source having durations of a few nanoseconds (laser flash photolysis) are much more widespread. These techniques are well known, and their properties, pitfalls, and limitations have been described.13–15
DERIVATION OF THE RATE LAW FOR KETO–ENOL EQUILIBRATION
Activation energies for unimolecular 1,3-hydrogen shifts connecting ketones and enols are prohibitive, so that thermodynamically unstable enols can survive indefinitely in the gas phase or in dry, aprotic solvents. Ketones are weak carbon acids and oxygen bases; enols are oxygen acids and carbon bases. In aqueous solution, keto–enol tautomerization proceeds by proton transfer involving solvent water. In the absence of buffers, three reaction pathways compete, as shown in Scheme 2. Four species participate in the tautomerization reaction, the ketone (K, e.g., acetone), the protonated ketone (K), the enol (E), and its anion (E). These species are connected through two thermodynamic cycles. The Gibbs free energies for the individual elementary reactions r of any cycle must add up to naught, Equation (2). SDr Go ¼ 2:3RTSpKr ¼ 0
ð2Þ
OH K
Ka
E
k0 + kOH cOH
K K KE kH cH + k0
O
OH
′E k0′E + kOH cOH
K ′K
K
rate determining E
′K
k0 + kH c H
O
E E
Ka
E
Scheme 2
Acid-, base-, and ‘‘uncatalyzed’’ reaction paths of keto–enol tautomerism.
328
J. WIRZ
For the cycle K ! E ! E þ H ! K we get pKE þ pKEa pKK a ¼ 0, where are the acidity KE is the equilibrium constant of enolization and KEa and KK a is defined in the direction opposite to the constants of E and K, respectively; KK a must be subtracted. Similarly, the equilibrium last process of the cycle so that pKK a constant for carbon deprotonation of the protonated ketone, K ! E þ H, can K be replaced by pKE þ pKK a , where pKa is the acidity constant of K . Thus, the equilibrium properties of Scheme 2 are fully defined by the three equilibrium constants KE, KEa , and KK a . We turn to the kinetic parameters. When an enol E is rapidly generated in a concentration cE(t = 0) exceeding its equilibrium concentration cE(1), the decrease of cE(t) may be followed in time by, for example, some absorbance change as in flash photolysis. Deprotonation or protonation of carbon atoms is generally slow relative to the equilibration of oxygen acids with their conjugate bases. Therefore, carbon acids and bases have been called pseudo-acids and pseudo-bases. Proton transfer reactions involving carbon are the ratedetermining elementary steps of the tautomerization reactions. A shaded oblique line is drawn across these reactions in Scheme 2. Thus we posit that the protonation equilibria on oxygen that are associated with the ionization constants KEa and are established at all times during the much slower tautomerization reacKK a tions. This assumption leads to a pH-dependent first-order rate law for keto–enol tautomerization reactions, Equation (14), which will be derived below and is found to hold in general. The pre-equilibrium assumption adopted for oxygen acids is, thereby, amply justified. We define equilibrium constants as concentration quotients, as in Equation (3) for KEa and KK a . Provided that the experiments are done at low and constant ionic strengths, I £ 0.1 M, these can be converted to thermodynamic constants, Ka, using known or estimated activity coefficients.16 KaE ¼ cE ðtÞcH =cE ðtÞ and KaK ¼ cK ðtÞcH =cK ðtÞ
ð3Þ
The total concentration of the enol and its anion is cE;tot ðtÞ cE ðtÞ þ cE ðtÞ; inserting Equation (3) we can express the concentrations cE and cE as a function of proton concentration cH, Equation (4). cE ð t Þ ¼
KaE
cH KE cE;tot ðtÞ and cE ðtÞ ¼ E a cE;tot ðtÞ þ cH Ka þ cH
ð4Þ
Protons and hydroxyl ions are not consumed by the reaction K Ð E. A temporary shift in the relative concentrations of K and E may, however, lead to a change in proton concentration cH due to rapid equilibration with K and E, respectively. To avoid this complication, the conditions are generally chosen such that cH remains essentially constant during the reaction by using either a large excess of acid or base, or by the addition of buffers in near-neutral solutions (pH = 7 4). However, the addition of buffers usually
KINETIC STUDIES OF KETO–ENOL TAUTOMERIC EQUILIBRIA
329
accelerates the rates of tautomerization. We first consider reactions taking place in wholly aqueous solutions, that is, in the absence of buffers. The handling of rate constants obtained with buffered solutions will be discussed in section ‘‘General Acid and General Base Catalysis’’. To derive the general rate law for keto–enol equilibration, we consider each of the rate-determining elementary reaction steps shown in Scheme 2 separately, beginning with enol ketonization reactions. The relevant rate constants for the and kK rate-determining ketonization reactions are kK 0 for C-protonation of H 0K E by H and solvent water, respectively, and kH and k0K 0 for C-protonation of E by H and water (Scheme 2). We use primed symbols k0 for the rate constants referring to ketonization of the anion E. As we shall see in a moment 0K E [Equation (7)], the terms kK 0 and kH Ka are both independent of pH and may K be combined to a single term kuc . The associated, seemingly ‘‘uncatalyzed’’ reactions are therefore kinetically indistinguishable and additional information is required to determine, which of the corresponding mechanisms is the dominant one (see section ‘‘Mechanism of the ‘Uncatalyzed’ Reaction’’). We assume that the rate-determining reactions shown in Scheme 2 are elementary reactions, so that the corresponding rate laws are equal to the product of a rate constant and the concentrations of the reacting species. Acid-catalyzed ketonization The rate for ketone formation by carbon protonation of the enol E is given by Equation (5), where the right-hand expression is obtained by substituting cE(t) using Equation (4). K K vK H ¼ kH cH cE ðtÞ ¼ kH cH
cH cE;tot ðtÞ KaE þ cH
ð5Þ
Base-catalyzed ketonization Pre-equilibrium ionization of E generates the more reactive anion E, which may be protonated on carbon by the general acid water in the rate-determining step, Equation (6). For pH values well below pKK a , the concentration cH is much greater than KEa , which may thus be neglected in the denominator of Equation (6). The rate of this reaction is then inversely proportional to cH, i.e., proportional to cOH . This ‘‘apparent’’ base catalysis saturates at pH values above pKEa , when E is converted to E. The concentration cH then becomes much smaller than KEa and may be neglected in the denominator of Equation (6). 0
0
K K vK OH ¼ k0 cE ðtÞ ¼ k0
KaE
KaE cE;tot ðtÞ þ cH
ð6Þ
330
J. WIRZ
‘‘Uncatalyzed’’ ketonization At pH values near neutral, a pH-independent rate of ketonization is frequently observed, which may be attributed to several different mechanisms (see section ‘‘Mechanism of the ‘Uncatalyzed’ Reaction’’): carbon protonation of E by water or a concerted transfer of the enol proton to carbon through one or more solvent molecules, and carbon protonation of E by the proton, Equation (7). For pH << pKEa , the right-hand expression becomes independent of cH. 0 0K K K K E K ¼ k c ð t Þ þ k k þ k vK cH cE ðtÞ ¼ E 0 0 0 a H H
KaE
cH cE;tot ðtÞ þ cH
ð7Þ
Summing up the rates of these competing reaction paths, Equations (5–7), one obtains the total rate of enol ketonization, Equation (8). Note that vK refers exclusively to the forward reaction E ! K. v ¼ K
kK 0
þ
0
kHK KaE
þ
kK H cH
þ
0
k0K
KaE cH cE;tot ðtÞ ¼ kK cE;tot ðtÞ cH KaE þ cH
ð8Þ
The rather complex expression preceding cE,tot(t) is nothing but a collection of constants for a given proton concentration cH. Thus, Equation (8) represents a first-order rate law with a pH-dependent rate constant kK. 0K K K E , k0K The three independent rate constants kK 0 , and kuc ¼ k0 þ kH Ka fully H determine the kinetic properties of Scheme 2, because the rate constants kEi for enolization are related* to those of the reverse reactions, Equation (9), where Kw is the ionization constant of water. We use primed symbols for the enolization of the neutral ketone K. In the rate equation for enolization, the terms k0E 0 and kEOH Kw =KK are kinetically indistinguishable (see Equation (10) below). a
aÞ kE0 ¼ KE KaK kK ; H
bÞ kEOH ¼ KE KaK kK 0 =Kw ;
cÞ k 0 ¼ KaK k
dÞ k OH ¼ KaK k 0 =Kw
0E
0K
H ;
0E
0K
ð9Þ
The rate of the reverse reactions, Equation (10), is derived in the same way using cK;tot ðtÞ cK ðtÞ þ cK ðtÞ and the ionization product of water, Kw = 1.59 1014 M2 (I = 0.1 M), to replace cOH by KW/cH. vE ¼
*
0
k0E þ kEOH
Kw KaK
þ
kE0 Kw KaK 0E c þ k cK;tot ðtÞ H OH cH KaK þ cH KaK
ð10Þ
In a system of connected reversible reactions at equilibrium, each reversible reaction is individually at equilibrium. This is the principle of microscopic reversibility or its corollary, the principle of detailed balance.
KINETIC STUDIES OF KETO–ENOL TAUTOMERIC EQUILIBRIA
331
Replacement of the rate constants kEi in Equation (10) by those of the reverse reactions kK i using Equation (9) gives Equation (11). Most ketones are < 0. Hence, cH in the denominator of Equation (11) very weak bases, pKK a in the normal pH range, i.e., the ratio may be neglected relative to KK a K K Ka =ðKa þ cH Þ is unity. vE ¼
kK 0 þk
0K
H
E 0K K KaK a K KaE þ kK cK;tot ðtÞ ¼ kE cK;tot ðtÞ cH þ k0 E H c H KaK þ cH
ð11Þ
The observed rate law Starting from an excess enol concentration at time t = 0, the observable decay of total enol concentration in time, Equation (12), is equal to the difference between the ketonization rate of the enol, vK [Equation (8)], and the enolization rate of the ketone, vE [Equation (11)]. Equilibrium (t = 1) is reached when vK = vE, i.e., when –dcE,tot(t)/dt = 0. dcE;tot ðtÞ=dt ¼ vK vE ¼ kK cE;tot ðtÞ kE cK;tot ðtÞ
ð12Þ
The time-dependent concentrations cE,tot(t) and cK,tot(t) are related by mass conservation, cE,tot(t) þ cK,tot(t) = cE,tot(1) þ cK,tot(1) = const. Substituting cK,tot(t) by cE,tot(1) þ cK,tot(1) – cE,tot(t) and using the relation cE,tot(1)/cK,tot(1) = kE/kK one obtains Equation (13).
dcE;tot ðtÞ=dt ¼ kE þ kK cE;tot ðtÞ cE;tot ð1Þ
ð13Þ
Integration gives the rate law for the decay of enol to its equilibrium concentration cE,tot(1), Equation (14).
E K cE;tot ðtÞ ¼ cE;tot ð0Þ cE;tot ð1Þ e ðk þk Þt þ cE;tot ð1Þ
ð14Þ
Thus the approach to equilibrium always follows a first-order rate law, Equation (14), with the pH-dependent rate constant kobs = kE þ kK. Figure 1 shows the concentration changes in time starting from a 1M solution of pure enol (full line) and of pure ketone (dashed line). The individual, unidirectional rate constants kE and kK can be determined as follows: For most ketones the equilibrium enol concentration is quite small, i.e., KE = cE(1)/ cK(1) << 1. Hence kE << kK [Equation (1)], so that enol ketonization is practically irreversible and kE may be neglected, kobs kK. The rate constant of enolization kE, on the other hand, is equal to the observed rate constant of reactions for which enolization is rate-determining, such as ketone bromination (Scheme 2).
332
J. WIRZ
Fig. 1 Time-dependent concentrations of cE,tot(t), starting from pure enol (full line), and pure ketone (dashed line), Equation (14).
HALOGEN TITRATION METHOD
Some ketones such as -dicarbonyls contain substantial amounts of the enol at equilibrium. For example, acetylacetone in aqueous solutions contains 13% of 4-hydroxypent-3-en-2-one, which is stabilized both by an intramolecular hydrogen bond and the inductive effect of the remaining carbonyl group.17 When bromine is added to such a solution, a portion is initially consumed very rapidly by the enol that is already present at equilibrium. The ketone remaining after consumption of the enol reacts more slowly via rate-determining enolization. The slow consumption of bromine is readily measured by optical absorption. In acidic solutions containing a large excess of the ketone the slow reaction follows a zero-order rate law; the rate is independent of bromine concentration, because any enol formed is rapidly trapped by bromine (Scheme 1). In this case, the amount of enol present at equilibrium may be determined as the difference between the amount of bromine added and that determined by extrapolation of the observed rate law to time zero, as is shown schematically in Fig. 2.
Fig. 2 Bromine titration method.
KINETIC STUDIES OF KETO–ENOL TAUTOMERIC EQUILIBRIA
333
This technique, called ‘‘bromine titration method’’, was extensively used by K.H. Meyer in the early twentieth century.18 It was later extended to determine the enol content of simple ketones using faster flow methods combined with more sensitive potentiometric measurements of bromine uptake, but this technique sometimes produced apparent enol contents that were far too high, such as the enol content of acetone of 2.5 104% that is frequently quoted in older textbooks of organic chemistry. The excessive values so obtained have been attributed to the presence of small amounts of impurities reacting with bromine.
pH–RATE PROFILES
The dependencies of kobs [Equation (14)], kE [Equation (11)], and kK [Equation (8)] on proton concentration are usually displayed in log–log plots called pH–rate profiles, which allow one to identify the reaction paths dominating at various pH values as well as the parameters of the rate law, namely the acidity constants Ka and the elementary rate constants of the rate-determining steps. Figure 3 shows pH–rate profiles of kE (dashed line), kK (thin full line, coincides with kobs below pH 17), and kobs = kE þ kK (thick gray line), which were plotted using Equations (8) and (11) with the six relevant kinetic and thermodynamic parameters that have been determined for acetophenone (see Table 1 in section ‘‘Examples’’).4,19–23 It is worth spending some time to interpret and digest the curves shown in Fig. 3. The acid-catalyzed reaction paths dominate at pH values below 3 (marked by the symbol ‘‘a’’). In region ‘‘a,’’ the slope of the curves equals 1
_
Fig. 3 pH–rate profiles for kK (—, Equation (8)), kE (- - -, Equation (11)) and kobs = kK þ kE ( ) of acetophenone in aqueous solution.
Table 1 Kinetic and thermodynamic parameters determined for various tautomeric equilibria in aqueous solution at 25C. The symbols for the rate constants k and the equilibrium constants K are explained in the text (first paragraph of section ‘‘Examples’’). Acidity constants are concentration quotients of ionization at ionic strength I = 0.1 M Stable tautomer Acetone Butan-2-one Butan-2-one 3-Methylbutan-2-one 3-Methylbutan-2-one 3,3-Dimethylbutan-2-one
Unstable tautomer
Propen-2-ol 2-Buten-2-ol 1-Buten-2-ol 3-Methyl-1-buten-2-ol 3-Methyl-2-buten-2-ol 3,3-Dimethyl-1-buten2-ol Pentan-3-one 2-Penten-3-ol Cyclopentanone Cyclopenten-1-ol Cyclohexanone Cyclohexen-1-ol Cycloheptanone Cyclohepten-1-ol 2,4-Dimethylpentan-3-one 2,4-Dimethylpent-1-en3-ol Acetophenone a-Hydroxystyrene Isobutyrophenone 1-Phenylisobuten-1-ol 1-Tetralone 3,4H-Naphthalen-1-ol 1-Indanone Indene-3-ol 2-Indanone Indene-2-ol Isochroman-4-one 1H-2-Benzopyran-4-ol Acetoacetate Acetoacetate enol 4,4,4Trifluoroacetoacetate Trifluoroacetoacetate enol Oxocyclohexane-2Cyclohexen-1-ol-2carboxylate carboxylate Oxocyclopentane-2Cyclopenten-1-ol-2carboxylate carboxylate
pKE 8.33 7.51 8.76 8.60 7.33 8.76
1 1 kK s ) H/(M
1 kK uc /s
pKEa
pKK a
10.94
3.06 3.48 3.48 3.63 3.63 3.48
5.38 103 839 6.30 103 5.93 103 233 7.51 103
3.88
793 5.3 103 577 4.0 103 97.5
3.87
1.25 103 2.14 180 904 3.36 0.090 1.28 105 7.44 102
0.18 5.1 104 1.1 102 0.26 0.207
0.077
0
k 0K/s1 5.0 104
Referencesa 20, 48, 48, 48, 48, 48,
46, 47 49 49 49 49 49
48, 48, 48, 48, 48,
49 49 49 49 49
7.43 7.94 6.38 8.00 7.52
11.7
7.96 6.48 7.31 7.48 3.84 5.26 2.91 0.61
10.35 11.78 10.82 9.48 8.36 10.13 13.18 9.95
1.99
14.53
1.35 104
2.32 105 18.0
56
3.00
12.41
2.41 105
2.57 102 484
57
1.8 102 2.12 103
7.2 103 69 743 501 6.95 10.8 9.06 102 3.2 102
4, 20–23 50 51 52 53 51 54 55
3,3,5,5-Tetramethyloxocyclopentane-2carboxylate Oxocyclobutane-2carboxylate Phenol Phenol 1-Naphthol 1-Naphthol 9-Anthrone Acetaldehyde Isobutyraldehyde 2-Phenylacetaldehyde 2-Phenylacetaldehyde 2,2-Diphenylacetaldehyde Cyclopentadienyl-1carboxylic acid Cyclopentadienyl-1carboxylate
3,3,5,5-Tetramethylcyclopenten-1-ol-2carboxylate Cyclobuten-1-ol-2carboxylate Cyclohexa-2,4-dienone Cyclohexa-2,5-dienone Benzo[b]cyclohexa-2,5dienone Benzo[b]cyclohexa-2,4dienone 9-Anthrol Vinyl alcohol 2-Methylpropen-1-ol cis-2-phenylethen-1-ol trans-2-phenylethen-1ol 2,2-Diphenylethen-1-ol Fulvenediol Fulvenediol anion
1-Indene-3-carboxylic acid Benzofulvenediol 1-Indene-3-carboxylate Benzofulvenediol anion
1.83
14.4
7.60 104
1.74 103 310
58
5.97
8.47
1.59 107
12.8
319
59
12.73 11.0 6.2
9.84 9.84 9.25
1.0 107 3.0 107 5.7 105
7.1 1010 8.4 1010 1.3 107
4.1 1011
7.1
9.25
2.8 105
5.7 107
7.8 108
2.14 6.23 3.86 3.35 3.07
7.84 10.50 11.63 9.76 9.46
0.032 33 0.59 0.190 0.0745
1.8 103 0.039 4.0 104
8.3 103 882 6.6 4.1 1.33
44 44 Wirz J et al., unpublished Wirz J et al., unpublished 33, 60 61 62 40 40
0.98 8.4
9.40 1.31
2.1 103
7.0 104 1.1 108
0.106
5.0
8.7
9.3 6.6
1.90 8.3
4.71
2.2 107
4.50
2.21 10
1.0 107
3
7
2.8 105 105
34 36, 37 (Almstead JIK and Wirz J, unpublished) 36, 37 (Almstead JIK and Wirz J, unpublished) 36 36
Table 1 (continued ) pKE
pKEa
Fluorene-9-carboxylic acid Fluorene-9-carboxylate
Dibenzofulvenediol
9.67
2.01
Dibenzofulvenediol anion a-Cyano-,dihydroxy-styrene anion a,,Trihydroxystyrene a,-Dihydroxy-methoxystyrene -Amino-a,dihydroxystyrene 2,6-dimethyl-4hydroxy-1,3,5heptatriene Phenylethynol Phenylethynamine N-Pentafluorophenylphenylethynamine 3H-Indole Enamine tautomer
8.24
9.61
11.67
1.25 108
6.49
8.70
8.22
2.09 107
16.19
6.39
Mandelic acid Methyl mandelate Mandelamide Diisobutenyl ketone (phorone) Phenylketene Phenylketenimine N-Pentafluorophenylphenylketenimine 1H-Indole 2-(20 ,40 -Dinitrobenzyl) pyridine 2-Nitrotoluene a
aci-Nitro tautomer
k 0K/s1
Referencesa
1.23 106
9.03 103
6.55 15.88
8.40
1.7 10
7.2
10.84
200
63 3.22 103
63
2.53 104
64
3.89 102
1.7 105
65, 66
5.24 10
4.20 10
67
2.56 10
68
2.6
378
69
2 107b)
2.52 106
30
2
6
5 6
£2.8 £18c) 10.23
8.9 102
1.08
6.52 105
38, 39 41 42
5.8 8.0
5.94
4.9 106 5.8 105
0.207 17
0.09
70 32, 45
17
3.57
1.3 105
1.16
31
The pKK values of protonated ketones were taken from Reference 19. a 9 1 1 Calculated from the observed rate constant k0K s , Equation (18). H = 1.34 10 M c 6 1 1 11 1 0K E Calculated from the observed rate constant kK ¼ k K =K s assuming k0K W = 6.5 10 M 0 0 £ 1 10 s . a OH b
0
K 1 1 1 kH /(M s ) kK uc /s
Unstable tautomer
Phenylcyanoacetate
pKK a
Stable tautomer
KINETIC STUDIES OF KETO–ENOL TAUTOMERIC EQUILIBRIA
337
because the rate constants kE and kK are directly proportional to acid c of Equations concentration cH. This is due to the dominant terms kK H H (8) and (11). Because the acidity constant of enols, KEa , is usually much smaller than cH at pH < 3, the ratio cH =ðKEa þ cH Þ of Equation (8) amounts to <0 unity. On the other hand, protonated ketones are very strong acids, pKK a so that, in moderately strong acidic solutions, the term cH in the denominator of Equation (11) can be neglected relative to KK a . Acid catalysis of enolization K saturates for pH pKa ; a further increase in acid concentration no longer accelerates enolization when the ketone is quantitatively converted to its conjugate acid. However, this saturation is rarely observed at pH values > 0. In the areas ‘‘b’’ (pH > 7) and ‘‘u’’ (pH 5) the contributions of the basecatalyzed and ‘‘uncatalyzed’’ reactions dominate, respectively. The slopes in region ‘‘b’’ are þ1 (the rates are proportional to base concentration cOH with E ¼ k0K an apparent rate coefficient kK 0 Ka =KW for base catalysis), but base OH catalysis of ketonization saturates at pH pKEa , when the pre-equilibrium of 0K the enol shifts to the enolate so that kK obs approaches k0 , the first-order rate constant for the protonation of E by water, Equation (6). The pKEa values of simple enols are usually around 9–11. The curves for log(kK/s1) and log(kE/s1) of acetophenone are parallel in << pH << pKEa and the vertical distance between them the range pKK a then equals pKE = log(kK/s1) log(kE/s1). Most ketones are very weak < 0, so that the parameter KK does not affect the shape of bases, pKK a a the pH–rate profiles in the range pH > 1. Base catalysis of ketonization saturates at pH = pKEa , while the rate of enolization continues to rise, so that the curves for kE and kK eventually cross at higher pH. At still higher pH, the rate E constant kE exceeds that of kK = k0 K 0 , and kobs follows k . The crossing point, E K K for which k = k , lies at pH = pKa = 18.3 for acetophenone (Fig. 3), which is outside the accessible pH range when ionic strength I is limited to 0.1 M, but pKK a is readily calculated from Equation (2). The rates of ketonization are usually easier to determine (by flash photolysis) than the much slower rates of enolization that require laborious conventional methods such as measuring bromination kinetics and analysis of the reaction products. Thus the shape of the profile is conveniently explored by flash photolysis over a wide range of pH for kK, and only a single point on the lower curve is then required to determine the enolization constant KE. A single reaction path dominates at most pH values, and in these regions the curves are straight lines with slopes of 1, 0, or þ1, corresponding to acid catalysis, uncatalyzed reaction, and base catalysis, respectively. The mechanistic implications of positive curvature (increasing slope) and of negative curvature (decreasing slope) differ fundamentally from each other. pH–rate profiles are readily interpreted with the aid of the following rules.24
338
J. WIRZ
1. Positive curvature indicates a change in the reaction mechanism. In the areas of positive curvature, two reaction paths with different pH-dependence are competitive. The two regions of positive curvature near the bottom of the two curves in Fig. 3 indicate a change from the acid-catalyzed to the uncatalyzed path (around pH 4), and from the uncatalyzed to the base-catalyzed reaction (pH 6). 2. The same reaction mechanism operates in the regions to the left and right of negative curvature. In general, negative curvature can arise from two causes: (a) Pre-equilibria: As we have seen, acid catalysis of ketone enolization saturates around pH = pKK a , and base catalysis of enol ketonization E saturates around pH = pKa . Thus, the acidity constants of reactive intermediates participating in pre-equilibria can be determined by nonlinear least-squares fitting of the kinetic equations to the experimental data. (b) A change in the rate-determining step of a reaction can also give rise to negative curvature, when the pH-dependencies of the two steps differ. This case is rarely encountered in keto–enol tautomerization. However, when very low halogen concentrations are used, the secondorder reaction of enol trapping does eventually become the ratedetermining step of ketone halogenation. Quite accurate enolization constants of some simple ketones have been derived in this way, based on the assumption that halogen trapping is diffusion-controlled, as indicated by the fact that the second-order rate constants of chlorination, bromination, and iodination were found to be nearly the same.25
GENERAL ACID AND GENERAL BASE CATALYSIS
The addition of buffers is required to maintain constant pH during the reaction when experiments are to be carried out in the range 3 < pH < 11. However, keto–enol tautomerization reactions usually exhibit so-called ‘‘general’’ acid and base catalysis.†,26 The observed rate acceleration with increasing buffer concentration implies that the components of the buffer participate in some rate-determining step of the reaction. In most cases, the rate of reaction increases linearly with increasing buffer concentration at constant buffer ratio, cHB/cB = const (Fig. 4a). Reaction rate constants applying to wholly aqueous (i.e., unbuffered) solutions are required for pH–rate profiles. These can be obtained by linear extrapolation of a buffer dilution plot to zero buffer concentration. To determine the individual contributions of the general acid and base components of
†
‘‘General’’ acid catalysis is distinguished from ‘‘specific’’ acid catalysis, which applies when a general acid participates only in pre- or post-equilibrium steps; then only the proton concentration cH appears in the rate law.
KINETIC STUDIES OF KETO–ENOL TAUTOMERIC EQUILIBRIA
339
Fig. 4 (a) Buffer dilution plot; (b) buffer slopes as a function of buffer ratio.
the buffer, the slopes of several dilution series obtained at different buffer ratios are plotted against the mole ratios xHA = cHA/(cHA + cA ) of the buffers (Fig. 4b). Linear extrapolation to xHA = 0 and 1 then gives the catalytic coefficients kA and kHA, respectively. In general, both coefficients kA and kHA are found to be different from zero, although they may be difficult to determine accurately, when they are small compared to the rate coefficients of the solvent-derived species. It may be surprising that the coefficient for general base-catalyzed ketoniza, should differ from zero, because only general acids accelerate the tion, kK A rate-determining steps of ketonization by carbon protonation of E and E. Correspondingly, only general bases accelerate the rate-determining steps of enolization by deprotonation of the ketone or of its conjugate acid. Let us take a look at ketonization, which may occur either by direct protonation of the enol by HA (upper line of Scheme 3) or by pre-equilibrium ionization of the enol, followed by rate-determining carbon protonation of the enolate by HA (lower line). Thus, two terms must be added to the rate law of ketonization, Equation (8), and the buffer slopes are given by Equation (15).
@kK @cHA
¼
kK HA
þ
0
K kHA
cH
KaE cH
cH KaE þ cH
ð15Þ
K
OH
OH +A
kHA
OH
+ HA
K = KaE/KaHA
+A
k'HA K
O
+ HA
O
+A
Scheme 3 Rate-determining reactions giving rise to general acid catalysis of ketonization.
340
J. WIRZ
E In the first term, the rate constant kK HA is multiplied by cH =ðKa þ cH Þ, the fraction of total enol present in neutral form E, and in the second term, k0K HA is multiplied by KEa =ðKEa þ cH Þ, the fraction of total enol present in basic form E [Equation (4)]. The observed coefficient for general base catalysis kK A is now seen to arise from the pre-equilibrium reaction shown in the second line ðKEa =KHA of Scheme 3. Replacing ðKEa =cH ÞcHA by a ÞcA we find 0K K E HA kA ¼kHA Ka =Ka . Thus, pre-equilibrium deprotonation of the enol by the general base followed by carbon protonation of the ensuing enol anion is operationally equivalent to general base catalysis. At high buffer concentrations, positive curvature may be observed in buffer dilution plots, indicating that the general acid and base are simultaneously participating in the rate-determining step.27 In such a case, the rate law must be expanded by third-order terms. Furthermore, plots of buffer slopes versus xHB may be nonlinear, when the unstable tautomer is a diprotic acid as, for example, the aci-nitro tautomer of nitrobenzene.28 Buffer catalysis has been applied to induce chiral induction by enantioselective protonation; remarkable enantiomeric excess was achieved in the photodeconjugation of a,-unsaturated ketones and esters by using chiral catalysts for the ketonization of photoenols in aprotic solvents.29
3
Examples
The six parameters defining the kinetic and thermodynamic properties of tautomerization reactions that have been determined for a representative selection of carbon acids are collected in Table 1. The column headed by the symbol kK uc contains the observed pH-independent, ‘‘uncatalyzed’’ terms, K 0K E ¼k þ k kK H Ka , of the ketonization rate law [Equation (8)]. In general, uc 0 the unprimed symbols k refer to rate constants of the neutral enol tautomer and the primed symbol k0K 0 refers to the rate constant for the reaction of enol anion with water (cf. Scheme 2). However, when the stable tautomer is designated as an anion in the left-hand column of Table 1 (e.g., acetoacetate), the unprimed symbols in the header refer to rate or equilibrium constants of the enol anion and the primed symbol k0K 0 to the rate constant of the enol dianion. The acidity constants of the neutral ketone, formed by C-protonation of the enol anion, are then listed in the column headed by the symbol pKK a . To determine these data, the unstable tautomers were mostly generated by flash photolysis in order to measure their relaxation kinetics in aqueous solution at various pH. Some prototype precursors for the photochemical generation of unstable tautomers are shown in Scheme 4. In a few cases they are formed directly by irradiation of the stable form either by intramolecular photoenolization such as in 2-alkylacetophenones,30 2-nitrobenzyl derivatives28,31 such as 2-(20 ,40 -dinitrobenzyl)pyridine,32 or by light-induced proton transfer to solvent water, as in the case of 9-anthrone.33
KINETIC STUDIES OF KETO–ENOL TAUTOMERIC EQUILIBRIA O
O
CH3
OH
+
OH
hν
hν
CH2
OH
OH
O
2
+
341 CH2
OH
O hν Ar
Ar
OH/NH2 O
OH/NH2
+ CO
O H
hν
C O
+ H
O O
O N2
hν
C
HO
OH
H2O
–N2 O
CH2R
Ph
hν – RCH = CH2
HO
HO
OH
Ph
OH
C O Ph
O
Scheme 4 Prototype reactions used for the generation of unstable tautomers by flash photolysis.
Let us have a look at some instructive pH–rate profiles. That for acetophenone was already discussed in the section ‘‘pH–Rate Profiles’’ (Fig. 3). Its general shape is characteristic for the behavior of the enols of simple ketones and aldehydes. The enolization constants of aldehydes tend to be higher than those of ketones; compare, for example, pKE(acetone) = 8.33 and pKE(acetaldehyde) = 6.23. This is in line with the well-known stabilizing effect of alkyl substitution on double bonds, in particular of the polar C¼O bond. aSubstitution of ketones and aldehydes by alkyl or, better still, by aryl groups further stabilizes the enol, so that the enol content of 2,2-diphenylacetaldehyde reaches 10%.34 The enolization constants of carboxylic acids to form enediols are generally still lower than those of ketones. The pKE of acetic acid is about 20.35 Due to the relatively high acidity of 1,1-enediols, the enol content of carboxylate anions is somewhat higher. When the carboxylate is attached to cyclopentadienyl, a strong mesomeric electron acceptor, the conjugate acid of the enol, fulvene-1,1-diol, becomes a strong acid, pKa = 1.3, and the pKE of the enol anion is reduced to 5.0 (Almstead JIK and Wirz J, Unpublished data).36,37
342
J. WIRZ
The pH–rate profiles of the enol of 1-indene-3-carboxylic acid and of its ketene precursor, formed from either 1-diazo-2(1H)naphthalenone or 2-diazo-1(2H)naphthalenone by photochemical deazotization and Wolff rearrangement, are shown in Fig. 5.36 The first and second acidity constants of the diol, pKEa = 1.9 and pK0E a = 8.3, are evident from the downward 1 =s Þ at these pH values. The photo-Wolff rearrangecurvature of log ðkK obs ment of diazonaphthoquinones is the active principle of Novolak photoresists. Ynols and ynamines are the enol tautomers of ketenes and ketenimines, respectively. They were generated by CO photoelimination from the corresponding cyclopropenones (Scheme 4). Flash photolysis of phenylhydroxycyclopropenone produced transient absorption in the near UV that was monitored at 270 nm and exhibited a biexponential decay.38,39 The pH–rate profile and solvent isotope effects served to identify the first of these intermediates as the phenylynolate ion and the second as phenylketene; the identity of the ketene was also confirmed by independent generation through photo-Wolff reaction of benzoyldiazomethane. The kinetic behavior of phenylynolate is shown in Fig. 6. Protonation of the anion to the less reactive neutral phenylynol should produce saturation of acid catalysis. No indication of curvature was seen down to pH 2.8, where the limit in time resolution of the nanosecond apparatus was reached. This sets an upper limit of pKa £ 2.8 on the acid dissociation constant of phenylynol, which is a remarkable result: it makes phenylynol at least 7 pKa units more acidic than its double bond analogue, the enol of phenylacetaldehyde, PhCH=CHOH,40 which, in turn, is some 7 units more acidic than saturated alcohols. With hindsight, such a pKa difference seems quite reasonable; it is reminiscent of the well-known greater acidity of acetylenic C–H bonds over ethylenic C–H bonds. Both effects may be attributed to charge
Fig. 5 pH–rate profile of benzofulvene-1,1-diol, the enol of 1-indene-3-carboxylic acid, and its ketene precursor.36
KINETIC STUDIES OF KETO–ENOL TAUTOMERIC EQUILIBRIA
343
Fig. 6 pH–rate profile for the decay of phenylynol in aqueous solution.39
delocalization and especially to the increasing s-character and, hence, electronegativity, of carbon with increasing unsaturation. Similarly, ynamines are much stronger acids than enamines and alkylamines.8,41–43 Saturation of base catalysis allowed the determination of the NH acidity constant of N-(pentafluorophenyl)phenylethynamine in aqueous solution, pKEa =10.23.42 Aromatic enols, that is, phenols, are generally more stable than their ketone tautomers. The pH–rate profile for the enolization reaction of 2,4cyclohexadienone to parent phenol is shown in Fig. 7.44 The rate constant kK of the reverse reaction was determined at pH = 1 by measuring the rate of isotopic exchange and correcting for isotope effects to determine the enoliza¼ 5:4 1012 , pKE = 12.73. The dashed line in tion constant KE ¼ kEH =kK H
Fig. 7 pH–rate profiles for the enolization of 2,4-cyclohexadienone (upper curve) and for the reverse ketonization reaction (lower curve). Note that ordinate scale is shifted upward by 6.5 units for log(k) values below 3.44
344
J. WIRZ
the lower part of Fig. 7 shows the pH–rate profile of kK as calculated by determined at pH = 1. For pH values Equation (8) using the single value of kK H below pKEa = 9.8, where the neutral forms of the ketone and phenol predominate, the two curves are parallel, separated by the distance pKE. At pH values above pKEa , the phenol ionizes and kK begins to fall off (slope of 1). This is an unusual case where the addition of base actually inhibits the rate of tautomerization. The phenolate is protonated by hydronium ions and the rate increases with acid concentration in the pH range 11–9. Acid catalysis saturates when phenolate is neutralized at pH < pKEa = 9.8, because it is then compensated by the inverse dependence of the phenolate concentration on proton concentration. Above pH 11 the protonation of phenolate by water becomes dominant. The ‘‘uncatalyzed’’ regions of phenol tautomerization cover an unusually wide range from pH 3 to 10. The reason for this dominance of the uncatalyzed reaction, which is barely detectable in the pH–rate profiles of simple ketones (Fig. 3) and is absent in carboxylic acids (Fig. 5), will become clear from the linear free-energy relationship discussed in section ‘‘The Marcus Model of Proton Transfer’’. The predominant reaction of the ketone in the flat central 3 1 region is CH ionization by protonation of water, k0E 0 = 3.8 10 s . Owing to the large driving force of enolization, the dienone is a remarkably strong carbon acid: pKEa ¼ pKE þ pKEa ¼ 2:9, which is comparable to the acidity of HCl. The well-known photochromic tautomerism of 2-(20 ,40 -dinitrobenzyl) pyridine (CH, Scheme 5) was investigated by flash photolysis in aqueous
NO2
+H
N HO
N
O
OH hν
OH
NO2
H
CHNH
CHNH+
NO2
NO2
pK a,c
N
OH
pK a,c ≈ –0.6
pK T ≈ 14.5
+H = 4.18
N
NO2
CH
NO2
CNO–
NH
pK T = 8.0
hν
+ 2H CH pK a,c = 13.9 N O
N
O
420 nm
NH
pK a,c = 5.9
NO2
NO2
+H N
N H
HO
N
NHOH
O
pK a,c
<0
H
NO2
520 nm
NHOH+
NH
Scheme 5 Tautomerization reactions of 2-(20 ,40 -dinitrobenzyl)pyridine: a lightactivated proton shuttle.32
KINETIC STUDIES OF KETO–ENOL TAUTOMERIC EQUILIBRIA
345
Fig. 8 pH–rate profiles for the decay rate constant kin obs of NH and CNO (—) and for in the reverse reaction kobs (– –), see Scheme 5. Reproduced by permission from Reference 32.
solution in view of its potential application as a light-activated proton pump.32 Irradiation of CH yields the enamine tautomer NH (max = 520 nm) that rapidly equilibrates with its conjugate base CNO (max = 420 nm). Transient absorption in the visible region was formed within 30 ns and decayed by first-order kinetics. The pH–rate profile for the first-order decay rate constant of NH and NH CNO, kin obs (Fig. 8), determines the acidity constant of NH, pKa = 5.94. Rate were measured by More O’Ferrall and constants of the reverse reaction kout obs gave the tautomerizaQuirke45 using halogen trapping. Combination with kin obs = 8.0. tion constant pKNH T
4
Rate–equilibrium relationships
THE BRØNSTED RELATION, STATISTICAL FACTORS, AND THE ACIDITY OF SOLVENT-DERIVED SPECIES (H AND H2O)
Keto–enol tautomerization reactions usually exhibit general acid and general base catalysis (section ‘‘General Acid and General Base Catalysis’’). The rate coefficients for general acid catalysis, kHA, determined from a series of buffer dilution plots (Fig. 4) tend to obey a linear log–log relationship to the acidity
346
J. WIRZ
constants KHA of the catalysts. Similarly, the coefficients of general base a HA of the buffer catalysis kA are related to the basicity constants KA b ¼ Kw =Ka bases, as was first reported by Brønsted and Pedersen in 1924.71 Taking account of the appropriate statistical factors p and q,72,73 the Brønsted relations may be written as in Equation (16).74,75
HA kHA qKa ¼ log GA þ log p pA pKb kA pKw ¼ log GB þ log ¼ log GB þ log log q q qKaHA log
ð16Þ
The factor p is equal to the number of equivalent acidic hydrogens in a given general acid HA and the factor q represents the number of equivalent sites for proton attachment at the conjugate base A, GA and GA are constants for a given reaction, and the Brønsted parameters and are considered to be constant for a series of buffers with varying acidity or basicity. A plot of log(kHA/p) versus log(qKHA a /p) should therefore be linear with a slope of . This hypothesis has been amply confirmed. Equation (16) represents a linear free energy relationship for general acid and base catais equal to the free energy of ionization of the lysis, because 2.3RTpKHA a general acid HA. Rate theories generally require rate–equilibrium relationships to be curved rather than linear (see section ‘‘Mechanism of the ‘Uncatalyzed’ Reaction’’). Brønsted and Pedersen already noted that the bimolecular rate coefficients kA cannot increase indefinitely with increasing base strength of the catalyst, because they will eventually be limited by the rate of diffusion. Slight variation of the slope becomes perceptible when a wide range of general acids is used.20,50 The variation of becomes quite evident when general acid or base catalysis is compared for substrates with widely different free energies of reaction. Brønsted slopes , determined in each case with a series of general acids, versus the free energies DrG for C-protonation of enols or enolates are given in Table 2 and plotted in Fig. 9. To determine DrG, the acidity constants of the general acids used in the corresponding Brønsted plots were averaged. The Brønsted exponent increases from about 0.2 for strongly exergonic reactions (C-protonation of phenylethynolate) to 0.8 for strongly endergonic reactions (protonation of 1-naphthol at carbon atom 4). The observed increase of the Brønsted slope with increasing free energy of reaction is an exemplification of the Hammond postulate, because the Brønsted parameter may be regarded as a measure of the extent of proton transfer in the transition state: highly exergonic reactions have an early transition state ( ! 0) and endergonic reactions have a late transition state ( ! 1). The empirical correlation of the parameters with the reaction free energies DrG shown in Fig. 9 will be recast in terms of the Marcus model of proton transfer at the end of section ‘‘The Marcus Model of Proton Transfer’’.
KINETIC STUDIES OF KETO–ENOL TAUTOMERIC EQUILIBRIA
347
Table 2 Brønsted parameters and average reaction free energies DrG of the reactions E þ HA ! K þ A and E þ HA ! K þ A
Enolate Acetophenone enolate Isobutyrophenone enolate 1-Naphtholate – 4Hnaphthone Phenylynolate Phenolate – 2,4cyclohexadienone Isochroman-4-one enolate 9-Anthrolate Mandelamide enolate Enol Acetophenone enol Isobutyrophenone enol 1-Naphthol – 4Hnaphthone
DrG/(kJ mol1) a
calcb
References
0.32 0.37 0.62
83.5 83.3 0.0
0.31 0.31 0.50
0.25 0.67
109.0 52.7
0.25 0.62
20 50 Wirz J et al., unpublished work 39 44
0.47 0.56 0.31
47.9 26.3 97.1
0.39 0.44 0.28
51 33 68
DrG/(kJ mol1) a
calcb
0.50 0.58 0.85
0.7 6.8c) 77.0d)
0.49 0.52 0.67
References 20 50 Wirz J et al., unpublished work
a
Calculated from the data given in Table 1. Calculated using Equation (20). pKK a = 3.9 was assumed. d pKK a = 3.6 was assumed. b c
1.0 0.8
α
0.6 0.4 0.2
ΔrGo/(kJ mol–1)
0.0 –100
–50
0
50
100
Fig. 9 Variation of the Brønsted parameter for general acid catalysis of enol ketonization with the free energy change DG for carbon protonation of enols (o) and enolates (•). The data are taken from Table 2.
348
J. WIRZ
If one includes the solvent-derived acids H and H2O in a Brønsted plot, they often deviate substantially from the regression line of general acids. The rate constants predicted from the regression tend to be larger than the observed values. What is the reason for these discrepancies? To begin with, it should be mentioned that the ‘‘pKa’’ values of the proton and of water are 0 (by definition) and about 14.0 (i.e., equal to pKw) and not 1.74 and 15.74, as is erroneously stated in most textbooks of organic chemistry. The latter values originate from the inclusion of the concentration cH2O = 55.5 M, log (55.5) = 1.74, in the equilibrium constants corresponding to reaction equations such as Equation (17). H2 O ! H þ HO
ð17Þ
The derivation of the law of mass action from the second law of thermodynamics defines equilibrium constants K in terms of activities. For dilute solutions and low ionic strengths, the numerical values of the molar concentration quotients of the solutes, if necessary amended by activity coefficients, are acceptable approximations to K [Equation (3)]. However, there exists no justification for using the numerical value of a solvent’s molar concentration as an approximation for the pure solvent’s activity, which is unity by definition.76,77 Thus, firstly, the choice of the pure solvent as the reference state for the definition of activities of solutes in fact impairs a fair comparison of the activity of dilute solutes such as general acids to the activity of the solvent itself. Secondly, the observed first-order rate constants k0 or k00 for the reaction of a solute with the solvent water are usually converted to second-order rate constants by division through the concentration of water, kH2 O ¼ k0 =cH2 O , for a comparison with the second-order rate coefficients kHA. Again, it is questionable whether the formal kH2 O coefficients so calculated may be compared with truly bimolecular rate constants kHA for the reactions with dilute general acids HA. It is then no surprise that the values for the rate coefficients determined for the catalytic activity of solvent-derived acids scatter rather widely, often by one or two orders of magnitude, from the regression lines of general acids.74 Hydronium ion catalytic coefficients for enolization and ketonization of simple aldehydes and ketones correlate with the enolization equilibrium constants pKE.48 The slopes of the two correlations are of opposite sign (–0.17 and 0.83, respectively), ketonization being considerably more sensitive to a change in the driving force.
MECHANISM OF THE ‘‘UNCATALYZED’’ REACTION
pH–Rate profiles frequently exhibit a more or less pronounced flat portion at pH values near neutral, where tautomerization is catalyzed neither by acid nor by base. In the case of phenol (Fig. 7), the ‘‘uncatalyzed’’ reaction dominates in
KINETIC STUDIES OF KETO–ENOL TAUTOMERIC EQUILIBRIA
349
the range of 4 £ pH £ 10. Several kinetically indistinguishable, pH-independent mechanisms may be considered as pathways of tautomerization. Facile intramolecular 1,5-H shifts are observed in the ketonization of 1,3-dienols (see, e.g., the entry phorone in Table 1). Intramolecular 1,3-H shifts, on the other hand, are ruled out on the basis of the prohibitively high activation energies that are unanimously predicted by calculations. Indeed, enols are kinetically stable in dry solvents or in the gas phase. Clearly, the solvent participates in these reactions. Water being amphoteric, it might intervene (a) as a general acid, (b) as a general base, or (c) by promoting a ‘‘concerted’’ transfer of two protons through a bridge of one or more water molecules (Scheme 6). Rate constants of ketonization of acetophenone enol along paths (a) and (b) have been be estimated using the Brønsted Equation (16).20 Those predicted for path (a) are orders of magnitude below the observed rate constant kK uc = 0.18 s1, while those for path (b) were found to be in reasonable agreement with experiment. The concerted mechanism (c) does not satisfactorily account for structure–reactivity relationships observed in aqueous solution. It may, however, well be the dominant mechanism in aprotic solvents containing small amounts of water. In the next section we will show that for most compounds, the pH0K K E independent terms kK uc ¼ k0 þ kH Ka [Equation (8)] determined in aqueous solution can be attributed to water reacting as a general base, path (b), that corresponds to the second term, where k0K H is the rate constant for proton addition to E. 0
kuc » kHK KaE
ð18Þ
Ketonization along path (b) liberates a proton in the pre-equilibrium step and the proton is removed by subsequent protonation of E. While the rate of the second, rate-determining step is directly proportional to the concentrations cE and cH, the concentration cE is itself inversely proportional to cH as long
OH + OH
k0K
KaK /Kw
a OH
KaE
O
+
k H' K c H
H
O
b c
O
H
O H
H
‡
HH
Scheme 6
Reaction paths considered for the ‘‘uncatalyzed’’ term kK uc.
350
J. WIRZ
as cH >> KEa [Equation (4)], so that the overall contribution of this path to the overall rate of reaction is pH-independent.
THE MARCUS MODEL OF PROTON TRANSFER
The experimental ketonization rate constants kK collected in Table 1 cover a range of 20 orders of magnitude. A logarithmic plot against the corresponding reaction free energies DrG reveals that these data follow a systematic, nonlinear trend, Fig. 10. The free energy of reaction associated with a given rate constant is determined by the equilibrium constant of that reaction. Thus, for the reaction , filled circles •, center), we have DrG = 2.3RT(pKE þ E þ H ! K (kK H )]; for the reaction E þ H ! K (k0K pKK a H , triangles r, upper left), E DrG = 2.3RT(pKE þ pKa ); for the protonation of enolates by water, E þ E H2O ! K þ HO (k0K 0 , triangles D, lower right), DrG = 2.3RT(pKE þ pKa – pKw); finally, for the reaction of enols with water, E þ H2O ! K þ HO (k0 K, empty circles *, lower right), DrG = 2.3RT(pKE þ pKK a – pKw). Statistical factors (section ‘‘The Brønsted Relation, Statistical Factors, and the Acidity of Solvent-Derived Species (H and H2O)’’) were taken into account, i.e., the rate constants were divided by the number of equivalent basic carbon atoms of the enol (e.g., q = 1 for acetone enol and q = 2 for phenol reacting to cyclohexa-2,5-dienone) and the free energy terms DrG/(2.3RT) were corrected by –log(p/q), where p is the number of equivalent acidic protons in the ketone
log k 10 ΔrG‡/(2.3RT )
0
–10
–25 –20 –15 –10
–5
0
5
10 15 20 ΔrG o/(2.3RT )
Fig. 10 Empirical relationship between the logarithm of the proton transfer rate constants (Table 1) and the corresponding free energies of reaction DrG. Triangles 1 1 1 s ). Filled circles (•): kK /(M1 s1). Empty circles (O): kK (5): k0K 0 /s . H /(M H 0K 1 Triangles (D): k0 /s . The solid line was obtained by fitting of the Marcus Equation (19).
KINETIC STUDIES OF KETO–ENOL TAUTOMERIC EQUILIBRIA
351
(e.g., p = 6 for acetone). These corrections are small compared to the variation of the rate constants. The dotted line shown in the upper part of Fig. 10 represents the free-energy relationship expected for ‘‘normal’’ bases, in which the nucleophilic center is an O or N heteroatom (‘‘Eigen’’-curve78); exergonic reactions are diffusion-controlled (kd 1011 M1 s1) and the rates of endergonic reactions decrease with a slope of 1 versus DrG/(2.3RT). The rate constants of the carbon bases (‘‘pseudo’’-bases) studied here are much lower than predicted by the Eigen curve, particularly in the region around DrG = 0, where the difference amounts to some 10 orders of magnitude. The systematic trend of the rate data shown in Fig. 10 is reasonably well captured by the Marcus expression for proton transfer,79 which takes the simple form of Equation (19) when work terms are omitted.80 !2 k Dr G‡ Dr G o ‡ ‡ ; where Dr G ¼ Dr G0 1 þ log ¼ ð19Þ ln ð10ÞRT kd 4Dr G‡0 The parameter DrG0‡ is called the ‘‘intrinsic’’ barrier, the barrier of a thermoneutral reaction, DrG = 0. The rate of diffusion was assumed as kd = 1 1011 M1 s1. Nonlinear least-squares fitting of Equation (19) to the set of data gave DrG0‡ = 55.6 0.7 kJ mol1. In an earlier treatment using a smaller set of data we had obtained DrG0‡ = 57 2 kJ mol1.7 In most cases, the rate constants kucK were converted to k0K H [Equation (18)] assuming that mechanism (b) of Scheme 6 accounts for the uncatalyzed reaction. Clearly, the rate constant kK uc for phorone should not be converted to , because the uncatalyzed reaction is due to an intramolecular 1,5-H shift k0K H rather than to pre-equilibrium ionization of the enol. Conversion of kK 0 = 2.6 11 1 1 = 1.8 10 M s , which is higher than any of the s1 would give k0K H values observed for simple enols and more than two orders of magnitude higher than that predicted by the Marcus equation for k0K H . Similar arguments apply to the six a-carboxy-substituted ketones that have been studied by Kresge and coworkers (entries acetoacetate to oxocyclobutane-2-carboxylate in Table 1). Kresge already noted that the rate constants kucK observed for the ‘‘uncatalyzed’’ ketonization of some of these compounds would give unrealistically high calculated values for k0K H near or above 1011 M1 s1 using Equation (18). Indeed, these calculated values of k0K H are about two orders of magnitude above those expected from the Marcus relation except that for 4,4,4-trifluoroacetate. The rate constants kK uc observed for the formation of these a-carboxy-substituted ketones are, however, close to K those expected for the protonation of the neutral enols by water, kK uc = k0 . The modest amount of scatter in Fig. 10 is remarkable, considering that it includes four different reaction types (carbon protonation of enols or enolates by hydronium ions or by water) and a wide range of substrates. The standard deviation between the 62 observed values of log kK and those calculated by Equation (19) is 0.95.
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The acidity constants of protonated ketones, pKK a , are needed to deter, mine the free energy of reaction associated with the rate constants kK H K ). Most ketones are very weak bases, pK < DrG = 2.3RT(pKE þ pKK a a cannot be determined from the pH–rate 0, so that the acidity constant KK a profile in the range 1 < pH < 13 (see Equation (11) and Fig. 3). The acidity of a few simple ketones were determined in highly concentrated constants KK a acid solutions.19 Also, carbon protonation of the enols of carboxylates listed in Table 1 (entries cyclopentadienyl 1-carboxylate to phenylcyanoacetate) give the neutral carboxylic acids, the carbon acidities of which are known and are listed in the column headed pKK a . As can be seen from Fig. 10, the observed rate K constants kH for carbon protonation of these enols (8 data points marked by the symbol • in Fig. 10) accurately follow the overall relationship that is defined 0K mostly by the data points for k0K H and k0 . We can thus reverse the process by assuming that the Marcus relationship determined above holds for the protonato estimate the acidity tion of enols and use the experimental rate constants kK H constants KK of ketones via the fitted Marcus relation, Equation (19). This a procedure indicates, for example, that protonated 2,4-cyclohexadienone is less acidic than simple oxygen-protonated ketones, pKK a = 1.3. Marcus’ rate theory is useful to rationalize the connection between reactivity and the slope of Brønsted plots. The derivative of Equation (19) with respect to DrG is the slope of the Marcus curve, which corresponds to the Brønsted exponent for a given free energy of reaction DrG, Equation (20).74,80 ¼
@Dr G‡ @Dr Go
p ;T
¼
1þ
Dr G o
! =2
4Dr G‡0
ð20Þ
The Brønsted parameter varies substantially over the large range of DrG covered by the experimental data collected in Fig. 10; it ranges from 0.2 for the most reactive enolates (phenylethynol anion) to about 0.8 for the least reactive compound (1-naphthol). The -values calculated by Equation (20) are in satisfactory agreement with those determined experimentally from Brønsted plots of general acid catalysis (Table 2). The second derivative of Equation (19) with respect to DrG, Equation (21), represents the change of with increasing DrG. Using the fitted value of DrG0‡ = 55.6 kJ mol1, one obtains @/@DrG = 0.22 103 mol kJ1. The slope of Fig. 9 amounts to (0.28 0.03) 103 mol kJ1. @ 2 Dr G ‡ @ ½ Dr
Go 2
!
¼ p; T
@ @Dr Go
¼ p; T
1 8Dr G0‡
ð21Þ
Using these relations, the rate coefficients for specific and general acid catalysis, kH and kHA, of any keto–enol tautomeric reaction can be predicted from the appropriate free energy of reaction DrG. The required
KINETIC STUDIES OF KETO–ENOL TAUTOMERIC EQUILIBRIA
353
log(k/s–1) 5
5 OH
0
0 kucK
–5 kucK
0
2
k0'K
kH+K
4
6
8
10 12 14 pH
k0'K
kobs K kH+K
–5
kobs K
–10 –15
O
O
OH
–10 –15
0
2
4
6
8
10 12 14 pH
Fig. 11 Effect of Brønsted on the shape of the pH–rate profile of ketonization.
thermochemical data can be estimated using group additivity rules81,82 or quantum chemical calculations. Equation (20) also rationalizes the fact that the ‘‘uncatalyzed’’, pH-independent portion of pH–rate profiles is marginal for ketones and absent for carboxylic acids with low enol content ( ! 0), but dominates the pH profile of phenol ( ! 1). The pH-independent contribution is generally due to the reaction E þ H ! K, which corresponds to the most exergonic reaction. The corresponding rate constants k0K H are approaching the limit of diffusion control for simple ketones and are therefore much less sensitive to changes in DrG than and k0K the acid- and base-catalyzed branches of the pH profiles due to kK 0 . As H an example, the pH–rate profiles for the ketonization of phenol and acetophenone enol are shown in Fig. 11 (thick lines), together with the contributions of 0K E the three individual terms of Equation (9) (dotted lines: kK uc ¼ kH Ka ; dashed 0K K lines: kH ; long dashed lines: k0 ). Clearly, the uncatalyzed term that is due to the fastest rate constant k0K H increases less than the others when going to the much more exergonic ketonization of acetophenone enol, so that it is marginalized. The extended pH-independent branch seen in the pH profile of phenylynol (Fig. 6) has an entirely different origin: due to the high acidity of the ynol, pKEa <2.7, the ynol anion is predominant over the whole observable pH range, and the pH-independent process observed above pH 5 is its protonation by solvent water, E ! K þ HO.
5
Conclusion and outlook
Flash photolysis has provided a wealth of kinetic and thermodynamic data for tautomerization reactions. Equilibrium constants of enolization, KE, spanning a range of 30 orders of magnitude, have thereby been determined accurately as the ratio of the rate constants of enolization, kE, and of ketonization, kK. Nowadays, tautomerization constants KE can be predicted with useful
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accuracy by performing ab initio or density functional theory calculations. Free energy relationships based on empirical data can then be used to estimate the lifetime of unstable tautomers in wholly aqueous solutions and in aqueous buffers. These studies have uncovered some remarkable findings such as the CH acidity of 2,4-cyclohexadienone, pKEa = – 2.9, or the unusually high acidities of ethynols and ethynamines. The analysis of these data provides reliable assignments for the elementary reactions that govern tautomerization reactions and how they depend on pH.
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.
Erlenmeyer E. Chem Ber 1880;13:305–10. Lapworth A. J Chem Soc 1904;85:30–42. Hochstrasser R, Kresge AJ, Schepp NP, Wirz J. J Am Chem Soc 1988;110:7875–6. Haspra P, Sutter A, Wirz J. Angew Chem Int Ed 1978;18:617–9. Keefe JR, Kresge AJ, Kinetics and mechanism of enolization and ketonization. In: Rappoport Z, editor. The chemistry of enols. Chichester: Wiley; 1990. pp. 399–480. Kresge AJ. Chem Soc Rev 1996:275–80. Wirz J. Pure Appl Chem 1998;70:2221–32. Chiang Y, Kresge AJ, Paine SW, Popik VV. J Phys Org Chem 1996;9:361–70. Wirz J. Chem Unserer Zeit 1998;32:311–22. Kresge AJ. Acc Chem Res 1990;23:43–8. Norrish RGW, Porter G. Nature 1949;164:658. Porter G, Flash photolysis. In: Friess SL, Lewis ES, Weissberger A, editors. Techniques of organic chemistry, Part 2. New York: Interscience; 1963; Vol. VII. pp. 1055–106. Bonneau R, Wirz J, Zuberbu¨hler AD. Pure Appl Chem 1997;69:979–92. Scaiano JC. Nanosecond laser flash photolysis: a tool for physical organic chemistry. In: Moss RA, Platz MS, Jones M, Jr., editors. Reactive intermediate chemistry. Hoboken, New Jersey: John Wiley & Sons; 2004. pp. 847–71. Kla´n P, Wirz J. Photochemistry of organic compounds: from concepts to practice. Chichester: Wiley; 2009. p. 563. Bates RG. Determination of pH. Theory and practise. New York: Wiley; 1973. Emsley J, Freeman NJ. J Mol Struct 1987;161:193–204. Meyer KH. Chem Ber 1912;45:2843–64. Bagno A, Lucchini V, Scorrano G. J Phys Chem 1991;95:345–52. Chiang Y, Kresge AJ, Santaballa JA, Wirz J. J Am Chem Soc 1988;110:5506–10. Chiang Y, Kresge AJ, Wirz J. J Am Chem Soc 1984;106:6392–5. Keefe JR, Kresge AJ, Toullec J. Can. J Chem 1986;64:1224–7. Chiang Y, Kresge AJ, Capponi M, Wirz J. Helv Chim Acta 1986;69:1331–2. Loudon GM. J Chem Educ 1991;68:973–84. Toullec J. Adv. Phys. Org. Chem 1982;18:1–77. Keefe JR, Kresge AJ. In: Bernasconi CF, editor. Techniques of chemistry, investigations of rates and mechanisms of reactions. New York: Wiley; 1986; Vol. 6, part 1, Chapter XI. Hegarty AF, Dowling J, Eustace SJ, McGarraghy H. J Am Chem Soc 1998;120:2290–6. Il’ichev YV, Schwo¨rer MA, Wirz J. J Am Chem Soc 2004;126:4581–95.
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29. He´nin F, Le´tinois S, Muzart J, Wirz J. Photochem. Photobiol. Sci 2006;5:426–31, and references therein. 30. Haag R, Wirz J, Wagner PJ. Helv Chim Acta 1977;60:2595–607. 31. Schwo¨rer M, Wirz J. Helv. Chim. Acta 2001;84:1441–58. 32. Goeschen C, Herges R, Richter J, Tokarczyk B, Wirz J. Helv. Chim. Acta 2009; 92:1909–22. 33. Freiermuth B, Hellrung B, Peterli S, Schultz M-F, Wintgens D, Wirz J. Helv. Chim. Acta 2001;84:3796–809. 34. Chiang Y, Kresge AJ, Krogh ET. J Am Chem Soc 1988;110:2600–7. 35. Guthrie JP. Can J Chem 1993;71:2123–28. 36. Almstead JIK, Urwyler B, Wirz J. J Am Chem Soc 1994;116:954–60. 37. Urwyler B, Wirz J. Angew. Chem., Int. Ed. Engl 1990;29:790–2. 38. Chiang Y, Kresge AJ, Hochstrasser R, Wirz J. J Am Chem Soc 1989;111:2355–7. 39. Chiang Y, Kresge AJ, Popik VV. J Am Chem Soc 1995;117:9165–71. 40. Chiang Y, Kresge AJ, Walsh PA, Yin Y. J Chem Soc Chem Commun 1989:869–71. 41. Chiang Y, Grant AS, Kresge AJ, Pruszynski P, Schepp NP, Wirz J. Angew. Chem., Int. Ed. Engl 1991;30:1356–58. 42. Chiang Y, Grant AS, Guo H-X, Kresge AJ, Paine SW. J Org Chem 1997;62:5363–70. 43. Andraos J, Chiang Y, Grant AS, Guo H-X, Kresge AJ. J Am Chem Soc 1994;116:7411–2. 44. Capponi M, Gut IG, Hellrung B, Persy G, Wirz J. Can. J. Chem 1999;77:605–13. 45. More O’Ferrall R, Quirke AP. Tetrahedron Lett 1989;30:4885–8. 46. Chiang Y, Kresge AJ, Tang YS, Wirz J. J Am Chem Soc 1984;106:460–2. 47. Chiang Y, Kresge AJ, Schepp NP. J Am Chem Soc 1989;111:3977–80. 48. Keeffe JR, Kresge AJ, Schepp NP. J Am Chem Soc 1990;112:4862–8. 49. Keeffe JR, Kresge AJ, Schepp NP. J Am Chem Soc 1988;110:1993–5. 50. Pruszynski P, Chiang Y, Kresge AJ, Schepp NP, Walsh PA. J Phys Chem 1986;90:3760–6. 51. Chiang Y, Kresge AJ, Meng Q, More O’Ferrall RA, Zhu Y. J Am Chem Soc 2001;123:11562–9. 52. Jefferson EA, Keefe JR, Kresge AJ. J Chem Soc Perkin Trans 2 1995:2041–6. 53. Keefe JR, Kresge AJ, Yin Y. J Am Chem Soc 1988;110:8201–6. 54. Chiang Y, Guo H-X, Kresge AJ, Tee OS. J Am Chem Soc 1996;118:3386–91. 55. Chiang Y, Kresge AJ, Meng Q, Morita Y, Yamamoto Y. J Am Chem Soc 1999;121:8345–351. 56. Chang JA, Kresge AJ, Nikolaev VA, Popik VV. J Am Chem Soc 2003;2003:6478–84. 57. Chiang Y, Kresge AJ, Nikolaev VA, Popik VV. J Am Chem Soc 1997;119:11183–90. 58. Chiang Y, Kresge AJ, Nikolaev VA, Onyido I, Zeng X. Can. J. Chem 2005;83:68–76. 59. Chang JA, Chiang Y, Keefe JR, Kresge AJ, Nikolaev VA, Popik VV. J Org Chem 2006;71:4460–7. 60. McCann GM, McDonnell CM, Magris L, More O’Ferrall RA. J Chem Soc Perkin Trans 2 2002:784–95. 61. Chiang Y, Hojatti M, Keeffe JR, Kresge AJ, Schepp NP, Wirz J. J Am Chem Soc 1987;109:4000–9. 62. Chiang Y, Kresge AJ, Walsh PA. J Am Chem Soc 1986;108:6314–40. 63. Andraos J, Chiang Y, Kresge AJ, Popik VV. J Am Chem Soc 1997;119:8417–24. 64. Andraos J, Chiang Y, Kresge AJ, Pojarlieff IG, Schepp NP, Wirz J. J Am Chem Soc 1994;116:73–81. 65. Chiang Y, Kresge AJ, Popik VV, Schepp NP. J Am Chem Soc 1997;119:10203–12. 66. Chiang Y, Kresge AJ, Pruszynski P, Schepp NP, Wirz J. Angew. Chem., Int. Ed. Engl 1990;102:810–2. 67. Chiang Y, Kresge AJ, Schepp NP, Xie R-Q. J Org Chem 2000;65:1175–80.
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68. Chiang Y, Guo H-X, Kresge AJ, Richard JP, Toth K. J Am Chem Soc 2003;125:187–94. 69. Capponi, M. Bestimmung von Keto-Enol Gleichgewichten mittels Blitzlichtphotolyse: Phoron und Phenol. PhD thesis. Switzerland: University of Basel; 1986. 70. Gut IG, Wirz J. Angew. Chem., Int. Ed. Engl 1994;33:1153–6. 71. Brønsted JN, Pedersen K. Z Phys Chem 1924;108:185–235. 72. Brønsted JN. Chem Rev 1928;5:231–338. 73. Bishop DM, Laidler KJ. J Chem Phys 1965;42:1688–91. 74. Kresge AJ. Chem Soc Rev 1973;2:475–503. 75. Bell RP. The proton in chemistry. London: Chapman and Hall; 1973. 76. Keeports D. J Chem Educ 2005;82:999. 77. Keeports D. J Chem Educ 2006;83:1290. 78. Eigen M. Angew. Chem 1963;75:489–508. 79. Marcus RA. J Phys Chem 1968;72:891–9. 80. Cohen AO, Marcus RA. J Phys Chem 1968;72:4249–56. 81. Benson SW, Cruickshank FR, Golden DM, Haugen GR, O’Neal HE, Rodgers AS, et al. Chem. Rev 1968;68:279–324. 82. Guthrie JP. J Phys Chem A 2001;105:9196–202.
The role of pre-association in Brønsted acid-catalyzed decarboxylation and related processes RONALD KLUGER and SCOTT O.C. MUNDLE Davenport Chemical Laboratories, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada 1 2 3 4 5 6 7 8
Catalysis and reversibility 357 Catalysis of decarboxylation 359 Decarboxylation, internal return, and directionality 360 Pre-association 361 Catalyzing thiamin diphosphate catalysis 362 12 C/13C kinetic isotope effects and pre-association catalysis 366 Implications of blocking reversion for enzyme catalysis 368 OMP decarboxylase – decarboxylation and protonation of orotidine monophosphate 369 9 General trends in catalyzed decarboxylation 370 10 Decarboxylation of aromatic carboxylic acids 371 11 Decarboxylation of 3-ketoacids 372 12 Conclusions 373 References 374
1
Catalysis and reversibility
The most common view of the operation of a successful catalyst is that it makes available lower energy transition states by associating with the reactant and maintaining the interaction throughout the pathway leading to the desired product.1 Another role for a catalyst is to provide an alternative route from an intermediate that competes effectively against the normal reversal that returns to the reactant from the intermediate.2 This increases the net rate of product formation without changing the nature of the initial transition state.3 In this review, we focus on a simple unimolecular reaction, decarboxylation, where a carboxyl group is replaced by a proton and carbon dioxide is formed.4 While the barrier to a decarboxylation reaction is normally seen as being the activation energy for cleavage of the carbon– carbon bond, we find another important factor that controls the rate of the reaction is the extent to which the step that produces carbon dioxide is reversible.3 Where this is the case, catalysis that promotes separation of the 357 ADVANCES IN PHYSICAL ORGANIC CHEMISTRY VOLUME 44 ISSN: 0065-3160 DOI: 10.1016/S0065-3160(08)44007-8
2010 Elsevier Ltd. All rights reserved
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R. KLUGER AND S.O.C. MUNDLE
immediate products of decarboxylation can cause a significant acceleration in the observed rate of reaction. In a reaction that converts a single stable molecule into two reactive molecules, catalysis of the forward reaction will be limited by the extent of the reverse reaction, which by the principle of microscopic reversibility must proceed through the same transition state. If there is no (rapid) subsequent reaction of the products, the catalyst will establish a pseudo-equilibrium between reactants and intermediates, with the formation of the ultimate product controlled by slower subsequent processes. On the other hand, if the products separate rapidly or react with other species (or catalysts) that generate the final product at a rate that is competitive with that of reversion to reactants, the overall rate of product formation will increase. Thus, the reaction of the product of the first step with a third entity can be the key to enhancing the rate, along with the conventionally expected stabilization of the transition state. In the extreme, if the reaction is made irreversible by a process that prevents the products from recombining, the net rate of product formation is greatly facilitated, allowing the full effect of catalysis to be observed in the net rate of transformation. The availability of routes that promote the forward reaction requires catalytic species be present in the vicinity of the initially formed complex because diffusion is expected to be slower than the separation of the immediate products. While such a situation is unusual with small catalysts, it is likely to be common with large catalysts, such as enzymes, where a catalytic array is present once the substrate has become associated (Scheme 1). The rate of a reaction involving a high-energy intermediate appears to depend on an observed first-order rate constant associated with the formation of the product (or disappearance of reactant), which can be expressed in a simplified manner in most cases by applying the steady-state approximation as kobs = k1k2/(k1 þ k2). The overall forward reaction (that includes steps associated with k1 and k2) is significantly suppressed to the extent that k1 is comparable in magnitude to k2. In the case of decarboxylation, we propose that the reaction can be accelerated by a catalyst that is capable of effectively
k1
A
A‡
k2 Products
k–1 ±C A·C
k1 k–1
A‡ · C
k3
Products
Scheme 1 The rate constant k1 leading to the transition state A‡ is not affected by association with catalyst C. However, the reaction rate in the forward direction in the presence of C (k3) is greater than k2, favoring product formation rather than reversion to reactants.
PRE-ASSOCIATION CATALYSIS OF DECARBOXYLATION O R1 R2
Scheme 2
O R3
k1
R1
k–1
R2
O C R3
k2
O
AH
359
R1 H
R2
+ CO2
R3
Two-step mechanism involving reversible decarboxylation.
competing with the reversion step associated with k1. This will make the net forward reaction rate larger (Scheme 2).
2
Catalysis of decarboxylation
Decarboxylation of activated carboxylates provides an illustration of the modes of catalysis where a single reactant is converted initially to two reactive products. Breaking of the carbon–carbon bond that leads to the formation of carbon dioxide leaves behind a carbanion, which is typically a highly energetic species. The energies of transition states leading to the formation of carbanions and carbon dioxide are differentiated by the carbanion that is generated, with carbon dioxide providing stability that helps to drive the reaction in terms of enthalpy and whose separation promotes the reaction entropically. In general, in cases where the carbanion can be stabilized by catalytic intervention, as in the initial conversion of a 2-ketoacid to a cyanohydrin, the transition state leading to its formation will be stabilized. In addition, the stability of the carbanion generated by loss of carbon dioxide also depends on its molecular environment. The rate of decarboxylation of pyridine-2carboxylic acid is enhanced in a nonpolar environment as the zwitterionic ground state is destabilized and the less polar transition state is stabilized.5 Miller and Wolfenden6 compared the rates of decarboxylation of the substrate of orotidine-50 -monophosphate decarboxylase (OMPDC) in quantitative detail, on and off the enzyme. They showed that the apparent unimolecular rate constant of decarboxylation of the substrate when bound to the enzyme is about 1015 times greater than the decarboxylation process in the absence of the enzyme. Further studies confirm that the enzyme-promoted reaction does not involve additional intermediates or covalent alterations of the substrate. The reaction consists of carbon dioxide being formed and the resulting carbanion becoming protonated. Since thermodynamic barriers are not altered by catalysis, the energy of the carbanion must be a component that reflects the energy of the environment in which it is created, one in which the carbanion that is formed is selectively stabilized. Richard and coworkers7 showed that proton exchange from UMP in the presence of OMPDC, which requires formation of the carbanion that is generated by decarboxylation, occurs more readily when bound to the protein but is too slow to observe in the absence of protein. In the case of that enzyme, there is
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no means of stabilizing the carbanion by delocalization or addition of acids or bases. Yet, the enzyme-catalyzed reaction proceeds rapidly, indicating that the environment created by the protein is critical. The difference in rates is seen as a measure of the difference in pKA on and off the enzyme. However, unless there is a way to stabilize the carbanion specifically, the difference can be a reflection of different mechanisms for exchange in the two systems. If a carbanion is thermodynamically accessible, but is subject to rapid quenching by internal return of CO2 in the case of decarboxylation, or by a proton in carboxylation, or in a hydrogen/deuterium exchange reaction, then the carbanionic intermediate off the enzyme would give the appearance of greater basicity than its thermodynamic value would predict. The localized character of the carbanion at the 6-position of UMP requires that the proton that is removed by a base in solution initially remains closely associated, and therefore, to a great extent be transferred to the carbanion. This reduces the rate of exchange and creates a discrepancy between kinetic and thermodynamic acidities.
3
Decarboxylation, internal return, and directionality
By examination of the stereochemical consequences of decarboxylation, Cram and Haberfield8 obtained evidence for internal return of carbon dioxide to the carbanion, affecting the stereochemical outcome of these reactions. It is reasonable to consider that the barrier for the combination of the carbanion and carbon dioxide may be comparable to or lower than that for diffusion, in which case the reverse reaction will be a kinetically significant component in the overall rate of reaction. In such a case, a catalyst cannot deal with the direction of the reaction – if it lowers the transition state energy for the forward reaction, conservation of energy demands that it also lower the barrier for the reverse reaction. The energy for addition of the carbanion to carbon dioxide is also inherent. The reaction should occur readily if the reaction partners have reduced entropy. Jencks and coworkers9 noted that a likely route for catalysis of carboxylation reactions (replacement of a proton by a carboxyl group) is the generation of ‘‘low entropy’’ carbon dioxide by a reaction of ATP and bicarbonate adjacent to N10 of biotin. This way of promoting carboxylation produces a situation which is precisely what is created at the stage of the initial formation of products in decarboxylation reactions. Since there is no directional momentum, the proximity of ‘‘low entropy’’ carbon dioxide and a nucleophile similarly will slow the reaction in the direction of decarboxylation. The same authors suggest that for decarboxylation reactions, nucleophilic addition to carbon dioxide in an enzyme’s active site would prevent re-addition and promote the forward reaction if the addition product is itself sufficiently unstable. Introducing directionality that favors product formation in a decarboxylation reaction should provide a reliable path to acceleration: the immediate
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361
products are carbon dioxide and a carbanion and they must become separated to have the reaction proceed. If either wins a competition with the reverse the reaction, the rate of the forward reaction is increased as a consequence of increased throughput.10
4
Pre-association
In order for an interventional catalyst to have an effect on the rate, it must accelerate the net rate of diffusion (the physical process of diffusion will not change but the reversion will be slowed). It must either make carbon dioxide or the carbanion less reactive. Since the process that slows reversion must compete with diffusion, it cannot itself be diffusion-limited. This can be achieved by the reaction being intramolecular or by the catalyst being associated with the reactant prior to the formation of the initial products, a process known as pre-association.11–16 Enzyme-catalyzed reactions involve specific, rapid combination of substrate and enzyme to form a complex that is rapidly converted to products through transition states that are controlled by the enzyme’s environment. Since enzymes are homogeneous chemical catalysts, we expect them to operate by routes that parallel some of the same processes in reactions that do not involve enzymes. The relative magnitude of enzymic and nonenzymic catalytic parameters has been called ‘‘catalytic proficiency’’ by Wolfenden6,17–24 and this has been a subject of intense current interest.7,25–32 Wolfenden noted that while nonenzymic reactions have diverse rates, enzyme-catalyzed processes are highly evolved to be comparable in rate, no matter how slow their nonenzymic counterparts. The transition state-stabilizing power of the rapid enzymic process can be held up for comparison with a particularly slow nonenzymic reaction that is brought about through addition of a large amount of heating. In particular, comparisons of the rates of enzyme-catalyzed process and spontaneous nonenzymic reaction produce dramatically large ratios. The range of catalytic proficiencies for enzymes suggests that there are features of catalysis in enzymes that involve factors other than stabilization of transition states. One important distinction is that the enzyme active site contains catalytic groups that are able to access reactive intermediates, while intermediates formed in solution have lifetimes that are less than the time needed for a reagent to diffuse to the site of the reaction.33 In the enzyme, groups are initially associated with the bound substrate in a specific array and continue to be available through the course of the reaction. Diffusional introduction of catalytic groups is overcome by pre-association of the catalysts and reactant prior to the formation of any reactive intermediate. This accesses modes of catalysis that are not possible if the catalyst and intermediate must become associated after the intermediate has formed.
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R. KLUGER AND S.O.C. MUNDLE
A clear statement of the conditions for such catalysis comes from Jencks and coworkers16 with respect to proton transfer: ‘‘in the limiting case of the pre-association mechanism the catalyst and reactants come together in a fast preliminary step, after which the chemical steps occur without further equilibration of intermediates or the transition state with respect to proton transfer to or from other components of the solution.’’ In such a case, the catalyst must be present in order to compete with other reactions. Venkatasubban and Schowen34 provided a key refinement in which they specify that the role of a pre-associated catalyst is to quench a reactive intermediate. Since the catalyst does not participate in stabilizing the transition state it has another role and a special name: ‘‘The [catalyst] is a ‘‘spectator’’ during the bond fission, and the catalysis is of the type we have called spectator catalysis. . . It is conceivable that the diffusional approach of BH to the tetrahedral adduct is the rate-limiting step.’’ With this general introduction as background, we will focus on the pre-association mechanisms in decarboxylation reactions, an area where such a possibility has only been recently recognized.
5
Catalyzing thiamin diphosphate catalysis
Decarboxylation of 2-ketoacids is a key metabolic reaction whose enzymic catalysis requires alteration of the inherent reactivity of the substrate. Direct loss of carbon dioxide from 2-ketoacids would lead to acyl carbanions: these species must be high in energy and have yet to be observed in solution. The acyl carbanion is avoided by addition of enzyme-bound thiamin diphosphate (ThDP) cofactor to the carbonyl group of the substrate, reversing the substrates’s carbonyl polarity and setting up the carboxylate ion for facilitated decarboxylation.35–39 In addition, combination with the protein provides substrate specificity and the general advantage of reduced translational entropy to enhance the addition process.40,41 The covalent intermediate undergoes cleavage of the carbon–carbon bond of the carboxylate group, resulting in the production of carbon dioxide and a residual acyl carbanion equivalent that can be delocalized for stability as an analogue of a 2-iminocarbanion. Protonation of the carbanion and elimination of the aldehyde result in an overall substitution of a proton for carbon dioxide. There are significant differences in the reactivity of synthetic intermediate analogues for these reactions and the corresponding intermediates in the enzymic system. Lienhard and coworkers42,43 reported that the rate of decarboxylation of 2-(1-carboxy-1-hydroxyethyl)-3,4-dimethylthiazolium chloride is very fast relative to pyruvate (whose reaction is too slow to observe) but slower than the enzymic decarboxylation of pyruvate decarboxylase (PDC) by a factor of 105. Similar observations of a ‘‘catalytic gap’’ were seen for the rate of decarboxylation of lactylthiamin compared to PDC and the
PRE-ASSOCIATION CATALYSIS OF DECARBOXYLATION
363
decarboxylation of mandelylthiamin (MTh) compared to benzoylformate decarboxylase (BFD).44–46 Based on the conventional analysis of the mechanism of decarboxylation of thiamin-derived intermediates, there is no role for a catalyst in the carbon– carbon bond-breaking step of this reaction. The thiazolium nitrogen is at its maximum electron deficiency with no available coordination sites. Ultimately, there is no place for a proton or other cation to position itself in order to promote the reaction by stabilizing a transition state that resembles the product of the reaction. Since there is no role for an acid, base, or metal to accelerate the decarboxylation of these intermediates by stabilizing the transition state for C–C bond-breaking, the means by which this could be achieved became a source of interest and speculation. Lienhard and coworkers42,43 suggested that the additional acceleration observed for the enzyme could occur if there was a way to transfer the initial covalent intermediate into an environment of reduced polarity in the active site. This was supported by evidence of rate accelerations of 2-(1-carboxy-1hydroxyethyl)-3,4-dimethylthiazolium chloride in solvents of reduced polarity. It is reasonable that a local hydrophobic microenvironment could destabilize the ground state of the charged carboxylate ion and stabilize the delocalized transition state based on nonenzymic models. However, pyruvate is a small molecule; there will be little binding energy available for desolvation that would accelerate the reaction. Furthermore, the cofactor does not dissociate and therefore its binding energy is not available for catalysis. BFD shows an even greater acceleration (106) relative to the spontaneous decarboxylation of MTh in solution; yet it has a very polar binding site for both the substrate and cofactor.47 While polarity may be a component of the acceleration mediated through transition state stabilization and ground state destabilization, it is not likely to be the principal source of catalysis of the reaction of the intermediate, at least in the case of BFD. The decarboxylation step in ThDP-derived intermediates has usually been formulated as occurring in a single irreversible step: C–C bond-breaking and rehybridization produces a molecule of carbon dioxide and a carbanion (or other leaving group) that rapidly separate. However, the major barrier to the reverse reaction in many reactions, carboxylation of a carbanion, has been presented (see above) as being largely entropic, with addition of the carbanion to an adjacent molecule of carbon dioxide being very rapid.9 In decarboxylation reactions, carbon dioxide must initially form adjacent to a reactive carbanion. Therefore, the reverse reaction, carboxylation of the carbanion should be a kinetically significant process affecting the observed forward rate, reducing the net rate of diffusional separation without affecting the rate constant for the diffusion step itself. As noted earlier, the conversion of benzoylformic acid to benzaldehyde is catalyzed by the thiamin diphosphate (ThDP)-dependent enzyme BFD. The proposed catalytic mechanism proceeds through two covalent
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intermediates: 2-(2-mandelyl)ThDP (MThDP) formed from the addition of ThDP to benzoylformic acid and 2-(1-hydroxybenzyl)TDP (HBnThDP generated from protonation of the carbanion formed subsequent to decarboxylation (Scheme 3). Model studies have shown that a third product resulting from the fragmentation of HBnTh into DMAP and PTK can also be formed,48,49 and that this process is suppressed by the enzyme (Scheme 4). H3C
N
NH2
N
(CH2)2OP2O63–
S
H3C
NH2 –CO2
CH3
N
N OH
O
H3C CH3
N
+H+
N HO
N
CH3 N HO
(CH2)2OP2O63–
S
NH2
N
O–
O
O
ThDP
(CH2)2OP2O63–
S H
MThDP
HBnThDP
H3C
N
NH2 CH3
N
N O
H
(CH2)2OP2O63–
S
H
Scheme 3 Thiamin diphosphate-dependent decarboxylation of benzoylformic acid to benzaldehyde. Reprinted with permission from Reference 50. Copyright 2006 American Chemical Society. H3C
N
NH2
N
H3C
OH–
HO H
(CH2)2OH
S
NH2
N
CH3 N
N
H3C
N
NH2
N
CH3
CH3
N
N
O H
(CH2)2OH
S
H O H
HBnTh –H+ H3C H
N
(CH2)2OH S Thiamin
H+ NH2
N
NH2 N
CH3
O
N HO H
S
(CH2)2OH
H3C
CH3 N
CH3 N
+
S
(CH2)2OH
H DMAP
PTK
Scheme 4 Competing routes from HBnTh: elimination of benzaldehyde versus fragmentation. Reprinted with permission from Reference 50. Copyright 2006 American Chemical Society.
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365
The decarboxylation of MTh is promoted exclusively by the conjugate acid of pyridine-based buffers.10,50 The fragmentation reaction is also suppressed by these buffers. A logical mechanism that accounts for this phenomenon involves pre-association of the catalyst and reactant (Scheme 5).3 The nature of the interaction between the pyridinium ion catalyst and MTh is likely to involve p-stacking of the phenyl group derived from the substrate. The importance of the phenyl group in MTh arises from the observation that there is no catalysis by pyridinium on LTh, the intermediate found on PDC, with a methyl group replacing the phenyl group at C2a. The possibility of cation-p interactions between the positive charge of pyridinium ion and the phenyl group in an orthogonal orientation was analyzed in terms of the steric effect on catalysis for C-alkyl derivatives of the catalyst at the 2 and 6 positions. This interaction would be impeded by the presence of the alkyl groups. Therefore, the catalyst is likely to be held with its ring plane parallel to the ring of the substrate with the proton proximal to the C2a position poised for transfer (Scheme 5). The proposed mechanism involves pre-association of the catalyst and MTh, forming a weak complex; the weak nature of the interaction is consistent with the inability of the catalytic process to be saturated at high concentrations of pyridinium. Once associated, the acidic group can react with the nascent carbanion formed upon decarboxylation, thereby catalyzing the departure of carbon dioxide by preventing reversal, providing an enhanced forward commitment.
A
H3C
R
H3C
R
H3C
R
R′ N
S
R N
S
R′ N
S
H
N
OH – O C
N
OH
H
N
C O
O
OH O
H
O
C O HBnTh
MTh H3C
R
H3C
R
R′ N
S
R′ N
S
B OH – O C O
O C OH
R = –(CH2)2OH R′=
NH2 N
O N
CH3
Scheme 5 Pre-association mechanism involving p-stacking in the decarboxylation of MTh. Reprinted with permission from Reference 50. Copyright 2006 American Chemical Society.
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R. KLUGER AND S.O.C. MUNDLE
An alternative mechanism for catalysis involves electrostatic stabilization by the positively charged pyridinium ion through a similar pre-association mechanism. However, reactions in the presence of N-ethyl pyridinium show no enhancement.50 Although we can expect that the steric bulk of the N-ethyl group would be a less efficient catalyst, if the stabilization of the transition state were completely electrostatic, some level of catalysis would be observed.
6
12
C/13C kinetic isotope effects and pre-association catalysis
Kinetic evidence implicates a pre-association mechanism for catalysis that supports decarboxylation involving reversible formation of a complex of CO2 and the carbanionic product.50 The catalyst is able to accelerate the reaction by competing for the carbanion. Such a situation would routinely be available in an enzyme active site.37 The complex cannot be observed spectroscopically because of its short lifetime and low concentration. However, catalysis after C–C bond-breaking should alter the observed 12 C/13C kinetic isotope effects (CKIE). In decarboxylation reactions, where the process is purely dissociative (in the absence of a bond acceptor), the isotope effect on the bond-breaking step can be approximated as a product of the zero-point energy and the imaginary frequency factor, which are related to the vibrational frequencies in the ground state and transition state.51–53 While it may be possible to relate the magnitude of the observed CKIE to the structure and bond lengths (or position on the reaction coordinate) the results have been inconsistent in a variety of systems and do not apply to multistep processes.54–56 Another approach that evolved from the complexity of enzyme-catalyzed processes is that the magnitude of a CKIE is proportional to the sum of those processes surrounding the isotopically sensitive step.57,58 This allows for the application of the steady state to CKIE for more complex reactions that proceed through multiple transition states.59,60 In those cases, the intrinsic CKIE associated with the bondbreaking step (k1) would have a similar maximum for all decarboxylation reactions that proceed through the same mechanism. Therefore, the variation in magnitude that is observed for decarboxylation reactions would arise from the sum of the reversible processes surrounding the carbon–carbon bondbreaking event as all involve the same intrinsic process. We apply the concept of catalytic commitment, as proposed by Northrop, O’Leary, and Cleland for multistep enzyme-catalyzed processes, to nonenzymic decarboxylation for comparison.52 The interpretation of CKIEs for decarboxylation reactions is dependent upon whether the process is viewed as a single-step or multi-step process. In a single-step mechanism, carbon– carbon bond-breaking is not affected by any other rate-limiting process. In this case, the CKIE for a particular compound will be constant under a standard set of conditions. Substantial changes in bond order must occur in the
PRE-ASSOCIATION CATALYSIS OF DECARBOXYLATION
367
transition state in order to perturb this value.55 As noted earlier, in a multistep process, microscopic reversibility requires that the carbon dioxide that forms adjacent to the accompanying carbanion (or equivalent) will be subject to attack by the carbanion. Reversal (carboxylation of the carbanion) could be a kinetically significant process affecting the observed forward rate, reducing the net rate of diffusional separation, without affecting the rate constant for the diffusion step itself, and this will affect the observed CKIE. The rate constant for C–C bond cleavage will be subject to a significant primary CKIE, enriching the initially formed CO2 in 12C. However, to the extent that the reversion step is comparable to or faster than the separation step, the observed CKIE will be smaller than the intrinsic CKIE. An important consequence of this mechanism is that it predicts that if departure of CO2 is partially rate limiting, a catalyst that effectively makes product separation faster will increase the magnitude of the observed CKIE. We have reported that the apparent CKIE for the decarboxylation of MTh increases in the presence of the pyridine.3 The CKIE for the pyridine-catalyzed pathway is 6.6%, compared to 5.8% for the uncatalyzed reaction. Initial C–C bond cleavage (k1) is expected to have a maximum CKIE value that arises from the difference in energy from the ground state to the transition state, which will not be affected by the catalyst. Carboxylation of the carbanion (k-1) will also be subject to a CKIE (Scheme 6). While the precise magnitude of this CKIE is unknown, it will be lower than that for k1, as the reaction from the high-energy intermediate will be less selective among isotopically differing reaction partners. If k2 is simply the separation of CO2 from the carbanion, it will have no CKIE since diffusion does not depend on isotopic mass. However, to the extent that reversibility causes accumulation of the intermediate subject to carboxylation (k1), it will reduce the apparent CKIE. R
R′ N HO
S
Ph
O– O
k1 k–1
1
R
R′ N HO
S O
Ph
kpyr
C O
R
R′ N HO
N+ H
Ph
S H C O
H2O+
O
k2 R = CH2CH2OH NH2 R′ =
R
R′ N HO
S
N Ph N+ H
2 H
Scheme 6 Decarboxylation of MTh (1) to HBnTh (2), showing protonated pyridine capturing the carbanion, preventing reversion. Reprinted with permission from Reference 3. Copyright 2009 American Chemical Society.
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R. KLUGER AND S.O.C. MUNDLE
The observed change in the apparent CKIE for the reaction in the presence of pyridine supports this mechanism. Since the catalyst cannot affect k1, the increase results from a change in the balance between k1 and subsequent steps that increases the forward commitment of the reaction. If we use the standard assumption that the transition state for C–C bond-breaking (associated with k1) is the point on the reaction coordinate where the C–C bond is completely broken, the CKIE will be comparable for all three compounds, regardless of the activation barrier. Therefore, a change in the observed CKIE can only result from changes in k1 and k2.
7
Implications of blocking reversion for enzyme catalysis
The million-fold difference in rates for the C–C bond-breaking step in model decarboxylation reactions for thiamin systems and their very similar enzyme intermediates might be understood in terms of the enzyme being able to overcome the reverse reaction with great efficiency. Since the reaction occurs within an active site, where proton donors and/or electron acceptors are available without diffusion to quench the carbanion, separation of carbon dioxide can be more efficient. This increases the overall throughput, increasing the observed rate of the reaction. We can consider decarboxylation reactions in terms that are analogous to those in proton transfer reactions: the reactivity of the carbanion in carboxylation reactions is analogous to internal return observed in proton transfer reactions from Brønsted acids. Kresge61 estimated that the rate constant for protonation of the acetylide anion, a localized carbanion (pKA 21), is the same as the diffusional limit (1010 M1 s1). However, achieving this rate is highly dependent on the extent of localization of the carbanion. Jordan62 has shown that intermediates in thiazolium derivatives are also likely to be localized carbanions, which implies that protonation of these intermediates could occur at rates approaching those of other localized carbanions. In the enzyme-catalyzed reaction, a tetrahedral array at the carbonylderived portion of the ThDP-conjugate intermediates is enforced throughout the catalytic cycle.63 This is not possible for analogous reactions in solution. Therefore, carboxylation of the carbanion would occur more readily on the enzyme. Although this seems counterproductive, the enzyme also prevents internal return and catalyzes the reaction by rapid proton transfer from a residue poised for the reaction (or by addition or oxidation, depending on the reaction catalyzed). The alternative, a mechanism proceeding through a stabilized enamine, may provide a lower energy path; however, that path would not lead to products with the lowest possible barrier.
PRE-ASSOCIATION CATALYSIS OF DECARBOXYLATION
8
369
OMP decarboxylase – decarboxylation and protonation of orotidine monophosphate
We summarized some fundamental aspects of OMPDC earlier in this review. The detailed mechanism can be regarded in terms of the reactive components in the mechanism. Ealick and Begley64 proposed an alternative mechanism in which the highly basic carbanion resulting from the loss of carbon dioxide from OMP is avoided by a concerted electrophilic substitution process on the enzyme; a proton is added to the carbanion prior to formation of carbon dioxide. This concerted pathway would be lower in energy if the negative charge at carbon did not develop completely in the transition state. However, Richard and coworkers29 ruled out this possibility through evaluation of the selectivity of the intermediate toward hydrogen and deuterium in the solvent. They showed that there is no discrimination between H and D in a mixture of water and deuterium oxide – therefore the proton transfer is not part of the C–C bond-breaking step, which would be expected were it involved in the rate-determining step of the reaction. Various schemes to make the initial carbanion less basic through protonation of the substrate have been shown to be inconsistent with structural and reactivity data. The idea that the carboxylate of the substrate is destabilized by close interaction with a carboxylate from a side chain of the protein, a case of electrostatic stress of the substrate as a result of strain in the enzyme (Fersht65 states that stress occurs in a substrate from electrostatic or steric interactions, while a macromolecule can assume a strained state that induces the stress), was the result of the examination of structure of OMP decarboxylase.66 Gao and coworkers66 calculations suggest that the breaking of the C–C bond involves simply making the local energy greater. This leads to the spontaneous release of CO2 while a nearby protonated lysine side chain transfers a proton to the nascent carbanion upon its formation. Examination of Gao and coworkers66 calculated energy diagram shows that there is little or no barrier to the combination of carbon dioxide with the carbanion (Fig. 1). Therefore, the protonation event prevents reversal of the decarboxylation. Gao and coworkers66 proposed that binding energy of the substrate and protein is utilized to promote the reaction, which is the Circe Effect as proposed by Jencks67: the ground state of the reactant is specifically destabilized by electrostatic stress in a manner that leads to formation of the transition state. Richard and coworkers25 have shown that the components of the substrate in separate pieces can achieve the same effect, and it is consistent with this view. Such a process is only possible with a bound reactant and would not apply in solution. However, a further aspect of the mechanism, proposed by Gao and coworkers66,68 is that the adjacent protonated lysine serves to protonate the nascent carbanion. This prevents the carbon dioxide generated
370
R. KLUGER AND S.O.C. MUNDLE PMF for the Orotate Decarboxylation Reaction Free Energy (kcal mol–1)
45 Aqueous solution
35 25 15 Orotidylate decarboxylase
5 –5 1
2
3
5 4 R(C6–CO2)
6
7
Fig. 1 Computed free energy reaction profiles for the decarboxylation of OMP in water and in the wild-type enzyme ODCase. Reprinted with permission from Reference 66. Copyright 2000 National Academy of Sciences.
in the bond-breaking process from being captured. The proton source can compete with carbon dioxide in trapping a carbanion and thus accelerate a decarboxylation reaction by blocking its reversal as presented in the first part of this chapter.
9
General trends in catalyzed decarboxylation
We have presented specific cases with evidence that decarboxylation may be a multistep process from which the internal return of carbon dioxide can affect the observed rate of reaction. We have also discussed the mechanism of OMP decarboxylase, where these conclusions may provide additional insight into the mechanism of catalysis employed by the enzyme. There are many other cases that may benefit from applying these principles. For example, Strassner and coworkers69 investigated the enantio-selective decarboxylation of 2-cyano-2-(6-methoxy-naphth-2-yl)propionic acid and concluded from computational analysis that protonation and decarboxylation occur through a concerted mechanism. However, rather than proceeding through an impossibly high-energy five-coordinate carbon, if the catalyst were pre-associated to the face opposite the carboxyl group, the planar intermediate could be rapidly protonated (Scheme 7). This system should be able to undergo pre-association-based catalysis through aromatic stacking.
PRE-ASSOCIATION CATALYSIS OF DECARBOXYLATION
N H
R
CN
N
R
371
CN H
CO2– CO2 N
N
O R=
Scheme 7 Alternative mechanism for asymmetric decarboxylation of 2-cyano2-(6-methoxy-naphth-2-yl)propionic acid in the synthesis of NaproxenTM involving a pre-association mechanism.
10 Decarboxylation of aromatic carboxylic acids We can also consider cases where pre-association would not accelerate a reaction. The decarboxylation of aromatic-ring-substituted carboxylic acids typically involves initial protonation of the a-carbon, followed by carbon– carbon bond-breaking from a carboxylate ion.70 The resulting carbanions in these systems are typically very weak bases and are rapidly incorporated into the ring for re-aromatization. Kresge and coworkers71 reported pKA values for substituted protonated benzene derivatives ranging from 3 to 11, and 23 for unsubstituted protonated benzene. These cases are not expected to be greatly affected by internal return; the rate of carboxylation of the carbanions will be slow. Similarly, in decarboxylation reactions of these acids, the C–C bond of the carboxyl group once broken is expected to lead to a carbanion with similar characteristics as that achieved by the loss of a proton from protonated benzene (Scheme 8). The very weakly basic carbanion
H ±H
H
pKa ~ –23 CO2H
H ±H
CO2H
+ CO2
Scheme 8 Comparison of protonation of benzene with decarboxylation of benzene. Both cases are expected to generate very weak carbanions.
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R. KLUGER AND S.O.C. MUNDLE
NH
O C + HA + H2O OH
+ H NH
OH C OH OH
OH
HO + NH
O H
+
H3O+ + CO2
Scheme 9 Mechanism of decarboxylation via addition of water to the carboxyl group of pyrrole-2-carboxylic acid. Reprinted with permission from Reference 73. Copyright 2009 American Chemical Society.
generated in these cases is not expected to be reactive. This behavior is highlighted in the analogous aromatic acid decarboxylases. The majority of these decarboxylases do not catalyze the corresponding carboxylation reaction. In the few examples that catalyze carboxylation, the equilibrium lies far toward decarboxylation.72 We have presented evidence that pyrrole-2-carboxylic acid decarboxylates in acid via the addition of water to the carboxyl group, rather than by direct formation of CO2.73 This leads to the formation of the conjugate acid of carbonic acid, C(OH)3þ, which rapidly dissociates into protonated water and carbon dioxide (Scheme 9). The pKA for protonation of the a-carbon acid of pyrrole is 3.8.74 Although this mechanism of decarboxylation is more complex than the typical dissociative mechanism generating carbon dioxide, the weak carbanion formed will be a poor nucleophile and will not be subject to internal return. However, this leads to a point of interest, in that an enzyme catalyzes the decarboxylation and carboxylation of pyrrole2-carboxylic acid and pyrrole respectively.75 In the decarboxylation reaction, unlike the case of 2-ketoacids, the enzyme cannot access the potential catalysis available from preventing the internal return from a highly basic carbanion, which could be the reason that the rates of decarboxylation are more comparable to those in solution. Therefore, the enzyme cannot achieve further acceleration of decarboxylation. In the carboxylation of pyrrole, the absence of a reactive carbanion will also make the reaction more difficult; however, in this case it occurs more readily than with other aromatic acid decarboxylases. Another general application is the decarboxylation of compounds related to pyrrole-2-carboxylic acid, such indole-2-carboxylic acid. The observed decarboxylation by microwave irradiation could simply result from the addition of water to the carboxyl group.76–78
11 Decarboxylation of 3-ketoacids Some of the best-known examples of decarboxylation in organic chemistry include the conversion of 3-ketoacids to ketones in the acetoacetic ester synthesis and the conversion of malonate derivatives to substituted carboxylic
PRE-ASSOCIATION CATALYSIS OF DECARBOXYLATION
373
acids in the malonic ester synthesis. These reactions are often formulated as a concerted process in which the proton of the carboxyl group is transferred to the b-carbonyl as the formation of carbon dioxide occurs through carbon–carbon bond cleavage.79 An alternative representation involves initial tautomerization by formation of the zwitterion in which the b-carbonyl is protonated and the carboxyl is ionized with the resulting process involving only carbon–carbon bond cleavage.80 Guthrie81 has considered the details of the latter process in terms of his No Barrier Theory, where further aspects of the reaction are included in considering the mechanism, specifically changes in hybridization at carbon centers during the course of the reaction. He concluded that rehybridization is concerted with bond cleavage. In this case, the carbanion adjacent to the nascent carbon dioxide is extremely weak as it becomes the enol prior to bondbreaking. The reactivity of enols was shown by Kresge61 to be very low with little carbanion character. Therefore, upon breaking the carbon–carbon bond in the decarboxylation of these acids, the adjacent leaving group possesses minimal carbanion character and will not be subject to significant carboxylation by carbon dioxide. Alternatively, if decarboxylation leads to the enolate, which has carbanion character, the internal return of CO2 would become a competing factor. In biochemical decarboxylation reactions where the reactant contains a 3-keto group, the e-amino group of a lysyl side chain of the protein backbone can form an iminium derivative with the substrate.82 Upon loss of carbon dioxide, the delocalized, weakly basic product will not react faster than carbon dioxide can separate. Benner83 showed that the stereochemical consequence of decarboxylation of acetoacetate by acetoacetate decarboxylase involves protonation of the product from either face, consistent with a passive, uncatalyzed step, which is consistent with the view we have presented.
12 Conclusions Pre-association by a proton donor or electron acceptor can be a novel catalytic component in decarboxylation reactions. The mechanism is readily available in biochemical systems but is difficult to achieve in solution as the preassociation requires specific interactions. As instances are found, they provide important information on the mode of catalysis. This review is dedicated to Jerry Kresge, our long-time colleague, whose ideas on the limits of proton transfer provide the basis for the extension to decarboxylation. We thank NSERC Canada for support through a Discovery Grant.
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AUTHOR INDEX Abatjoglon, A. G., 250 Abboud, J. L., 148, 160 Abdur-Rashid, K., 143 Abe, M., 198, 199 Abeygunawardana, C., 4 Aboud, J.-L. M., 19, 20, 22, 25, 49 Abu-Dari, K., 2 Abu-Freih, A., 20, 75 Acheson, S. A., 361 Addepalli, S. V., 192 Agarwal, A., 37, 63 Ahern, D. G., 154 Ahmed, M., 52 Ahonen, A.-K., 11 Ahrens, M.-L., 226 Aida, M., 193, 201, 205, 210, 211 Alavosus, T. J., 96 Alder, R. W., 68 Aldridge, T. E., 90 Aleshi, P., 226, 238, 242, 243 Alewood, D., 13 Alewood, P. F., 13 Ali, M., 253, 256, 258, 304, 305, 308 Alkorta, I., 19, 20, 22, 25 Allen, A. D., 25, 34, 46, 60 Allen, P. R., 68 Allinger, N. L., 159 Almstead, J. I. K., 341 Al-Quatomi, S., 251, 252 Alston, W. C., II., 136, 159, 236 Ammal, S. C., 193, 201, 204, 208 Amyes, T. L., 19, 20, 27, 30, 31, 32, 33, 34, 35, 37, 39, 40, 49, 51, 53, 58, 68, 69, 70, 74, 75, 76, 80, 84, 85, 88, 89, 90, 108, 236, 309, 311, 359, 361, 369 An, J. Y., 372 Anand, S., 187 Andersen, N. H., 10 Anderson, V. E., 124, 136, 153, 157 Andraos, J., 336, 343 Andreeva, T. P., 63 Andre´s, J., 214, 215
Anet, F. A. L., 184 Angelici, R. J., 67 Angelini, G., 237 Anslyn, E. V., 236 Antipova, I. V., 164 Appel, R., 101 Appeloig, Y., 20, 69, 75 Appleby, T. C., 369 A˚qvist, J., 160 Arad, D., 250 Araki, M., 154 Araki, T., 153 Arduengo, A. J., 68, 69 Argile, A., 95, 113 Ariga, T., 49, 76 Arima, K., 49, 76 Armstrong, K. B., 129 Arnett, E. M., 24, 53, 136 Asada, T., 215 Asakura, M., 130 Astrand, P.-O., 211 Atherton, J. H., 294 Atkins, T. J., 164 Aue, D. H., 20, 22, 32 Aumann, R., 307 Ausfelder, F., 200 Ausloos, P., 147 Aviyente, V., 201 Ayala, P. Y., 201, 204 Azizian, K., 313 Bagnell, L., 372 Bagno, A., 28, 30, 49, 52, 53, 100, 333, 352 Baidya, M., 105 Baker, B. W., 155 Baker, J., 201 Bakken, V., 187, 201, 206 Balaban, A. T., 146 Baldwin, J. E., 177, 178, 184 Bamberger, E., 37 Bamford, C. H., 371 Banait, N., 20, 31, 73, 75, 91, 92, 108, 110
377
378 Banait, N. S., 31, 32, 91, 107, 308 Barbosa, R., 230 Bares, J. E., 250 Barker, B., 57 Barletta, G. L., 230, 232 Barnes, D. J., 135 Barnett, S. A., 361, 369 Bartell, L. S., 156 Bartl, J., 31, 97, 98, 100, 101 Bartmess, J. E., 147, 159, 250 Barton, A., 90 Bartunik, H., 368 Bary, Y., 135, 138, 139 Basilevski, M. V., 189, 209 Bates, R. G., 134, 157, 328 Batiz-Hernandez, H., 128 Batts, B. D., 138, 148, 166 Bausher, L. P., 68 Baykov, A. A., 11 Bayles, J. W., 143 Bearne, S. L., 361 Bederke, R., 97, 101 Begley, T. P., 369 Bei, L., 74 Beinert, H., 4, 5 Bekele, T., 196 Belfield, K. D., 177, 178 Bell, A. F., 136, 153, 157 Bell, J. B., 361 Bell, R. P., 52, 53, 95, 134, 156, 157, 230, 346 Bellobono, I. R., 138, 148 Belogurov, G. A., 11 Beltrame, P., 138, 148 Benchekroun, Y., 155 Bender, B. R., 146 Benner, S. A., 373 Benson, S. W., 24, 353 Bentley, T. W., 28, 30, 73 Berg, U., 108 Bergman, R. G., 198, 199 Bergset, J. M., 152 Bergstrom, R. G., 52 Berheide, M., 368 Berkner, K. L., 6 Bernardi, F., 250, 275 Bernasconi, C., 137
AUTHOR INDEX Bernasconi, C. F., 67, 81, 82, 110, 113, 223, 225, 226, 230, 232, 237, 238, 242, 243, 246, 247, 248, 249, 250, 251, 252, 253, 255, 256, 257, 258, 259, 260, 261, 262, 266, 268, 269, 270, 271, 273, 274, 275, 276, 280, 282, 283, 285, 286, 287, 288, 290, 292, 293, 298, 299, 303, 304, 305, 306, 307, 308, 309 Bernheim, R. A., 128 Bertani, R. J., 42 Berti, G., 62 Bertolasi, V., 2 Bertra´n, J., 201, 204, 214, 215 Berweger, C. D., 191 Best, M. D., 236 Bethell, D., 20 Bhattacharya, S., 259, 308 Bierbaum, B. V., 191 Bierbaum, V. M., 147 Bigeleisen, J., 125, 142, 366 Billing, G. D., 211 Binning, R. C., Jr., 211 Bird, C. W., 259, 285, 286 Birney, D. M., 201 Bishop, D. M., 346 Biton, R., 20, 75 Bittener, E. W., 24 Blacker, D. J., 60 Blacker, J., 309 Blakemore, P. R., 130 Blanksby, S. J., 191 Blotny, G., 235 Boehme, C., 69 Bohlmann, F., 163 Bolton, K., 181, 183, 211 Bonneau, R., 327 Borden, W. T., 183, 190 Bordwell, F. G., 82, 230, 250 Borodkin, G. I., 63 Borodkin, S., 63 Bosch, E., 201 Bothner-By, A. A., 136 Bott, R., 8 Bourne, N., 361 Bowden, K., 230 Bowers, M. T., 20, 22, 32 Boyd, D. R., 30, 31, 37, 60, 61, 63, 309 Boyd, W. A., 145
AUTHOR INDEX Boyle, W. J., Jr., 82, 230 Boys, S. F., 275 Brandt, P., 63 Brannigan, I. N., 30, 31 Brant, S. R., 242, 307 Brauman, J. I., 25, 142, 186, 187, 275 Brazier, J. L., 155 Breslow, R., 30, 362, 363 Breugst, M., 93, 95, 104, 105 Bron, J., 143, 157 Brønsted, J. N., 336, 346 Brotzel, F., 103, 105 Brouillard, R., 52 Brown, B. R., 357 Brown, D. A., 67 Brown, E. V., 359 Brown, S. D., 243 Brown, W. G., 64 Bruice, T. C., 2 Bruning, M., 368 Bruns, R. E., 157 Brynda, J., 13 Bueker, H.-H., 211 Bug, T., 98, 100, 101 Bugg, T. D., 37 Buhl, M., 66, 67 Bull, H. G., 52 Buncel, E., 242, 243, 250, 307, 308 Bunnell, R. D., 226, 238, 242 Bunnett, J. F., 36, 225 Bunting, J. W., 62, 82, 232, 235, 243 Bunton, C. A., 65, 66 Burfeindt, J., 100 Burger, S. K., 214 Burggraf, L. W., 201 Burk, R. M., 149 Buschek, J., 31 Busetto, L., 67 Bushick, R. D., 136 Bushmelev, V. A., 63 Byrne, B., 60, 309 Byun, K. L., 369 Cablewski, T., 372 Caldin, E. F., 87 Camden, J. P., 200 Canalini, G., 62
379 Cannes, C., 242, 307 Cannizzaro, C., 201 Cantwell, N. H., 359 Cao, P. P., 365, 366 Capponi, M., 333, 334, 335, 336 Capponi, N., 55 Caramella, P., 201 Carey, A. R. E., 95, 113, 251, 252 Carloni, P., 12 Carpenter, B. K., 175, 176, 177, 178, 179, 180, 183, 187, 190, 211 Carrasco, N., 65 Carrat, S., 153 Carter, C. W., Jr., 8 Carter, E. A., 213 Carter, G. E., 73 Cashen, M. J., 52 Cassidy, C. S., 8 Castan˜o, O., 201 Castejon, H., 250 Caussignac, C., 153 Ceccon, A., 62, 66 C¸elebi-O¨lc¸u¨m, N., 201 Chambreau, S. D., 199 Chan, C., 85 Chan, K., 361, 369 Chan, K. K., 359, 361 Chang, E., 210, 212 Chang, H. W., 30 Chang, J. A., 334, 335 Chang, P. S., 152 Chatrousse, A.-P., 226, 230, 235, 242, 307, 308 Chawia, N., 200 Chen, H. J., 42, 371 Chen, K. H., 159 Chen, W., 187, 211 Chen, X., 110, 299, 303, 306 Chen, Z., 283, 286, 291, 292 Cheng, J.-P., 68 Cheon, S., 210, 212 Chiang, Y., 25, 46, 52, 57, 59, 75, 142, 326, 333, 334, 335, 336, 341, 342, 343, 346, 372 Chin, J., 363 Chioiu, A. S., 200 Chiraleu, F., 146 Cho, Y. J., 212
380 Christian, C. F., 196 Chu, Y., 68 Chu, Y. C., 103 Chwang, W. J., 36, 47 Cistola, D. P., 127 Clark, T., 250 Cleland, W. W., 1, 2, 4, 5, 6, 8, 15, 124, 128, 132, 143, 366 Clifton, J. R., 3 Coates, L., 13 Cockerill, A. F., 225 Codding, S. J., 308 Coe, M., 52 Cohen, A. O., 351, 352 Cohen, T., 136 Compton, R. G., 371 Connor, R. E., 65, 75 Cook, P. F., 132 Cooks, R. G., 148 Coop, I. E., 156 Cooper, J. B., 13 Cooperman, B. S., 11 Cordes, E. H., 361 Cordier, C., 65 Corminboeuf, C., 283, 286, 291, 292 Cossı´ o, F. P., 291 Costentin, C., 272, 315 Courtney, M. C., 33, 34, 75 Covington, A. K., 146 Cox, J. P., 294 Cox, M. M., 361 Cox, R. A., 28, 30, 31, 38, 44, 45, 100 Cozens, F. L., 31, 32, 49, 85, 104 Crabtree, R. F. H., 66 Craig, B. N., 152 Cram, D. J., 360 Crampton, M. R., 294 Creary, X., 90 Croisat, D., 226 Crooks, J. E., 157, 226 Crosby, J., 362, 363 Crugeiras, J., 73, 92, 93, 105, 109, 110, 361 Cruickshank, F. R., 24, 353 Csizmadia, I. G., 250 Cuevas, G., 250 Culliemore, J. C., 53, 68 Culliemore, P. A., 53 Custo´dio, R., 157
AUTHOR INDEX Cvetanovic, R. J., 145 Cybulski, S. M., 277 Cyra´nski, M. K., 283, 286 D’Anna, F., 53 Dai, T., 206 Dalton, H., 37, 60, 309 Danovich, D., 201, 204, 206 Dargel, T. K., 146 Das, A., 13 Das, P. K., 20, 33, 34, 35 Dautraix, S., 155 Da´valos., J. Z., 148., 160 Davalos., J. Z., 19., 20., 22., 25 Davidson, E. R., 185 Davis, L., 14 Davis, L. P., 201 de Jong, W. A., 192 De Maria, P., 53 De Ridder, J. J., 154 de Weck, G., 255 De´sage, M., 155 Debbert, S. L., 190 Deeter, S., 53 DeFrees, D. J., 146, 147, 148, 159, 162, 163 Degani, I., 62 Dega-Szafran, Z., 261 Degorre, F., 242, 307 Dehareng, D., 201 Dell’Erba, C., 53 DeMaria, P., 237 Denegri, B., 105 Deng, H., 68 Denisov, G. S., 156 Deno, N. C., 29, 30 Depristo, A. E., 201 DePuy, C. H., 147 deRossi, R. H., 308 Devine, D. B., 28 Devlin, J. L., III., 146 Dewan, J. C., 14 Dewar, M. J. S., 291 Dey, J., 27, 36, 41, 42, 45, 75 Dfietze, P. E., 72 Dietze, P. E., 35 Diffenbach, R. A., 20 Dinnocenzo, J. P., 315
AUTHOR INDEX Dive, G., 201 Diver, S. T., 68, 69, 70 Dixon, D. A., 69 Doan, L., 59, 76 Doering, W. v. E., 28, 62 Dombek, B. D., 67 Dong, Y., 130, 131, 136, 137, 141, 154, 157, 160, 161, 163, 166 Dostrovsky, I., 35 Do¨tz, K. H., 255, 307 Doubleday, C., Jr., 180, 181, 182, 183, 184 Dowling, J., 340 Drake, A. F., 60 Drake, D. A., 142 Dransfeld, A., 292 Drees, M., 370 Drevko, B. I., 164 Drewes, R., 177, 178 Drewry, J. J., 365, 366 Drucker, G. F., 250 Drueckhammer, D. G., 5 Dubois, J.-E., 52 Duffield, G. L., 294 Dulich, F., 65 Duncan, F. J., 145 Duncan, J. A., 190 Duncan, M. W., 155 Dunlap, C. A., 10 Dupuis, M., 193, 201, 205, 210, 211 Duroki, R., 14 Duus, F., 151 Dybala-Defratyka, A., 366, 367 Dziembowska, T., 128 Eaborn, C., 46, 63 Eagle, H., 153 Ealick, S. E., 369 Eberlin, M. N., 148, 160 Eck, D. L., 36 Edman, C., 361 Eichhorn, C., 200, 210 Eigen, M., 226, 351 El Amour, H., 65 El-Alaoui, M., 53 Elbert, S. T., 201 Elias, M., 14 Eliel, E. L., 250 Elison, C., 136
381 Elliott, H. W., 136 Ellison, G. B., 191 Ellison, S. L. R., 128 Emmons, W. D., 142 Emokpae, T. A., 63 Emsley, J., 2, 332 Engelt, K. M., 314 Epstein, L. M., 143 Erde´lyi, M., 130, 139, 161, 164, 165 Erlenmeyer, E., 325 Erskine, P. T., 13 Ess, D. H., 201 Eur, J., 9 Eustace, S. J., 340 Evans, M. G., 291 Evans, W. L., 29, 30 Eyring, H., 84 Fabian, M. A., 129, 130 Fabian, W. M. F., 312 Fabrichniy, I. P., 11 Fabry, M., 13 Fahey, R. C., 142 Fainberg, A. H., 72 Fairchild, D. E., 226, 232, 238, 242, 243, 246, 251 Falconer, W. E., 145 Fang, S., 183 Farid, S., 315 Farneth, W. E., 275 Farrell, P. G., 226, 235 Fassberg, J., 299 Fattahi, A., 59 Fattal, E., 213 Faucher, N., 243, 250 Fazio, F., 154 Fedorov, A. A., 359, 361 Fedorov, E. V., 359, 361 Fendrich, G., 242, 307 Fernandez, I., 291 Ferrall, P., 230 Ferrer, J.-L., 13 Ferretti, V., 2 Fersht, A., 369 Fierman, M. B., 152 Filer, C. N., 153, 154 Fischer, E. O., 307 Fischer, H., 260, 261, 307
382 Fischer, H. P., 207 Fitzpatrick, N. J., 67 Fitzwater, S., 156 Fleurat-Lessard, P., 215 Flores, F. X., 305, 307, 308 Fochi, R., 62 Fogel, P., 235 Fong, T. P., 143 Fontana, A., 53, 237 Foote, C. S., 201 Forsyth, D. A., 131, 149 Forsythe, K. M., 211 Fournier, B., 14 Freedberg, D. I., 150, 184 Freeman, N. J., 332 Freiermuth, B., 55, 335, 340 Frekel, M., 72, 73 Frenking, G., 69 Frey, P. A., 1, 2, 8, 15, 253 Freyberg, D. P., 2 Frick, L., 8 Fridovich, I., 373 Fridovich-Keil, J. L., 11 Friedman, M. A., 313 Frutos, L. M., 201 Fujii, Y., 153 Fujio, M., 30, 31, 33, 34, 37, 40, 49, 59, 76, 103 Fujita, M., 49 Fukata, G., 95, 113 Fukuzawa, K., 215 Funke, C. W., 155 Furuhama, A., 211 Futakawa, T., 130 Gabbay, S., 159 Gadosy, T. A., 45 Gajewski, J. J., 113, 185 Gal, J. F., 146 Gallardo, I., 201, 204 Galvin, M., 67 Gambaro, A., 62, 66 Gandler, J. R., 230, 242, 305, 307 Ganshow, G., 8 Gantilov, Yu, G., 63 Gao, J., 214, 316, 369 Garcı´ a-Rı´ o, L., 248, 249, 305, 306, 307 Garcia-Viloca, M., 214, 316
AUTHOR INDEX Gassman, P. G., 1 Gavrilina, L. V., 155 Gawlita, E., 136, 153, 157 Gedge, S., 28 Geerke, D. P., 214 Gelb, M. H., 10 George, T. F., 201 Gerhold, J., 250 Gerlt, J. A., 1, 3, 15, 361, 363, 369 Ghobrial, D., 45 Giblin, D., 148 Gilboa, H., 135, 138, 139 Gill, P. M. W., 201 Gilli, G., 2 Gilli, P., 2 Girard, L., 65 Gittis, A. G., 4 Glass, W. K., 67 Glasstone, S., 84 Glukhoutsev, M. N., 259, 285 Goddard, R., 307 Goeschen, C., 336, 340, 344, 345 Golbik, R., 11, 12, 368 Golbon, P., 46 Gold, M. A., 230 Gold, V., 20, 32, 35, 36, 40, 87 Golden, D. M., 24, 353 Golding, P. D., 135 Golubev, N. S., 156 Gona´lez-Lafont, A`., 201, 214 Gorath, G., 100 Gordon, M. S., 201 Goronski, J. K., 60 Goto, T., 163 Gotta, M. F., 97, 98, 100 Goumont, R., 243, 250 Govind, N., 213 Gozzo, F. C., 148, 160 Grabis, U., 97 Grabowski, J. J., 147 Grace, J. T., 30 Grainger, S., 230 Granados, A. M., 308 Grant, A. S., 336, 343 Grauel, H., 146 Gray, S. K., 211 Greaves, B., 143 Greenwald, E. J., 201, 203
AUTHOR INDEX Grehn, L., 129, 135, 136, 140, 154 Grieg, C. C., 53 Grob, C. A., 207 Groh, S., 360, 363 Gronert, S., 262, 268, 269, 270, 273, 277, 283, 286, 313 Gronheid, R., 49, 76 Gross, M. L., 148 Groves, P. T., 29 Gruen, L. C., 32, 35, 36, 40 Grunwald, E., 28, 230 Gruselle, M., 65 Gruttadauria, M., 53 Gu, Z., 5 Guadagnini, P. H., 157 Guir, F., 242, 307 Gunsteren, W. F., 191 Gunter, J. C., 258 Guo, H.-X., 334, 336, 343 Gusev, D. G., 143 Gut, I. G., 55, 335, 335, 343 Guthrie, J. P., 23, 24, 48, 51, 53, 67, 68, 72, 73, 86, 341, 353, 373 Haag, R., 340 Haake, P., 68 Haas, M. J., 147 Haber, M. T., 308 Haberfield, P., 360 Hafner, A., 255 Hagen, G., 98, 100 Hagen, R., 128 Hakka, L. E., 371 Hakka, L. E., 42 Halevi, E. A., 124, 134, 135, 138, 139, 140, 145, 156, 166 Haley, K., 136, 159, 236 Hall, G. E., 211 Hall, R. E., 73, 94, 95 Halle´, J.-C., 226 Hamaguchi, M., 198, 199 Hamilton, J. A., 127 Hammes-Schiffer, S., 126, 165 Hammond, G. S., 95, 208 Hampel, N., 104 Hand, M. V., 60, 309 Hang, C., 201, 203, 207, 214 Hanley, J. A., 149
383 Hansch, C., 243, 255, 273, 302 Hansen, H. J., 145 Hansen, P. E., 128, 149, 151 Haran, E. N., 156 Harcourt, M., 95, 113 Harcourt, M. P., 27, 75 Hari, S. P., 128 Harris, J. M., 73, 94, 95 Harris, N., 262, 268, 271, 272, 277 Harrison, A. G., 147 Hartmann, A. A., 250 Hasako, T., 49, 76 Hase, W. L., 181, 182, 183, 184, 187, 189, 192, 200, 210, 211, 212 Hasegawa, H., 201, 208 Hasegawa, T., 206 Haspra, P., 326, 333, 334 Hassell, A., 361 Hasselman, D., 177, 178 Hassner, D. Z., 159 Hasson, M. S., 363 Hatoum, H. N., 90 Hattox, S. E., 154 Haugen, G. R., 24, 353 Hawkinson, D. C., 235 Hawthorne, M. F., 142 Hayes, R. L., 213 He´nin, F.,340 Heckl, B., 307 Hegarty, A. F., 90, 340 Hegedus, L. S., 255 Hehre, W. J., 49, 140, 144, 146, 147, 156, 159, 162, 163 Heidrich, D., 201 Heikinheimo, P., 11 Heine, T., 291 Heinekey, D. M., 143 Heinemann, C., 69 Heinemann, G., 144 Helgaker, T., 211 Hellrung, B., 55, 335, 340, 343 Hengge, A. C., 124, 143 Herek, J. L., 181 Herges, R., 291, 336, 340, 344, 345 Hering, N., 98, 100 Herndon, W. C., 34 Herreros, M., 49 Herschlag, D., 2, 308
384 Hertwig, R. H., 146 Heys, J. R., 155 Hibbert, F., 2, 226 Hibdon, S. A., 226 Higginbotham, H. K., 156 Hinckley, C. C., 145 Hine, J., 21, 26, 28, 72, 73, 311 Hinman, J. G., 143 Hinterding, P., 307 Hirani, S. I. J., 230 Hirano, T., 201, 211 Hirao, K., 201, 211 Hiraoka, K., 22 Hirose, M., 14, 201 Hoang, T. X., 164 Hochstrasser, R., 326, 336, 342 Hoffman, B. M., 4 Hofmann, M., 104 Hofmann, R., 307 Hojatti, M., 335 Holden, H. M., 9, 11 Honer, H., 30 Honig, E. D., 65, 96 Hopkins, A., 361 Hopkinson, A. C., 250 Horejsi, M., 13 Hori, Y., 49, 76 Horsley, W. J., 127 Horvat, C. M., 361 Hosoya, K., 153, 154 Hosur, M. V., 13 Houk, K. N., 83, 180, 184, 185, 201 Hristov, I., 215 Hrovat, D. A., 183, 190 Hu, H., 214 Hu, Q., 361, 363, 365, 366 Hu, S.-H., 13 Huang, L. L., 252, 253 Hubbard, J. W., 155 Hubner, G., 11, 12 Humphrey, J. S., Jr., 142 Hupe, D. J., 242, 307 Hupe, S. J., 242, 307 Huskey, W. P., 230, 232 Igarashi, M., 189, 210 Ikeda, G., 365, 366 Ikegami, T., 153
AUTHOR INDEX Ikeo, E., 215 Il’ichev, Y. V., 340 Imker, H. J., 359, 361 Inadomi, Y., 215 Ingold, C. K., 20 Ingold, K., 210 Inoue, H., 49, 76 Intharathep, P., 214 Irrgang, B., 98, 100 Irwin, R. S., 145 Ishida, T., 153 Ishikawa, T., 210, 215 Ishikawa, Y., 211 Ishiwata, A., 206 Iverson, B. B., 2 Iyer, P. S., 150 Jacob, G., 226 Jaffe, M., 150 Jagannadham, V., 33, 49, 75, 76, 85, 311 Jagow, R. H., 142 Jameson, C. J., 128, 156 Janker, B., 98, 100 Janssen, M. U., 152 Jaouen, G., 65 Jaruzelski, J. J., 29, 30 Jaye, A. A., 14 Jefferson, E. A., 334 Jeffrey, G. A., 160 Jelsch, C., 14 Jemmis, E. D., 311 Jencks, D. A., 225 Jencks, W. P., 20, 31, 32, 33, 34, 35, 40, 51, 52, 53, 68, 72, 75, 88, 95, 96, 108, 113, 225, 230, 232, 242, 243, 250, 269, 307, 308, 361, 362, 363, 369 Jensen, H. J. A., 211 Jerina, D. M., 59, 76 Jessop, P. G., 143 Jia, G., 143 Jia, Z. S., 46, 63 Jiao, A., 292 Jiao, H., 34, 291 Johnson, C. D., 53 Jones, D. A. K., 64 Jones, M. E., 361 Jordan, F., 230, 232
AUTHOR INDEX Juaristi, E., 250 Juric, S., 105 Kaatze, U., 31, 34, 35 Kabo, G. J., 72, 73 Kaerner, A., 128 Kallarakal, A. T., 3 Kamikubo, H., 14 Kaminski, Yu, L., 155 Kanagasabapathy, V. M., 31, 32, 91, 107 Kanagasabapthy, V. H., 308 Kanavarioti, A., 243 Kandanarachichi, P., 314 Kane-Maguire, L. A. P., 65, 96 Kanski, R., 136, 159 Kanzian, T., 104 Kaplan, E. D., 164 Karri, P., 143 Kasho, V. N., 11 Kaspersen, F. M., 155 Kass, S. R., 59 Kato, S., 192, 191 Kaumanns, O., 101 Kauski, R., 236 Kawai, H., 292 Kebarle, P., 22 Keefe, J. R., 326, 333, 334, 335, 338, 348 Keeffe, J. R., 20, 30, 31, 33, 34, 37, 40, 48, 50, 59, 60, 61, 69, 70, 87, 224, 230, 236, 251, 262, 268, 269, 270, 273 Keeports, D., 348 Kelly, S. C., 30, 31, 37, 60, 63, 309 Kempf, B., 20, 97, 100, 101 Kennedy, M. C., 4, 5 Kenyon, G. L., 3, 363 Keresztes, I., 187 Kern, D., 11, 12 Ketner, R. J., 110, 299, 303, 306 Kevill, D. N., 104 Khan, S. I., 152 Kiffer, D., 242, 307 Kiirend, E., 129, 135, 136, 140, 154 Kilian, J., 70 Killion, R. B., Jr., 110, 299 Kim, C., 313 Kim, C. K., 262, 268 Kim, C.-S., 364 Kim, H., 9
385 Kim, J. K., 147, 159 Kim, Y.-J., 68, 143, 152 Kimata, K., 153 Kiran, V., 64, 66 Kirby, A. J., 162, 311 Kirmse, W., 69, 70 Kitamura, T., 20, 31 Kitamura, Y., 266 Kitaura, K., 215 Kittredge, K. W., 238, 243, 247, 248, 249, 250, 252, 253, 305, 307, 308 Kizilian, E., 243, 250 Kla´n, P., 327 Klarner, F.-G., 177, 178 Kleiber, L., 370 Klein, F. S., 35 Klein, H. S., 134, 157, 165 Klein, P. D., 154 Kliner, D. A. V., 226, 238, 243 Klippenstein, S. J., 211 Kluger, R., 357, 361, 362, 363, 364, 365, 366, 367, 369, 372 Knapp, M., 8 Knight, W. B., 128 Knowles, J. R., 3 Kobayashi, S., 20, 31, 49, 76, 91, 92, 103, 104, 105 Koch, W., 137, 146 Koehler, K., 52 Koga, K., 49, 76 Kohen, A., 316 Kolmodin, K., 160 Komeiji, Y., 210, 215 Ko´nˇa, J., 312 Koo, C. W., 3 Kopelevich, M., 150 Koptyug, V. A., 63 Korobeinicheva, I. K., 63 Kos, A. J., 250 Kouba, J. E., 371 Kouba, J. E., 42 Kovalevsky, A., 13 Koyano, Y., 215 Kozarich, J. W., 3 Krauss, W. A., 201 Kreevoy, M. M., 1, 4, 5, 6, 15 Kreissl, F. R., 307 Kreiter, C. G., 307
386 Kresge, A. J., 25, 30, 42, 46, 51, 52, 56, 57, 59, 75, 81, 95, 107, 124, 125, 142, 144, 224, 230, 236, 237, 242, 248, 251, 266, 307, 326, 333, 334, 335, 338, 341, 342, 343, 346, 348, 368, 371, 373 Krishna, P., 148 Krishnamurthy, V. V., 150 Kristjansdottir, S. S., 143 Krogh, E. T., 335, 341 Kronja, O., 105, 151 Kru¨ger, C., 307 Krygowski, T. M., 283, 286 Kudavalli, J., 60, 61 Kudavalli, J. S., 20 Kudelin, B. K., 155 Kuhn, O., 65, 66, 97 Kuhn, P., 8 Kumar, G. A., 2 Kumar, R., 372 Kumar, V., 372 Kumeda, Y., 201, 211 Kuperman, J., 130, 139, 161, 164, 165 Kurihara, K., 14 Kurosaki, Y., 211 Kurtz, H. A., 63 Kurz, L., 5 Kuwata, K. T., 201 Kwit, M., 60 La John, L. A., 250 Laali, K. K., 19, 59 Lacrampe-Couloume, G., 357, 365, 367 Lad, C., 361 Lahankar, S. A., 199 Laidler, K. J., 84, 346 Lakhdar, S., 105 Lal, K., 66 Laloi, M., 242, 307 Lam, J. F., 364 Landau, S. E., 143 Landesman, H., 146 Landro, J. A., 3 Lang, G., 102, 105, 106, 113 Lang, R. W., 145 Lantz, M., 136, 153, 157 Lapworth, A., 325 Larsen, F. K., 2 Larsen, R. W., 53
AUTHOR INDEX Larsen, T. S., 314 Lau, C.-P., 143 Lau, J. S., 143 Lauble, H., 4, 5 Laurie, V. W., 156 Laursen, R., 136 Lawlor, D. A., 20, 30, 33, 37, 38, 40, 44, 60, 61, 62, 77, 88, 89 Le Gue´vel, E., 242, 307, 308 Le´tinois, S., 340 Leach, A. G., 201 Leckey, N. T., 66 Lee, I., 262, 268 Lee, J. C., 230 Lee, J. M., 313 Lee, S. K., 199 Lee, Y.-G., 75, 76, 85 Leffler, J. E., 28, 208, 230 Lehn, J.-M., 250 Lehtihuhta, E., 11 Lelie`vre, J., 230, 235 Lemek, T., 101 Lennartz, H. W., 190 Leo, A., 243, 255, 273, 302 Le´once, E., 153 Levi, B. A., 147, 148, 159, 163 Lewis, B. E., 124, 155, 163 Lewis, C. A., 361 Lewis, E. S., 78, 83 Leyes, A. E., 248, 249, 253, 255, 256, 305 Li, G., 184, 210, 211 Li, J., 104, 201, 206 Li, X., 201, 206, 211 Lias, S. G., 147 Liberman, J., 130, 139, 161, 164, 165 Lichtin, N. N., 144 Lide, D. R., Jr., 157 Lidwell, O. M., 95 Liebman, J. F., 59 Liebschner, D., 14 Lield, K. R., 214 Lien, M. H., 250 Lienhard, G. E., 362, 363 Liese, A., 368 Limbach, H. H., 153, 156 Lin, B., 59, 76 Lin, J., 8 Lin, S.-S., 19, 20, 37, 39, 88, 90
AUTHOR INDEX Lindner, W., 153 Lippmaa, E., 129, 135, 136, 140, 154 Lipscomb, W. N., 9 Lipton, M. A., 196 Litovitz, A. E., 187 Liu, G., 315 Liu, K., 5 Lluch, J. M., 151, 201, 214 Lo Meo, P., 53 Lockley, W. J. S., 154 Lodder, G., 49, 76, 298 Lodi, P. J., 3 Lodter, W., 37 Loendorf, A. J., 143 Logue, M. W., 373 Loh, S., 2 Lomas, J. S., 49 Long, F. A., 29, 42 Looker, M. R., 155 Loos, R., 91, 92, 101, 104 Lo´pez, J. G., 192 Lorance, E., 226, 238, 242, 243 Loudon, G. M., 334, 337 Lourderaj, U., 192, 200, 210 Love, P., 145 Lu, F., 305 Lu, Z., 214 Lucas, P., 149 Lucchini, V., 36, 46, 47, 48, 52, 53, 333, 352 Lucius, R., 101 Luisandre´s, J., 201 Luzhkov, V. B., 160 Lyons, B. A., 179, 211 Ma, S., 316 Maass, G., 226 Maccoll, A., 366 MacCormack, A. C., 19, 20, 30, 31, 34, 36, 38, 40, 42, 46, 48 Machiguchi, T., 206 Madsen, G. K. H., 2 Maerker, C., 292 Magnier, E., 243, 250 Magris, L., 55, 335 Mahale, S., 13 Mahler, J. E., 64 Maier, N. M., 153
387 Major, D. T., 214 Malone, J. F., 60 Manassen, J., 35 Mangini, A., 250 Mann, D. J., 192 Marcus, R. A., 78, 107, 224, 236, 351, 352 Mareda, J., 49 Maria, P.-C., 146 Mariappan, S. V. S., 128 Markey, S. P., 155 Markley, J. L., 8 Marquez, V. E., 8 Marsh, K. N., 72, 73 Martı´ , S., 214, 215 Martin, D. P., 5 Martins-Costa, M. T. C., 214 Marziano, A., 42 Masters, C. F., 155 Mathivanan, N., 31, 33, 34, 73, 85 Matos, M. A. R., 59 Matsson, O., 124, 366, 367 Matthews, B. W., 9 Mayer, M. G., 125 Mayr, H., 20, 21, 23, 31, 32, 65, 66, 67, 83, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 113 McAllister, M. A., 2, 34 McCann, G. M., 55, 335 McClelland, R. A., 19, 20, 28, 31, 32, 33, 34, 45, 49, 52, 73, 74, 75, 77, 85, 91, 92, 97, 104, 106, 107, 108, 110, 308, 314 McCloskey, J. A., 154 McCollum, J. G., 250 McCormack, A. C., 33, 34, 75 McDermott, A., 5 McDonnell, C. M., 19, 20, 30, 31, 34, 36, 38, 40, 42, 46, 48, 55, 67, 335 McGarraghy, H., 340 McGlinchey, M. J., 65 McIver, R. T., Jr., 147, 159 McLeish, M. J., 363 McMahon, T. B., 147, 159 McMordie, R. A. S., 37 McMurry, J., 249 Meech, S. R., 14 Mefford, I. N., 155 Meller, J., 153
388 Meloche, H. P., 15 Meng, Q., 334 Metiu, H., 201 Meyer, D., 368 Meyer, K. H., 333 Meyer, M. P., 201 Mhala, M. M., 66 Midha, K. K., 155 Mikami, B., 14 Mikkelsen, K. V., 211 Mikosch, J., 200, 210 Milburn, M., 361 Mildvan, A. S., 4 Milicevic, S. D., 130 Millam, J. M., 187, 211 Miller, B. G., 359, 361 Miller, W. B., 68 Miller, W. B. T., 134 Millot, C., 214 Mills, N. S., 34 Minami, Y., 211 Minato, T., 206 Mindl, J., 29, 30 Minegishi, S., 91, 92, 96, 103, 104, 105 Minkin, V. I., 259, 285 Miranda, M. S., 59 Mirza, S. P., 148 Mishima, M., 33, 49, 76, 266 Mitra, B., 3 Mizersi, T., 90 Mo, Y., 34, 369 Mochizuki, Y., 210, 215 Modena, G., 36, 46, 47, 48, 49, 298 Modro, A., 85 Moffat, J. R., 66 Moliner, V., 214, 215 Moniot, S., 14 Montan˜ez, R. L., 226, 238, 242, 243 Monzingo, A. F., 9 Mookerjee, P. K., 26, 72, 73 Moore, C., 143 Morais, V. M. F., 59 Moran, D., 291 Moran, M., 58, 84 Morao, I., 291 More O’Ferrall, R., 334, 336, 345
AUTHOR INDEX More, O’Ferrall, R. A., 19, 20, 21, 27, 28, 30, 31, 33, 34, 36, 37, 38, 40, 41, 42, 44, 45, 46, 48, 50, 51, 52, 53, 54, 55, 59, 60, 61, 63, 67, 69, 70, 75, 77, 78, 83, 88, 89, 95, 100, 113, 124, 225, 235, 250, 251, 252, 269, 311 Moreira, J. A., 252, 253 Morene, G., 201, 204 Moreno, M., 151, 201 Morey, J., 230 Morita, Y., 334 Morris, R. H., 143 Morrow, J. R., 361 Morton, T. H., 373 Moutier, G., 242, 307 Moutiers, G., 226, 308 Moylan, C. R., 142, 275 Mueller, T., 69 Muenter, J. S., 156 Mulholland, A. J., 214 Muller, K.-H., 65, 66, 67, 94 Muller, M., 100 Muller, P., 19, 20, 22, 25, 49 Muller, T. J. J., 65 Mu¨ller-Plathe, F., 191 Mullikan, R. S., 64 Mullin, A. S., 226, 238, 243 Mundle, S. O. C., 357, 365, 367, 372 Mun˜oz-Caro, C., 148, 160 Murphy, D. G., 21, 54 Murr, B. L., 144 Murray, B. A., 251, 252, 311 Murray, C. J., 136, 159, 232, 236, 242, 243, 250, 307 Muscate, A., 363 Mustanir., 266 Mustyakimov, M., 13 Muzart, J., 340 Myles, A. A., 13 Mylonakis, S. G., 30, 56 Nagae, Y., 215 Nagai, T., 198, 199 Nagaoka, M., 215 Nagasawa, T., 372 Nagase, S., 82 Nagy, S. M., 63 Naito, I., 20, 31
AUTHOR INDEX Nakaishi, M., 198, 199 Nakamura, C., 242, 307 Nakamura, T., 198, 199 Nakanishi, K., 163 Nakanno, T., 215 Nakano, T., 210, 215 Nappa, J., 14 Nazaretian, K. L., 308 Neef, H., 11, 12 Nelson, A., 152 Nemoto, T., 215 Nendel, M., 184, 185, 201 Netz, A., 65 Neumann, T. E., 193 Nevy, J. B., 235 Newman, K. E., 146 Newton, M. D., 160 Ni, J. X., 226, 238, 243 Nicholas, K. M., 65, 75 Nicolaisen, F. M., 149 Nielson, J. B., 143 Nikolaev, V. A., 334, 335 Nimura, N., 14 Nin˜o, A., 148, 160 Nolte, C., 105 Nomura, K., 154 Norrish, R. G. W., 326 Norrman, K., 147, 159 Northcott, D., 138, 147, 166 Northrop, D. B., 12, 13, 357, 366 Norton, J. R., 143 Notario, R., 49 Noto, A., 53 Nourse, B. D., 148 Novak, M., 30, 33, 34, 40 Novi, M., 53 Nowlan, V. J., 36, 47 Nummela, J. A., 187 Nussim, M., 134, 138, 139, 140, 166 Nymand, T., 211 O’Brien, D. M., 21, 54 O’Connell, E. L.15 O’Donoghue, A. C., 19, 20, 27, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 45, 46, 48, 51, 59, 75, 88, 90 O’Leary, D. J., 152 O’Leary, M. H., 366
389 O’Neal, H. E., 24, 353 Oae, S., 250 Oakenful, D. G., 361, 362 Ochiai, M., 49, 76 Offerhaus, R., 190 Ofial, A. R., 20, 21, 23, 32, 65, 66, 67, 83, 94, 97, 100, 101, 102, 105, 113 Ohashi, M., 163 Ohki, T., 154 Ohkita, M., 292 Ohno, A., 250 Ohta, B. K., 130, 138, 139, 161, 164, 165 Oishi, Y., 215 Oki, M., 130 Okuyama, M., 292 Okuyama, T., 49, 76 Okyama, T., 298 Olah, G. A., 19, 150 Olechno, J. D., 155 Oliveira, A. E., 157 Omura, H., 372 Onak, T. P., 146 Onyido, I., 335 Oppenheimer, N. J., 132 Ortiz, J. J., 361 Osten, H. J., 128, 156 Osterheld, H. T., 186, 187 Otto, R., 200, 210 Paabo, M., 134, 157 Page, M., 184 Page, M. I., 362, 363 Pai, E. F., 369 Paine, S. W., 336, 343 Pak, M. V., 126, 135 Palmeiro, R., 201 Palmer, C. A., 230 Pan, Y., 2 Panda, M., 243, 247 Pande, K. C., 63 Paneth, P., 136, 153, 157, 366, 367 Paneth, P. J., 366 Paralis, R. E., 37 Park, D.-H., 10 Parkin, G., 143 Parks, J. M., 214 Paschalis, P., 226, 238
390 Pattenden, L. K., 13 Patz, M., 97, 99, 100 Paul, M. A., 29 Paul, S. O., 143 Pearson, R. G., 93, 94 Pedersen, S., 181 Pehk, T., 129, 135, 136, 140, 154 Peigneux, A., 226 Pelet, S., 67 Pellerite, M. J., 275 Pentin Yu, A., 164 Perdoncin, J., 84 Perera, H., 130 Pe´rez-Lorenzo, M., 243, 259, 260, 308 Perillo, G., 53 Peroni, D., 52, 55 Perrin, C. L., 125, 129, 130, 131, 136, 137, 138, 139, 141, 143, 152, 154, 157, 158, 160, 161, 163, 164, 165, 166, 313 Persy, G., 55, 335, 343 Peslherbe, G. H., 181, 183, 210 Peter, E. A., 159 Peterli, M. F., 55 Peterli, S., 335, 340 Peterson, H. J., 29 Peterson, T. H., 179, 211 Petit, R., 64 Petsko, G. A., 3 Pezacki, J. P., 364 Pfeifer, J., 179, 211 Pham, T. V., 74, 75 Phan, T. B., 93, 95, 103, 104, 105 Piana, S., 12 Pierini, M., 237 Piez, K. A., 153 Pirinccioglu, N., 38, 40, 44, 46, 75 Pitchko, V., 86 Pitt, C. G., 63 Plapp, B. V., 10, 11 Pohjanjoki, P., 11 Pohl, E. R., 242, 307 Poi, M. J., 10 Pojarlieff, I. G., 336 Pollack, R. M., 230, 235, 373 Pollack, S. K., 147, 148, 159, 163 Polovnikova, L. S., 363 Pomerantz, A., 200 Popik, V. V., 326, 336, 339, 342, 343
AUTHOR INDEX Porter, G., 326, 327 Pottel, R., 31, 34, 35 Pouet, M.-J., 226 Powell, M. F., 124 Prabhakar, S., 148 Prakash, G. K. S., 19, 150 Prall, M., 291 Pramata, J., 236 Pranata, J., 136, 159 Prapansiri, V., 149 Prashar, V., 13 Price, C. C., 250 Pross, A., 49, 95, 104, 238, 255 Pruszynski, P., 334, 336, 343, 346 Pu, J., 316 Puchta, R., 283, 286, 291, 292 Quacchia, R. H., 29 Quadrelli, P., 201 Quapp, W., 201 Quintanilla, E., 148, 160 Quirke, A. P., 336, 345 Quirke, R. P., 53 Rabb, D. M., 152 Rabenstein, D. L., 128 Raber, D. J., 73, 94, 95 Raczynska, E. D., 146 Radom, L., 49 Radzicka, A., 361 Ragains. M. L., 255, 259, 282, 283, 285, 286, 292, 299 Ragnarsson, U., 129, 135, 136, 140, 154 Ramaswamy, S., 10 Ramquet, M.-N., 201 Rao, K. N., 144 Rao, S. N., 20, 30, 31, 34, 36, 37, 38, 40, 42, 44, 46, 48, 60, 61, 63, 77, 88, 89 Rapoport, H., 136 Rappoport, Z., 96, 110, 298, 299, 303, 306, 368 Rathgeber, S., 357, 361, 365, 367 Rau, D., 65, 66, 94 Raudenbusch, W., 207 Ravid, B., 145, 156 Raymond, K. N., 2 Reagan, M. T., 29, 30 Reed, A. E., 311
AUTHOR INDEX Reid, E. E., 357 Reid, R. C., 13 Reinhardt, L. A., 8 Rekowski, V., 190 Remington, S. J., 5 Ren, D., 45 Resnick, S. M., 37 Reuben, J., 148 Reyes, A., 126, 165 Reyes, M. B., 179 Reys, M. B., 179 Rezacova, P., 13 Rheingold, A. L., 143 Rice, D. J., 27, 75, 76, 85 Richard, J. P., 19, 20, 27, 30, 31, 32, 33, 34, 35, 37, 39, 40, 49, 58, 68, 69, 70, 72, 73, 74, 75, 76, 78, 79, 80, 82, 84, 85, 88, 89, 90, 92, 93, 94, 95, 96, 101, 105, 108, 109, 110, 236, 308, 309, 311, 336, 361, 369 Richler, D., 102 Richter, J., 336, 340, 344, 345 Rickborn, B., 37 Ridder, L., 214 Riedle, E., 105 Rieke, C. A., 64 Rietjens, I. M. C., 214 Rife, J. E., 132 Rios, A., 361 Rishavy, M. A., 6 Rissing, P.-J., 201 Ritchie, C. D., 20, 21, 66, 71, 75, 92, 95 Rivas, F. M., 68, 69, 70 Riveiros, E., 361 Roberts, J. D., 128 Robertson, R. E., 138, 139, 141, 147, 166 Robinson, M. J. T., 128 Robinson, R. A. J., 134, 157 Roca, M., 214, 215 Rochester, C. H., 29 Rode, B. M., 214 Rodgers, A. S., 24, 353 Rodriguez-Dafonte, P., 308 Roganov, G. N., 72, 73 Rohde, C., 250 Rohrer, J. S., 155 Romanin, A., 62, 66 Ron, A., 134, 138, 139, 140, 166
391 Ronayne, K. L., 14 Ross, J., 201 Rostkowski, M., 366, 367 Roth, J., 152 Roth, W. R., 190 Rothenburg, M. E., 20, 31, 32, 33, 34, 40, 88, 96 Roychaudhuri, D. K., 164 Rozwadowski, Z., 128 Rozzell, J. D., 373 Ruddat, V., 257, 260, 261 Ruedenberg, K., 201 Ruffalo, R., 65 Ruiz-Lo´pez, M. F., 214 Ruszczycky, M. W., 153 Ruud, K., 211 Ryaboy, V. M., 189, 209 Rybalova, T. V., 63 Rzepa, H. S., 159 Sabatier, P., 357 Sacchettini, J. C., 14 Sacksteder, K. A., 8 Saenger, W., 2 Sagarik, K., 214 Saines, G., 29 Sakanishi, Y., 49 Salahub, D. R., 211 Salamin, M., 65 Salvesen, K., 361, 362 Salzner, U., 27 Sander, E. G., 52 Sanders, J. K. M., 145 Sano, K., 20 Santaballa, J. A., 333, 334, 346 Sastry, G. N., 201, 204 Sato, M., 201, 208, 210, 215, 266, 286, 287, 288, 290 Sato, Y., 30, 56 Sauers, C. K., 360, 363 Saunders, M., 24, 150 Saunders, O. L., 230 Saunders, W. H., Jr., 225, 262, 268, 271, 272, 274, 277, 279, 366 Save´ant, J.-M., 201, 204, 272, 315 Sayal, P. K., 67 Sayer, J. M., 361 Scaiano, J. C., 327
392 Schade, C., 97, 101 Schaple, L. H., 102, 106, 113 Schaumburg, K., 149 Scheiner, S., 277 Schepp, N. P., 309, 326, 334, 335, 336, 340, 346, 348 Scher, C., 156 Schimerlik, M. I., 132 Schindele, C., 83 Schiott, B., 2 Schlegel, H. B., 187, 201, 204, 206, 211, 250 Schleyer, P. v. R., 27, 64, 66, 94, 95, 250, 283, 286, 291, 292, 311 Schlierf, C., 65 Schmidhammer, U., 105 Schnabel, W., 20, 31 Schneider, R., 97, 101 Schowen, R. L., 362 Schramm, V. L., 124, 155, 163 Schreiner, P. R., 291 Schriesheim, A., 29, 30 Schro¨der, D., 146, 148 Schroeder, G., 261 Schubert, U., 307 Schubert, W. M., 29, 30 Schug, K. A., 153 Schultz, M.-F., 335, 340 Schulz, D. Z., 55 Schulze, J., 42 Schumacher, A. J., 31, 34, 35 Schwarz, H., 69, 148 Schwo¨rer, M., 336, 340 Scleyer, P. v. R., 34 Scorrano, G., 28, 30, 52, 53, 84, 100, 333, 352 Scott, B. S., 93 Scott, J. M. W., 135 Scott, K., 14 Sedlacek, J., 13 Sekhar, V. C., 11 Selc¸uki, S., 201 Semialjac, M., 148 Sen Sharma, D. K., 22 Serianni, A. S., 151 Serre, L., 13 Shah, V. J., 3
AUTHOR INDEX Shaik, S., 201, 204, 206, 262, 268, 271, 272, 277 Shaik, S. S., 238 Shainyan, B. A., 298 Shakirov, M. M., 63 Shan, S.-ou, 2 Shapiro, I., 146 Sharma, A., 372 Sharma, N., 372 Sharma, N. D., 37, 60 Sharma, R. B., 22 Shen, C. S., 78, 83 Shen, K. K-. W., 198, 199 Sherwood Lollar, B., 357, 365, 367 Shi, Y., 255 Shimizu, N., 14 Shiner, V. J., Jr., 144, 193 Short, S., 361 Short, S. A., 8 Shubin, V. G., 63 Shubina, E. S., 143 Shukla, D., 315 Shvarev, A., 130 Siani, G., 237 Sidorov, V. I., 63 Siehl, H. U., 151 Siehl, U., 19, 49 Sierra, M. A., 291 Silbey, R., 201 Simion, D. V., 64, 66 Simkin, B. Y., 259, 285 Singleton, D. A., 196, 201, 203, 207, 214, 211 Sinha, A. K., 372 Sinnott, M. L., 129, 314 Skibsted, U., 151 Skvortsov, I. M., 164 Slegt, M., 49, 76 Small, D. M., 127 Smallwood, C. J., 2 Smith, G. V., 145 Smyth, T., 363 Snowden, T. S., 236 Sobel, H., 93, 94 Soltis, S. M., 8 Song, K., 189, 210, 211, 212 Songstad, J., 93, 94 Sørensen, P. E., 314
AUTHOR INDEX Sorenson, S., 53 Sorenson, T. S., 64, 66 Sowinski, G., 136 Sperling, D., 185 Sperling, E. M. G., 155 Spillet, R. E., 46 Spinelli, D., 53 Spinner, E., 138, 148, 166 Spitznagel, G., 250 Springsteen, J., 53 Sptiznagel, G. W., 311 Spunta, G., 62 Stahl, F., 291 Stanoiu, I. I., 146 Stavascik, J., 37 Steenken, S., 20, 31, 32, 33, 34, 49, 52, 70, 73, 75, 85, 91, 92, 97, 104, 107, 108, 110, 308 Stefanidis, D., 82, 232, 243 Steiner, T., 2 Sternlicht, H., 127 Steven, J. A., 294 Stevens, I. M., 309 Stevens, I. W., 75, 80, 309 Stewart, R., 87 Stone, R., 362, 363 Stoner-Ma, D., 14 Storer, J. W., 185 Stouracova, R., 13 Stout, C. D., 4, 5 Strassner, T., 370 Strauss, C. R., 372 Streiter, A., 105 Streitwieser, A. Jr., 61, 68, 134, 142, 157, 165, 250 Stronach, M. W., 243, 247 Stubblefield, V., 74, 309 Sueda, T., 49 Suhrada, C. P., 180, 201 Suits, A. G., 199 Summerhays, K. D., 49, 147, 148, 159, 163 Sun, L., 189, 210, 211, 212 Sun, W., 226, 248, 249, 253, 256 Sunko, D. E., 140, 144, 162, 163 Sustmann, R., 190 Sutter, A., 326, 333, 334 Suzuki, S., 142
393 Suzuki, T., 292 Swain, C. G., 93 Sweigart, D. A., 65, 96, 162 Syzmanski, M. J., 201, 203 Szafran, M., 261 Szczepanik, P. A., 154 Szele, I., 140 Szymanski, P., 101 Taagepera, M., 49, 147, 148, 159, 163 Tachikawa, H., 189, 210, 211 Taft, R. W., Jr., 20, 49, 145, 146, 147, 148, 159, 163, 243, 251, 255, 273, 274, 302 Tagaki, W., 250 Tait, J. J., 361 Tajima, N., 201 Takano, K., 211 Takayanagi, T., 211 Taketsugu, T., 201, 211 Takino, T., 49 Takka, R. M., 308 Talalay, P., 4 Tanaka, N., 153, 154 Tang, Y. S., 334 Taniguchi, H., 20, 31 TaShma, R., 96 Taylor, R., 46, 63 Tchapla, A., 153 Tee, O. S., 334 Teplyakov, A., 11 Terashima, S., 206 Terrier, F., 226, 230, 235, 238, 242, 243, 250, 307, 308 Thibblin, A., 38, 40, 44, 46, 63, 75 Thiel, S., 214 Thiel, W., 214 Thoburn, J. D., 125, 143, 157, 158 Thoden, J. B., 11 Thoene, M., 8 Thomas, H. D., 159 Thornton, E. R., 153, 164, 209 Thweatt, D., 184 Tidwell, T. T., 25, 34, 36, 46, 47, 60 Ting, J. Y., 92 Tittmann, K., 11, 12, 362, 366 Tobin, J. B., 1, 8, 253 Tokarczyk, B., 336, 340, 344, 345 Tokuyasu, T., 105
394 Toma, L., 201 Tomanicek, S., 13 Tomaszewski, J. W., 10 Tonachini, G., 250 Tong, H., 14 Tonge, P. J., 14, 136, 153, 157 Tongraar, A., 214 Topsom, R. D., 49, 251, 273, 274 Torres, L., 151 Tortato, C., 42 Toteva, M. M., 19, 20, 31, 35, 37, 39, 40, 58, 72, 73, 75, 84, 88, 89, 90, 92, 93, 94, 105, 109, 110, 309, 311 Toth, K., 68, 69, 70, 336, 361, 369 Toullec, J., 53, 333, 334, 338 Townsend, D., 199 Toyota, S., 130 Trainor, R. W., 372 Traylor, T. G., 313 Trippel, S., 200, 210 Tronrud, D. E., 9 Truhlar, D. G., 316 Tsang, W. Y., 361 Tsuij, T., 292 Tsuji, Y., 19, 20, 37, 39, 88, 89, 90 Tsuno, Y., 33, 49, 76, 103 Tuan, H.-F., 13 Tun˜o´n, I., 214, 215 Tuominen, V., 11 Turkina, M. V., 11 Turowski, M., 153 Tyndall, J. D. A., 13 Uebayasi, M., 215 Ueno, Y., 215 Uggerud, E., 211 Urwyler, B., 335, 341 Usher, K. C., 5 Ussing, B. R., 201, 207, 211, 214 Usui, S., 49, 76 Vairamani, M., 148 Vaisserman, J., 65 Valleix, A., 153 Valtazanos, P., 201 Van der Linde, W., 138, 139, 141 van der Vlugt, D., 49, 76 van Eikema Hommes, W. J. R., 292
AUTHOR INDEX Van Verth, J. E., 262, 274, 279 Van Doren, J. M., 147 van Gunsteren, W. F., 214 Van Hal, H. J. M., 154 van Rooy, F. A. M., 155 Van Sickle, D. E., 142 Vande Linde, S. R., 212 VanVerth, J. E., 92 Vasquez, T. E., Jr., 152 Vayner, G., 192 Vecera, M., 29, 30 Venkatasubban, K. S., 362 Venzo, A., 62, 66 Vervoort, J., 214 Vichard, D., 226 Villarica, K. A., 184 Virtanen, P. O. I., 66, 71, 75 Vitullo, P., 30, 56 Vitullo, V. P., 373 Vivarelli, P., 250 Vogel, P., 150 Vontor, T., 108 Vrcek, V., 151 Vyacheslav, G., 63 Wade, D., 153 Wagenaars, G. N., 155 Waghorne, W. E., 51 Wagner, P. J., 340 Wakselman, C., 243, 250 Walsh, P. A., 334, 335, 342, 346 Wan, P., 57 Wang, H., 210, 255 Wang, L., 277 Wangbo, M.-H., 250 Wannese, C. S., 283, 286, 291, 292 Wartik, T., 145 Washabaugh, M. W., 68 Watts, W. E., 64, 65, 66 Weaver, L. H., 9 Weber, J., 291 Weeks, D. P., 51 Wei, D., 211 Wei, W., 262, 268, 271, 272, 277 Weimer, M., 370 Weiss, K., 307 Weiss, P. M., 128 Wenkert, E., 164
AUTHOR INDEX Wenzel, P. J., 232, 238, 260, 261, 262, 266, 268, 269, 270, 271, 273, 274, 275, 276, 280, 282, 283, 285, 286, 292 Werner, H., 307 Werst, M. M., 4 Wesendrup, R., 146 Westaway, K. C., 124, 366, 367 Westheimer, F. H., 373 Westler, W. M., 8 Westmaier, H., 104 Weston, R. E., Jr., 124 Whalen, D., 59, 76 Whalen, D. L., 59, 76 Whipple, E. B., 372 Whitt, S. A., 1, 8 Wiberg, K. B., 250 Wickersham, B. M., 152 Wieser, M., 372 Wiest, O., 185 Wight, P., 294 Wilgis, F. P., 193 Wilhoit, R. C., 72, 73 William, J. E., 250 Williams, A., 361 Williams, D. H., 145 Williams, G., 20, 35 Williams, I. H., 159 Williams, K. B., 78, 88, 101, 95 Williams, N. H., 361 Williams, R. E., 146 Williams, R. V., 63 Williams, S. J. J., 68 Windus, T. L., 201 Winstein, S., 72 Wintgens, D., 335, 340 Wipf, G., 250 Wirz, J., 55, 309, 326, 327, 333, 334, 335, 336, 340, 341, 342, 343, 344, 345, 346 Wodzinksi, S., 235 Wohlers, T. M., 11 Wolf, J. F., 49, 146 Wolfe, S., 250 Wolfe, V. E., 90 Wolfenden, R., 359, 361 Wolfenden, R. V., 8 Wolfsberg, M., 159, 366 Wollweber, D., 190 Wong, B., 53
395 Wood, B. M., 359, 361, 369 Wood, S. P., 13 Wu, D., 242, 307 Wu, N., 369 Wulff, W. D., 255 Wurthwein, E. U., 102, 106, 113 Xiang, S., 8 Xiao, L., 242, 307 Xie, H.-Q., 226 Xie, R.-Q., 336 Yagi, H., 59, 76 Yamabe, S., 206 Yamaguchi, A., 154 Yamaguchi, S., 14 Yamakawa, N., 153 Yamamoto, Y., 334 Yamaoka, R., 154 Yamataka, H., 82, 193, 201, 204, 205, 208, 210, 211, 215, 266, 286, 287, 288, 290 Yamataka, Y., 49, 76 Yan, J., 53 Yan, K., 248, 249 Yanai, T., 201 Yang, C., 8 Yang, C.-M., 364 Yang, J.-R., 131 Yang, S.-Y., 215 Yang, W., 214 Yao, X., 230 Yates, K., 28, 100 Yeung, P. K. F., 155 Yin, Y., 334, 335, 342 York, D. M., 214 Yoshida, T., 372 Yoshimura, N., 266, 286, 287, 288, 290 Yoshimura, T., 154 Young, P. R., 20, 31, 95 Yuan, C., 10 Yuan, Y., 361 Zahradnik, P., 312 Zajicek, J., 151 Zakharov, L. N., 130 Zeng, X., 335 Zergenyi, J., 207 Zewail, A. H., 181
396 Zhang, J. X., 200, 210 Zhang, W. Y., 149 Zhang, X., 199 Zhao, Q., 4 Zheng, H., 226, 238, 242, 243, 260 Zhong, Z., 236 Zhou, C., 201 Zhu, L., 212 Zhu, Y., 57, 59, 75, 151, 334
AUTHOR INDEX Ziegler, T., 215 Zimmerman, H., 291 Zollinger, H., 137 Zoloff Michoff, M. E., 308 Zou, Y., 230, 232 Zrinski, I., 51, 52, 55 Zuberbu¨hler, A. D., 327 Zuilhof, H., 49, 76
Cumulative Index of Authors Abboud, J.-L.M., 37, 57 Ahlberg, P., 19, 223 Alabugin, I., 42, 1 Albery, W.J., 16, 87; 28, 139 Alden, J.A., 32, 1 Alkorta, I., 37, 57 Allinger, N.I., 13, 1 Amyes, T.L., 35, 67; 39, 1 Anbar, M., 7, 115 Antoniou, D., 41, 317 Arnett, E.M., 13, 83; 28, 45 Ballester, M., 25, 267 Bard, A.J., 13, 155 Basner, J., 41, 317 Baumgarten, M., 28, 1 Beer, P.D., 31, I Bell, R.P., 4, 1 Bennett, J.E., 8, 1 Bentley, T.W., 8, 151; 14, 1 Berg, U., 25, 1 Berger, S., 16, 239 Bernasconi, C.F., 27, 119; 37, 137, 44, 223 Berreau, L.M., 41, 81 Berti, P.J., 37, 239 Bethell, D., 7, 153; 10, 53 Blackburn, G.M., 31, 249 Blandamer, M.J., 14, 203 Bohne, C., 42, 167 Bond, A.M., 32, 1 Borosky, G. L., 43, 135 Bowden, K., 28, 171 Brand, J.C.D., 1, 365 Bra¨ ndstro¨ m, A., 15, 267 Braun-Sand, S., 40, 201 Breiner, B., 42, 1 Brinker, U.H., 40, 1 Brinkman, M.R., 10, 53 Brown, H.C., 1, 35 Brown, R.S., 42, 271
Buncel, E., 14, 133 Bunton, C.A., 21, 213 Buurma, N. J., 43, 1 Cabell-Whiting, P.W., 10, 129 Cacace, F., 8, 79 Capon, B., 21, 37 Carter, R.E., 10, 1 Chen, Z., 31, 1 Cleland, W.W., 44, 1 Clennan, E.L., 42, 225 Collins, C.J., 2, 1 Compton, R.G., 32, 1 Cornelisse, J., 11, 225 Cox, R.A., 35, 1 Crampton, M.R., 7, 211 Datta, A., 31, 249 Da´ valos, J.Z., 37, 57 Davidson, R.S., 19, 1; 20, 191 de Gunst, G.P., 11, 225 de Jong, F., 7, 279 Denham, H., 31, 249 Desvergne, J.P., 15, 63 Detty, M.R., 39, 79 Dosunmu, M.I., 21, 37 Drechsler, U., 37, 315 Eberson, K., 12, 1; 18, 79; 31, 91 Eberson, U., 36, 59 Ekland, J.C., 32, 1 Eldik, R.V., 41, 1 Emsley, J., 26, 255 Engdahl, C., 19, 223 Farnum, D.G., 11, 123 Fendler, E.J., 8, 271 Fendler, J.H., 8, 271; 13, 279 Ferguson, G., 1, 203 Fields, E.K., 6, 1 Fife, T.H., 11, 1 Fleischmann, M., 10, 155
397
Frey, H.M., 4, 147 Fujio, M., 32, 267 Gale, P.A., 31, 1 Gao, J., 38, 161 Garcia-Viloca, M., 38, 161 Gilbert, B.C., 5, 53 Gillespie, R.J., 9, 1 Glover, S.A., 42, 35 Gold, V., 7, 259 Goodin, J.W., 20, 191 Gould, I.R., 20, 1 Greenwood, H.H., 4, 73 Gritsan, N.P., 36, 255 Gudmundsdottir, A. D., 43, 39 Hadad, C. M., 43, 79 Hamilton, T.D., 40, 109 Hammerich, O., 20, 55 Harvey, N.G., 28, 45 Hasegawa, M., 30, 117 Havjnga, E., 11, 225 Hayes, C. J., 43, 79 Henderson, R.A., 23, 1 Henderson, S., 23, 1 Hengge, A.C., 40, 49 Hibbert, F., 22, 113; 26, 255 Hine, J., 15, 1 Hogen-Esch, T.E., 15, 153 Hogeveen, H., 10, 29, 129 Horenstein, N.A., 41, 277 Hubbard, C.D., 41, 1 Huber, W., 28, 1 Ireland, J.F., 12, 131 Iwamura, H., 26, 179 Johnson, S.L., 5, 237 Johnstone, R.A.W., 8, 151 Jonsa¨ ll, G., 19, 223 Jose´ , S.M., 21, 197 Kemp, G., 20, 191 Kice, J.L., 17, 65 Kirby, A.J., 17, 183; 29, 87
398 Kitagawa, T., 30, 173 Kluger, R., 44, 357 Kluger, R.H., 25, 99 Kochi, J.K., 29, 185; 35, 193 Kohnstam, G., 5, 121 Korolev, V.A., 30, 1 Korth, H.-G., 26, 131 Kramer, G.M., 11, 177 Kreevoy, M.M., 6, 63; 16, 87 Kunitake, T., 17, 435 Kurtz, H.A., 29, 273 Laali, K.K., 43, 135 Le Fe` vre, R.J.W., 3, 1 Ledwith, A., 13, 155 Lee, I., 27, 57 Lee, J.K., 38, 183 Liler, M., 11, 267 Lin, S.-S., 35, 67, 351 Lodder, G., 37, 1 Logan, M.E., 39, 79 Long, F.A., 1, 1 Lu¨ ning, U., 30, 63 Maccoll, A., 3, 91 MacGillivray, L.R., 40, 109 McWeeny, R., 4, 73 Manderville, R.A., 43, 177 Mandolini, L., 22, 1 Manoharan, M., 42, 1 Maran, F., 36, 85 Matsson, O., 31, 143 Melander, L., 10, 1 Merle, J. K., 43, 79 Mile, B., 8, 1 Miller, S.I., 6, 185 Mo, Y., 38, 161 Modena, G., 9, 185 More O’Ferrall, R.A., 5, 331 Morsi, S.E., 15, 63 Mu¨llen, K., 28, 1 Mu¨ller, P., 37, 57 Mundle, S.O.C., 44, 357 Muthukrishnan, S., 43, 39 Nefedov, O.M., 30, 1 Nelsen, S.F., 41, 185
CUMULATIVE INDEX OF AUTHORS Neta, P., 12, 223 Neverov, A.A., 42, 271 Nibbering, N.M.M., 24, 1 Norman, R.O.C., 5, 33 Novak, M., 36, 167 Nu´ ne˜ z, S., 41, 317 Nyberg, K., 12, 1 O’Donoghue, A.M.C., 35, 67 O’Ferrall, R.M., 44, 19 Okamoto, K., 30, 173 Okuyama, T., 37, 1 Olah, G.A., 4, 305 Olsson, M.H.M., 40, 201 Oxgaard, J., 38, 87 Paddon-Row, M.N., 38, 1 Page, M.I., 23, 165 Parker, A.J., 5, 173 Parker, V.D., 19, 131; 20, 55 Peel, T.E., 9, 1 Perkampus, H.H., 4, 195 Perkins, M.J., 17, 1 Perrin, C.L., 44, 123 Pittman, C.U., Jr., 4, 305 Platz, M.S., 36, 255 Pletcher, D., 10, 155 Poulsen, T.D., 38, 161 Prakash, G.K.S., 43, 219 Pross, A., 14, 69; 21, 99 Quintanilla, E., 37, 57 Rajagopal, S., 36, 167 Rajca, A., 40, 153 Ramirez, F., 9, 25 Rappoport, Z., 7, 1; 27, 239 Rathore, R., 35, 193 Reddy, V. P., 43, 219 Reeves, L.W., 3, 187 Reinboudt, D.N., 17, 279 Richard, J.P., 35, 67; 39, 1 Ridd, J.H., 16, 1 Riveros, J.M., 21, 197 Robertson, J.M., 1, 203 Romesberg, F.E., 39, 27 Rose, P.L., 28, 45 Rosenberg, M.G., 40, 1 Rosenthal, S.N., 13, 279
Rotello, V.M., 37, 3l5 Ruasse, M.-F., 28, 207 Russell, G.A., 23, 271 Saettel, N.j., 38, 87 Samuel, D., 3, 123 Sanchez, M. de N. de M., 21, 37 Sandstro¨ m, J., 25, 1 Sankaranarayanan, J., 43, 39 Save´ ant, J.-M., 26, 1; 35, 117 Savelli, G., 22, 213 Schaleger, L.L., 1, 1 Scheraga, H.A., 6, 103 Schleyer, P., von R., 14, 1 Schmidt, S.P., 18, 187 Schowen, R.L., 39, 27 Schuster, G.B., 18, 187; 22, 311 Schwartz, S.D., 41, 317 Scorrano, G., 13, 83 Shatenshtein, A.I., 1, 156 Shine, H.J., 13, 155 Shinkai, S., 17, 435 Siehl, H.-U., 23, 63 Siehl, H-U., 42, 125 Silver, B.L., 3, 123 Simonyi, M., 9, 127 Sinnott, M.L., 24, 113 Speranza, M., 39, 147 Stock, L.M., 1, 35 Strassner, T., 38, 131 Sugawara, T., 32, 219 Sustmann, R., 26, 131 Symons, M.C.R., 1, 284 Takashima, K., 21, 197 Takasu, I., 32, 219 Takeuchi, K., 30, 173 Tamara, C.S. Pace, 42, 167 Tanaka, K.S.E., 37, 239 Tantillo, D.J., 38, 183 Ta-Shma, R., 27, 239 Tedder, J.M., 16, 51 Tee, O.S., 29, 1 Thatcher, G.R.J., 25, 99 Thomas, A., 8, 1 Thomas, J.M., 15, 63
CUMULATIVE INDEX OF AUTHORS Tidwell, T.T., 36, 1 Tonellato, U., 9, 185 Toteva, M.M., 35, 67; 39, 1 Toullec, J., 18, 1 Tsuji, Y., 35, 67; 39, 1 Tsuno, Y., 32, 267 Tu¨ do¨ s, F., 9, 127 Turner, D.W., 4, 31 Turro, N.J., 20, 1 Ugi, I., 9, 25 Walton, J.C., 16, 51 Ward, B., 8, 1 Warshel, A., 40, 201
Watt, C.I.F., 24, 57 Wayner, D.D.M., 36, 85 Wentworth, P., 31, 249 Westaway, K.C., 31, 143; 41, 219 Westheimer, F.H., 21, 1 Whalen, D.L., 40, 247 Whalley, E., 2, 93 Wiest, O., 38, 87 Williams, A., 27, 1 Williams, D.L.H., 19, 381 Williams, J.M., Jr., 6, 63 Williams, J.O., 16, 159 Williams, K.B., 35, 67
399 Williams, R.V., 29, 273 Williamson, D.G., 1, 365 Wilson, H., 14, 133 Wirz, J., 44, 325 Wolf, A.P., 2, 201 Wolff, J.J., 32, 121 Workentin, M.S., 36, 85 Wortmaan, R., 32, 121 Wyatt, P.A.H., 12, 131 Yamataka, H., 44, 173 Zimmt, M.B., 20, 1 Zipse, H., 38, 111 Zollinger, H., 2, 163 Zuman, P., 5, 1
Cumulative Index of Titles
Abstraction, hydrogen atom, from O—H bonds, 9, 127 Acid–base behaviour macroeycles and other concave structures, 30, 63 Acid–base properties of electronically excited states of organic molecules, 12, 131 Acid solutions, strong, spectroscopic observation of alkylcarbonium ions in, 4, 305 Acids, reactions of aliphatic diazo compounds with, 5, 331 Acids, strong aqueous, protonation and solvation in, 13, 83 Acids and bases, oxygen and nitrogen in aqueous solution, mechanisms of proton transfer between, 22, 113 Activation, entropies of, and mechanisms of reactions in solution, 1, 1 Activation, heat capacities of, and their uses in mechanistic studies, 5, 121 Activation, volumes of, use for determining reaction mechanisms, 2, 93 Addition reactions, gas-phase radical directive effects in, 16, 51 Aliphatic diazo compounds, reactions with acids, 5, 331 Alkene oxidation reactions by metal-oxo compounds, 38, 131 Alkyl and analogous groups, static and dynamic stereochemistry of, 25, 1 Alkylcarbonium ions, spectroscopic observation in strong acid solutions, 4, 305 Ambident conjugated systems, alternative protonation sites in, 11, 267 Ammonia liquid, isotope exchange reactions of organic compounds in, 1, S56 Anions, organic, gas-phase reactions of, 24, 1 Antibiotics, b-lactam, the mechanisms of reactions of, 23, 165 Aqueous mixtures, kinetics of organic reactions in water and, 14, 203 Aromatic photosubstitution, nucleophilic, 11, 225 Aromatic substitution, a quantitative treatment of directive effects in, 1, 35 Aromatic substitution reactions, hydrogen isotope effects in, 2, 163 Aromatic systems, planar and non-planar, 1, 203 N-Arylnitrenium ions, 36, 167 Aryl halides and related compounds, photochemistry of, 20, 191 Arynes, mechanisms of formation and reactions at high temperatures, 6, 1 A-SE2 reactions, developments In the study of, 6, 63 Base catalysis, general, of ester hydrolysis and related reactions, 5, 237 Basicity of unsaturated compounds, 4, 195 Bimolecular substitution reactions in protic and dipolar aprotic solvents, 5, 173 Bond breaking, 35, 117 Bond formation, 35, 117 Bromination, electrophilic, of carbon–carbon double bonds: structure, solvent and mechanisms, 28, 207 I3C NMR spectroscopy in macromolecular systems of biochemical interest, 13, 279 Captodative effect, the, 26, 131 Carbanion reactions, ion-pairing effects in, 15, 153
401
402
CUMULATIVE INDEX OF TITLES
Carbene chemistry, structure and mechanism in, 7, 163 Carbenes generated within cyclodextrins and zeolites, 40, 1, 353 Carbenes having aryl substituents, structure and reactivity of, 22, 311 Carbocation rearrangements, degenerate, 19, 223 Carbocationic systems, the Yukawa–Tsuno relationship in, 32, 267 Carbocations, partitioning between addition of nucleophiles and deprotonation, 35, 67 Carbocations, thermodynamic stabilities of, 37, 57 Carbon atoms, energetic, reactions with organic compounds, 3, 201 Carbon monoxide, reactivity of carbonium ions towards, 10, 29 Carbonium ions, gaseous, from the decay of tritiated molecules, 8, 79 Carbonium ions, photochemistry of, 10, 129 Carbonium ions, reactivity towards carbon monoxide, 10, 29 Carbonium ions (alkyl), spectroscopic observation in strong acid solutions, 4, 305 Carbonyl compounds, reversible hydration of, 4, 1 Carbonyl compounds, simple, enolisation and related reactions of, 18, 1 Carboxylic acids, tetrahedral intermediates derived from, spectroscopic detection and investigation of their properties, 21, 37 Catalysis, by micelles, membranes and other aqueous aggregates as models of enzyme action, 17, 435 Catalysis, enzymatic, physical organic model systems and the problem of, 11, 1 Catalysis, general base and nucleophilic, of ester hydrolysis and related reactions, 5, 237 Catalysis, micellar, in organic reactions; kinetic and mechanistic implications, 8, 271 Catalysis, phase-transfer by quaternary ammonium salts, 15, 267 Catalytic antibodies, 31, 249 Cation radicals, in solution, formation, properties and reactions of, 13, 155 Cation radicals, organic, in solution, and mechanisms of reactions of, 20, 55 Cations, vinyl, 9, 135 Chain molecules, intramolecular reactions of, 22, 1 Chain processes, free radical, in aliphatic systems involving an electron transfer reaction, 23, 271 Charge density-NMR chemical shift correlation in organic ions, 11, 125 Charge distribution and charge separation in radical rearrangement reactions, 38, 111 Chemically induced dynamic nuclear spin polarization and its applications, 10, 53 Chemiluminesance of organic compounds, 18, 187 The chemistry of reactive radical intermediates in combustion and the atmosphere, 43, 79 Chiral clusters in the gas phase, 39, 147 Chirality and molecular recognition in monolayers at the air–water interface, 28, 45 CIDNP and its applications, 10, 53 Computer modeling of enzyme catalysis and its relationship to concepts in physical organic chemistry, 40, 201 Computational studies of alkene oxidation reactions by metal-oxo compounds, 38, 131 Computational studies on the mechanism of orotidine monophosphate decarboxylase, 38, 183 Conduction, electrical, in organic solids, 16, 159 Configuration mixing model: a general approach to organic reactivity, 21, 99 Conformations of polypeptides, calculations of, 6, 103
CUMULATIVE INDEX OF TITLES
403
Conjugated molecules, reactivity indices, in, 4, 73 Cross-interaction constants and transition-state structure in solution, 27, 57 Crown-ether complexes, stability and reactivity of, 17, 279 Crystalographic approaches to transition state structures, 29, 87 Cycloaromatization reactions: the testing ground for theory and experiment, 42, 1 Cyclodextrins and other catalysts, the stabilisation of transition states by, 29, 1 D2O—H2O mixtures, protolytic processes in, 7, 259 Degenerate carbocation rearrangements, 19, 223 Deuterium kinetic isotope effects, secondary, and transition state structure, 31, 143 Diazo compounds, aliphatic, reactions with acids, 5, 331 Diffusion control and pre-association in nitrosation, nitration, and halogenation, 16, 1 Dimethyl sulphoxide, physical organic chemistry of reactions, in, 14, 133 Diolefin crystals, photodimerization and photopolymerization of, 30, 117 Dipolar aptotic and protic solvents, rates of bimolecular substitution reactions in, 5, 173 Directive effects, in aromatic substitution, a quantitative treatment of, 1, 35 Directive effects, in gas-phase radical addition reactions, 16, 51 Discovery of mechanisms of enzyme action 1947-1963, 21, 1 Displacement reactions, gas-phase nucleophilic, 21, 197 Donor/acceptor organizations, 35, 193 Double bonds, carbon–carbon, electrophilic bromination of: structure, solvent and mechanism, 28, 171 Dynamics for the reactions of ion pair intermediates of solvolysis, 39, 1 Dynamics of guest binding to supramolecular systems: techniques and selected examples, 42, 167 Effect of enzyme dynamics on catalytic activity, 41, 317 Effective charge and transition-state structure in solution, 27, 1 Effective molarities of intramolecular reactions, 17, 183 Electrical conduction in organic solids, 16, 159 Electrochemical methods, study of reactive intermediates by, 19, 131 Electrochemical recognition of charged and neutral guest species by redox-active receptor molecules, 31, 1 Electrochemistry, organic, structure and mechanism in, 12, 1 Electrode processes, physical parameters for the control of, 10, 155 Electron donor–acceptor complexes, electron transfer in the thermal and photochemical activation of, in organic and organometallic reactions, 29, 185 Electron spin resonance, identification of organic free radicals, 1, 284 Electron spin resonance, studies of short-lived organic radicals, 5, 23 Electron storage and transfer in organic redox systems with multiple electrophores, 28, 1 Electron transfer, 35, 117 Electron transfer, in thermal and photochemical activation of electron donor-acceptor complexes in organic and organometallic reactions, 29, 185 Electron transfer, long range and orbital interactions, 38, 1 Electron transfer reactions within s- and p-bridged nitrogen-centered intervalence radical ions, 41, 185
404
CUMULATIVE INDEX OF TITLES
Electron-transfer, single, and nucleophilic substitution, 26, 1 Electron-transfer, spin trapping and, 31, 91 Electron-transfer paradigm for organic reactivity, 35, 193 Electron-transfer reaction, free radical chain processes in aliphatic systems involving an, 23, 271 Electron-transfer reactions, in organic chemistry, 18, 79 Electronically excited molecules, structure of, 1, 365 Electronically excited states of organic molecules, acid-base properties of, 12, 131 Energetic tritium and carbon atoms, reactions of, with organic compounds, 2, 201 Enolisation of simple carbonyl compounds and related reactions, 18, 1 Entropies of activation and mechanisms of reactions in solution, 1, 1 Enzymatic catalysis, physical organic model systems and the problem of, 11, 1 Enzyme action, catalysis of micelles, membranes and other aqueous aggregates as models of, 17, 435 Enzyme action, discovery of the mechanisms of, 1947–1963, 21, 1 Equilibrating systems, isotope effects in NMR spectra of, 23, 63 Equilibrium constants, NMR measurements of, as a function of temperature, 3, 187 Ester hydrolysis, general base and nucleophitic catalysis, 5, 237 Ester hydrolysis, neighbouring group participation by carbonyl groups in, 28, 171 Excess acidities, 35, 1 Exchange reactions, hydrogen isotope, of organic compounds in liquid ammonia, 1, 156 Exchange reactions, oxygen isotope, of organic compounds, 2, 123 Excited complexes, chemistry of, 19, 1 Excited molecular, structure of electronically, 3, 365 Finite molecular assemblies in the organic solid state: toward engineering properties of solids, 40, 109 Fischer carbene complexes, 37, 137 Force-field methods, calculation of molecular structure and energy by, 13, 1 Free radical chain processes in aliphatic systems involving an electron-transfer reaction, 23, 271 Free Radicals 1900–2000, The Gomberg Century, 36, 1 Free radicals, and their reactions at low temperature using a rotating cryostat, study of, 8, 1 Free radicals, identification by electron spin resonance, 1, 284 Gas-phase heterolysis, 3, 91 Gas-phase nucleophilic displacement reactions, 21, 197 Gas-phase pyrolysis of small-ring hydrocarbons, 4, 147 Gas-phase reactions of organic anions, 24, 1 Gaseous carbonium ions from the decay of tritiated molecules, 8, 79 General base and nucleophilic catalysis of ester hydrolysis and related reactions, 5, 237 The Gomberg Century: Free Radicals 1900–2000, 36, 1 Gomberg and the Nobel Prize, 36, 59 H2O—D2O mixtures, protolytic processes in, 7, 259 Halides, aryl, and related compounds, photochemistry of, 20, 191
CUMULATIVE INDEX OF TITLES
405
Halogenation, nitrosation, and nitration, diffusion control and pre-association in, 16, 1 Heat capacities of activation and their uses in mechanistic studies, 5, 121 Heterolysis, gas-phase, 3, 91 High-spin organic molecules and spin alignment in organic molecular assemblies, 26, 179 Homoaromaticity, 29, 273 How does structure determine organic reactivity, 35, 67 Hydrated electrons, reactions of, with organic compounds, 7, 115 Hydration, reversible, of carbonyl compounds, 4, 1 Hydride shifts and transfers, 24, 57 Hydrocarbon radical cations, structure and reactivity of, 38, 87 Hydrocarbons, small-ring, gas-phase pyrolysis of, 4, 147 Hydrogen atom abstraction from 0—H bonds, 9, 127 Hydrogen bonding and chemical reactivity, 26, 255 Hydrogen isotope effects in aromatic substitution reactions, 2, 163 Hydrogen isotope exchange reactions of organic compounds in liquid ammonia, 1, 156 Hydrolysis, ester, and related reactions, general base and nucleophilic catalysis of, 5, 237 Interface, the air-water, chirality and molecular recognition in monolayers at, 28, 45 Intermediates, reactive, study of, by electrochemical methods, 19, 131 Intermediates, tetrahedral, derived from carboxylic acids, spectroscopic detection and investigation of their properties, 21, 37 Intramolecular reactions, effective molarities for, 17, 183 Intramolecular reactions, of chain molecules, 22, 1 Ionic dissociation of carbon-carbon a-bonds in hydrocarbons and the formation of authentic hydrocarbon salts, 30, 173 Ionization potentials, 4, 31 Ion-pairing effects in carbanion reactions, 15, 153 Ions, organic, charge density-NMR chemical shift correlations, 11, 125 Isomerization, permutational, of pentavalent phosphorus compounds, 9, 25 Isotope effects and quantum tunneling in enzyme-catalyzed hydrogen transfer. Part I. The experimental basis, 39, 27 Isotope effects, hydrogen, in aromatic substitution reactions, 2, 163 Isotope effects, magnetic, magnetic field effects and, on the products of organic reactions, 20, 1 Isotope effects, on NMR spectra of equilibrating systems, 23, 63 Isotope effects, steric, experiments on the nature of, 10, 1 Isotope exchange reactions, hydrogen, of organic compounds in liquid ammonia, 1, 150 Isotope exchange reactions, oxygen, of organic compounds, 3, 123 Isotopes and organic reaction mechanisms, 2, 1 Kinetic medium effects on organic reactions in aqueous colloidal solutions, 43, 1 Kinetics, and mechanisms of reactions of organic cation radicals in solution, 20, 55 Kinetics and mechanism of the dissociative reduction of C—X and X—X bonds (X¼O, S), 36, 85 Kinetic and mechanistic studies of the reactivity Zn–Ohn (n = 1 or 2) species in small molecule analogs of zinc-containing metalloenzymes, 41, 81
406
CUMULATIVE INDEX OF TITLES
Kinetics and spectroscopy of substituted phenylnitrenes, 36, 255 Kinetics, of organic reactions in water and aqueous mixtures, 14, 203 Kinetics, reaction, polarography and, 5, 1 Kinetic studies of keto–enol and other tautomeric equilibria by flash photolysis, 44, 325 -Lactam antibiotics, mechanisms of reactions, 23, 165 Least nuclear motion, principle of, 15, 1 The low-barrier hydrogen bond in enzymic catalysis, 44, 1 Macrocyles and other concave structures, acid-base behaviour in, 30, 63 Macromolecular systems of biochemical interest, 13C NMR spectroscopy in, 13, 279 Magnetic field and magnetic isotope effects on the products of organic reactions, 20, 1 Mass spectrometry, mechanisms and structure in: a comparison with other chemical processes, 8, 152 Matrix infrared spectroscopy of intermediates with low coordinated carbon silicon and germanium atoms, 30, 1 Mechanism and reactivity in reactions of organic oxyacids of sulphur and their anhydrides, 17, 65 Mechanism and structure, in carbene chemistry, 7, 153 Mechanism and structure, in mass spectrometry: a comparison with other chemical processes, 8, 152 Mechanism and structure, in organic electrochemistry, 12, 1 Mechanism of the dissociative reduction of C—X and X—X bonds (X¼O, S), kinetics and, 36, 85 Mechanisms for nucleophilic aliphatic substitution at glycosides, 41, 277 Mechanisms of hydrolysis and rearrangements of epoxides, 40, 247 Mechanisms of oxygenations in zeolites, 42, 225 Mechanisms, nitrosation, 19, 381 Mechanisms, of proton transfer between oxygen and nitrogen acids and bases in aqueous solutions, 22, 113 Mechanisms, organic reaction, isotopes and, 2, 1 Mechanisms of reaction, in solution, entropies of activation and, 1, 1 Mechanisms of reaction, of -lactam antibiotics, 23, 165 Mechanisms of solvolytic reactions, medium effects on the rates and, 14, 10 Mechanistic analysis, perspectives in modern voltammeter: basic concepts and, 32, 1 Mechanistic applications of the reactivity–selectivity principle, 14, 69 Mechanistic studies, heat capacities of activation and their use, 5, 121 Mechanistic studies on enzyme-catalyzed phosphoryl transfer, 40, 49 Medium effects on the rates and mechanisms of solvolytic reactions, 14, 1 Meisenheimer complexes, 7, 211 Metal-catalyzed alcoholysis reactions of carboxylate and organophosphorus esters, 42, 271 Metal complexes, the nucleophilicity of towards organic molecules, 23, 1 Methyl transfer reactions, 16, 87 Micellar catalysis in organic reactions: kinetic and mechanistic implications, 8, 271 Micelles, aqueous, and similar assemblies, organic reactivity in, 22, 213
CUMULATIVE INDEX OF TITLES
407
Micelles, membranes and other aqueous aggregates, catalysis by, as models of enzyme action, 17, 435 Molecular dynamics simulations and mechanism of organic reactions: non-TST behaviors, 44, 173 Molecular recognition, chirality and, in monolayers at the air-water interface, 28, 45 Molecular structure and energy, calculation of, by force-field methods, 13, 1 N-Acyloxy-N-alkoxyamides – structure, properties, reactivity and biological activity, 42, 35 N-Arylnitrinium ions, 36, 167 Neighbouring group participation by carbonyl groups in ester hydrolysis, 28, 171 Nitration, nitrosation, and halogenation, diffusion control and pre-association in, 16, 1 Nitrosation, mechanisms, 19, 381 Nitrosation, nitration, and halogenation, diffusion control and pre-association in, 16, 1 NMR chemical shift-charge density correlations, 11, 125 NMR measurements of reaction velocities and equilibrium constants as a function of temperature, 3, 187 NMR spectra of equilibriating systems, isotope effects on, 23, 63 NMR spectroscopy, 13C, in macromolecular systems of biochemical interest, 13, 279 Nobel Prize, Gomberg and the, 36, 59 Non-linear optics, organic materials for second-order, 32, 121 Non-planar and planar aromatic systems, 1, 203 Norbornyl cation: reappraisal of structure, 11, 179 Nuclear magnetic relaxation, recent problems and progress, 16, 239 Nuclear magnetic resonance see NMR Nuclear motion, principle of least, 15, 1 Nuclear motion, the principle of least, and the theory of stereoelectronic control, 24, 113 Nucleophiles, partitioning of carbocations between addition and deprotonation, 35, 67 Nucleophili aromatic photolabstitution, 11, 225 Nucleophilic catalysis of ester hydrolysis and related reactions, 5, 237 Nucleophilic displacement reactions, gas-phase, 21, 197 Nucleophili substitution, in phosphate esters, mechanism and catalysis of, 25, 99 Nucleophilic substitution, single electron transfer and, 26, 1 Nucleophilic substitution reactions in aqueous solution, 38, 161 Nuckophilic vinylic substitution, 7, 1 Nucleophilic vinylic substitution and vinyl cation intermediates in the reactions of vinyl iodonium salts, 37, 1 Nucleophilicity of metal complexes towards organic molecules, 23, 1 O—H bonds, hydrogen atom abstraction from, 9, 127 One- and two-electron oxidations and reductions of organoselenium and organotellurium compounds, 39, 79 Orbital interactions and long-range electron transfer, 38, 1 Organic materials for second-order non-linear optics, 32, 121 Organic reactivity, electron-transfer paradigm for, 35, 193 Organic reactivity, structure determination of, 35, 67 Orotidine monophosphate decarboxylase, the mechanism of, 38, 183
408
CUMULATIVE INDEX OF TITLES
Oxyacids of sulphur and their anhydrides, mechanisms and reactivity in reactions of organic, 17, 65 Oxygen isotope exchange reactions of organic compounds, 3, 123 Partitioning of carbocations between addition of nucleophiles and deprotonation, 35, 67 Perchloro-organic chemistry: structure, spectroscopy and reaction pathways, 25, 267 Permutations isomerization of pentavalent phosphorus compounds, 9, 25 Phase-transfer catalysis by quaternary ammonium salts, 15, 267 Phenylnitrenes, Kinetics and spectroscopy of substituted, 36, 255 Phosphate esters, mechanism and catalysis of nuclcophilic substitution in, 25, 99 Phosphorus compounds, pentavalent, turnstile rearrangement and pseudoration in permutational isomerization, 9, 25 Photochemistry, of aryl halides and related compounds, 20, 191 Photochemistry, of carbonium ions, 9, 129 Photodimerization and photopolymerization of diolefin crystals, 30, 117 Photoremovable protecting groups based on photoenolization, 43, 39 Photosubstitution, nucleophilic aromatic, 11, 225 Planar and non-planar aromatic systems, 1, 203 Polarizability, molecular refractivity and, 3, 1 Polarography and reaction kinetics, 5, 1 Polypeptides, calculations of conformations of, 6, 103 Pre-association, diffusion control and, in nitrosation, nitration, and halogenation, 16, 1 Principle of non-perfect synchronization, 27, 119 The principle of nonperfect synchronization: recent developments, 44, 223 Products of organic reactions, magnetic field and magnetic isotope effects on, 30, 1 Protic and dipolar aprotic solvents, rates of bimolecular substitution reactions in, 5, 173 Protolytic processes in H2O—D2O mixtures, 7, 259 Proton transfer between oxygen and nitrogen acids and bases in aqueous solution, mechanisms of, 22, 113 Protonation and solvation in strong aqueous acids, 13, 83 Protonation sites in ambident conjugated systems, 11, 267 Pseudorotation in isomerization of pentavalent phosphorus compounds, 9, 25 Pyrolysis, gas-phase, of small-ring hydrocarbons, 4, 147 Radiation techniques, application to the study of organic radicals, 12, 223 Radical addition reactions, gas-phase, directive effects in, 16, 51 Radical rearrangement reactions, charge distribution and charge separation in, 38, 111 Radicals, cation in solution, formation, properties and reactions of, 13, 155 Radicals, organic application of radiation techniques, 12, 223 Radicals, organic cation, in solution kinetics and mechanisms of reaction of, 20, 55 Radicals, organic free, identification by electron spin resonance, 1, 284 Radicals, short-lived organic, electron spin resonance studios of, 5, 53 Rates and mechanisms of solvolytic reactions, medium effects on, 14, 1 Reaction kinetics, polarography and, 5, 1 Reaction mechanisms, in solution, entropies of activation and, 1, 1 Reaction mechanisms, use of volumes of activation for determining, 2, 93
CUMULATIVE INDEX OF TITLES
409
Reaction velocities and equilibrium constants, NMR measurements of, as a function of temperature, 3, 187 Reactions, in dimethyl sulphoxide, physical organic chemistry of, 14, 133 Reactions, of hydrated electrons with organic compounds, 7, 115 Reactive intermediates, study of, by electrochemical methods, 19, 131 Reactivity, organic, a general approach to; she configuration mixing model, 21, 99 Reactivity indices in conjugated molecules, 4, 73 Reactivity-selectivity principle and its mechanistic applications, 14, 69 Rearrangements, degenerate carbocation, 19, 223 Recent studies of persistent carbodications, 43, 219 Receptor molecules, redox-active, electrochemical recognition of charged and neutral guest species by, 31, 1 Redox and recognition processes, interplay between, 37, 315 Redox systems, organic, with multiple electrophores, electron storage and transfer in, 28, 1 Reduction of C—X and X—X bonds (X¼O, S), kinetics and mechanism of the dissociative, 36, 85 Refractivity, molecular, and polarizability, 3, 1 Relaxation, nuclear magnetic, recent problems and progress, 16, 239 The role of pre-association in Br½nsted acid-catalyzed decarboxylation and related processes, 44, 357 Secondary equilibrium isotope effects on acidity, 44, 123 Selectivity of solvolyses and aqueous alcohols and related mixtures, solvent-induced changes in, 27, 239 Short-lived organic radicals, electron spin resonance studies of, 5, 53 Small-ring hydrocarbons, gas-phase pyrolysis of, 4, 147 Solid state, tautomerism in the, 32, 129 Solid-state chemistry, topochemical phenomena in, 15, 63 Solids, organic, electrical conduction in, 16, 159 Solutions, reactions in, entropies of activation and mechanisms, 1, 1 Solvation and protonation in strong aqueous acids, 13, 83 Solvent effects, reaction coordinates, and reorganization energies on nucleophilic substitution reactions in aqueous solution, 38, 161 Solvent, protic and dipolar aprotic, rates of bimolecular substitution-reactions in, 5, 173 Solvent-induced changes in the selectivity of solvolyses in aqueous alcohols and related mixtures, 27, 239 Solvolytic reactions, medium effects on the rates and mechanisms of, 14, 1 Spectroscopic detection of tetrahedral intermediates derived from carboxylic acids and the investigation of their properties, 21, 37 Spectroscopic observations ofalkylcarbonium ions in strong acid solutions, 4, 305 Spectroscopy, 13C NMR in macromolecular systems of biochemical interest, 13, 279 Spectroscopy of substituted phenylnitrenes, kinetics and, 36, 255 Spin alignment, in organic molecular assemblies, high-spin organic molecules and, 26, 179 Spin trapping, 17, 1
410
CUMULATIVE INDEX OF TITLES
Spin trapping, and electron transfer, 31, 91 Stable carbocations and onium ions from polycondensed aromatic and heteroaromatic compounds as models for biological electrophiles and DNA-transalkylating agents, 43, 135 Stabilities and Reactivities of Carbocations, 44, 19 Stability and reactivity of crown-ether complexes, 17, 279 Stereochemistry, static and dynamic, of alkyl and analogous groups, 25, 1 Stereoelectronic control, the principle of least nuclear motion and the theory of, 24, 113 Stereoselection in elementary steps of organic reactions, 6, 185 Steric isotope effects, experiments on the nature of, 10, 1 Structural and biological impact of radical addition reactions with DNA nucleobases, 43, 177 Structure, determination of organic reactivity, 35, 67 Structure and mechanism, in curbene chemistry, 7, 153 Structure and mechanism, in organic electrochemistry, 12, 1 Structure and reactivity of carbencs having aryl substitutents, 22, 311 Structure and reactivity of hydrocarbon radical cations, 38, 87 Structure of electronically excited molecules, 1, 365 Substitution, aromatic, a quantitative treatment of directive effects in, 1, 35 Substitution, nueleophilic vinylic, 7, 1 Substitution reactions, aromatic, hydrogen isotope effects in, 2, 163 Substitution reactions, bimolecular, in protic and dipolar aprotic solvents, 5, 173 Sulphur, organic oxyacids of, and their anhydrides, mechanisms and reactivity in reactions of, 17, 65 Superacid systems, 9, 1 Tautomerism in the solid state, 32, 219 Temperature, NMR measurements of reaction velocities and equilibrium constants as a function of, 3, 187 Tetrahedral intermediates, derived from carboxylic acids, spectroscopic detection and the investigation of their properties, 21, 37 The interplay between experiment and theory: computational NMR spectroscopy of carbocations, 42, 125 The interpretation and mechanistic significance of activation volumes for organometallic reactions, 41, 1 The physical organic chemistry of very high-spin polyradicals, 40, 153 Thermodynamic stabilities of carbocations, 37, 57 Topochemical phenomena in solid-slate chemistry, 15, 63 Transition state analysis using multiple kinetic isotope effects, 37, 239 Transition state structure, crystallographic approaches to, 29, 87 Transition state structure, in solution, effective charge and, 27, 1 Transition stale structure, secondary deuterium isotope effects and, 31, 143 Transition states, structure in solution, cross-interaction constants and, 27, 57 Transition states, the stabilization of by cyclodextrins and other catalysts, 29, 1 Transition states, theory revisited, 28, 139 Tritiated molecules, gaseous carbonium ions from the decay of, 8, 79 Tritium atoms, energetic reactions with organic compounds, 2, 201 Turnstile rearrangements in isomerization of pentavalent phosphorus compounds, 9, 25
CUMULATIVE INDEX OF TITLES
411
Unsaturated compounds, basicity of, 4, 195 Using kinetic isotope effects to determine the structure of the transition states of SN2 reactions, 41, 219 Vinyl cation intermediates, 37, 1 Vinyl cations, 9, 185 Vinyl iodonium salts, 37, 1 Vinylic substitution, nuclephilic, 7, 1; 37, 1 Voltammetry, perspectives in modern: basic concepts and mechanistic analysis, 32, 1 Volumes of activation, use of, for determining reaction mechanisms, 2, 93 Water and aqueous mixtures, kinetics of organic reactions in, 14, 203 Yukawa–Tsuno relationship in carborationic systems, the, 32, 267
SUBJECT INDEX
Note: The letter ‘f’ following the locators refer to figures cited in the text. Acetal derived alkoxycarbocations trapping, 31 Acetoacetic ester synthesis, 372 Acetone: bromination rate of, 325–6 radical cation, 186, 187 Acetyl-CoA enolization, 5 Acetylene and methyl acetylene, hydration rate constants, 48 Acetyl fluoride, 149 Acid–base catalysis, 14–15 see also Low-barrier hydrogen bond Acid-catalyzed ester hydrolysis, 53 Acid solution: dissociation constant, medium effects on, 29 dissociation constants of arenonium ions, 56 interpretation of UV–visible spectra in concentrated, 30 Aconitase mechanism, 4, 5f Adamantyl and norbornyl chloride, preassociation processes, 72–3 Alcohol: alcohol–alkene equilibrium constant, 90 carbocation, 33 free energies of formation, 73 p-substituted a-trifluoromethyl benzyl cations, reaction with, 108 Aldehyde: keto–enol equilibrium constants and free energies of formation, 48 protonation of, 54 Alkenes: epoxidation of, 313 hydration, 36 nucleophilic additions, 293 and correlation with proton transfers, 293–5
intramolecular hydrogen bonding, effect of, 295 polarizable nucleophiles, 297–8 polar substituents, effect of, 296–7 steric effects, 296 2-Alkylacetophenones, 340 Allylic bromination of o-acylated tetralol, 37 Amines: Mayr’s study on, 110 reactivities of, 96 2-Amino-3-ketobutryate-CoA ligase NMR spectrum, 13–14 Anomeric effect, 311 9-Anthrone, 340 Antiaromaticity for fluorenyl cation, 34 Aqueous solution: free energies of formation in, 24–5 and hydride affinity scale, 22–3 pH–rate profile for decay of phenylynol in, 343f pKR values for alkyl cations in, 26 Arenonium ion: acid dissociation constants of, 56 aromatic hyperconjugation, 61 hyperaromaticity of, 59–64 intermediates of electrophilic aromatic substitution, 37 and secondary benzylic carbocations, correlation line, 77f stabilized by C–H hyperconjugation, 61 Aromatic carboxylic acids decarboxylation, 371–2 Aromatic enols, 343 Aromatic hydrate acid-catalyzed dehydration, 40 Aromaticity effect on intrinsic barriers, 258–61 Aromatic stabilization energies (ASEs), 283
413
414 Arylnitromethanes, deprotonation of, 230 Arylnitromethanes deprotonation, 230 ASEs see Aromatic stabilization energies (ASEs) Aspartic proteases, 12 X-ray and neutron diffraction studies of, 13 Asymmetrical PES, 201 Autoprotolysis constant for water, 21–2 Avoided intermediate on IRC: [3,3]sigmatropy, 189–90 SN2 reaction, 189 Azide: equilibrium measurements, 76 ion trapping, 31 ‘‘Azide-clock’’ methods, 32 Beckmann rearrangement, 201, 207–9 Bell–Evans–Polanyi relationship, 95 Benzene: aromaticity of benzenonium ion, 62 1,4-benzene hydrate, stability of, 45 benzhydryl cations electrophilic parameters for, 97 E values for, 97–8 Mayr’s plot, E parameters against pKR, 106 reaction, p-nucleophiles with, 98f and benzoannelation, 61–2 cyclic benzylic carbocations effects of oxygen substituents on stabilities of, 59 o-quinone methide, neutral and acidcatalyzed hydrolysis, 59 oxygen substituents and, 58 protonation and decarboxylation, comparison of, 371 rate constant, 38 trihydroxy-substituted and methoxy-substituted, 56 ring substituted benzenes, Cox’s extrapolation of rate constants, 45 Benzene cis-1,2-dihydrodiols, acidcatalyzed aromatization of, 309–10 Benzofulvene-1,1-diol, pH-rate profile, 342
SUBJECT INDEX Benzoic-d5 acid, 134 Benzoylformate decarboxylase (BFD), 363 Benzoylformic acid, 364 Benzylideneacetylacetone, 295 1-Benzyl-1-methoxy-2-nitroethylenes, 258 Benzyltriflones, 250 Berry pseudorotation, 201 Bicyclo[3.2.0]hept-2-ene, 177 Bimodal lifetime distribution, 179 Bohlmann bands, 163, 164 Boltzmann constant, 84 sampling, 207 Bond breaking, 86–7 Born–Oppenheimer approximation, 124, 126, 155, 156 trajectories, 213 Bromine titration method see Halogen titration method Brønsted coefficients, 235 Brønsted a and b values, 229–30 evidence of imbalance, 229 aCH greater than bB, 231–2 aCH less than bB, 232–4 p-acceptors stabilizing, 234 proton transfers, 230 Z-substituent and, 230 Bronsted exponent for base catalysis, 95 Buffer: catalysis, 340 dilution plot, 339f Bunting and Stefanidis’s expression, 82–3 Butane: butyl cations heats of formation, 25 stabilities, 24 free energies of formation, 26 Carbanions stability, 359 Carbene: dipolar electron distribution for, 71 energies of number of, 70 singlet stabilities comparison of, 70 stability, 68–9 Carbocations: reactions of, 309–11
SUBJECT INDEX reactivity of, 76 hard and soft nucleophiles, 110–12 nucleophiles other than water, 90–105 nucleophilic reactions with water, 77–87 structure and, 105–10 with water as base, 87–90 stabilities of alkyl cations, 46–8 arenonium ions, 37–41 b-oxygen substituents, 59–64 diffusion-controlled trapping, 31–2 equilibrium constants for hydration, 41–2 equilibrium measurements of pKR, 28–30 forming reactions, 32–5 halide and azide ion equilibria, 71–6 kinetic methods for determining pKR, 30–1 measures of, 21–8 metal-coordinated carbocations, 64–8 methyl cation, 49–51 oxygen ring substituents, 57–9 oxygen substituent effects on arenonium ions, 55–7 oxygen-substituted, 51–5 as protonated carbenes, 68–71 rate–equilibrium correlations, 42–6 solvent relaxation and hydration equilibria, 35–7 vinyl cations, 48–9 Carbon acids: deprotonation by secondary alicyclic amines, 227–8 proton transfers and intrinsic rate constants, 226–9 Carbon group contributions, 26 Carbon-to-carbon proton transfer, Costentin/Save´ant analysis on, 272 Carboxylate anions: p-substituted a-trifluoromethyl benzyl cations, reaction with, 108
415 Carboxyl inhibitor, 5 Carboxypeptidase mechanism, 9 CASPT2(4,4)/6-31G*//CASSCF (4,4)/6-31G* calculations, 180 Catalysis role, 357 Catalytic gap, 362 Catalytic proficiency, 361 12 C/13C kinetic isotope effects (CKIE), 366–8 C–D bond length, 124 Charge-transfer (CT) interaction energies, 217 Chemical shifts, 127–8, 152 accurate determination of, 130 of allenic esters, 145 of aniline and anilinium ion, 131 nuclear shielding and, 156 of undeuterated and deuterated isotopologues, 129 Chiral alcohol racemization, 32–3 CH3Y/CH2=Y– systems, 261–2 Costentin/Save´ant analysis, 272 gas phase acidities and reaction barriers, 273–9 imbalance, evidence of, 262–8 More O’Ferrall–Jencks diagrams, 269–71 valence bond analysis of imbalance, 271–2 Chymotrypsin mechanism, 7f Circe effect, 369 Citrate synthase mechanism, 5, 6f CKIE see 12C/13C kinetic isotope effects (CKIE) ‘‘Clock’’ methods, 31 13 C NMR resonances, 124 C–N rotation, 125 Common ion rate depression of hydrolysis, 51 C¸-complex, 202 Computational study: at B3LYP/6-31G**, 196 with DFT methods, 207 on reactions of formaldehyde anion radicals, 204 for type II SN2, limitation, 210 at (U)B3LYP/6-31G*, 198
416 Computational study: (Continued) at UHF or UB3LYP level of theory, 202 see also ET/SN2 bifurcation Conductivity, 127 Conformational analysis, 130 see also Nuclear magnetic resonance (NMR) Conformational equilibrium, 149 Costentin/Save´ant analysis, 272 see also CH3Y/CH2=Y– systems Cr(CO)3-coordinated benzylic carbocation, 64–8 CXY–CHD rotation, 178 2-Cyano-2-(6-methoxy-naphth-2-yl) propionic acid: asymmetric decarboxylation, 371 enantio-selective decarboxylation, 370 Cycloaddition, 201 of cyclopentadiene, 214 reactions of ketenes, 206, 214 Cyclohexadienol preparation, 37 2,4-Cyclohexadienone enolization pH–rate profiles, 343 Cyclohexadienyl cation stabilities, 23 Cyclopentadiene: 1,3,5-Cycloheptatriene-7-d, 150 and ketenes, cycloaddition, 214 Cyclopentene (CP), 184 cyclopentane-1,3-diyl radical, 179 Cytidine deaminase structure, 9f Deazetization, 201 Decarboxylation, 357 of aromatic carboxylic acids, 371–2 blocking reversion for enzyme catalysis, implications of, 368 carbanion, formation and stability of, 359–60 catalysis of, 360 catalyst role, 357–9 CKIE and pre-association catalysis, 366–8 directionality in, 360–1 of 3-ketoacids, 372–3 pre-association mechanisms in, 362 and protonation of OMP decarboxylase, 369–70
SUBJECT INDEX of pyridine-2- carboxylic acid, 359 thiamin diphosphate catalysis, catalyzing of, 362–6 trends in catalyzed decarboxylation, 370–1 Degenerate rearrangement of bicyclo [3.1.0]hex-2-ene, 180 Delocalized valence bond method (DVB), 272 Deprotonation process, 128, 142, 150, 155, 159, 160, 162, 163 acetaldehyde, 236 arylnitromethanes, 230 dimethyl-9-fluorenylsulfonium ion, 250 Fischer carbene complexes, 248–9 methyl and benzylic mono carbonyl compounds, 236–7 nitroalkanes, 237, 248, 269 2-nitrocyclohexanone, 237 2-nitro-4-Z-phenylacetonitrile, 258 pentacarbonyl-(cyclobutenylidene) chromium complexes, 260–1 PhCH2CH2NO2, 247 2-tetralone, substituent, 235–6 Deuteration, 129, 136, 142, 144, 154, 160, 165 Deuterium-induced isotope: effects on amine basicities, 139 shift, 149 Diaza-[2.2.1]bicycloheptane, 179 Diazonaphthoquinones, 342 2,2-Dichloropropionate, 8 Diels–Alder reaction, 291 Diffusion-controlled trapping of carbocations, 31–2 Diffusion trap, 31 Dihedral angle, 164 Dihydroaromatic molecules oxidative fermentation, 37 o-Dimethyl cumyl carbocation, 90 Dimethyl-9-fluorenylsulfonium ion, 250 Dimethyl sulfoxide (DMSO), 130 2-(20 ,40 -Dinitrobenzyl)pyridine tautomerization reactions, 340, 344 Diosmacyclobutane complex, 146
SUBJECT INDEX Di-pentamethylbenzhydryl cation: deprotonation, 90 nucleophilic and elimination reactions, 90 Dipole moment, 156, 165 p-Donor effects, 253–8, 260, 297, 299, 302, 306, 317 Dynamic bifurcation: Beckmann rearrangement, 207–9 cycloaddition, 206–7 ET/SN2 bifurcation, 204–6 Dynamics effect, 180 on chemical reaction, 175, 176 dynamics trajectories, 204 electron withdrawing substituent (CO2Me), role in, 199 emerged from trajectory calculations, 175 non minimum energy pathway due to, 191 non statistical, 187 role of, 176 on stepwise PES, 178 Electron density, 124 Electrophilicity scale for carbocations, 22 Ene reactions, 198, 203 cyclization reaction, 196 of 2-pentene, 204 of simple alkenes, 201 Energy: diagrams for hydrogen bonds, 2 randomization, 179 Enolization reactions, 3–6 see also Low-barrier hydrogen bond Enzyme-catalyzed reactions, 361 implications of blocking reversion for, 368 Equilibrium constants: for carbocation formation, 28 of enolization, 326 for hydration, 41–2 for isomerization of alkenes, 47 for phenanthrene hydrate, 40 for sulfur nucleophile, 111 Ethylene protonation rate constant, 47 Ethyl heats of formation, 25
417 ET/SN2 bifurcation, 204–6 ET-SN2 borderline reaction, 201 EXC factor, 125 Eyring expression, 84 equation, 224 Facilitated tetrahedral intermediate formation, 6–10 see also Low-barrier hydrogen bond Fe(CO)3-cooordinated cyclohexadienyl cation, 67 Finite element interpolation, 191 Fischer carbene complexes: acidities of, 254–5 deprotonation of, 248–9 nucleophilic substitution of and desolvation of nucleophile, 307–8 intrinsic rate constants for, 303–7 transition state imbalances in, 307 see also Principle of nonperfect synchronization 19 F isotope shift, 131 Flash photolysis, 326–7 generation of carbocations, 32 unstable tautomers, 341f see also Keto–enol tautomerization reactions kinetics Flash vacuum thermolysis, 187 Flavylium ion derivatives, 28 FMO-MD simulations, 215 9-Formylfluorene (FlCHCHO) with hydroxylamine reaction, 54 Free energies of formation, 23 Friedel–Crafts reaction, 101, 104 F-Strain, 296 F-Type trajectories, 209 Full quantum MD simulation, in water, 215–17 Gas phase: carbocation stabilities in, 25 SNV reactions, 312 General acid and general base catalysis see Keto–enol tautomerization reactions kinetics
418 Group additivity schemes by Benson, 24–5 Guthrie’s ‘‘no barrier’’ plot construction, 86, 87f Halide: and acetate ions with quinone methide comparison, 110–11 and azide ion equilibria azide ions, 75–6 bromide and fluoride ions, 75 chloride ions, 71–4 Halogen titration method, 332–3 Hammond postulate, 95 Hard and soft nucleophilicity, 112 Hartree–Fock calculations, 153 H148D mutants of green fluorescent protein, 14 Heats of formation of carbocations, 24 Heavy-atom isotope effects: on acidities, 143–4 see also Isotope effects (IEs) Hemiacetal anion, decomposition of, 314 Henderson–Hasselbalch equation, 127 Hen ovotransferrin structure, 14 Hessian-based predictor-corrector method, 187 Heterolysis 3D map, 194f HIA see Hydride ion affinity (HIA) High-performance liquid chromatography (HPLC), 32 analysis of carbocation formation in alcohol–water mixtures, 33 Human immunodeficiency virus (HIV-1) proteases, calculation on, 12–13 Hydration reaction, 29 Hydride ion affinity (HIA), 22–3 of carbocations, 26 free energies of formation, 26 plot of, 50f Hydrocarbons Guthrie’s values, 26 b-Hydrogen atoms carbocations, 35–6 Hydrogen bonding, 152, 153 energy diagrams for, 2 f hydrogen-bonded complex, 136 low fractionation factors, 2 O–O and O–N bonds in, 2
SUBJECT INDEX oxygens in, 2 properties of, 1–2 Hydrogen isotope exchange measurements, 38 Hydroxy- and methoxy-substituted benzenes Kresge’s extensive measurements of protonation, 30 p-Hydroxybenzyl alcohol and acetate, flash photolysis, 57 1-Hydroxy-1,2-dihydro-naphthalene preparation, 37 10-Hydroxyphenanthrenonium ion ratio of cis/trans dihydrodiol products, 60–1 1-Hydroxy-1,2,3,4tetrahydronaphthalene, 37 Hyperaromaticity, 63 Hyperconjugation, 63, 145, 147, 148, 163, 247–9 adding electron density into, 162 in cationic conjugate acids, 162 favoring CH3 a to carbocation and, 150 by H into vacant p orbital on boron, 145 removing electron density from, 162 stabilize CH3–Cþ fragment, 142, 144 stabilizing interaction between, 162 weaken C–H (or C–D) bond, 159 Imbalanced transition state, in reaction, 225 Brønsted coefficients and, 229–35 deprotonation of arylnitromethanes, 230 Imidazolyl carbene heat of hydrogenation, 69 Indole-2-carboxylic acid, 372 Inductive effect, 124, 164–6 Intramolecular hydrogen bonding, at transition state, 236 Intramolecular SN2 reaction, 312–13 Intramolecular vibrational energy redistribution (IVR), 181 Intrinsic barrier, 224 rate constant, 225 effect of adjacent polar substituents on, 244–5
SUBJECT INDEX electrostatic effects on, 251–3 p-donor effect on, 255–6 polarizability effects on, 249–51 in proton transfers from carbon acids, 226–8 solvent effects on, 238–42 and transition state imbalances, factors affecting, 238 aromaticity, 258–61 electrostatic effects, 251–3 hyperconjugation, 247–9 p-donor effects, 253–8 polar effect of adjacent substituents, 243–7 polar effect of remote substituents, 242–3 polarizability, 249–51 solvation, 238–42 Ion cyclotron resonance (ICR), 146 Ionic fragmentation reaction, 191–2 Ionic molecular rearrangement, 193–6 Ipso protonation, 147 Isobutene equilibrium constant for hydration, 36 Isomerizations, 178, 201 of benzylideneanilines, 204 Isopropyl heats of formation, 25 Isotope effects (IEs), 123 on acidity, 124 of aliphatic deuterium on acidity, 138 in chromatographic separations, 124 on conformational and, 124 due to synperiplanar deuterium, 140 on enzyme-catalyzed reactions, 124 isotopic substitutions, 124 isotopologues, 124 theory of, 125–6 see also Secondary isotope effects Isotope exchange with 18O-labeled water, 32–3 Isotopomers, 124, 130 Keeffe/Kresge correlation, 251–3 Ketoacids: 2-ketoacids, decarboxylation of, 362 3-ketoacids, 372–3 Keto–enol equilibria for phenol, 55
419 Keto/enol isomerization, 186 Keto–enol tautomerization reactions kinetics, 187, 325–6 and examples, 340–5 flash photolysis, for study of, 326–7 and general acid and general base catalysis, 338–40 halogen titration method, 332–3 kinetic and thermodynamic parameters, for tautomeric equilibria, 334–6 pH–rate profiles, 333, 337–8 rate–equilibrium relationships Brønsted relations and acidity of solvent-derived species, 345–8 Marcus model of proton transfer, 350–3 uncatalyzed reaction, mechanism of, 348–50 rate law for keto–enol equilibration, derivation of, 327–32 acid-catalyzed ketonization, 329 base-catalyzed ketonization, 329 enolization rate of ketone, 330–1 ketonization rate of enol, 330 observed rate law, 331 uncatalyzed ketonization, 330 unstable tautomers by flash photolysis, generation of, 340–1 Ketone: keto–enol equilibrium constants and free energies of formation, 48 ketonization, 349 protonation equilibria, 54 Ketosteroid isomerase enzyme, 3 Kinetic IEs, defined, 124–5 Kinetic method application for pKa and pKR for carbocations, 31 Kresge model, 237 Laser flash photolysis use, 31 Leffler–Hammond principle, 208 Lennard-Jones 12-6 potential energy functions, 183 Lewis acid, 144, 145 Lewis acid–base complexation, 146
420 Lewis acidity see Electrophilicity scale for carbocations Lewis bases, 144, 145 Liver alcohol dehydrogenase reaction, 10 hydrogen bond, changes in, 11f Localized valence bond method (LVB), 271 Low-barrier hydrogen bond, 1 between aspartates of HIV protease, 13 in enzymatic reactions acid–base catalysis, 14–15 aspartic proteases, 12–13 enolization reactions, 3–6 facilitated proton ionization, 10–12 facilitated tetrahedral intermediate formation, 6–10 Glu50 and bound thiamin-PP, formation of, 12 NMR chemical shifts for protons in, 10 photoactive yellow protein, neutron crystallography study of, 14 Malonic ester synthesis, 373 Mandelate racemase enolization, 3 Mandelylthiamin (MTh) decarboxylation, 367 pre-association mechanism involving p-stacking in, 365 Marcus model: Marcus curvature, 236 Marcus equation, 82–3, 224 potential energy barrier, 78f of proton transfer, 350–3 rate theory, 352 Mayr’s scheme, 102–5 Metal-coordinated carbocations, 64–8 p-Methoxystyrene data, 30 a-Methoxystyrenes hydration, 95 Molecular dynamics (MD): analyses, by using model PES, 176 simulations, 175 two-dimensional plots of, 208f Molecular orbital (MO) calculations, 175 More O’Ferrall–Jencks diagrams, 269–71 Morphine, 136 Mukaiyama aldol cross couplings, 101
SUBJECT INDEX Naphthalene rate constant, 38 NaproxenTM synthesis, 371 NCCH2Y/NCCH=Y– systems, 280 Negative hyperconjugation, 163, 165, 250 Neutral dibenzothiophene, Mayr’s N values and rate constants, 104 Neutron diffraction of crystals, 2 Nicholas propargylation, 101 Nitroalkane anomaly, 248 Nitrogen-substituted carbocations reactivity, 110 ‘‘No barrier theory’’, 86–7, 373 Nonhydroxylic solvents heat of formation, 24 Non-IRC reaction pathway, 190 cyclopropyl radical ring-opening, 192–3 ene reaction, 196–8 ionic fragmentation reaction, 191–2 ionic molecular rearrangement, 193–6 photoisomerization, of cis-stilbene, 191 thermal denitrogenation, 198–9 unimolecular dissociation, 199 SN2 reaction, 200 Nonlinearity of IEs on trimethylamine basicities, 141f Nonstatistical barrier recrossing, 211 cycloaddition of cyclopentadiene and, 214 SN2 reactions, 212–13 direct dynamics simulation, 212–13 quasiclassical direct dynamics trajectories, 212 for SN2 nucleophilic substitution, 212 vinilydene to acetylene rearrangement, 213 Nonstatistical product distribution: acetone radical cation, dissociation of, 186–7 degenerate rearrangement of, 180–1 MD analyses, using model PES, 176 reaction of diaza-[2.2.1] bicycloheptane to, 179–80 [1,3]sigmatropic migration, of bicyclo[3.2.0]hept2-ene, 177–8
SUBJECT INDEX rearrangement, of vinylcyclopropane to, 184–6 trimethylene, chemistry of, 181–4 WOLFF rearrangement, 187–8 Norbornene, 177 Northrop mechanism, 13 Novolak photoresists, 342 N-protonation, 163 Nuclear magnetic resonance (NMR): pH titration, 127–8 titration, 124, 128–30, 131f, 132 Nuclear mass, 124 Nucleophile affinities of carbocations, 21 Nucleophilic vinylic substitution reactions, 298–303 O’Ferrall–Jencks diagram for deprotonation of nitroalkane, 269f, 270f 18 O IEs on acidities, 143–4 One-dimensional quadratic energy profiles, 86–7 Orotidine-50 -monophosphate decarboxylase (OMPDC), 359–60 decarboxylation and protonation, 369–70 Orthocarbonates hydrolysis, 314 Oxygen-substituted carbocations: effects on arenonium ions, 55–7 hyperaromaticity, 59–64 a-oxygen substituents, 51–5 and quinone methides, 57–9 Path bifurcation, 200 asymmetrical and symmetrical PES, 201f ene reactions, 201–4 dynamics effect on, 204 TS giving products through, 201 violating TS-based reaction theory, 209 Perepoxide, 201 Pericyclic reactions, aromaticity in, 291 PES see Potential energy surface (PES) Phenanthrene hydrate equilibrium constant, 40 Phenol: C-protonation of, 55
421 hydroxy and methoxy substituents, 56 phenol-d5, 134 Phosphate-binding protein X-ray structure, 14 Phosphine nucleophiles reactivities, 96 Phospholipase A2 with bound phosphonate inhibitor structure, 10f Phosphonate inhibitors, 10 Photoisomerization of cis-stilbene, 191 Photolytic generation of carbocations, 32 Photo-Wolff rearrangement, 342 PMF see Potential mean force (PMF) PNS see Principle of nonperfect synchronization Polar effect: of adjacent substituents, 243–7 of remote substituents, 242–3 Potential energy: calculations, 185, 190 contour map, 193 variation of, 195 Potential energy surface (PES), 175 Potential mean force (PMF), 214 Potentiometric titration, 127 Pre-association, 361–2 see also Decarboxylation Pressure effect on product distribution, 179 Primary isotope effects, 123 Principle of imperfect synchronization (PIS) see Principle of nonperfect synchronization Principle of nonperfect synchronization, 223, 225–6, 316–19 and enzyme-catalyzed hydride transfer, 316 epoxidation of alkenes and, 313–14 Fischer carbene complexes, nucleophilic substitution of, 303 and desolvation of nucleophile, 307–8 intrinsic rate constants for, 303–7 transition state imbalances in, 307 gas phase SNV reactions, 312 and hemiacetal decomposition, 314 intramolecular SN2 reaction, 312–13 intrinsic barriers, 224
422 Principle of nonperfect synchronization, (Continued) nucleophilic additions to alkenes, 293 and correlation with proton transfers, 293–5 intramolecular hydrogen bonding, effect of, 295 polarizable nucleophiles, 297–8 polar substituents, effect of, 296–7 steric effects, 296 nucleophilic vinylic substitution (SNV) reactions, 298–303 product/reactant destabilization factors, 225 stabilizing factors, 225 radical reactions and, 315 and reactions involving carbocations, 309–11 transition state imbalances and, 224–5 Propane: free energies of formation, 26 rate constant for, 47 Propargyl reactant complex structure, 66 2-Propenol, 325 Protium, 123, 124, 164 Protonated carbenes carbocations, 68–71 Protonation, 124, 129, 130, 131, 142, 160, 164 of deuterated amine, 147 reactions, 36 see also Deprotonation process; N-protonation; Zero-point energy (ZPE) Proton loss from carbocations, 68 Proton transfers in gas phase, ab initio calculations, 261 aromatic and anti-aromatic systems, 282–90 decoupling of aromaticity development from charge delocalization, 290–1 CH3Y/CH2=Y– systems, 261–2 Costentin/Save´ant analysis, 272 gas phase acidities and reaction barriers, 273–9 imbalance, evidence of, 262–8 More O’Ferrall–Jencks diagrams, 269–71
SUBJECT INDEX valence bond analysis of imbalance, 271–2 NCCH2Y/NCCH=Y– systems, 280–1 Pseudomonas putida, mutant strain (UV4), 37 Pseudorotation, 201 Pyramidalization, 125 Pyridine-based buffers, 365 Pyrrole-2-carboxylic acid, mechanism of decarboxylation, 372 Pyruvate, 362–3 pyruvate decarboxylase, 11 low-barrier hydrogen bond between, 12f QM/MM methodology for chemical reactions, 214–15 Q-Switched laser, 327 Quasiclassical direct dynamics trajectories, 210, 212 see also SN2 reactions Quasiclassical trajectory: calculations, 179, 180, 199 simulations, 184 see also Nonstatistical product distribution Quasiclassical TS sampling, 185 Quinone methides, 57–9 Radical reactions, 315 Raman spectrum, 157 Rate constants for deuterium/tritium exchange of aromatic molecules, 38 Rate–equilibrium: correlations for deprotonation of carbocations, 42–6 relationship by Marcus, 111 Redlich–Teller product rule, 125 Rehybridization, 86–7 Reverse deprotonation reactions, 36 Reversible decarboxylation two-step mechanism, 359 Rice–Rampsperger–Kassel–Marcus (RRKM) theory, 181 Ring-opening reaction of cyclopropyl radical, 192–3 Ring strain, 313, 317
SUBJECT INDEX Ring substituted benzenes, Cox’s extrapolation of rate constants, 45 Ritchie’s Nþ equation, 97, 103 Schmidt reaction mechanism, 76 sec-Butyl heats of formation, 25 Secondary deuterium isotope effects: on acidities of amino acids, 140 of anilines, 140 of anilinium ions ArNH3þ, 137 of carboxylic acids, 134, 135, 137 CH acids, 142–3 NH acids, 136–42 OH acids, 134–6 of phenols, 137 Secondary equilibrium IEs on amine basicity, 138–9 methodology, 127 equilibrium perturbation, 132–3 NMR pH titration, 127–8 NMR titration, 128–32 pH titration, 127 scope, 123–5 theory, 125–6 Secondary isotope effects: on acidity, origin of, 157 computations, 159–62 evidence from, 157–8 frequency changes, cause of, 162–4 inductive effect, 164–6 in chromatography, 153–5 on conformational equilibrium, 148–50 on gas-phase acidity and basicity, 146–8 on hydrogen bonding, 152–3 on Lewis acid–Lewis base interactions, 144–6 on molecular structure, 155–7 on tautomeric equilibria, 150–2 Self-consistent field valence bond (VBSCF) method, 271 Semiquantitative model of reactivity in electrophile–nucleophile reactions, 102f Shaik–Pross model, 238
423 see also Valance bond configurationmixing model Sigmatropic isomerization, 179, 201 Sigmatropic migration, 177 see also Nonstatistical product distribution [3,3] Sigmatropic rearrangement of 1,2,6heptatriene, 189–90 [1,3] Sigmatropic rearrangement of VCP, 184 Singel-well hydrogen bond, 2 SN2 reactions: of CH3Cl with Cl, 211 of CH3F with nucleophiles X, 189 of methyl halides, 209–10 at molecular level, 200 quasiclassical direct dynamics trajectories, 210 semi-empirical AM1 theory, 210 type I and type II, 211 in water, 210–11, 215–17 see also Full quantum MD simulation, in water Soft–soft interaction, 297, 307, 317 Solution phase proton transfers and PNS: delocalization and constraints on transition state Kresge model, 237 Shaik–Pross model, 238 intrinsic barriers and transition state imbalances, factors affecting, 238 aromaticity, 258–61 electrostatic effects, 251–3 hyperconjugation, 247–9 p-donor effects, 253–8 polar effect of adjacent substituents, 243–7 polar effect of remote substituents, 242–3 polarizability, 249–51 solvation, 238–42 resonance effects, 226, 235–7 Brønsted coefficients, imbalance based on, 229–30 carbon acids, deprotonation by secondary alicyclic amines, 227–8
424 Solution phase proton transfers and PNS: (Continued) proton transfers from carbon acids, and intrinsic rate constants, 226–9 Solvation, 238–42 Solvolysis reactions, 38–9, 144 Spectator catalysis, 362 Statistical reaction theory (TST), 180 Stereoselection, 179 Steric crowding, 291 Structure-based free energy relationships, 30 Styrene, hydration and protonation in thermodynamic cycle, 29 Subtilisin structure, 8 Sulfur nucleophile equilibrium constant, 112 Swain–Scott equation, 94, 105 Symmetrical PES, 201 Taft equations, analysis of acidities and barriers, 274 Tautomerization reactions see Keto–enol tautomerization reactions kinetics Tautomers, 150 tautomeric equilibria, 150–2 Tetramethyl ethylene alkylation, 100 Thermal denitrogenation, 198–9 Thermolysin mechanism, 9f Thiamin diphosphate (ThDP), 362 competing routes from HBnTh, 364 dependent decarboxylation of benzoylformic acid to benzaldehyde, 364 mechanism of decarboxylation, 363 Thioacetylacetone, 151 Trajectory calculations, 175, 178, 182, 189 on analytical PES fitted to, 212 for cyclopropane stereomutation, 183 on PES, 204 for proton transfer, and ionization in water cluster, 211 see also Dynamics effect Trajectory simulations, 180 trans-1,3-cyclohexanediol, 148 Transition states (TSs), 174
SUBJECT INDEX aromaticity indices, 287–8 region of PES, 185 Transition state theory (TST), 176 Trapping carbocation with azide ion, 32 Trifluoroethanol (TFE)–H2O mixtures and diffusion trap, 31 2,4,6-Trimethylbenzyl unstable carbocations, 30 Trimethylene, 181–4 ab initio MRCI calculations, 181 cyclopropane and propene branching ratio, 183–4 dynamics simulations, 183 lifetime distribution, calculation, 182 trajectory calculations, 183 Triose-P isomerase enzyme, 3 mechanism of, 4f Tropylium ion, 28 UDP-galactose 4-epimerase, 11 Unimolecular dissociation of laserexcited formaldehyde, 199–200 Unstable carbocations, 35 Unstrained hydrocarbons energies, 24 Valance bond configuration-mixing model, 238, 271 Valence bond analysis of imbalance, 271–2 Valley-ridge inflection (VRI) point, 201 Vibrational spectroscopy, 157–8 vibrational frequencies, 125, 158 Vinilydene to acetylene rearrangement, 213–14 Vinyl cations mechanistic chemistry, 48–9 Vinylcyclopropane (VCP), 184 Vitamin K-dependent carboxylase, 5 Water: as base, 87–90 charge-transfer interaction energies, 217f correlations of nucleophilic reactivity, 92–6 decarboxylation of OMP in, 370f equilibrium measurements in, 24 estimates of intrinsic reaction barriers, 83–5 extrapolations of pKR in, 30
SUBJECT INDEX hard and soft nucleophiles, 110–12 initial water droplet, 216f intrinsic barriers for carbocation reactions, 79–82 linearity of log plots, 82–3 Marcus analysis, 78–9 Mayr’s work, extensions of, 102–5 no barrier calculations, 86–7 nucleophile–electrophile reactions and synthesis, 96–102 nucleophilic reactions with, 77, 90, 91f, 92 reactivity, selectivity and transition state structure, 105–10 rotational relaxation constant of, 35 solvolysis rate constant in, 72–3 Wheland-type intermediates, 63 Wild-type enzyme ODCase:
425 free energy reaction profiles, 370 Wittig and Mannich reactions, 101 WOLFF rearrangement, 187–8 see also Nonstatistical product distribution Woodward–Hoffmann rule, 177 Yeast pyrophosphatase, 11 Ynamines, 342–3 Ynols, 342 Yukawa–Tsuno correlation of substituent effects, 34 Zero-point energy (ZPE), 124, 126, 160, 161f, 163, 177, 182, 203 Zn-bound water, 9 Zwitterion, 201 and intramolecular hydrogen bond, 295
