Advances in Physical Organic Chemistry, Volume 04

Advances in

Physical Organic Chemistry

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Advances in

Physical Organic Chemistry Edited by

V. GOLD Department of Chemistry King’s College, University of London

VOLUME 4

1966

Academic Press, London and New York

ACADEMIC PRESS INC. (LONDON) LTD. Berkeley Square House Berkeley Square, London, W.l

U.S. EditiolL publislld by ACADEMIC PRESS INC. 111 Fifth Avenue New York, New York 10003

Copyright @ 1966 by Academic Press Inc. (London) Ltd.

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CONTRIBUTORS TO VOLUME 4 R. P. BELL,Physical Chemistry Laboratory, Oxford, England H. M. FREY,Chemistry Department, Southampton University, England H. H. GREENWOOD,Quantum Theory Group, University of Keele, Xtaffrdshire, England R. MCWEENY, Quantum Th,eoryGroup, University of Keele, Staffordshire, England GEORGEA. OLAH, Department of Chemistry, Western Reserve University, Cleveland, Ohio, U.S.A.

H. H. PERKAMPUS, Department of Molecular Spectroscopy of the Institute for Organic Chemistry, Technische Hochschule, Braunschweig, Germany CHARLESU. PITTMAN, JR., Department of Chemistry, Western Reserve University, Cleveland, Ohio, U.S.A.

D. W. TURNER, Department of Chemistry, Imperial College of Science and Technology, University of London, England

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CONTENTS CONTRIBUTORS TO VOLUME 4

.

.

v

The Reversible Hydration of Carbonyl Compounds R. P. BELL I. Introduction . 11. Hydration Equilibrium Constants . 111. Acidity of Carbonyl Hydrates . IV. Kinetics of Hydration and Dehydration Reactions References .

. .

.

1 2 12 16 27

I. Introduction . . 11. The Measurement of Ionization Potentials . . 111. Molecular Structure Dependence of Ionization Potentials References . .

31 35 46 69

. .

Ionization Potentials D. W. TURNER

Reactivity Indices in Conjugated Molecules: The Present Position H. H. GREENWOOD and R. MCWEENY I. Introduction . 11. Some Applications of the Indices . 111. Properties of the Secular Equations . IV. The Isolated Molecule Method . V. The Localization Method . VI. Relationship between the Indices . VII. Frontier Orbital and Charge Transfer Theories Vii

.

.

. . . . . .

73 81 88 95 102 107 112

viii

CONTENTS

VIII. The Physical Basis of Reactivity Indices . IX. Reactivity Indices in Many-Electron Theory . X. Conclusions and Future Prospects References .

118 129 141 143

.

The Gas Phase Pyrolyses of Some Small Ring Hydrocarbons H. M. PREY I. Introduction . 11. Cyclopropane . 111. Alkylcyclopropanes . IV. Unsaturated Cyclopropanes . V. Bicyclopropyl . VI. Bicyclic Systems Containing Cyclopropane Rings . VII. Tricyclic Systems Containing Two Cyclopropane Rings VIII. Cyclopropene . IX. Systems Containing Four-membered Rings . X. Unsaturated Cyclobutanes . XI. Bicyclic Compounds Containing Cyclobutane Rings XII. Tricyclic Systems Containing a Cyclobutane Ring XIII. Cyclobutene . XIV. Bicyclobutenes . XV. Tricyclic Systems Containing Cyclobutene Rings . XVI. Conclusion . References .

.

. .

148 148 151 155 165 165 169 170 170 175 180 183 183 188 189 190 191

The Basicity of Unsaturated Com pounds H.-H. PERKAMPUS 195 I. Definition of Basicity . 200 11. The Structure of the Proton Addition Complexes . 111. Methods for Determining the Basicity of Unsaturated Hydrocarbons . 232 IV. Basicity Scale and Basicity Constants of Unsaturated 262 Compounds . V. Theoretical Treatment of Proton Addition Complexes . 284 VI. Supplementary Remarks . 297 References . 300

ix

CONTENTS

Spectroscopic Observation of Al kylcarbonium Ions in Strong Acid Solutions GEORGEA. OLAH and CHARLESU. PITTMAN,JR. I. Introduction . 11. Remarks on Nomenclature 111. Alkyl Halide-Lewis Acid Halide Systems . IV. Alcohols and Olefins in Strong Bronsted Acids V. Cyclopropylcarbonium Ions . VI. Alkylarylcarbonium Ions . References .

AUTHORINDEX. CUMULATIVEINDEX OF AUTHORS CUMULATIVE INDEX OF TITLES .

. . . . . .

305 307 307 324 333 338 345

.

349

.

. 357

.

357

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THE REVERSIBLE HYDRATION OF CARBONYL COMPOUNDS R. P. BELL

Physical Chemistry Laboratory, Oxford, England I. Introduction 11. Hydration Equilibrium Constants . A. Experimental Methods . B. Results and Discussion C. Isotope Effects on Hydration Equilibria 111. Acidity of Carbonyl Hydrates . A. Experimental Methods B. Results and Discussion IV. Kinetics of Hydration and Dehydration Reactions A. Historical B. Mechanism and Relation to other Reactions C. Experimental Methods D. Catalytic Behaviour . E. IsotopeEffects . F. The Hydration of Carbon Dioxide . References .

.

. .

.

.

.

.

I

. . .

2 2 7 12 12 12 14 16 16 16 19 22 26 26 27

. . . . . . . . . . . .

I. INTRODUCTION THEformation of stable solid hydrates is well known for aldehydes and ketones containing several electronegative substituents and for some diand triketones. The classical example is chloral hydrate, for which there is direct evidence from proton magnetic resonance measurements (Bishopand Richards, 1959) and from Raman spectra (Hibben, 1931) for the gem-diol formula CCl,.CH(OH)2, rather than any looser mode of hydration. The majority of carbonyl compounds do not give solid hydrates, except sometimes a t low temperatures, but there is frequently evidence for the reaction RlR2C0 + H20+R1R2C(OH)2 in aqueous solvents: this is accompanied by the disappearance or weakening of the characteristic U.V. absorption band of the carbonyl group at about 280 mp, again confirming the nature of the hydrate. This reaction represents the simplest example of the important class of reversible additions to the carbonyl group. The present review

2

R. P. BELL

attempts to summarize our present knowledge of the equilibrium constants and kinetics of these reactions, with special reference to recent work. Such equilibria are undoubtedly of importance in interpreting the chemical and biological reactivity of carbonyl compounds in aqueous solution, and they have proved kinetically very convenient for studying problems of homogeneous catalysis. 11. HYDRATION EQUILIBRIUM CONSTANTS

A. Experimental Methods 1. Historical

Most of our information about the thermodynamics of hydration relates to solutions in water, and aqueous solutions of acetaldehyde have been widely investigated. The presence of considerable proportion of CHs.CH(OH), in these solutions was first suggested by Ramsay and Young (1886) on the basis of the unusually large evolution of heat (about 5 kcal mole-I) accompanying the dissolution of acetaldehyde in water. Perkin (1887) made the same observation, and reported erroneously that an initial absorption of heat is followed by a larger evolution. He also noted that dilute aqueous solutions of acetaldehyde are denser than pure water, although pure acetaldehyde has a density of about 0.8. Density measurements over a range of temperatures (Homfray, 1905) indicated that the degree of hydration diminished with rise of temperature, in conformity with the sign of the observed heat change, but gave no quantitative information. 2. Ultra-violet absorption

The commonest modern method for determining the degree of hydration is to measure the intensity of the broad nlr* carbonyl absorption band at about 280 mp, which disappears on hydration. Early measurements (Schou, 1926, 1929; HBrold and Wolf, 1929, 1931) show considerable discrepancies, but the results of later workers are in reasonable agreement. The main uncertainty lies in the value to be assigned to em, the maximum extinction coefficient of the unhydrated carbonyl compound, which varies between 12 and 80 for different compounds. This is commonly taken as the value measured in a non-hydroxylic solvent such as hexane or cyclohexane,but this is not strictly valid, sincethe intensities of n-n* transitionsvary somewhat with the solvent (see e.g. Dertooz and Nasielki, 1961) ;moreover, since the shape of the band and the value of em are also solvent-dependent it may make some difference whether the extinction coefficients are compared at the same wavelength, a t the respective maxima, or in terms of the band area. Special difficulties arise

REVERSIBLE HYDRATION O F CARBONYL COMPOUNDS

3

with substances such as biacetyl, where there are several maxima and the spectrum changes in a complicated manner on hydration (Bell and McDougall, 1960). For a series of aldehydes the assumption has been made (Rumpf and Bloch, 1951)that em is the same as for aqueous solutions of ketones of similar structure, which are very little hydrated. It is occasionally possible to obtain an independent check on the correct value of em. Bell and Clunie (19528) measured the U.V. absorption of aqueous acetaldehyde solutions in the temperature range 0"-54" C, and also studied the heat changes on dissolving acetaldehyde in water at 0" C and 25"C, a calorimeter with rapid response being used. Since the hydration reaction in pure water has a half-time of about 1 min at 25" C and 8 min at O"C, the heat evolved during the first second could be identified with the physical heat of solution, AHs. Calorimetric measurements were also made in very dilute alkali, in which the hydration reaction has a half-time < 0.01 sec : the heat evolved in these experiments is AH8+ (1- a)AHh,where a is the equilibrium degree of dissociation of the hydrate and AHh the enthalpy change for the hydration reaction in solution. By assuming a value for em, the spectrophotometric measurements can be used to calculate a at each temperature, and a plot of logcr/(l -a) against 1/T then gives AHh. The same plot can be used to interpolate values of a at 0" C and 25" C, and these values used to determine a second value of AHh from the calorimetric values of (1 - cr)AHh at 0" C and 25" C. If the correct value of em has been chosen, there will be agreement between AHhfrom the isochore and the calorimetric values at both temperatures (assumingthat both AHh and em are sensibly constant over the temperature range concerned). This method gave em = 17.0 f 0.2 at 278 mp for aqueous acetaldehyde, compared with E,,, = 16.2 a t 288 mp for hexane solutions: in this instance the use of the latter value would have produced an error of only a few per cent in a. A less setisfactory method is to choose em so as to produce a linear plot of logK, against 1/27 (Gruen and McTigue, 1963a). These uncertainties may well produce errors of up to l0-20% in the derived equilibrium constants. Compounds which are almost completely hydrated in pure water are more readily studied in dioxan +water mixtures, which have been used by Rumpf and Bloch (1951)and by Federlin (1952)who used the volume concentrations of water to relate the results to those in pure water. Bell and McDougall (1960) studied 1,3-dichloroacetone at 25"-53"C in dioxan-water mixtures containing 10-100 wt. yo water (mole fraction xHaO ; activity uIInO), and found that Z ~ , ~ ~1C a) / ( varied much less with solvent compositionthan did uHsOcr/( 1 - E ) :this suggests that the activity coefficientsof the species concerned cancel to a considerableextent as the medium is changed from pure water. The same authors studied the

4

R . P. B E L L

dissociation of O ~ O O ~ M - O ~ O chloral ~M hydrate solutions in cyclohexane, but the equilibrium constant which they obtained cannot be compared with those in aqueous media. It may be noted that if an aqueous solution of a carbonyl compound shows absorption a t about 280 mp which is unaffected by the addition of dioxan or by change of temperature, this provides evidence that the compound is very little hydrated (Bell and Wright, 1961). 3. Raman and nuclear magnetic resonance spectroscopy

Measurements of Raman spectra should in principle distinguish between hydrated and unhydrated species in solution, but rather concentrated solutions must be used, and little work has yet been done. The measurements of Matsushima (1963) on aqueous acetaldehyde are in qualitative accord with other methods. Proton magnetic resonance measurements offer greater possibilities. The spectrum of pure acetaldehyde contains a doublet due to the methyl group, and a quartet from the hydrogen of the aldehyde group. Aqueous solutions of acetaldehyde give these same two peaks, with reduced intensities, and also two new peaks due to CH, .CH(OH)2(Lombardi and Sogo, 1960; Fujiwara and Fujiwara, 1963; Ahrens and Strehlow, 1965). The extent of dissociation of the hydrate follows from the relative areas of the two sets of peaks, most accurately from those arising from the methyl group. Similar measurements have been made for isobutyraldehyde (Hine et al., 1965). The advantage of this method is that the areas of the peaks are directly proportional to the numbers of hydrogen atoms concerned, thus avoiding the calibration which is necessary for most spectroscopic methods. The appearance of separate signals for the two species RlR2C0 and RIR,CH( OH), shows that their interconversion must be relatively slow, and in the presence of sufficient concentrations of catalyst (for example, hydrogen or hydroxide ions) only one set of peaks is observed. The use of N.M.R. measurements for studying the kinetics of the interconversion is mentioned in the second part of this review. In principle, N.M.R. measurements can be used to determine the reaction velocity in both directions, leading to an independent estimate of the equilibrium position : this has been done for acetaldehyde (Evans et al., 1965). This method may be particularly useful for detecting small extents of hydration, for example for acetone, which is normally regarded as unhydrated. Preliminary measurements by Hine and Redding (1964) of the N.M.R. spectrum at 60 Mc/s of a 20% solution of acetone in water (H20or D20)show a weak signal 48 c/s upfield from that due to acetone. The attribution of this signal to Me,C(OH), is confirmed by the fact that

REVERSIBLE HYDRATION O F CARBONYL COMPOUNDS

5

it is broadened by 0 . 0 1 0 perchloric ~ acid and is undetectable in 0 . 1 acid, ~ in which the interconversion of the two forms should be very fast. By comparing the area of the peak with that of a neighbouring 13C satellite the proportion of hydrate in dilute aqueous acetone can be estimated as 0.2 & 0.1%. 4. Polarography

Polarography has been applied mainly to study the rate of the reaction CH2(OH)2+CH20+H20 (see Section IV, C), the equilibrium position being assumed, but in principle it can also be used to determine equilibrium constants provided that the degree of dissociation of the hydrate is small and the rate of dissociation not too high. The most accurate method employs oscillographic polarography. Valenta ( 1960) used triangular pulses of short duration with unbuffered formaldehyde solutions: under these conditions a measure is obtained of the concentration of unhydrated aldehyde, since methylene glycol (which is not directly reducible) does not have time to dissociate appreciably in the time of a pulse. Less accurate results for unbuffered formaldehyde solutions were obtained by Landqvist (1955). 5. Miscellaneous methods

Many physical properties of solutions of carbonyl compounds will be modified by hydration, and in principle might be used to determine its extent. An attempt to use the refractive index of aqueous acetaldehyde solutions for this purpose (Lauder, 1948) led to the erroneous conclusion that the degree of hydration is small. The partial vapour pressure of carbonyl compounds over their aqueous solutions will be reduced by hydration, since the gem-diols will have a lower volatility because of hydrogen-bonding to water, and will be more completely dissociated in the vapour-phase in the absence of a high concentration of water molecules. If it is assumed that the systems obey Raoult's law (or some other theoretical relation) then the observed partial pressure and vapour composition can be used to calculate the degree of dissociation of the hydrate both in the vapour and in the liquid phase. This procedure has so far been applied only to formaldehyde (Piret and Hall, 1949; Iliceto, 1954) and for the equilibrium in solution gives a result in agreement with other methods (see Table 1). It is interesting to note that methylene glycol is incompletely dissociated in the vapour phase : for example, K p is 1 atm at about 50' C. All the other gem-diolsare likely to be completely dissociated in the vapour under attainable conditions. It has recently been shown (HQnaff,1963; Bell and Evans, 1966) that under suitable conditions the reaction of various carbonyl reagents (e.g.

R . P. B E L L

6

hydrazine, hydroxylamine, semicarbazide, bisulphite) with unhydrated carbonyl compounds may be faster than the establishment of the hydration equilibrium. If the reaction is followed continuously, for example, spectrophotometrically, carbonyl reagent added to an aqueous solution will react almost instantaneously with the unhydrated compound, followed by a slow subsequent reaction determined by the rate of dissociation of the hydrate. The proportion of unhydrated compound is then determined by extrapolating the reaction curve back to zero time : this method has so far been applied only to acetaldehyde (see Table 1). The occurrence of isotopic exchange of “0 between water and carbony1 compounds has been observed to take place slowly with acetone (Cohn and Urey, 1938) and much more rapidly with acetaldehyde (Herbert and Lauder, 1938). This gives qualitative evidence for reversible hydration (since no other reasonable mechanism exists for isotopic exchange), but gives no quantitative information about the equilibrium position. Similarly, the fact that lS0exchange occurs in the unhydrolysed ester during the hydrolysis of carboxylic esters (Bender, 1951) shows that the species RC(OH),OR’ is a stabIe intermediate rather than a transition state. The hydration of carbon dioxide according to the scheme

is a special case of the reactions considered here, and has been much investigated. (For a review, see Edsall and Wyman, 1958.) The small proportion of carbon dioxide which is hydrated (about 0.2%) makes it difficult to measure the equilibrium constant directly. The most accurate equilibrium determinations (Wissbrunn et al., 1954) depend upon conductivity measurements at high field strengths. A powerful electrostatic field displaces the equilibrium H2C03+H++ HCO, to an extent which depends upon the equiIibrium constant. This dependence can be predicted theoretically, and the theoretical expressions tested with acids of known dissociation constant. Since the experimental method uses pulses of high field-strength and short duration, the equilibria H20 C02+H2C03 and H20+ C02+H+ + HCO, are not appreciably displaced, so that the observed field can be used to derive the “true” dissociation constant of carbonic acid, and hence the extent of hydration of carbon dioxide.

+

REVERSIBLE HYDRATION O F CARBONYL COMPOUNDS

7

B. Results and Discussion 1. Compilation of results The available information on equilibrium constants is collected in Table 1. Since they relate mainly to dilute aqueous solutions, they are expressed as Kd= [R1R2CO]/[R1R2C(OH),],and are independent of the concentration scale used. The values given for constanta measured in aqueous dioxan represent Kd= xH,o[RlR2CO]/[RlRzC(OH)z],where xHaO is the mole fraction of water. The values of AH are derived from the temperature coefficient of K d , except for acetaldehyde, where a confirmatory calorimetric value is also available. The Table does not include the early measurements of HBrold (1932). When corrected to 25" C, with AH = 6 kcal mole-l, his values for the chloroacetones and for biacetyl agree with those given in the Table,l but his measurements for five aliphatic aldehydes differ considerably from later work ; in particular, the variation of Kd with chain-length is in the opposite direction. Other values given by HBrold (converted to 25°C) are for MeC(OH),.CH,Br (& = 0-96)and for MeC(OH), .CH20H (Kd= 6.7). The species CH2(0H)2and MeCH(OH)2have been studied by a number of authors and methods, and the results call for special comment. The most accurate value for methylene glycol is probably that of Valenta (1960) from oscillographic polarography. Study by spectrophotometry suffers fmm two difficulties, the very low concentration of free aldehyde and the difficulty of estimating a value for E,. Bieber and Trumpler (1947b) used 0 . 8 7 ~solutions of formaldehyde in a 70-cm optical cell at 54", 58" and 64" C and assumed E,,, = 12.5 by extrapolation from higher aliphatic aldehydes. Their results were consistent with AH = 14.6 kcal mole-', which they used to make a long extrapolation to Kd= at 25" C. Gruen and McTigue (1963a)used 3.4-13.3 M solutions in a 1-cm cell at 25"-90°C and chose ~ , = 7 as giving the best linear at 25" C and AH = 5.7 plot of logK, against 1/T, leading to K , = kcal mole-l. Their value of em seems improbably low, and AH=5.7 kcal mole-l implies a standard entropy change of 5.4 e.u. for formaldehyde, compared with 19 to 27 e.u. foranumber of otheraldehydes, including chloral. It seems likely that the interpretation of their results is vitiated by polymerization to (CH20H)20,or higher polymers :thus Bezzi et al. (1 951)have estimated from vapour pressure data that solutionsof the concentrations used by Gruen and McTigue contain only 30-70% of 1 No temperature is specified by HBrold. but later work from the same laboratory (Gauditz, 1941) is stated to be at 18' C.

TOLE 1 Dissociation Constants for gem-Diols in Aqueous Solution ~

K d

Substance

CHZC1. CH(0H)z MeCHz .CHCl .CH(OH)2 (CHza)zC(OH)z MeCHz .CBrz.CH(OH)z Me(CH&. CHCl.CH(OH)z MezCCl. CH(0H)z MeCHz. CHBr .CH(0H)z MeC(0H)z.COMe Me(CHz)&HBr. CH(0H)z MeC(0H)p. CHClz MeC(0H)z.COzH MeCH(0H)z

Method

U.V. Polerog. Polarog. U.V. U.V. v.p. U.V. U.V. U.V. U.V.

u v.

U.V. U.V. U.V. U.V. U.V. U .v. U.V. U.V. U.V. U.V. N.M.R. N.M.R. N.M.R. N.M.R. Chem.

Temperature "C 25 t o 90 20

20

- 18 t o

25 23 25

obs 3.6 x 10-5 5.5 x 10-4* ~a

54 t o 64 25 to 90 30 to 60 20 20 25 t o 68 20 20 20 20 25 t o 53 20 25 t o 53 25 20 18 to 54 20 25 t o 90 25

+27

at 25'

10-4

5.3 x 10-4t I x 10-3$ 4.5 x 10-48 0.027 11 0.063 [I 0.10

c calc

3.6 x 10-5 9.0x 10-4

a e

1.08

f

0.007

f

w

f

W

9

f

f f

0.50

f"

0.6

h i

9

j

k a

0.67

1

0.81

m n

0.81** 0.82ti 0.67

R

0.002

0.1911

0.651 0.6i 0.827

a b C

0.1611

0.42 7 0 %

Reference

d

O.ll/j 0.27 / / 0.30 0.35 11 0.35

AH kcal mole-'

8 0

M

F

F

MeCHz. C(OH)2.CO2H MezCH. C(0H)z.COzH MeCHa .CH(OH)z MeC(0H)Z.CHzCl Me(CHz)2CH(OH)z

U.V. U.V. U.V. U.V. U.V. U.V. U.V. N.M.R. N.M.R. Cond.

25 25 25 to 90 25 to 53 25 t o 90 20 25 to 90 25 t o 35 25

0.71 1.0 1.4 1-6 2.1 2.611 2.3 1.6 ea. 5 x 102 3.9 x 103

1-6 2.0 5.0 7.0

5 x lo2

6.5 2.0 7.1

-

7.3 6.5

-

2.7

h h a 9

a

f

a

P P r

Gruen and McTigue, 1963a. b Valenta, 1960. c Landqvist, 1955. d Bieber and Triimpler, 1947b. C niceto, 1954. Federlin, 1952. 0 Bell and McDouga11, 1960. h Strehlow, 1962. Rumpf end Bloch, 1951. f Bell and Clunie, 1952a. Edwards et aZ., 1962. 'Lombardi and Sogo, 1960. Fujiwara and Fujiwara, 1963. "Evans et al., 1965. Bell and Hine and Redding, 1964. 'Wissbrunn et al., 1954. ' Ahrens and Strehlow, 1965. Evans, 1966. Hine et aZ., 1965. 5

f

'

* Calculated from value at 20' C, with A H = 9 kcal mole-'. t Calculated from values at 54"-64' C, with A H = 8 kcal mole-'. 3 34-13.3

M solutions, probably partly polymerized. $ Calculated from value at 30' C, with AH =8 kcal mole-'. 11 Calculated from measurements at 20" C in dioxan containing 12.5% and 25% water. Constants converted to pure water by multiplying by mole fraction of water, and to 25" with AH = 6 kcal mole-'. 7 Calculated from value at 20" C, with AH = 5 kcal mole-1. ** From ratio of forward and reverse rates. tt Calculated from value at 23" C with A H = 5 kcal mole-'.

W

10

R . P. B E L L

monomer at 35" c. Support for the polarographic value of Kd comes from an analysis of vapour pressure data by Iliceto (1954), who finds, after at 25", A H = 8.0 kcal mole-l ; allowing for polymerization, K , = 4.5 x if the latter value is used to extrapolate the measurements of Bieber and at 25"C. Trumpler (retaining E,,, = 12.5) we arrive a t K , = 5.3 x It thus seems safe to conclude that Kd = 5( 0.5) x for this substance. It may be noted that attempts to estimate A H from calorimetric measurements of the heat of solution of formaldehyde (Walker, 1933)are inconclusive because of the unknown heat of mixing of liquid formaldehyde and water to give a solution containing unhydrated CH20. For the equilibrium between acetaldehyde and MeCH(OH), several methods agree in giving K p 0 . 7 at 25" C. The value 1-08given by Gruen and McTigue (1963a) is the only discrepant one, and this is due to their choice of em = 14.5 (obtained by the method described in the last paragraph), compared with ,,€, = 17.0 found by Bell and Clunie (1952a) and E,,, = 16.2 in hexane. It is commonly found (seee.g. Dertooz and Nasielski, 1961)that the carbonyl absorption of ketones, which are not appreciably hydrated, is stronger in water than in hydrocarbon solvents, and it seems likely that the value of E,,, used by Gruen and McTigue is considerably too low. Moreover,the effect of an erroneous value of€,,,will increase with rise of temperature, so that the derived value of A H will be too high. The same considerations apply to the values given by Gruen and McTigue for other aliphatic aldehydes, which show an unexpected increase of A H with chain length. The values in the Table are those given by the authors, but in converting the results of Federlin (1952)from 20"to 25"C we have used a uniform value of A H = 6.0 kcal mole-l. Ahrens and Strehlow (1965) have used the broadening of N.M.R. lines to investigate aqueous solutions containing 1-4 to 56 mole % acetaldehyde. Their values of Kd increase with aldehyde concentration ; this may be partly because of the decrease in water activity a t high aldehyde concentrations, but may also be related to the presence of the hemihydrate (MeCHOH)20in concentrated solutions. Their value for low concentrations (given in Table 1) is in good agreement with other methods. 1. Discussion of results

An examination of Table 1 shows that the value of Kd is decreased by the presence of electron-attracting substituents, and increased by bulky groups. The former effect can be attributed to de-stabilization of the carbonyl compound, and the latter to steric strain in the diol. It is therefore of interest to compare the observed values of Kd with the polar and steric substituent constants CT*and E, derived by Taft (1952, 1953,

REVERSIBLE HYDRATION O F CARBONYL COMPOUNDS

11

1956; see also Leffler and Grunwald, 1963) from the rates of acid and alkaline hydrolysis of aliphatic esters. The values of Kd (calc.)in Table 1 are &om the expression

log Kd = 2.70 - 2.6 U* - 1.3 E, (1) where the summation involves both the substituents in R,R,C(OH),, the methyl group representing the standard (u*=O, E8=0). The agreement is fair, and many of the compounds for which experimental substituent constants are not available give values of Kd in the expected region. Apart from the rates of alkaline ester hydrolysis, on which the substituent constants are based, the only other reaction for which a quantitative correlation with both polar and steric constants has been demonstrated is the very similar methanolysis of Z-menthyl esters in presence of methoxide ions (Pavelich and Taft, 1957). Similar relations should hold for the equilibrium constants of other reactions involving addition to the carbonyl group, but these reactions are often complicated by subsequent loss of water, and few systematic data are available for aliphatic systems. The equilibrium constants measured by Gubareva (1947) for the addition of bisulphite to aliphatic aldehydes and ketones show qualitatively the importance of both polar and steric factors. It should be noted that the last term of equation (1) implies the summation of steric substituents for two groups attached to the same carbon atom. This is not normally a valid procedure, since steric effects are not usually additive, but it appears to work fairly well in the present instance. Since the a* values are of wide application, relations could no doubt be found between the degrees of hydration and many other properties of carbonyl compounds, though because of the importance of steric effects in the former such correlations will be of limited validity. Thus Bell and McDougall (1960) pointed out that the values of K d for formaldehyde, acetaldehyde and acetone were in the same order as the thermochemical stabilities of the carbonyl groups, as measured by Q(R,R,CH,)Q(R,R,CO), where Q is a heat of combustion or formation, but the necessary thermochemical values are not available for most of the substances in Table 1. The values of Adkins et al. (1949) for redox potentials of systems RIRzCO- RIRzCHOH also show some correlation with Kd, though the experimental conditions are very different (toluene solutions at 60" C). Similarly, since the infra-red carbonyl frequencies correlate well with u* for many aliphatic aldehydes and ketones (Sullivan and Sadler, 1957) these frequencies will also be roughly related to the degrees of hydration, though the spectral frequencies do not reflect any steric interactions. The very small extent of hydration of carbon dioxide cannot be

12

R. P. BELL

accounted for within the above frame-work, but is clearly related to the great stability of the unhydrated species, as revealed by its heat of formation and bond length. It can in fact be included in the thermochemical series noted by Bell and McDougall (1960), as is shown by the following heats of formation : Q(CH4)- Q(CH20) = 9.8 kcd, Q(C2He)- Q(MeCHO)= 19.4 kcal, Q(C3Hs)-Q(Me&O) =27 kcal, &?(CH4)- Q(C02) =40 kcal

K ~ ( c H ~ ( o H )= ~ )5 x 10-4 Kd(MeCH(OH)2)=0.7 Kd(Me&(OH)Z) = 5 x lo2 K ~ ( o c ( o H ) ~ ) = 4 x 103

C. Isotope Effects on Hydration Equilibria There is a limited amount of information on the extent of hydration of aldehydes in deuterium oxide. Gruen and McTigue (1963a) concluded that Kdfor five aliphatic aldehydes at 25" C is 16% to 25 % smaller in D20 than in HzO, the differences between the different aldehydes being probably within experimental error. They also find that AH is smaller in D20, so that the change in Kd appears as an entropy effect, but i t is doubtful whether this is firmly established. Edwards et al. (1962) found a somewhat smaller effect (10%) for acetaldehyde at 20"C. Pocker (1960) has also reported a 10% effect in the same direction for acetaldehyde in water at 0" and in 9 : 1 dioxanlwater at 25' C, but does not mention his experimental method. Because of the change of solvent involved it is difficult to give even a qualitative interpretation of this isotope effect. Both the diol and the water molecule formed by its dissociation will be hydrogen-bonded to the solvent, and the overall effect presumably reflects the balance of rather complex changes of zero-point energy which depend upon the mass of the hydrogen isotope. The hydrogen atoms on carbon atoms adjacent to a carbonyl group can exchange with the solvent, but such exchange is slow in neutral solution and is unlikely to have taken place appreciably in the measurements quoted above. In this connection it is interesting to note that Jones and Bender (1960)have reported secondary deuterium isotope effects of up to 40% for analogous equilibria such as (CD,)&O + MeOH$(CD,),C(OH)OMe, though their equilibrium constants show considerable variations and a trend with concentration. 111. ACIDITYOF CARBONYL HYDRATES

A. Experimental Methods The gem-diols are considerably stronger acids than the glycols or the monohydric alcohols, and the equilibrium R1R2C(OH),+ R,R,C(OH)O- + Hf can be investigated in alkaline aqueous solutions.

REVERSIBLE HYDRATION OF CARBONYL COMPOUNDS

13

The anion can also be thought of as being formed by the addition of a hydroxide ion to the unhydrated carbonyl compound, and the following constants may be defined [RiRzC(OH)O-l [H+l/[RiRzC(oH)zl =Ki [RiRaC(OH)O-I/[RiRaC(OH)al [OH-] =Kz [RiRaC(OH)O-][H+]/[RiRaCO] =K3 [R1RzC(OH)O-]/[RiRzCO] [OH-] =K4

with the obvious relations K z = K l / K w , K , = K 1 / K , , K 4= K l / K w K d where K d is the constant defined in the last section. If K , is large and unknown it may be possible to determine only K , and K 4 of the above constants. It should be pointed out that many carbonyl compounds can also give rise to enolate ions, even when the equilibrium content, of enol is very low, and that most of the experimental methods employed do not discriminate between the two kinds of anion. It is probable that for simple aldehydes and ketones (the only classes whose acidity has been hitherto investigated) the amount of enolate ion is extremely small, but it would be desirable to check this independently, for example spectrophotometrically or by utilizing the rapid reaction of enolate ions with halogens. It has been reported (Taft and Cook, 1959) that hexafluoroacetylacetone and thenoyltrifluoroacetone, although quite strong acids in aqueous solution, appear to ionize very slowly in IMsodium hydroxide. As pointed out by Stewart and Van der Linden (1960) this is no doubt because the stable form of the ion is the enolate, which is formed slowly from the very small amount of unhydrated ketone present. The acidity of the gem-diols is not usually great enough to be determined by the usual methods of pH-measurement, though the pK of chloral hydrate (10.04) has been determined by potentiometric titration with a glass electrode (Bell and Onwood, 1962). A more useful general method is that employed by Ballinger and Long (1969,1960) for measuring the acidity of alcohols, which employs the change of conductivity of dilute sodium hydroxide solutions produced by the addition of a weak acid. It is necessary to know the mobility of the anion produced, but an approximate estimate is sufficient on account of the high mobility of the hydroxide ion. It is possible in principle to obtain both the anion mobility and the constant K 2from the conductivity measurements. This method has been applied to the hydrates of carbonyl compounds by Bell and McTigue (1960) and by Bell and Onwood (1962).l Many carbonyl compounds undergo slow condensation or reaction in alkaline solution, 1 Equation (3)of Bell and Onwood (1902)is actuallyvalid only if both the concentration of &on and that of added alkali are much smaller than that of the diol. This is not the case for all the measurements to which the equation was applied, but the resulting errors are small. Equation (3) also contains a misprint: the factor I,, - I,, should read I,, + I,.

14

R. P . B E L L

so that the observed conductivities must be extrapolated back to zero time : this is often a limitation to the application of the method. It is interesting to note that the anion mobilities thus obtained are all considerably smaller than those of the corresponding carboxylate ions, and the same is true of the anions of the alcohols studied by Ballinger and Long (1959, 1960). The difference may be due to the tetrahedral arrangement of groups round the carbon atom, as compared with the planar arrangement in a carboxylate ion, but it may also reflect the fact that the negative charge is concentrated on one oxygen atom rather than being shared between two, thus leading to increased solvation and a greater effective ionic size. If the solution contains an appreciable concentration of unhydrated carbonyl compound, the variation of carbonyl U.V. absorption with pH 1965). Simican be used to obtain K 4 (Bunnett et al., 1061; Hine et d., larly, in the weakly dissociated compounds X .CoH,.C(OH)2.CF, the variation of the aromatic absorption with pH provides a means of determining K 1 or K z (Stewart and Van der Linden, 1960). Since the reactivities of the species RIRzCO, R,R,C(OH), and R1R2C(OH)O-will normally be very different, the variation of reaction velocities with pH can sometimes give information about the equilibria involved. Thus Bunnett et al. (1961)showed that the alkaline cleavageof 2,6-dihalobenzaldehydesto m-dihalobenzenesand formate ion took place with an apparent fist-order velocity constant given by k' = k;K4[OH-l2/ (1 + K4[OH-]), where K 4(defined above) was measured independently by spectrophotometry, but could also have been derived from the kinetic results. I n this system there is no detectable amount of the unionized hydrate, and the cleavageis believed to involve reaction of the anion with another hydroxide ion. A similar kinetic investigation with chloral hydrate (Gustafsson and Johanson, 1948) leads to a value of pK1 (9.77) in fair agreement with that given in Table 2. Frequently the unhydrated carbonyl compound will be the most reactive species :thus measurements in this laboratory have shown that the velocity of the reaction CH2Cl.CHO + OH-+CH20H. CHO + C1- is proportional to the total aldehyde concentration and to the quantity [OH-]/( 1 + K,[OH-]), thus providing a means of determining K , . B. Results and Discussion Only a small number of substances have so far been investigated, and the available results are given in Table 2. These compounds should be more suitable than carboxylic acids for correlating acidity with inductive effects, since the negative charge is concentrated on one oxygen atom,

15

R E V E R S I B L E H Y D R A T I O N O F CARBONYL COMPOUND8

while in the carboxylate anions it is shared between two atoms, and the charge distribution may vary with the nature of the substituents and even with the solvent. (The same simple situation is of course also present with the alcohols, but few of these are sufficiently strong acids to be investigated accurately in aqueous solution.) Steric effects should be negligible. I n fact it was shown by Stewart and Van der Linden (1960) TABLE 2 Acid Strengths of gem-Diols in Water at 25"C

Ki = [RiR2C(OH)O-] [H+]/[RiRzC(OH)z] Substance

Method

pK1

Ref.

__ .___ ~

CH2(0H)z MeCH(OH)2 MezCH. CH(OH)2 CCls. CH(0H)z CaH5.C(OH)a.CF3 p-MeO.CaH4.C(OH)zCF3 p-Me.CaH4.C(0H)z.CFS m-Br.CeH4.C(OH)z.CFs m-NOa.CeH4.C(OH)a.CF3

~~

~

Conductivity Conductivity U.V. Conductivity U.V.

U.V. U.V. U.V.

U.V. ____

13.27 13.57 13.77 10.04 10.00 10.18 10.15 9.51 9.18

a a

b a C

C C C C

-

Bell and Onwood, 1962. b Hine et al., 1965. c Stewart and Van der Linden, 1960.

that the last five values in Table 2 correlate well with Hammett u-constants, and slightly better with the revised uO-constantsof Taft et al. (1959),in each case with p = 1.1. A similar correlation was found for the CHOH. CF3,with p = 1.0. the acidity of the carbinols X . CBH4. For the aliphatic compounds the appropriate substituent constant is u*, and the first four values in Table 2 correlate well with u* if p* = 1.4, which is identical with the value found by Ballinger and Long (1959,1960) for ten methanols with electronegative substituents. We can in fact include both the alcohols and the gem-diols in the same series if we take u* = 1.28 for the substituent OH and allow statistically for the number of OH-groups. Extrapolation of the values for gem-diols to u* = 0 gives pK- 14.5forMe2C(OH),.Sincethis speciesispresenttotheextentofonly about 0.2% in aqueous solutions of acetone (see Table l),these solutions would not be expected to show detectable acid properties, in agreement with experiment.

16

R. P . BELL

Iv. KINETICSO F HYDRATION AND DEHYDRATION REACTIONS A. Historical Although equilibrium in the system RlR2C0 + H,0+R1R2C(OH), is achieved rapidly a t ordinary temperatures, there has long been qualitative evidence that i t is not established instantaneously. Thus Perkin (1887) observed that when acetaldehyde and water are mixed the evolution of heat occurs over a period of several minutes : he also found that in measuring the densities of aqueous acetaldehyde solutions at different temperatures it was necessary to keep them at constant temperature for a considerable time before consistent results could be obtained. Brown and Pickering (1897) also observed the slow evolution of heat on mixing, and found that it was accelerated by the addition of small quantities of ammonia. They attributed this to the intermediate formation of aldehyde-ammonia, but it would now be explained in terms of catalysis by hydroxide ions. Cohn and Urey (1938) observed slow exchange between acetone and l80in water, which was accelerated by acids and bases: thiscanonlybedue to thepro~essMe~CO+H~O+Me~C(OH)~. Herbert and Lauder (1938) found that the rate of the corresponding exchange with acetaldehyde was much higher but still measurable. I n the same year Booth and Roughton (1938) measured the rate of hydration of carbon dioxide, and showed that it was catalysed by bases. Some years later both Vesely and Brdi6ka (1947) and Bieber and Triimpler (1947a) showed that the magnitude of the polarographic reduction current of aqueous formaldehyde solutions depended on the rate of dissociation of methylene glycol and varied with the pH of the solution. The first systematic study of the catalytic behaviour of this class of reaction was carried out by Bell and Higginson (1949) for the dissociation of MeCH(OH), in aqueous acetone. B. Mechanism and Relation to other Reactions The addition of water to a carbonyl group is a special case of the more general reaction R,R,CO + R30H+R,R2C(OH)OR3. Many reactions of this type have been studied kinetically and shown to be catalysed by acids or bases or both, for example the reversible formation of semiacetals (Dieckmann, 1916, 1917; Meadows and Darwent, 1952) the mutarotation of glucose (Lowry and Smith, 1927 ;Bronsted and Guggenheim, 1927) and the reversible dimerization of /3-hydroxyaldehydes and p-hydroxyketones (Bell and Baughan, 1937; Bell and Hirst, 1939). The last two reactions involve respectively the intramolecular and intermolecular making and breaking of semi-acetal linkages. Similar catalytic

17

REVERSIBLE HYDRATION O F CARBONYL COMPOUNDS

effects are found in the mutarotation of optically active a-keto-esters in alcoholic solution (McKenzie and Mitchell, 1929 ;McKenzie and Ritchie, 1931, 1932) and in exchange reactions between alcohols and esters (Alquier, 1943; Schaefgen et al., 1945), both of which presumably take place by the reversible addition of alcohol to the carbonyl group. All these reactions will have a common mechanism, which for the hydration reaction can be written as follows (Bell and Higginson, 1949) :

Acid Catalysis

+

\ +H ~ +OHB + /c(oH)oH2 + B\ + \ /C(OH)OHz + B- + /C(OH)z + HB >CO

(i) (ii)

Basic Catalysis

+ /C(OH)O-+HB \

)CO+H~O+B-

,C(OH)O\

+HB + )c(oH)~+ B-

(iii) (iv)

Of these four reactions (ii) and (iv)involve simple proton transfers to and from oxygen atoms, and experience shows that such equilibria will be set up very rapidly. The rate-limiting steps then become (i) and (iii), which involve greater structural changes and are likely to be slow. They are both formally termolecular reactions, and it is of interest to enquire whether either of them can be split up into consecutive bimolecular processes, one of which is rate-limiting. The only possibilities are as follows :

Reaction (i)

r

1

H B + H ~ O+ B - + H ~ o +

)CO+H.O+

I.+

$

/C:OH+H~O

+ /C(OH)OHz \

+

+ )C(OH)OH~

+

R . P. B E L L

18

Reaction (iii) B-+HzO )CO+OH-

[ )CO+HzO

p HB+OH-

+ )C(OH)O-

+

$

>C(O-)OHz

It appears that all these possibilities can be excluded. If reactions (a) or (9)were rate-limiting the reaction velocity would be independent of the concentration of the substrate, while reaction (e) (identical with (I)) would predict no catalysis by acids or bases. If reactions ( b ) , ( d ) or (h) determined the rate the reaction would show specific catalysis by hydrogen or hydroxide ions, in place of the general acid-base catalysis actually observed. Reactions (c), d f ) and (m) are unacceptable as rate-limiting processes, since they involve simple proton transfers to and from oxygen. Reactions 0’) and (k)might well be slow, but their rates would depend upon the nucleophilic reactivity of the catalyst towards carbon rather than on its basic strength towards a proton: as shown in Section IV,D it is the latter quantity which correlates closely with the observed rates. There is thus good evidence that the transition state contains a t least one molecule of water, and it has been suggested (Eigen, 1966) that a more reasonable physical picture is obtained if two more are included, when it becomes possible to replace the two steps (i)and (ii) or (iii) and (iv) by a concerted process involving a cyclic hydrogen-bonded transition state. The arguments for this proposal depend on a more detailed consideration of the rates of the individual processes concerned. I n the first place, if reasonable estimates are made of the equilibrium constants of reactions (ii) and (iv), it is found that for some catalysts the observed rates would demand velocity constants higher than the diffusion controlled value for the reverse of reactions (i) and (iii): in other words, there would be insufficient time for the species B- or HB to become free and move to the other oxygen atom of the hydrate. I n the second place, even if the required rate constants do not exceed the diffusion controlled values, they are so high that considerable curvature would be expected in the plots of log (catalytic constant) against pK for a series of catalysts. As shownin Section IV,F this curvature is not observed. There is thus a considerable

REVERSIBLE HYDRATION OF CARBONYL COMPOUNDS

19

amount of evidence for a concerted mechanism, including several water molecules, which for acid catalysis can be written H

H

0-H---

0-€I

I

I

,\

-

L

\

/"

No

H

H

H-oO--.H

I

I

I

\

/O

='\

R

0-H"

0-H

I

with a similar scheme for basic catalysis. Some variants on the above mechanism have been proposed. Gibert

+

(1954) has suggested that the species R,R,C: OH is formed by reaction

with an acidic species, and then reacts witheitherHzO or OH- to give the hydrate (cf. reactions (c) and (d) above). Under certain simplifying assumptions this scheme leads to the observed kinetic behaviour, but it predicts general acid-base catalysis only if proton-transfers to and from oxygen are rate-determining : moreover, it predicts a relation between the catalytic constants of an acid-base pair which is not observed in practice (Bell et al., 1956), Gruen and McTigue (1963b) have proposed

+

that in acid catalysis the species RIRzC:OH is formed reversibly, and then reacts in a rate-determining termolecular step with water and the conjugate base of the catalysing acid. This corresponds to a transition state of the same composition as the mechanism proposed above, but to a different arrangement of its components, i.e. d+

\ &

d-

..O - - - l i - - - J J

/ c.

8 -

_I H

,

\ /O---H---B

OH

ant1

C>,

-~

'0-H

I

H

A t present there appears to be no evidence which distinguishes between these two possibilities, and they become indistinguishable in terms of the cyclic transition states proposed above.

C. Experimental Methods Since water is normally present in large excess, the reaction can be characterized by two first-order velocity constants, kd for hydrate dissociation, and k, for hydration. Any method which measures the rate of approach to equilibrium will give an overall rate constant k = k d + k h ,

20

R. P. BELL

but some methods will give kd or Jch separately. They are of course related by kdlk),= Kd, the equilibrium constant for dissociation of the hydrate. The reactions are accompanied by a considerable volume change, and a dilatometric method was employed by Bell and Higginson (1949)) who added acetaldehyde-water mixtures (containing about equal quantities of MeCHO and MeCH(OH),) to an excess of acetone, and thus measured kd in presence of a large number of acid catalysts. The direct hydration of acetaldehyde in aqueous buffer solutions is inconveniently fast at room temperatures, but (kd+ kh)was measured dilatometrically at 0" C by Bell and Darwent (1950), who established the existence of general acid-base catalysjs. Lauder (1948)also gives data for the rate of hydration of acetaldehyde based on dilatometric and refractometric measurements. He did not realize the catalytic nature of the reaction, and worked in unbuffered solutions which presumably contained small but variable quantities of acetic acid : this may account for the erratic nature of his results and for the fact that his rates decrease with increasing temperature. It is more difficult to explain the fact that most of his recorded rates are considerably lower than the minimum (water-catalysed) velocity obtained by other methods. He used concentrated solutions of acetaldehyde, which may have contained considerable quantities of the hemihydrate (MeCHOH)20. The presence of this species has been recently suggested by Ahrens and Strehlow (1965) on the basis of N.M.R. spectra: there is evidence for the existence of analogous species in aqueous formaldehyde solutions (Bezzi et al., 1951),and the hemihydrate (CH2Cl.CHOH),O can be isolated as a solid (Natterer, 1882). The rate of heat evolution can be used to follow reactions with halflives down to a second or less. This method was h t applied by Bell and Clunie (1952b) to the hydration of acetaldehyde in aqueous acetate buffersat 0"C, and a more detailed study was made at 25" C by Bell et al. (1956). A similar method was later used by Gruen and McTigue (1963b) for other aldehydes. The appearance or disappearance of the U.V. absorption of the carbony1 group can in principle be used for kinetic measurements. Bell and Jensen (1961) applied this method to 1,3-dichloroacetone: the reaction is too fast in pure water, but proceeded a t a convenient rate in 5% water+dioxan mixtures, in which there is about 50% hydration at equilibrium, Catalysis by many acids and bases was observed. Much faster reactions can be studied by relaxation methods, and the pressurejump technique has been applied to the reaction MeC(OH)2.C02H+ MeCO.CO,H+H,O by Strehlow (1962).

REVERSIBLE HYDRATION O F CARBONYL COMPOUNDS

21

In the polarography of aqueous formaldehyde solutions the only reducible species is the unhydrated aldehyde, and under suitable conditions the observed current is dependent on the rate of dissociation of methylene glycol. This was f i s t shown by Vesely and BrdiEka (1 947) and by Bieber and Trumpler (1947a); later work (BrdiEka, 1955) demonstrated catalysis by borate and hydroxide ions, but no extensive study has been made by this method. An exact mathematical solution of the diffusion problem is difficult to obtain: a recent review has been given by BrdiEka (1960). For suitable substances the average life-time of the hydrated or unhydrated species can be deduced from the broadening of nuclear magnetic resonance lines. This has recently been applied to acetaldehyde (Evans et al., 1965; Ahrens and Strehlow, 1965) and to isobutyraldehyde (Hine and Houston, 1965); the velocities deduced for catalysis by hydrogen ions are in fair agreement with those obtained by other methods. It has been shown by HBnaff (1963)that the rate of reaction of several carbonyl reagents (bisulphite, hydrazine, phenylhydrazine, semicarbazide and hydroxylamine) with aqueous formaldehyde solutions is independent of the nature and concentration of the reagent, and is therefore determined by the rate of dehydration of methylene glycol. He obtained catalytic constants for hydrogen and hydroxide ions, and a detailed study of acid-base catalysis has been made by the same method by Bell and Evans (1966). I n principle the velocity of dehydration could be measured if a physical rather than a chemical method were available for removing the unhydrated carbonyl compound at a rate comparable to its hydration. It was claimed by Bieber and Trumpler (1947a) that this could be achieved by the removal of formaldehyde in a rapid gas stream, the rate of which appeared to be dependent on the pH of the solution. However, attempts to repeat their experiments have proved unsuccessful ; moreover, although they give no experimental details, calculation in terms of known kinetic and equilibrium constants shows that for a 1-ml liquid sample a gas flow of at least 30 litreslmin would be required to produce an appreciable perturbation of equilibrium conditions (Bell and Evans, 1966). It is thus clear that this method has no practical application, at least to formaldehyde solutions. The rate of exchange of l 8 0 between a carbonyl compound and water should give information about the velocity of the reversible hydration process, as shown in the early work of Cohn and Urey (1938)with acetone. Herbert and Lauder (1938) showed that isotopic exchange is faster with acetaldehyde, but no quantitative information was obtained. It would

22

R. P . B E L L

be of interest to carry out further studies on l*O exchange, and nuclear magnetic resonance measurements with "0 should give information about rapid exchanges.

D. Catalytic Behaviour Hydration and dehydration reactions have proved particularly convenient for studying catalysis by acids and bases over a wide range of structures and catalytic power. The results usually show a good correlation between acidic and basic catalytic constants (k, and kJ and the pK of the catalyst, accordingto the usual Bronstedrelations k,/p = G,(qK/p)", kJq = Q,(p/qK)@,where p and q are statistical corrections. (These statistical corrections have not always been applied consistently, but the discrepancies thus introduced are not serious.) The information so far obtained is summarized in Table 3, and comments on the individual reactions follow. TABLE 3 Hydration-dehydration Reactions at 25" C

n = number of catalysts

d = mean deviation of logk from linear relationship Solvent

Substance Acetaldehyde Acetaldehyde Acetaldehyde Formaldehyde Formaldehyde 1,3-Dichloro-acetone 1,3-Dichloro-acetone 1,3-Dichloro-acetone a c

Water Water 92.5% acetone Water Water 95% dioxan 95% dioxan 95% dioxan

Bell et al., 1956. Bell and Evans, 1966.

Catalyst type Ao,A+ BO, BA0 A", A+ BO, BA0 BO Bb d

PK

n

range

A

12 14 52 13 29 24 13 7

8 17

0.10 0.13 0.03 0.06 0.11 0.16 0.10 0.10

10

9 17 17 6 4

a o r p Ref. 0.54 0.45 0.54 0.23

a 6

0.46

c

0.27 0.50 0.50

d d

c

d

Bell and Higginson, 1949. Bell and Jensen, 1961.

1. Acetaldehyde

The catalytic constants for acids in aqueous solution correlate well with pK, and there is no apparent difference between uncharged and cation acids (carboxylic acids and pyridinium cations), though some steric inhibition is evident for 2,6-substituted pyridinium cations. The catalytic constants for bases behave somewhat more erratically, a.nd it has been suggested by Gruen and McTigue (1963b)that errors are intro-

REVERSIBLE HYDRATION O F CARBONYL COMPOUNDS

23

duced into the thermal method used for measuring the reaction velocities by the formation of addition compounds between acetaldehyde and the anions used as catalysts, for which there is some independent evidence. It may be significant that earlier measurements at 0' C by a dilatometric method (Bell and Darwent, 1950) gave a better correlation between kb and pK for seven bases of varying types, and further investigation would be desirable. The catalytic constants in 92.5% acetone have been correlated with pK-values in water, but essentially the same picture emerges if we use relative strengths in n-butanol, which has a dielectric constant similar to that of 92.5% acetone: these strengths are available for twenty-two of the acid catalysts used (Wooten and Hammett, 1935). The fifty-two acids included in Table 3 comprise carboxylic acids, phenols and NHacids, and somewhat better correlations are obtained by considering separately aliphatic carboxylic acids, aromatic carboxylic acids, and phenols. Large positive deviations (up to two powers of ten) were observed for oximes as catalysts, and large negative ones for nitroparaffins and the enols of /3-diketones : these substances are not included in the summary in Table 3.l Structural interpretations were originally suggested for these deviations (Bell and Higginson, 1949),but, at least in detail, they are often more ingenious than convincing. A recent report (Pocker and Meany, 1964) states that the enzyme carbonic anhydrase is a powerful catalyst for the reversible hydration of acetaldehyde, but no details have yet been published. 2. Formaldehyde

Apart from a limited amount of information from polarographic measurements (BrdiEka, 1955)catalytic data for this system have been obtained by using carbonyl reagents as scavengers, thus measuring the rate of dehydration of methylene glycol (HBnaff, 1963;Bell and Evans, 1966). The thirteen acids and twenty-nine bases listed in Table 3 include species derived from carboxylic acids and amines, and also inorganic species derived from arsenate, phosphite, phosphate, tellurate, borate, sulphite, sulphate and fluoride. Catalysts of all chemical types (including H,O+, HzO and OH-) confqrm to the same relationships, and there is little effect of charge, except that the anion acids HzPO;, HzPO; and HzAsO; show positive deviations of about 0.5 in logk. I n deriving the correlations in Table 3 the usual statistical factorsp and q have been used, but the general agreement is almost as good if they are omitted. The 1 The deviation reported for chloral hydrate as a catalyst disappears if wo use a more recent value of pK (Bell and Onwood, 1962). 2

.

24

R . P . BELL

independence of charge and structural type is in marked contrast to the behaviour reported for the hydration of carbon dioxide (see Section IV, F). 3. 1,3-Dichlmoacetone The catalytic constants measured in 95% aqueous dioxan have been compared with pK-values in water. The twenty-four acids referred to in Table 3 are mainly carboxylic acids, but also include nitric acid, o-chlorophenol and water. Two oximes show large positive deviations, and saccharin has considerably less catalytic activity than anticipated : these substances have not been included in the correlation. A number of “strong ” acids gave closely similar catalytic constantsHC1 (3.05), HBr (2.30), CBH6.S03H(2*30),MeS0,H (2*15),HC104 (1*25)-and the minor variations within this series are not in the expected order of acid strengths HCIOl HBr > HCI > C6H6.S03H> MeSOSH. Presumably all these acids are converted in solution to the hydronium ion, the catalytic power of which is somewhat modified by ion-pairing with different anions in the solvent of low dielectric constant. The catalytic constants observed are consistent with the conventional value pK = - 1.74 for H30+. The plot of logk against pK for basic catalysts gives two parallel straight lines, carboxylate anions being about 1000 times as effective as amine bases of the same pK. This can be largely attributed to the use of pK-values in water rather than in aqueous dioxan, since the equiIibrium RC02H+H,O+RCO, +H,O+ will be affected much more than R,NH++H20+R,N +H30+by a decrease in dielectric constant. (No such effect of charge is observed in the results for acetaldehyde and formaldehyde in aqueous solution, where both k and pK refer to the same solvent.) Some steric inhibition is again evident for 2,6-substituted pyridines.

=-

4. Comments on catalytic behaviour

The reversible hydration of carbonyl compounds shows an unusual degree of conformity to the Bronsted relation, both in the range of pK over which linearity is observed and in the lack of dependence on the charge or chemical nature of the catalyst. Eigen (1963) has produced much evidence to support the original contention of Bronsted and Pedersen (1923)that an apparently linear Bronsted plot represents only part of a continuous curve having slopes of unity and zero at its two extremities. Eigen refers to the unusually wide range of linearity observed in the mutarotation of glucose and in the dehydration of MeCH(OH)2,and attributes it to the fact that the rate-determining step

R E V E R S I B L E H Y D R A T I O N O F CARBONYL COMPOUNDS

25

is not a simple acid-base reaction, but is coupled with other processes such as the addition or removal of a water molecule. For this reason the absolute rate constants are relatively low even with very strong acids or bases, and diffusion-controlled rates are not approached for either the forward or the reverse reactions. As shown in Section IV,B, it is probably necessary to include several water molecules in the transition state, and the same arguments will apply. The absence of individual deviations due to variations of charge or chemical type can also be given a reasonable explanation. Conventional pK-values are defined in terms of equilibria for proton-transfers to and from the oxygen atom of water and steric effects will be neglibigle, whereas most of the reactions for which the Bronsted relation has been tested depend on proton transfers to or from carbon or nitrogen, and frequently involve the possibility of steric or other interactions between non-reacting groups. I n the reactions considered here the proton transfers take place to and from oxygen, and steric effects involving the catalyst will be small, especially if we accept the cyclic transition state suggested in Section IV,B: thus there should be a particularly close parallelism between the observed rate and the pK in water. Measurements by relaxation of the rapid reversible hydration of pyruvic acid (Eigen et al., 1962 ;Strehlow 1962) have producedinteresting results. Reactions involving the anions MeCO .CO, and MeC(OH),CO, make a negligible contribution, but the reaction MeCO .COzH + H20+ MeC(OH),. COzH is catalysed by hydrogen ions, pyruvic acid molecules and pyruvate ions. There is also a “spontaneous” rate, which (by comparison with the results for other hydration reactions) seems much too great to be interpreted as catalysis by water molecules. It was suggested by the authors that this part of the observed rate is due to intramolecular catalysis of the hydration process by the carboxyl group, and this explanation seems particularly likely in terms of a cyclic transition state containing two additional water molecules (see Section IV,B). It is of interest to note that intramolecular catalysis by the carboxylate group has also been established for the iodination of pyruvic acid and a number of other keto-carboxylic acids (Albery et al., 1965; Bell and Fluendy, 1963). I n these reactions the rate-determining step involvestheloss to the carboxylate group of a proton attached to carbon, and cyclic transition states can be constructed without the intervention of water molecules. Finally, it may be noted that the reversible addition of water to 2-hydroxypteridine is subject to general catalysis by acids and bases (Inoue and Perrin, 1962). The reaction here is -CH=N-+H20+ 4HOH-NHand the mechanism is presumably analogous to that of the hydration reactions discussed in this review.

26

R. P . B E L L

E. Isotope Eflects The only kinetic isotope effects so far reported for these reactions are those given by Pocker (1960), without experimental detail. He reports closely similar values for the rates of solvent-catalysed hydration of the species CH,. CHO, CD,. CHO, CH, .CDO and CD, .CDO in water at O°C ; the replacement of CH, by CD, increases the velocity by about 7%. The same effect is reported for solutions in deuterium oxide a t 0" C, presumably super-cooled. A comparison was also made of rates of hydration in H20 and D,O at O O C , giving the following values for k(H20)/k(D20)in presence of different catalysts :H+/D+,1-3;AcOH/AcOD, 2.5; AcO-, 2.3 ; H20/D20,3.6. Almost exactly the same ratios were obtained by measuring rates of dehydration at 25°C in dioxan containing 10% of H,O or D20and various catalysts. The presence of a considerablesolvent isotope effect is consistent with the mechanism given in Section IV,B, and i t would not be expected that substitution of deuterium on carbon would have an appreciable effect on the rate. It should be noted that the methyl group of acetaldehyde will exchange with the hydrogen of the solvent a t an appreciable rate, especially in presence of acids or bases. It is not clear whether such exchange had taken place in the above experiments.

F. The Hydration of Carbon Dioxide

A review of this reaction has recently been published (Edsall and Wyman, 1958), and only some particular points will be mentioned here. Early work a t 0' C (Booth and Roughton, 1938) showed that the absorption of carbon dioxide is catalysed by the anions of weak inorganic acids, and further catalytic constants (at 5°C) were obtained by Kiese and Hastings (1940). Two recent investigations at 0°C by flow techniques (Ho and Sturtevant, 1963; Gibbons and Edsall, 1963) are in good agreement as regards the rate of the uncatalysed reaction, but disagree on the existence of detectable catalysis by the ion HPOI-. A recent paper by Sharma and Danckwerts (1963) summarizes earlier results and adds new ones, catalytic constants being given for thirty-one bases. They conclude that there is a correlation between basic strength and catalytic power within a group of structurally similar catalysts, but that structural variations can cause wide deviations from this correlation, especially among inorganic anions with several oxygen atoms. This behaviour contrasts markedly with that of the hydration reactions discussed in the last section (especially the dehydration of methylene glycol), for which relations between acid-base strength and catalytic power are valid over

R E V E R S I B L E H Y D R A T I O N O F CARBONYL COMPOUNDS

27

wide variations of structure; it is therefore possible that the hydration of carbon dioxide involves some special mechanism. However, examination of the experimental data shows that many of the reported catalytic constants vary with pH (often by a factor of two to three, and sometimes by a factor of ten), while the values of different authors often disagree: for example, the value for the catalyst SO;- is given as 0.65-1-3 (Sharma and Danckwerts, 1963), 0-4-2.8 (Kiese and Hastings, 1940) and 1.9 (Booth and Roughton, 1938). It is possible that the gas absorption method does,not give a correct measure of the rates of the chemical processes invblved, and it seems premature to speculate until the experimental position is clearer. REFERENCES Adkins, H., Elofson, R. M., Rossow, A. G., and Robinson, C. C. (1949). J . Amer. Chem. SOC.71, 3622. Ahrens, M.-L., and Strehlow, H. (1965). Disc. Faraday SOC.39, 112. Albery, W. J., Bell, R. P., and Powell, A. L. (1965). Trans. Farad. SOC.61, 1194. Alquier, R. (1943). Bull. soc. chim. France ( 5 ) 10, 197. Ballinger, P., and Long, F. A. (1959). J . A m . Chem. SOC.81, 1050, 2347. Ballinger, P., and Long, F. A. (1960). J . A m . Chem. SOC.82, 795. Bell, R. P., and Baughan, E. C. (1937). J . Chem. SOC.1947. Bell, R. P., and Clunie, J. C. (1952a). Trans. Faraday SOC.48, 439. Bell, R. P., and Clunie, J. C. (1952b). Proc- Roy. SOC.212,33. Bell, R. P., and Darwent, B. de B. (1950). Trans. Faraday SOC.46, 34. Bell, R. P., and Evans, P. G. (1966). Proc. Roy. SOC.A, in the press. Bell, R. P., and Fluendy, M. A. D. (1963). Trans. Faruday SOC.59, 1623. Bell, R. P., and Higginson, W. C. E. (1949). Proc. Roy. SOC.A, 197, 141. Bell, R. P., and Hirst, J. P. H. (1939). J . Chem. SOC.1777. Bell, R. P., and Jensen, M. B. (1961). Proc. Roy. SOC.A, 261, 38. Bell, R. P., and McDougall, A. 0. (1960). Trans. Furaday SOC.56, 1281. Bell, R. P., and McTigue, (1960). J . Chem. SOC.2983. Bell, R. P., and Onwood, D. P. (1962). Trans. Faraday SOC.58, 1557. Bell, R. P., and Wright, G. A. (1961). Trans. Faraday Soc. 57, 1386. Bell, R. P., Rand, M. H., and Wynne-Jones, K. M. A. (1956). Trans. Faraday Soc. 52, 1093.

Bender, M. L. (1951). J . A m . Chem. SOC.73, 1626. Bezzi, S., Dallaporta, N., Giacometti, G., and Iliceto, A. (1951). Gnzz. chim. ital. 81, 915.

Bieber, R., and Triimpler, G. (1947a). Helw. Chim. Acta 30, 706. Bieber, R., and Trumpler, 0. (1947b). HeZw. Chim. Acta 30, 1860. Bishop, E. O., and Richards, R. E. (1959). Trans. Faraday Soc. 55, 1070. Booth, V. H., and Roughton, F. J. W. (1938). Biochem. J . 32,2049. BrdiEka, R. (1955). Collection Czechoslav. Chem. Commun. 20, 387. BrdiEka, R. (1960). “Advances in Polarography”, Pergamon Press, Oxford, p. 655. Bronsted, J. N., and Guggenheim, E. A. (1927). J . A m . Chem. SOC.49,2554. Bronsted, J. N., and Pedersen, K. J. (1923). 2. physikal. Chem. 108, 185. Brown, H. T., and Pickering, P. S. U. (1897). J . Chem. SOC.71, 774.

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Bunnett, J. F., Miles, J. H., and Nahabedian, K. V. (1961). J . Am. Chem.SOC. 83, 2512. Cohn, M., and Urey, H. C. (1938). J . Am. Chem.SOC. 60, 679. Dertooz, M., and Nasielski, J. (1961). Bull. SOC.chim. Belges, 70, 794. Dieckmann, W. (1916). Chem. Ber. 49, 2213. Dieckmann, W. (1917). Chem. Ber. 50, 1375. Edsall, J. T., and Wyman, J. (1958). “Biophysical Chemistry”, Academic Press, New York, Vol. I, Chap. 10. Edwards, J. O., Ibne-Ram, K. M., Choi, E. I.,and Rice, C. L. (1962). J.Phye. Chem. 66, 212. Eigen, M. (1963). Angew. Chem. 75,489. Eigen, M. (1965). Disc. Faraday Soc. 39, 7. Eigen, M., Kustin, K., and Strehlow, H. (1962). 2. physik. Chem. 31, 140. Evans, P. G., Kreevoy, M. M., and Miller, G. R. (1965). J . Phy8. Chem. 69,4325. Federlin, P. (1952). Compt. rend. 235, 44. Fujiwara, Y., and Fujiwara, S. (1963). Bull. Chem. SOC. Japan 36, 574. Gauditz, I. L. (1941). Z.phy&k. Chem. B , 48, 228. Gibbons, B. H., and Edsall, J. T. (1963). J . Biol. Chem. 238, 3502. Gibert, R. (1954). J . chim. phy8.51, 372. Gruen, L. C., and McTigue, P. T. (1963a). J . Chem. SOC.5217. Gruen, L. C., and McTigue, P. T. (1963b). J . Chem. SOC. 5224. Gubareva, M. A. (1947). Zhur. Obshchei. Khim. 17,2259. Gustafsson, C., and Johanson, M. (1948). Acta Chim. Scand. 2,42. HBnaff, P. L. (1963). Compt. rend. 256,1752. Herbert, J. B. M., and Lauder, I. (1938). Trans. Faraday Soc. 34, 432, 1219. Hbrold, W. (1932). 2.physik. Chem. B,, 18 265. HBrold, W., and Wolf, K. L. (1929). 2. physik. Chem. B, 5, 121. HBrold, W., and Wolf, K. L. (1931). 2. physik. Chem. B , 12, 165. Hibben, J. H. (1931). J . Am. Chem. Soc. 53, 2418. Hine, J., and Houston, J. G. (1965). J . Org. Chem. 30, 1328. Hine, J., and Redding, R. (1964). Personal communication. Hine, J., Houston, J. G., and Jensen, J. H. (1965). J . Org. Chem. 30, 1184. Ho, C., and Sturtevant, J. M. (1963). J . Biol. Chem. 238, 3499. Homfray, I. F. (1905). J . Chsm. SOC. 87, 1436. Iliceto, A. (1954). Qazz. chim. itul. 84, 536. Inoue, Y., and Perrin, D. D. (1962). J . Phys. Chem. 66, 1689. 82,6322. Jones, J. M., and Bender, M. L. (1960). J . Am. Chem.SOC. Kiese, M., and Hastings, A. B. (1940). J . Biol. Chem. 132, 267. Landqvist, N. (1955). Acta Chem. Scad. 9 , 867, 1127. Lander, I. (1948). Trans. Faraday SOC.44, 729. Leffler, J. E., and Grunwald, E. (1963). “Rates and Equilibria of Organic Reactions”, John Wiley, New York, Chap. 7. Lombardi, E., and Sogo, P. B. (1960). J . Chem. Phys.32,635. Lowry, T. M., and Smith, G. F. (1927). J . Chem. SOC.2539. Japan 36, 954. Matsushima, M. (1963). Bull. Chem. SOC. McKenzie, A., and Mitchell, A. G. (1929). Biochem. 2.208, 456. McKenzie, A., and Ritchie, P. D. (1931). Biochem. 2.231, 412; 237, 1. McKenzie, A., and Ritchie, P. D. (1932). Biochem. 2.250, 376. Meadows, G. W., and Darwent, B. de B. (1952). Trans. Faraday SOC. 48, 1015. Natterer, M. (1882). Monatsh. 3, 449.

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Pavelich, W. A., and Taft, R. W. (1957). J . A m . Chem. SOC.79, 4935. Perkin, W. H. (1887). J . Chem. SOC.51, 808. Piret, M. W. andHall, E. L. (1949). Ind. Eng. Chem. 41, 1277. Pocker, Y. (1960). Proc. Chem. SOC.17. Pocker, Y., and Meany, J. E. (1964). Abstracts, Amer. Chem. SOC.Meeting, Chicago, Sept. 1964. Ramsay, W., and Young, S. (1886). Phil. Trans. 177, 71. Rumpf, P., and Bloch, C. (1951). Compt. rend. 233, 1364. Schaefgen, J. R., Verhoek, F. H., and Newman, M. S. (1945). J . A m . Chem. Soc. 67, 253.

Schou, S. A. (1926). Compt. rend. 182, 965. Schou, S. A. (1929). J . Chim. phys. 26, 69. Sharma, A., and Danckwerts, P. V. (1963). Trans. Paraday SOC.59, 386. Stewart, R., and Van der Linden, R. (1960). Can. J . Chem. 38, 399. Strehlow, H. (1962). 2. Elektrochem. 66, 392. Sullivan, D. G. O., and Sadler, P. W. (1957). J . Chem. Soc. 4144. Taft, R. W. (1952). J . A m . Chem. Soc. 74, 2729, 3126. Taft, R. W. (1953). J . A m . Chem. SOC.75, 4538. Taft, R. W. (1966). “Steric Effects in Organic Chemistry”, ed. M. S. Newman, John Wiley, New York, Chap. 13. Taft, R. W., and Cook, E. H. (1959). J . A m . Chem. SOC.81,46. Taft, R. W., Ehrenson, S., Lewis, I. C., and Glick, R. E. (1959). J . A m . Chem. SOC. 81, 5352.

Valenta, P. (1960). Collection Czechoslav. Chem. Commun. 25, 853. Vesely, A., and BrdiEka, R. (1947). Collection Czechoslav. Chem. Commun. 12, 213. Walker, J. F. (1933). J . A m . Chem. SOC.55, 2821. Wissbrunn, K. F., French, D. M., and Patterson, A. (1954). J . Phys. Chem. 58,693. Wooten, L. A., and Hammett, L. P. (1935). J . A m . Chem. SOC.57,2289.

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IONIZATION POTENTIALS' D. W. TURNER Department of Chemistry, Imperial College of Xcience and Technology, University of London, England I. Introduction . 11. The Measurement of Ionization Potentials A. Historical . B. Recent Advances in Techiiique . 111. Molecular Structure Dependence of Ionization A. Introduction B. Amines . C. Alcohols and Ethers D. Aldehydes and Ketones . . E. Aromatic Compounds . F. Alkenes, Radicals and Alkanes. . References

.

.

.

31 35 35 39 46 46 47 50 62 65 63 69

Foreword Attempts to show the bearing of ionization potential data upon the electronic structure of complex organic molecules were greatly stimulated by the development of mass spectrometry which gave, quite easily, appearance potentials for a large number of molecular ions. More recently, notably in a review by Streitwieser (1963), the more readily reproducible photon impact values have begun to be employed. Lately, however, further advances in technique have given data on hitherto inaccessible higher ionization potentials and it seems worth while to see whether any clarification of previous uncertainties in interpretation can be expected from them. Owing to the still rather fragmentary coverage it has proved necessary to use both electron impact and photon impact results, though the one gives ideally vertical and the other adiabatic I.P. values. On the semi-empirical level of most of the arguments the difference is rather unimportant but should be borne in mind.

I. INTRODUCTION The Bohr theory of atomic structure allotted to each extra-nuclear electron within the atom a definite geometrical orbit and, more important, associated with each orbit a fixed total energy value. 1 We have used throughout the term ionizationpotentinl (I.P.)in preference to the more precise ionization energy on grounds of common usage.

2*

32

D . W . TURNER

Whilst the concept of definite geometrical orbits has been lost with the development of wave-mechanical pictures of atomic and, more recently, molecular structures, the idea of the existence of states of discrete energy or the existence of energy levels for extranuclear electrons in the field of one or more positive nuclei remains. It has become commonplace to make use of energy level diagrams to illustrate the manner in which the energies associated with the various orbitals (the wave mechanical equivalent of the Bohr orbits) are distributed on the energy scale. Such a diagram is illustrated in Pig. 1. This is constructed by placing a line for each orbital

lS’O-

- 1000

- 2000

‘\

- s-c-0 s: -

-

0:

- 20

S-C

-30

\-

c-0

- 40

1s.s-

FIa. 1. Orbital energy level diagram for carbon oxysulphide using theoretical values (Clementi, 1962). The deeper levels are essentially localized atomic orbitals. The energy scale is in electron volts, expanded on the right to show the valence shell structure.

spaced at distances proportional to the energy differences between orbitals. The absolute scale of energy is determined by the distances from a zero line correspondingto the energy of an electron a t an infinitely large distance from the central positive charge. The values used in the construction of Fig. 1 were theoretical (Clementi, 1962) and illustrate the occurrence of both large intervals between groups associated with differencesin principal quantum numbers n, and smaller intervals within each group or “shell”. The vertical scale is in the unit of energy most commonly used experimentally, the electron volt (e.v.), corresponding to the energy gained by an electron in traversing an electrostatic field whose limits differ in potential by 1 volt. The results of theoretical calculations are often expremed, however, in atomic units whose basis was originally the energy of ionization of the hydrogen atom, the Rydberg (R).Since the proton is light enough to contribute by its motion appreciably to the ionization energy, it has become the practice to employ units

IONIZATION POTENTIALS

33

based upon a hypothetically infinitely heavy (i.e. immobile) (‘proton” (Rm). The “double Rydberg” is also used and a recent rationalization proposed by Shull and Hall (1969) suggests replacing this by the Hartree ( H =me4/h2). The relation between these units and some practical units using the present values of rn, e, h, etc. are given in Table 1. TABLE1 Some Energy Units in Common Use 1 H = 27.210e.v. 1 R = 13.605e.v. 1 e.v. = 8,066 cm-1 1 e.v. = 23.06 kcal mole-1

The manner of fixing the absolute scale of energies in such a presentation equates the orbital energy (theoretically calculable) with the ionization potential, the energy necessary to remove to infinity or ionize an electron occupying the particular orbital in question. This is, briefly, Koopmans’ theorem. Whilst this is questionable in detail and is discussed further below, it is nevertheless true that there will be at least as many ionization potentials for a polyelectronic system as there are occupied orbitals. That there may be even more follows from the possibility of removing two electrons together or removing one and promoting another. The lowest ionization potential which can be observed, I , must relate to the removal of the most loosely bound electron (from the uppermost orbital level in such a diagram as Fig. 1 ) to leave the ion in an unexcited state. Kooprnans’ theorem. According to the concept of molecular orbitals developed from atomic orbitals (L.C.A.0.-M.O.) the electrons are allotted one at a time to spin orbitals of energy Ei which occur in pairs of equal Ei but of opposite spin i,bi (u),t,bi (p) until all available electrons are used up. Thus we can describe such a collection of occupied orbitals which form the molecule by the spectroscopic type of symbol a2,b2, . . . i2 . . . n.’, where the exponent shows the number of electrons in each twoelectron. orbital (i = & (u)t,hi p). Such a configuration on ionization affords a corresponding configuration with an electron missing from one of the spin orbitals: a2,b2 . . . i . . .n2 (i=a+n). I n the quantitative development of the structure in the self-consistent field approximation (S.C.F.) using the Hartree-Pock method the energy Ei is made up of three terms, one for the mean kinetic energy of the electron in i,hi, one for its mean potential energy in the field of the nuclei, and a correction term for the effect of all the other electrons, The total energy

34

D. W. TURNER

of the system would lose only these terms on removal of the ith electron so that the total energy of the ion is just Ei less than that of the molecule. Ei is thus equal to the negative of the ionization energy. It is somewhat artificial, however, to describe the effects of ionization so simply. The configuration of the ion is certainly not to be described accurately in terms of the same two-electron orbitals which were appropriate for the molecule. The presence of the positive charge results in altered ci values-the effective electronegativities of the constituent atoms-so that slightly altered atomic orbitals have to be used in the linear combination method. Further, the effects of electrostatic polarization in systems of mobile electrons can assume significant proportions, which amounts to saying that the positive hole left by the ith electron does not correspond exactly to t+hi. It is hardlysurprising, therefore, that ionization potentials calculated using Koopmans’ theorem have been found to be as much as 2-4 e.v. too large. Quite successful attempts to rectify this have been made by Hoyland and Goodman (1960) by allowing for deformation of both u- and n-electrons. Ehrenson (1962) similarly has shown that, using the w-technique (see p. 66), most of the deviations from Koopmans’ theorem come from the n-electrons and that an effective correction to the calculated value I only requires the use of the total number 7 of n-electrons: 1 = I - (7 - l)w/lo/q. This result is of considerable significance, for Koopmans’ theorem is of greatest value in the interpretation of data on higher ionization potentials. If it were to be found that the deviations were highly variable from one orbital to another within a particular system then the ionization potentials would not necessarily fall in the same order as the energies of the two-electron orbitals to which they relate. Fortunately this seems not to be the case. Examples are already to hand where predicted orbital energies from exact calculations agree well with observed ionization potentials and the associated bonding characters are in agreement with the experimental data. It seems that, though the flrst ionization potential predicted by Koopmans’ theorem may be in error by up to 4 e.v., rather similar deviations may appear for the higher values, so that the order and spacing of orbital energy levels can be inferred from ionizationpotential data. The energy associated with ionization processes is large since complete charge separation is involved. Most first ionization potentials are about 6-10 e.v. (140-280 kcal mole-l) and are thus much larger than bond energies, whilst the deepest valence shell electrons may have ionization potentials about three times greater (20-30 e.v.). Such high energies are not generally available chemically but the ionization energy is supplied by physical means, e.g. light (1) of the appropriate wavelength in the

35

IONIZATION POTENTIALS

vacuum ultraviolet region of the spectrum between 2000-400 e.v.).

M+hv

-+

A

(6-30

M++e

(1)

Alternatively the necessary energy can be supplied by the impact of electrons accelerated through the appropriate potential difference (2) or more subtly by collision with another positive (often atomic) ion with a higher recombination energy (the reverse of its ionization) (3).

M + e -+N++2e

M+X+

--f

M++X

(2) (3)

Although the energy required for ionization is so much larger than that associated with most chemical processes, considerable use has been made of ionization potential data in certain fields in which electron transfer, even if only partial, plays an important part. An early example (Compton, 1916) is to be found in attempts to relate minimum ionization potentials to the “looseness ” of the outermost molecular electrons requiredby dielectric theory. Subsequently in the years between 1928 and 1940 ionization-potential data were extensively used by R. S. Mulliken (c.f. Mulliken, 1935) in his development of the molecular orbital theory of the structure of simple molecules. With the increasing availability of reliable data associated with rapid developments in technique in the fields of vacuum ultraviolet and mass spectroscopy, attempts have been made to establish extensive correlations between ionization potentials on the one hand and polarographic oxidation potentials, the absorption spectra of charge-transfer species, basicities, and fluorescence quenching e&ts on the other, in all of which some degree of electron transfer from a donor molecule occurs. The effect of substituent groups in modifying ionization potentials has also been extensively examined in order to throw light on the manner of operation of substituent effects in general.

11. THEMEASUREMENT OF IONIZATION POTENTIALS A. Historical 1. The Hertz experiment

I n the first decade of the century a number of experiments were described which were interpreted as involving the ejection of molecular electrons and indicated the order of magnitude of the ionization poten-

36

D . W. TURNER

tials. These were particularly experiments with X-rays and with U.V.emitting discharge tubes. The first generally applicable method of more exact determination was described by Franck and Hertz (1913) and involved measuring the critical kinetic energies at which electrons were most likely to lose energy to the molecule under investigation. One such critical energy was of course the first molecular ionization potential but much early confusion sprang from the possibility of mere excitation resulting in characteristic critical kinetic energy values (Fig. 2).

1

FIG.2. Schematic representation of ionization ( I )and excitation ( E )potentials.

This experiment may be regarded as the forerunner of mass spectrometric appearance-potential determination in that both are threshold techniques, that is they depend on slow variation in the energy supplied by the impacting electron until a change in the electron-molecule interaction is observed. Thus, just as the Hertz experiment did not distinguish between excitation and ionization potentials, mass spectrometric appearance potential measurements are subject to similar ambiguities in interpretation as between ionization and autoionization. The Hertz experiment may also be regarded as the forerunner of the recently revived technique (Kuppermann et al., 1962) of electron loss spectroscopy applied to vapours. I n this, the characteristic energy losses (V,) are revealed as groups of scattered electrons of energy V, volts less than that of the incident beam whose energy is large compared with V , (see Fig. 3). Electron loss spectroscopy bears obvious similarities to Raman spectroscopy but, though ionization potentials are among the critical potentials detected, its greatest usefulness probably lies in the detection of excitation processes forbidden in optical absorption.

37

IONIZATION POTENTIALS Target molecule excited or ionised (VJ

Inelastic scatter

6

65

4.8

5

7.7

8.8

10 C

2 4 a x

=

3

(b) n

Y

2

\

U H Y

1

0

2

8

6

4

10

vc

FIG.3. (a) The inelastic scattering of electrons. (b) The energy loss spectrum for electron scattering by ethylene gas; 0 near 90'. (Reproduced with permission from Kupperman and Ruff, 1862.)

2 . Rydberg series molecular spectra

The ionization potential measurement to which the least ambiguity attaches is that which depends on the observation of a Rydberg series. Rydberg series stem from atomic spectroscopy. I n atomic spectra such series frequently form obvious features as groups of sharp, often intense lines showing a characteristic rapid convergence to shorter wavelengths up to a limit a t which they merge into a continuous absorption. Each line in such a series corresponds to the promotion of an electron to bound states of higher and higher principal quantum number n until, at the commencement of the continuum, it is just completely freed. The positions of the lines can be fitted to a series expression (4) v , ~= v, - R / ( n -

A)2

(4)

38

D. W . TURNER

where ( n - A ) is an effective quantum number. The sucess in fitting a number of observed lines to such a series is strong indication that a true ionization potential is associated with the limiting value v, . Rydberg series were detected in molecular spectra in the early 193O’s, notably by W. C. Price who showed that they arose from the outer electrons. These can usually be fairly well classified in terms of the structure of the molecule, e.g. non-bonding electrons on particular atoms or electrons of double bond systems. Non-bonding electrons give more nearly “atomic ” Rydberg series, with many numbers observable, and correspondingly accurate ionization potentials have been recorded. Most of the earlier measurements belong t o this class. The great difficulty lying in the way of extending these measurements to more complex molecules and to higher ionization potentials has been the rapidly increasing spectral complexity associated with the prescncc

FIG.4. Vacuum-ultra violet absorption spectrum of oxygen gas. The positions at which Rydberg series convergence limits occur are marked X-X. (We are indebted to Professor W. C. Price for this photograph.)

of many different types of electron and the many possible excitation processes available. Even for such a relatively simple molecule as oxygen the Rydberg series are not a t all obvious in the absorption spectrum (Fig. 4). Aside from the spectral complexity associated with polyelectronic molecules, the presence of many lines in the emission spectra of the Lyman continua used as backgrounds added to the early workers’ difficulties. 3. Mass-spectrometric appearance potentials

The combination of a mass analyzer with the electron impact apparatus enabled the scope of the pioneer work of Hertz, Lenard, Franck, and Lozier to be greatly extended, and results of less ambiguity were obtainahle. Such experiments lead in general to a curve relating the ion current

39

IONIZATION POTENTIALS

produced at each mass number to the potential used to accelerate the electron beam. Where such curves possessed a more or less distinct threshold in the case of the molecular ion, relative ionization potentials could be inferred. These were not in general absolute, though calibration using rare gases narrowed the range of uncertainty. The position of the threshold and the shape of the curve depended on so many instrumental variables that the results tended to lack absolute significance. Subsequently the shape of the curve above the threshold was given theoretical significance to provide an alternative method of calculation ionization potentials-the method of " critical slope ". The greatest advances in this direction have, however, probably been technical ones aimed at removing the instrumentally produced curvature and the uncertainties in and variability of electron energy.

B . Recent Advances in Technique 1. Photoionization cross-sectionmeasurement

It had long been recognized that some regions of strong continuous absorption, which appeared to be so-to-speaksuperimposedupon the more detailed vacuum ultraviolet absorption spectra of some simple molecules, were ascribable to ionization into a molecular ion, in its ground or an excited state, and an electron. I n many cases the long wavelength edge

M+e+MElectron copture M + hv --c M * Photo excitation

*

M+e-+M +e Electron excitation

+

M + hu -+ M+ e Photo ionization

M+e+M++2e Electron ionization M

+ hu -+ M t t + Photo double ionization

M+e+M+++3e Electrori double ionization

2e

M + h w - t Mt++ Photo triple ionization

+ 3e

FIG.5. Ideal formofexcitation cross-section((I) versusenergy ( E )functionsfordifferent fundamental processes.

of this continuum corresponded roughly to the limit of a Rydberg series or to an ionization potential inferred from electron impact measurement, but the presence of strong underlying intra-valence shell transitions prevented the general determination of ionization potentials from total absorption cross section measurements. I n 1953, however, Watanabe suggested a simple way of obtaining just the photoionization crosssection q, a function which theoretically has the form of a step

40

D . W. TURNER

at the ionization limit. This abrupt increase to a limiting value is to be contrasted with the continuous and, a t first, linear increase in ionization cross-section above the ionization potential expected for electron impact. The idealized forms of the variations of cross-section with energy for different types of excitation are shown in Fig. 5. The applicability of a step function to photoionization contributed largely to the success of Watanabe's method for measuring first ionization potentiaIs of awiderange of complex molecules (Watanabe, 1957). In addition, the values attracted greater confidence as to their absolute magnitudes since the energy of the excitation (=hv)was exactly defined by the monochromator setting, no uncertainties about contact potential variations arising. 2. Monoenergetic electron sources

It could be argued that by showing what can be done with one kind of monoenergetic excitation, the main contribution of photon impact I

Retardina

FIG.6. Potential distribution and electron kinetic energy functions in 8 simple ion source using the R.P.D. method (see text) : the effect of a variable retarding potential is shown Schematically.

studies has been to focus attention upon the problem of the precise form of the threshold laws and to stimulate work on monoenergetic electron sources. This problem has been approached in three ways. One method, first suggested by Fox and his associates (1 955), is known as the retarding potential difference (R.P.D.)method. I n this a retarding electrode at - V volts is included within the beam: electrons having energies up to

IONIZATION POTENTIALS

41

this value are repelled, and only the higher energy portions of the quasiMaxwellian distribution are passed on to be accelerated further (Fig. 6). If this electrode potential is slightly changed, the resultant variation in ionization is derived only from the electrons within this small energy range. With this apparatus an effective energy spread as low as 0.06 e.v. half-width has been achieved. An improved version has been described by Cloutier and Schiff (1959). Another method involves the use of an electrostatic or magnetic velocity selector (e.g. Marmet and Kerwin, 1960). The disadvantage of this type of instrument, which uses a narrow slit to select a particular group of electrons whose orbital radius is

Electron energy (eV)

!\'I

Pro. 7. Ionization efficiency curve for oxygen (a)obtained using monoecergetic electrons ( d E = f 0.06 e.v.)from anelectrostaticvelocityselector. The positionsof thresholds due to the ground state and vibrationallyexcitedstates of the 2Z7, ion are indicatedby the arrows (b). (Reproduced with permission from Brion, 1964.)

determined by the field magnitude is the very small output current obtainable. However, an energy spread as low as 0.03 e.v. has been achieved; about fifty times better than without velocity selection. Fox and others have also removed the effect of the uncertain contribution of this ion draw-out field to the electron energy by applying the draw-out and electron-accelerating potentials as alternate pulses (Frost and McDowell, 1955). With such refinements in technique the information which can be derived from electron impact experiments has become more exact and of a more detailed character. In simple molecules, for example, it has been

42

D . W. TURNER

possible to detect changes in slope, many of which relate to higher ionization potentials. I n the simplest it has even been possible to discern the “breaks ” associated with increases in the vibrational quantum number of the product ion. An example of this is seen for oxygen in Fig. 7. 3. Photoionization with mass analysis

Photoionization, as already pointed out, is characterized by a step function for ionization probability versus energy. The change in mode of ionization is thus much more easily detectable than for electron impact which produces only changes of slope. The combination of photon impact ion sources with mass analysis has been a major advance in technique since i t has allowed the direct study of formation and breakdown of excited ions. The first account of such an experiment was given by Hurzeler, Inghram and Morrison (1958) who employed the especially convenient Seya-Namioka type of monochromator, which had then just been described, in conjunction with a conventional magnetic sector mass

X

I

I

X

FIG.8. Vacuum monochromator and mass spectrometer combination. (Reproduced with permission from Hurzeler et al., 1958.) (A) Ultraviolet monochromator; (B) mass analyzer; (C) sections of ion source. The planes of the ultraviolet monochromator and the maw analyzer intersect at right angles along the line XX‘. 1, Discharge lamp; 2, window and entrance slit; 3, bellows for adjusting lamp; 4, micrometers for adjusting entrance slit; 5, light baffles; 6, grating; 7, grating micrometer; 8, pumping lead for monochromator; 9, light shutter; 10, micrometers for adjusting exit slits; 11, ion source pot; 12, gas inlet; 13, entrance slit of maw andyzer; 14, qumpinglead to ion source pot; 15, pumpmg lead to analyzer; 16, micrometers for adjusting exit slits of maw analyzer; 17, electron multiplier; 18, photoelectron suppressors; 19, exit slit of monochromator; 20, ionization chamber; 21, filament for producing ions by electron impact; 22, light monitoring plates; 23, gas inlet; and 24, ion gun.

IONIZATION POTENTIALS

43

spectrometer, (Fig. 8). Later instruments have employed a somewhat simpler combination using a time-of-flight mass spectrometer. It has, however, been common practice to isolate the gas in the light source from the ionization region by placing a LiF window either before or after the monochromator. This has the effect of limiting the photon energy accessible to the range below about 11.6 e.v. so that only the lowest ionic excitation levels have been accessible so far. Dibeler and Reese (1964) have however described a windowlessapparatus in which a large-capacity pumping system allowed the use of even several hundred millimetres pressure of rare gas in the light source. With this apparatus photoionization yield measurements with mass analysis have been extended to 14 e.v. A further draw-back has been that of low sensitivity; it has been estimated that when the full advantages of monochromatioity are realized, with spectral slit widths of ca. 0.001 e.v., only some 108particles enter the mass analyser as compared with perhaps 10l2in an electron impact experiment with velocity selection and up to 1014without velocity selection. N

4. Photoelectron spectroscopy I n November 1962 Professor M. Inghram remarked that much inform-

ation was being missed from impact studies by not studying simultaneously the electrons given off in the ionizing collision. As it happened, at about this time two laboratories had shown independently that the energy spectrum of photoemitted electrons contained a wealth of data and led directly to the higher ionization potentials. Vilesov et al. (1961)in Leningrad used a vacuum monochromator as the source of ionizing radiation separated by a LiF window from an ionization chamber containing a pair of cylindrical grids for electron velocity analysis. They were thus restricted to using photon energies less than 11 e.v. Turner and Al-Joboury (1962) at Imperial College, London, employed a windowless system with a helium resonance lamp as the source of monochromatic radiation (584 A=21.21 e.v.). The much more copious light output obtained with this arrangement made possible the direct recording of electron energy spectra which showed great detail, in particular ion vibrational structure. Furthermore the whole range of ionization potentials to 21-21 e.v. was covered. Both adiabatic and vertical ionization potentials should be derivable from photoelectron energy measurements, the former from the highest electron energy (within a group) and the latter from the energy of the most abundant electrons, i.e. from the peaks in the electron energy spectrum (Fig. 9a, b). (See for example the discussion in Al-Joboury and Turner 1963,1964). However, the present technique, using electron retardation by grids, introduces a

D. W. TURNER

44

characteristic asymmetry into the shapes of the bands in the electron energy spectra (Fig. 9c) so that only the adiabatic ionization potentials are readily derived (from the high electron-energy “edges)’). A large number of higher (as well as first) ionization potentials have now been measured in this way. Those which have also been measured from RydVertical I

M i a batic I

f

504r (b)

(a)

FIQ.9a, b. A portion of a photoelectron spectrum (idealized) showing (a) the identification of adiabatic and vertical ionization potentials with resolved ( 1 ) and unresolved (2) vibrational structures, (b) the identification of a higher adiabatic ionization potential with a “break”.

LJ IJ, 5

0

5

Electron-retarding potential

FIG. 9c. Photoelectron spectra for argon, krypton, and xenon, excited by the helium resonance line (684 A; 21.21 e.v.). Ionization energy increases from left to right within each section (see text).

berg series are in excellent agreement with them, but some significant disagreements with electron impact values have been noted and ascribed inter alia to the occurrence of autoionization in the latter case (v. AlJoboury and Turner, 1964; Al-Joboury et al., 1965). Future developments. It seems probable that a considerable increase in electron energy resolving power can be achieved without great loss in

IONIZATION POTENTIALS

45

sensitivity by using sector spectrometers which would also show advantages in giving “undistorted” spectra (see above). Some progress along these lines has already been made and the spectra obtained-an example is shown in Fig. 10-show promise of giving vertical ionization potentials and in favourable cases Franck-Condon factors directly.

Electron energy ( V )

FIG.10. Photoelectron spectrum of oxygen using the helium resonance line (21.21 e.v.) obtained with a magnetic electron energy analyser (May and Turner, unpublished work). Ionization energy increasing from left to right. The spectrum reveals four levels of ionization and the vibrational structure associated with each state of the ion can be clearly distinguished. This spectrum may be compared with that obtained using an electrostatic retarding field analyser (Al-Joboury et al., 1965).

5 . Ion-Molecule reactions

There is another way in which the large energy required for ionization of one molecule (1) can be supplied; that is by utilizing the recombination energy (R.E.) released upon neutralizing another ion (2). This was demonstrated by Kallmann and Rosen (1930)who showed the condition for charge exchange to occur to be just that R.E.(2) =I.P.(l). It is of course possible with ions of great velocity that during charge exchange the kinetic energy of the incident ion takes part in the process so that I.P.(l)may be somewhat greater than R.E.(2). Lindholm (1954) and his associates have developed this technique extensively and have described means (Fig. 1 1 ) whereby a wide variety of ions having a range of recombination energies can be produced and selected using one mass

46

D. W. T U R N E R

spectrometer, retarded to a low kinetic energy, and the collision products analysed in a second mass spectrometer. Magnef A -Ian

beam A in vertical plane Refording slits

source

Collision chamber---[ CallecforA

--

(Electraomelert

17

--I I

T

I o n beam B i n horizonlol plone

,

b-

Collector 8

4~iir;y

FIG. 11. Double mass spectrometer for investigation of dissociation after chargo exchange. The ions A in mass spectrometer A move in a vertical plane and the ions B move in a horizontal plane. The permanent magnet core is shown only in magnet A.

The results presented in the form of point-by-point plots of the ion abundance against the energy supplied (R.E.) give approximate fragment appearance potentials which can be related in some cases to higher ionization potentials. 6. Abbreviations

The following abbreviations are used to refer to the different methods in the tables of ionization potentials (I.P.):

E.I. P.I. P.S. R.P.D. S.

electron impact photoionization cross-section photoelectron spectroscopy retarding potential difference = spectroscopic

= = = =

111. MOLECULARSTRUCTURE DEPENDENCE

OF

IONIZATION POTENTIALS

A. Introduction By about 1930the orbital structure and ionization potentials for atoms were generally known in detail and had been related, for example, to chemical properties and periodic table regularities. In a series of papers of far-reaching importance, Mulliken (1935b) employed these atomic ionization potentials in construction of molecular orbitals, formulating rules which showed how bonding, non-bonding, and antibonding orbitals could be constructed from atomic orbitals of the appropriate energy and symmetry. I n particular, the idea was introduced that some electrons remained essentially localized in atomic-like orbitals, for example the

IONIZATION POTENTIALS

47

outer electrons of halogen in halogen acids and alkyl halides and the lone pair electrons of nitrogen, oxygen and sulphur in a variety of compounds. Since increasing bonding character waa associated with an increase in ionization potential, it seemed likely that, for compounds containing heteroatoms with lone pair electrons, these electrons occupied the highest energy orbitals, so that the first ionization potentials of such compounds pertained to the removal of one of these localized electrons. For such compounds the effects of structural changes can be expressed in terms of substituent effects, changes in grouping attached to the heteroatom being supposed to produce only a small perturbation in the essentially atomic character of the orbital in question. This is equivalent to saying that the “positive hole” left on ionization is largely confined to the heteroatom, and substituents are effective in part to the extent to which they assist positive charge dispersal, in addition to any effect due to raising or lowering of the non-bonding orbital energy in the unionized molecule.

B. Amines 1. First ionization potentials

The assumption of small perturbation is clearly justified in the case of TABLE 2 Adiabatic First Ionization Potentials of Amines (0.v.) Ammonia Methylamine Dimethylamine Trimethylamine Ethylamine Diethylamine Triethylamine n-Propylamine Di-n-propylamine Tri-n-propylamine i-Propylamine Di-i-propylamine n-Butylamine Di-n-butylamine t-Butylamine Benzylamine

10.15 8.97 8.24 7.82 8.86 8.01 7.50 8.78 7.84

7.23 8.72 7.73 8.71 7.69 8.64

8.70b

P.I. values, Watanabe et al. (1959). 0 P.S. value, Turner et al. unpublished result. The P.I. value usually quoted, 7.66 e.v. is probably much too low and may represent the energy for photodissociation. 0

48

D. W. TURNER

the aliphatic amines where the first ionization potential must relate to the loss of a nitrogen lone-pair electron since the first ionization potentials of the correspondingalkanes are nearly 3 e.v. higher. The amines have been rather fully investigated and an abundant body of data using different methods of investigation is available. The most accurate and selfconsistent values seem to be those measured by photoionization (Table 2). The effects of alkyl substitution are clearly cumulative to some degree, reflecting the degree of branching in the alkyl group close to the nitrogen atom. Kaufman and Koski (1 960) introduced a substituent constant sk to describe the change in ionization energy as each hydrogen atom of ammonia is replaced by alkyl radicals and showed that the values are group-characteristic, i.e. independent of the order of substitution. Some “saturation” was noted, sk changes going from R,NH, say, to R3N being less than for the change from NH, to RNH2. The saturation effects have also been rationalized empirically (Turner, 1962) in terms of inductive TABLE3 Stabilization energies (S) of the ground and ionized states of alkylethylenes referred to ethy1ene.a S(,,,,,)derived from A Y ( ~using ~ ~ the ~ ~observed ) changes in ionization potential (in e.v.) S(,,Ormd)

Propylene But- 1-ene But-2-ene (cis) But-2-ene (trans) 2-Methylpropene (Isobutene) Trimethylethylene Tetramethylethylene a

0.131 0.114 0.185

0.230 0.200 0.268 0.266

AZ

S(i00)

0.78 0.93 1.27 1.27 1.56 1.71 2.20

0.91 1.04 1.45 1.50 1.76 1.76 2.49

Data, from Isartcs et al. (1957).

polarization of the C-C and C-Helectronsof thealkylgroupsin the field of the nitrogen positive charge. Kaufman and Koski also considered that the ionization potentials of such amines reflected the Lewis basicities of the lone pair, free from steric effects which normally complicate discussion of structure-basicity correlations. They further argue, however, that ground stateinductive effects play the major part, largely on the grounds of correlation with Hammett u values. That is to say, alkyl groupings are most effective by raising the N lone-pair orbital energy. However, this seems to underestimate the great importance of polarization processes in the ion. Price has pointed out that, even in the alkylethylenes

49

IONIZATION POTENTIALS

where ground state resonance might be more important, substituent stabilization of the ground state is opposed to and small compared with the observed ionization potential changes (Table 3). The major part of the changes are ascribed to stabilization of the ion, values for which were derived. 2. Higher ionization potentials in amines The large difference in ionization potential between the nitrogen lone pair and the electrons of alkyl groupings has made it comparatively easy TABLE4 Ionization Potentials of Methylamine (e.v.) by Electron Impact and Photoelectron Spectroscopy Electron impact (R.P.D.)@

Photoelectron spectroscopyb

Estimatodc -~

9.45 0.08 12.35f0.10 13.90 0.30 17.70 f 0.70 21.75 f 0.20 23.75 f 0.70? a C

9.18 & 0.02 12.16f0.02 13.94+ 0.10 15.07 f0.10 16.57 0.02 19.89 f0.10

Collin (1961). Mulliken (1935a).

~

.-

11 (N:) 13.5 (C-N) 14.5 (C-H,CHz) 16 (NH2) 22 (CH2) 27 (N) b

Al-Joboury et al. (1964).

TABLE5 Tho second ionization potentials (e.v.)of aliphatic amines compared with first ionization potentials of the isoelectronic hydrocarbons

Primary Methylamine, Ethylamine, i-Propylamine, n-Butylamine, Secondary Dimethylamine, Diethylamine, Tertiary Trimethylamine, Triethylamine, b

Amine I2

Alkane I,

Diff.

cthano propano i-butane n-pentane

12.16 11.86 11.26 10.75

11.49 11.07 10.78 10.35a

0.67 0.79 0.48 0.40

propane n-pentane

12.88 11.08

11.49 10.35'

0.39 0.73

i-butane 3-ethyl-pentanc

1143 10.79

10.78 9.9b

0.85 0.9

From Watanabe et al. (1959). Estimated.

to observe the higher ionization potentials. Using the R.P.D. method (see p. 40) with electron impact, Collin (1961) has detected five higher potentials which compare surprisingly well (since they are vertical 1.P.s)

60

D . W. TURNER

with the adiabatic values measured by photoelectron spectroscopy. The results are compared in Table 4 with Mulliken's estimated values for the various molecular orbitals involved. The higher ionization potentials for the homologues of methylamine might be expected to reflect those of the corresponding isoelectronic hydrocarbons, but with some values increased by virtue of the greater nuclear charge of nitrogen. Some such effect can be seen for the second ionization potentials given in Table 5, measured by photoelectron spectroscopy.

C. Alcohols and Ethers Though there was little doubt in the case of amines that the heteroatom lone-pair electrons were the least firmly bound in the molecule, this assumption cannot generally be made with confidence when nitrogen is TABLE6 The Adiabatic Ionization Potentials of Aliphatic Alcohols (e.v.)

Methanol Ethanol Propan-1-01 Propan-2-01 Butan-1-01 Butan-8-01 2-Methylpropan-2-01 (t-butyl alcohol) Dimethyl ether Methyl ethyl ether Diethyl ether a b

10.85 10.50 10.1 10.1 10.1 10.1 9.7

10.83 10.63

12.33 11.81

14.67 12.80

17.23 15.69

17.38

10.00 9.81 9.63

Watanabe et al. (1959). Al-Joboury and Turner (1964) (see also Fig. 12).

replaced by oxygen, owing to the increase in ionization potentials associated with the larger nuclear charge of oxygen. Thus, there is only about 0-3-0.6 e.v. difference between the first ionization potentials of the aliphatic primary alcohols (Table 6 ) and the isoelectronic hydrocarbons. The second ionization potentials, however, seem to relate to the first ionization potentials of the corresponding hydrocarbons and thus are probably the ones to be associated with the hydrocarbon groupings moved

51

IONIZATION POTENTIALS

to higher values by the inductive effect of the heteroatom as before. The second ionization potentials in the pairs (1) methanol/methylamine, (2) ethanol/ethylamine, (3) diethyl ether/diethylamine are in fact very similar in each case: ( 1 ) 12.33/12.16, (2) 11.81/11.86, (3) 11.08/11-08e.v. The assignment of the first ionization to a non-bonding electron is also supported by the shape of the first (highest electron energy) peak in the photoelectron spectrum of methanol (Fig. 12). Confirmation of the

-

Electron energy (V)

FIG.12. Photoelectron spectrum of methanol vapour using the helium resonance line (21.21 e.v.). Ionization energy increases from left to right. T h e adiabatic ionization potentials measured (Al-Jobouryand Turner, 1964) are indicated by vertical arrows, and can be compared with (probably) vertical I.P. values derived from electron impact appearance potentials by Collin (1961) (dotted arrows).

general correctness of this view has been provided from a different quarter. Von Koch and Lindholm (1961) and Pettersson (1963) have shown that in charge-transfer reactions, the molecular ions of ethanol and propanol are produced by phosphorus ions (Pf) having recombination energies (10.48, 10-81 e.v.) only a little greater than the first ionization potentials of the alcohols, that is no bonding electron is transferred, e.g. +

CHS-CHZ-OH

+P+ -+ CHa-CHa-0-H

+P

(5)

On the other hand Xe+ (R.E. 12.13,13.44 e.v.) gives almost entirely mass 31, i.e. a bonding electron has been transferred: CH3-CHz-OH

+ Xe+

f --+

CH2=O-H

+ CH3 + X e

(6)

D. W. TURNER

52

D. Aldehydes and Ketones The effect of substituent groupings upon the first ionization potential of, at least, the aliphatic aldehydes and ketones does not seem to provide clear evidence for a choice between loss of a rr-electron from the C=O double bond or one of the oxygen lone-pair electrons. Concordant data for the homologous series of aliphatic ketones have been obtained by TABLE 7 The Adiabatic Ionization Potentials of Aldehydes and Ketones (e.v.) p.1.a

Formaldehyde Acetaldehyde Propionaldehyde Acetone Butan-2-one Pentan-2-one Hexan-2 -one Heptan-4-0110 Octan-4-one Nonan-5-0110 Decan-2-one 2,B-Dimethylbutan%One 2,2,4,4-Tetramethylpentme-3-one Cyclopentanone Cyclohexanone Camphor Acrolein But-2-enal Benzaldeh yde Acetophenone

P.S.

P.1.b

10.90 10.87 kO.03 kO.01 10.20 10.21 9.98 9.71 9.69 9.54 9.54 9.47 9.44 9.12 9.10 9.04 9.40

10.87

13.99

15.86

16.6

10.23 9.67

12.75 12.16

13.90 14.15

15.09 15.55

16.26 17.62

9.99

10.82

13.19

14.5G

15.94

19.05 19.88

9.18 8.65 9.42 9.14 8.71 10.10 9.73 9.51 9.77c

(See Table 8) (See Table 8)

P.I. = Photoionization cross section, (a)Vilesov, (1960); (b) Watanabe, (1957) P.S. = Photoelectron spectroscopy. D. W. Turner et al., unpublished work.

Vilesov (1960) and by Watanabe (1957) using photoionization (included in Table 7) which show effects due to alkyl substitution rather similar to those found in simple olefins. This might be taken to indicate loss of a 7r-electron. The changes produced by homologation are indeed appreciably larger than those found for the corresponding alcohols :

I 0 N IZA TI 0N P O T E N TI A L S

53

H H

However, the ready distortion of the n-electron system provides an additional mechanism whereby the charge dispersal can reach the substituents. The greater substituent effects in ketones compared to the alcohols are therefore equally consistent with the loss of an oxygen nonbonding electron. Unsaturated substituents which can conjugate with the carbonyl double bond do not have the expected large effect in reducing

I

I

t

I

I

\

,

,

,

.

,

,

,

,

,

Electron energy (V)

FIG.13. Photoelectronspectra of formaldehyde (a)and acrolein (b) vapours using the helium resonance line. Ionizationenergyincreasesfromleft to right. (D. P. May and D. W. Turner, unpublished work.)

the ionization potential, and acrolein (I.P. 10.10) even has a higher value than propionaldehyde (I.P. 9.98). Thus direct conjugation with the ionic centre is absent and in this case the electron-withdrawing inductive effect of the vinyl grouping is dominant. The photoelectron spectra of formaldehyde (Fig. 13) and acrolein show

D . W. T U R N E R

54

'85

I-

I800

16001

I

80

90

I

10 0

IP

II 0

1

12 0

eV

FIQ.14. Variation of VC=O with I.P.:0 ,class A; 0 , class B compounds I.P. Compound vc=o vc=o (in cc14) (gm) 1 COClz 1828 1813 11.57' 2 CHCla CO c1 1810 11-00= 3 CHs. CO. Cl 1822 1808 4 ace.OCHs 1795 1786 5 CHa CO OCaH5 1793 1780 6 CCla CO OCsH5 1787 1770 7 CHs. CO. OH 1785 10.35" 1768 8 CzHa .CO OH 1787 10.27' 1758 n-CsH7. CO O H 9 10.02' 1761 10 1777 (CHa0)zCO 1754 11 HCO .OCHs 1757 1734 12 CHa CO OCHs 1774 1751 10.31d 13 (CzH60)zCO 1767 1744 14 (i-C4Hg0)~C0 1744 15 1765 CHa CO OCaH5 10.10' 1740 16 n-CsH7CO.O-n-CsHg 1752 1735 17 C H a CHO 1752 10.21' 1733 18 CaHs. CHO 1757 9.86b 1738 19 n-C&. CHO 1745 9.81' 1729 20 i-C&. CHO 1742 9.72' 1729 21 CHa CO CHs 1742 1717 9.69" 22 CH3. CO CsH5 1742 9.54' 1722 23 CHs CO n-CsH7 1737 1717 9.39' 24 CHa CO n-C4H9 1734 9.38' 1718 25 Cyclohexanone 1742 1716 26 HCO N H z 1740 10*84* 1722 27 CHs :CH.CO. OH 10.70' 1721

. .

. .

. .

.

.

. .

. . .

. . .

. . . .

.

[continued onfacing page

55

IONIZATION POTENTIALS

that the first ionization is of a nearly non-bonding electron and that, at least in these instances, the oxygen lone pairs are the least tightly bound electrons. On the assumption that all the reported aldehyde first ionization potentials refer to the oxygen lone-pair electrons Cook (1958) has classified the effect of substituents into two classes, A and B, according to whether inductive or resonance effects predominate. Two different linear correlations (Fig. 14) were found between ionization potential and the carbonyl stretching frequency. Anomalies were noted for diacetyl, benzaldehyde and mesityl oxide, ascribed in the last instance to noncoplanarity interfering with resonance. It seems more likely, however, that in these cases the first ionization potential refers to 7r-electrons and higher values for the lone-pair electrons (as yet undetermined) might remove the anomalies.

E . Aromatic Compounds To some degree of approximation aromatic hydrocarbons can be considered to behave as electrically conducting bodies having a definable electrostatic capacity C, by virtue of the fact that the highest occupied orbitals extend over the whole molecule. The removal of an electron then charges this capacity and the work done is inversely proportional to C so that ionization potentials (Table 8) should fall rapidly and asymptotically to that of graphite as the molecular size increases. This approach has been developed quantitatively by Smith (1961). The calculated values however prove to be rather low but account in a general way for the low ionization potentials of, for example, circumanthracene CS2Hz2 (5.5 e.v.) and quaterrylene C,oHzo (4.9 e.v.) which approach that of 28

CH3.CO.CO.CH3

29 30

CH3. CO .NH2 CeH6.CHO

31 32 33 34 35 36 37 38 39 40 41 0

;;:I} 1717

9.25"

1714 1710

10.16d 9.51"

1704

10.10"

1700 1697 1696 1692 1689 1684 1668 1662 1649 1647

10.Ola 9.05" 9.73" 9.576 9.71b 9.1 I"*= 9.00' 8.80"

1725 1733 CH2:CH.CHO 1714} CH3.CO.NH.CH3 1718 (CH3)2C:CH.C0.CH3 1715 CH3.CH:CH.CHO 1715 CH3. CO .C B H ~ 1707 CH2: C H . CO. CH3 HCO.N(CH3)z CsH5. CO .CeHs C H B . C O . N ( C H ~ ) ~ 1689 CH3.CO.N(C2Htj)2 1678 CHs.CO.N(n-C4Hg)z

Watanahe (1967). b Morrison and Nicholson (1962). c W. C. Staele, quoted by d Higasi e l 02. (1966). e K. U. Ingold, quoted by Cook, (1968).

Cook (1968).

56

D . W. TURNER

graphite (4.40 e.v.). These last measurements were made by an interesting method based on Millikan's oil drop experiments (cf. Pope, 1962), the photoionization threshold for particles of the solids being detected from their motion in an electrostatic field. Though these values are not true molecular parameters they probably indicate the right order. 1. Benzene derivatives

There is no doubt that even in benzene itself the first ionization potential refers to the removal of a 7~ electron from the highest of the rr levels (7r2 7r3, el,) (doubly degenerate, Fig. 15). This has been amply

Orbital energy

FIQ.16. Occupied r orbital energy levels of benzene.

demonstrated spectroscopically (El-Sayed and Kasha, 1961). Also, the highest-energy band in the photoelectron energy spectrum of benzene vapour appears to be rather weakly bonding, as expected of rr electrons when compared with u electrons (Al-Joboury and Turner, 1964). It is less certain, however, whether the deeper rr level, 7r (alu)lies above or below the highest ulevel. The ionization potential found from the second Rydberg series is 11.489 e.v. and almost certainly relates to the deepest rr level (alu).Photoelectron spectroscopy shows no intermediate values but it is clear that there are other ionization potentials, presumably therefore u-electron ionization potentials, near 11 -5 e.v. The effect of substituents on the first ionization potential can be mainly inductive in character. Strongly electron withdrawing groups, such as -CHO, -NO2 or -CP3, which are meta directing lower the energy of, inter alia, the highest rr level (7r3, el,) causing an increase in ionization potential (Table 8). On the other hand, substituents having unshared electron pairs which can conjugate with the benzene ring can stabilize the positive ion by mesomeric charge transfer into the ring to cover up the

57

IONIZATION POTENTIALS

TABLE8 The Ionization Potentials of Benzene Derivatives (e.v.) Method

Benzene T,,, Benzene x , (upper) (lower)

{t.S.

Benzene Monosubstituted

{%If

-CN

{

-CF3

t.S.

P.I.

{::; * :{: ; {.::: {.;:

-CHO 4 0 . CH3

-c1 -Br -CHzOCH3

P.I.

-C=CH -CH3 -CHz. CH3 -1 -CHz. CHz .CHI -C4& (n,i -C4H9 (s,t)

{.:: {.::; P.I. P.I. P.I. P.I. P.I.

9.248 9.25 9.95 9.70 9-65, 10 9.683 697 9.68 9.51 9.46 9.27 9.24 9.07 8.99, 9.60 8.98 8.96, 9.59 8.85 8.82 8.77, 9.37 8.82 8.84, (9.15)a

11.489 11.49

11.76 11.92

11.48 11.63 11.88 11.8

11.17

8.77 8.73 8.72 8.69 8.68

z.

-CH=CHz -0Me

-CHz .NHz

(0)

-CH3, -CH3 (m)

3

10.68, 11-18

11.21

8.50

-CH3,-CH3

16.84 16.73

8.46, 9.34 11.30 {.;:; 8.35 11.29 10.29 (?C=C) {2.8.42, 9.18 8.20 8.20, 9.10 10.81 { 7.66 (See note t o Table 2) {p.': 8.70 11.19 7.71, 8.95 10.49 11.42 (?N) {s'.;p

-OH

-NH2 Disubstituted -CH3, -CHI

Other

(p)

P.I. P.S. P.I. P.S. P.I. P.S.

8.52 8.66, (9.01) 8.66 8.55, (9.0) 8.45 8.44, (9.4)

10.89 10.90 10.89

D. W . T U R N E R

58

TABLE S-Continued Method -CH3, -C1, ( p ) -CH3, -Br, ( 0 ) -CH3, -Br, ( p ) 5

Benzene x,, (upper)

P.I. P.I. P.I.

,

Benzene x , (lower)

Other

8.69 8.78 8.67

Values in parentheses tentative.

“positive hole”. Thus -OH and -NH2 groups lower the first ionization potential of benzene by 0.75 and 1.75 e.v. respectively. This is in contrast to the effect of oxygen and nitrogen upon alkyl group ionization potentials (see above) in which the inductive effect dominates, formal conjugation being absent. These effects of electron withdrawal from and release to the ring also find quantitative expression in the a+ substituent constants (Brown and Okamoto, 1957))and linear correlations between o+ values and ionization potentials have been reported (Crableand Kearns, 1962). More recently, the very strongly electrophilic reagent CF; has been shown to attack the benzene ring at a rate, k2, determined by an activation energy linearly related to the ionization potential of the benzene electrons in

1.2 1.11.0-

0.9 &?g

-g

0.8070.6 -

0.50.4 -

0‘3

0.2

8-6

9.0

9.4

9.8

10.2

lonizotion potentiol (eV)

FIG. 16. Ionization potential u8. log k4k1 of substituted benzenes: 1, CeHs-CN; 2, CeH5-NOz; 3, CeH5-COCH3; 4, CeH5-CI; 6, CeHs-Br; 6, C E H ~ - C ( C H ~ ) ~ ; 7, CeH5-H; 8, CeH5-I; 9, CeH5-CzHs; 10, CeH5--CH(CH3)2; 11, CeH5-CH3; 12, C&.-OH; 13, C&-OCH3. (Reproduced from Whitternore et al., 1962, with permission.)

IONIZATION POTENTIALS

59

substituted benzene derivatives. Thus a graph of log k2/kl against I.P. is linear (Fig. 16; kl is rate of attack on solvent). I n this reaction the transition state must involve almost complete one-electron transfer, analogous to gaseous ionization. A roughly equivalent viewpoint is to consider the charge dispersal in the positive ion by conjugating substituents to result from the delocalization in the molecule which conjugation produces. I n other words, the positive hole has the same distribution as i,h2, the electron density associated with the orbital that is losing the electron. The effect of a conjugating substituent (Fig. 17) is then to raise the energy levels of two of the three n orbitals (nl,n 2 )of the ring to an extent dependent upon its electronegativity. At the same time the substituent level is depressed. The thirdn orbital ( n s )originally , degenerate with n2,is largely unaffected since this has a node at the ring carbon atom bearing the substituent and, in the f i s t order, does not interact with it.

____-(x:

1

I

FIG.17. Perturbation (in a first approximation) of occupied m orbitals of benzene by a conjugating substituent X.

We would therefore expect to find in monosubstituted benzenes a second ionization potential, corresponding to the unperturbed orbital, at a value not very different from that of benzene ( 9.2 e.v.), as well as the higher value, corresponding to the lowest n-level ( n l ) ,and differing from the benzene nl-value by an amount similar to the first ionization potential difference. This has in fact been found in those compounds which have so far been studied by photoelectron spectroscopy (see Table 8). The simple monoalkylbenzenes and styrene have second ionization potentials in the range 9.0-9.1 e.v. Phenylacetylene has a second N

60

D . W. T U R N E R

ionization potential at 9.36 e.v. which probably reflects the marked electronegativity of the acetylenic grouping. The moving apart of the upper n levels n2 and n3 on perturbation should, for disubstituted benzenes, increase in the order o < m < p , and the separation of the first two ionization potentials of the xylenes is ordered in this way (AI, ortho = 0.50, meta = 0.55, para = 0-62e.v.). Somewhat larger intervals are found for the halogenated benzenes but the order remains the same. 2. Heterocyclic aromatic compounds a. Pyridine and other azabenzenes. The azabenzenes, compounds in

groups replace -CH= groups, often bear remarkable which -N= chemical spectroscopic similarities to the parent homocyclic hydrocarbons. This is associated with their being rr-isoelectronic with them. T ~ L9 E Ionization Potentials of HeterocyclicAromatic Compounds (e.v.) Pyridine 4-Picoline Pyridazine Pyrimidine Pyrazine

P.I. P.S. P.I. P.S. P.S. E.I.

(6.

P.I. E.I. P.S. E.I. E.I.

10.0 9.29 9.27 8.20 8.22 9.06 8.89 9.04 8.77 8-31 8.01

E.I. P.I. P.I.

9.31 8.91 8.68

P.S.

Pyrrole

Furan 2-Methylfuran 2,3-Dimethylfuran Furfwal Thiophene 2-Chlorothiophene

9.23 9.28 9.01 8.91 9.47

{E:.

10.54

12.22

13.43(?)

10.55 10-39

11.13 11.11

13.59 13.60

15.69 15.48

16.73 16.59

10.11

11.15

11.68

13.10

14.78

9.03

12.38

14.23

17.08

10.21

12.62

Pyridine has practically the same ionization potential as benzene ; it does not, however, necessarily follow that the first ionization potentials (Table 9) relate to an electron of the highest occupied n-orbital. These compounds are bases, though weaker than aliphatic amines, and parallels have been noted between base strength and ease of ionization (Nakajima and Pullman, 1968; Krishna and Chowdhury, 1963), which might indicate that the first ionization potential is that of a lone-pair

IONIZATION POTENTIALS

61

electron. Certainly the similar wavelengths for the n-m* (2700 d) and T+T* (2510 d)transitions in pyridine suggest that the nitrogen doublet and the highest rr orbitals are very similar in energy (Mason, 1959). The evidence from substituent effects is somewhat conflicting but the most systematic examination favours the ionization of a rr electron (Basila and Clancy, 1963). This is based upon a comparison between the effects of particular substituents on the electron impact ionization

1.P pyridines

FIG.18. Linear relationships between the ionization potentials of 4-substituted pyridines and the corresponding substituted benzenes (upper line -0-) and toluenes (lower line -X-). After Basila and Clancy (1963), electron impact data.

potentials of benzene, toluene and pyridine, the effect in either the benzene or toluene series being linearly related to that in the pyridine series (Fig. 18). It can be concludedthat the nitrogen atom produces a constant perturbation at least for substituents in the 4-position. Other experimental evidence leads to essentially the same conclusion regarding the rr ionization of pyridine. El Sayed and Kasha (1961) have detected Rydberg series in the absorption spectrum similar to those in benzene and ascribable to rr orbitals (9.266 e.v., a,; 11.56 e.v., b,) and, in addition, reported a fragmentary series leading to a third ionization potential of 10.3 e.v. which they ascribed to the nitrogen lone pair. Similar values are found by photoelectron spectroscopy which also indicated the 10.3 e.v. (10-54 e.v.) level to be only weakly bonding, N

D. W. TURNER

62

consistent with its assignment to a lone pair. The charge-transfer bands between azines and iodine appear to involve unshared-pair electrons of nitrogen and do not show a correlation with the first ionization potentials in the cases of pyrazine and pyrimidine (Krishna and Chowdhury, 1963).

It seems possible, however, that in the polyazines the order could be reversed, with n-electrons higher than rr-electrons, since the effect of heteroatoms in increasing the rr orbital ionization is likely to be cumulative. b. Pyrrole. I n this compound the nitrogen unshared pair of electrons is incorporated into the aromatic sextet. The effect upon degeneracy of the rr2, rr3 orbital is thus greater than in pyridine, giving a separation of

t

F

15

FIG.19. Comparison of the two lowest adiabatic ionization potentials in benzene with the three lowest in pyrrole and furan. The values arranged as an energy level diagram were obtained by photoelectron spectroscopy. (T. N. Radwan and D. W. Turner, unpublished work.)

-

0.8 e.v., so that all three occupied rr levels can be separately observed by photoelectron spectroscopy. I n furan one of the lone pairs is part of the aromatic sextet, the other is not. The greater electronegativity of oxygen leads to a larger rr2-7r3 level separation than in pyrrole (1.14 e.v.). The remaining non-bonding lone-pair orbital must be predominantly s in character and these electrons are much more tightly bound than in ordinary ethers. Figure 19 summarizes the orbital energy levels obtained

IONIZATION POTENTIALS

63

by photoelectron spectroscopy for the series of compounds from benzene to furan in which the effects of increasing electronegativity upon the TI levels is shown.

F. Alkenes, Radicals and Alkanes In the simple Hiickel molecular orbital theory of velectronic systems, molecular orbitals are derived by combinations of 2p orbitals, one from each bonded atom. All of the exchange integrals for bonded atoms are taken as equal and interactions between non-adjacent atoms are ignored. The energy Eiof each molecular orbital then has the form,

Ei = a + m i / l the coefficients mi being positive for bonding orbitals and negative for antibonding orbitals and taking the same number of values as there are contributing 2p atomic orbitals. This results in the series of orbital energy diagrams shown in Fig. 20. When the appropriate numbers of electrons

ff -2p

N -13

a u +j3 cc+2/3 a

b

a

b

FIG.20. 2psr molecular orbital energies in the Huckel approximation for simple radicals (a) and olefins (b).

are fed into these systems to maintain electrical neutrality we obtain, alternately, radicals (Fig. 20a) and olefins (Fig. 20b). The first ionization potential in each case should equal - a for the radicals and for the olefins a value greater than - a and decreasing towards - a as the number of double bonds increases. Whilst this accounts in a qualitative way for the fall in ionization potentials in a series of olefins (Table lo), the variation is larger than predicted and the radical ionization potentials (Table 11) vary over a range of more than 2 e.v. Part of these discrepanciesis obviously due to the use of constant a and equal /3 values. However, a major defect in the simple treatment is

64

D. W . T U R N E R

TABLE10 The Ionization Potentials of Alkenes (e.v.)

Mono-ole$ns Ethylene Propylene But-1-ene cis-But-2-ene trans-But-2-ene Z-Methylpropene (Isobutene) Pent-1-ene cis-Pent-2-ene trans-Pent-2-ene 2-Methylbut-1-me 3-Methylbut-1-me 2-Methylbut-2-ene Hex-1-ene trana-Hex-Z-ene trans-Hex-3-ene 2,3-Dimethylbut-2-ene 2-Ethylbut-1-ene Hept-1-ene Oct-1-ene Oct-2-ene Dec-1-ene

Method P.I. P.I. P.I. P.I. P.I. P.I.

10.516 9.73 9.58 9.24 9.13 8.95

P.I. E.I. E.I. P.I. P.I. P.I., s. P.I. E.I. E.I. P.I., s. E.I. E.I. E.I. E.I. E.I.

9.50 9.11 9.06 9.12 9.51 8.80 9.46 9.16 9.12 8.30 9.21 9.54 9.52 9.11 9.51

Allene 1,Z-Butadiene 1,2-Pentadiene 2,3-Pentadiene cis-1,3-Butadiene trans- 1,3-Butadiene 1,3-Pentadiene 1,4-Pentadiene Z-Methy1-1,3-butadiene 2,3-Dimethyl-butadiene 1,B-Hexadiene

P.I., s. E.I. E.I. E.I. S. S. E.I. E.I. P.I., s. P.I., s. E.I.

10.19 9.57 9.42 9.26 8.75 9.02 8.65 9.58 8.86 8.72 9.51

1,3,5-Hexatriene

S.

8.26

Tetruenes 1,3,5,7-0ctatetraene

S.

7.8

Cyclo-olefins Cyclopropene Cyclopentene Cyclohexene Cyclopentadiene Cyclohexadiene

E.I. P.I. P.I. S. S.

9.95 9.01 8.95 8.58 8.40 8.6 8.04

Dienes

Triener,

Cyclo-octatetraene

65

IONIZATION POTENTIALS

TABLE11 The Ionization Potentials of Some Radicals (e.v.) Aliphatic Methyl Ethyl 1-Propyl 2-Propyl n-Butyl i-Butyl S-Butyl t-Butyl

Fluoromethyl Difluoromethyl Trifluoromethyl Chloromethyl Dichloromethyl Trichloromethyl Bromomethyl Dibromomethyl Methylene Difluoromethylene Dichloromethylene Dibromomethylene Vinyl Ally1 Propargyl Formyl Acetyl Aromatic Phenyl Pentafluorophenyl Benzyl m-Cyanobenzyl m-Nitro p-cyan0 m-Fluoro p-Chloro p-Fluoro p-i-propyl p -Methoxyl 0-Xylyl m-Xylyl P-XYlYl Benzoyl

Method P.I., s. P.I. P.I., E.I. P.I. E.I. E.I. E.I. E.I. P.I. E.I. E.I. E.I. E.I. E.I. E.I. E.I. E.I. E.I. E.I. E.I. E.I. E.I. E.I. E.I. E.I. E.I.

9.84 8.78 7.80 7.77 8.11 8.35 7.93 7.4 7.19 9.35 9.45 10.15 9.32 9.30 8.78 9.30 8.13 11.9 13.30 13.10 10.11 9.4 8.16 8.25 9.88 8.08

E.I. E.I. E.I. E.I. E.I. E.I. E.I. E.I. E.I. E.I. E.I. E.I. E.I. E.I. E.I.

9.90 10.6 7.76 8.68 8.56 8.36 8.18 7.95 7.78 7.42 6.82 7.61 7-65 7-46 7.91

undoubtedly due to the neglect of electron repulsion effects which are different in molecule and ion. One way in which these can be allowed for is to choose empirical values of CL and /?to absorb the differences in electron repulsion. If the charge distribution in the ion (q, a t the rth atom) is 3*

66

D. W . T U R N E R

known from the distribution of the simple Huckel orbital or can be guessed at, individually modified o! values can then be used for each constituent atom to calculate an improved charge distribution, a process which can be reiterated using the new derived a values. This procedure, introduced by Wheland and Mann (1949), has been modified by Streitwieser (1961) who d e h e d the o! values in terms of a disposable parameter w (the so-called w technique) so that cr, = .o+w(1-!?r)ls

(7)

The best value of w is then found so that in a range of systems the best fit with ionization potential data is obtained. I n spite of its apparent simplicity this approach has been shown capable of removing the big discrepancies between simple Huckel M.O. values and experimental results. The improvement in results for simple n-systems is indicated in Fig. 21.

1.P calculated (eV)

FIG.21. Improvement in agreement between calculated and observed ionization potentials for simple T systems aa between values derived on the simple H.M.O. basis (left-handend of arrows) and those derived using the w technique (right-handend of arrows). See text. 1, Methyl; 2, Allyl; 3, Pentadienyl; 4, Benzyl; 6, Ethylene; 6, Butadiene; 7, Benzene; 8, Styrene; 9, Naphthalene; 10, Phenanthrene.

TABLE12 The Ionization Potentiah of Alkanes (e.v.)

Open chain Methane

Ethane Propane n-Butane i-Butane n-Pentene i-Pentane neo-Pentane n-Hexane i-Hexane 3-Methylpentane 2,3-Dimethylb~tane 2,Z-Dimethylb~tane n-Heptane Cycloalknee Cyclopropane

Methylcyclopmpane Cyclobutane Cyclopentane Cyclohexane Methylcyclohexane

5. P.I., P.S. P.I. P.S. P.I. P.S. P.I. P.S. P.I. P.S. P.I. P.I. P.I. P.I.

P.I. P.I. P.I. P.I. P.I.

{.;:;

{E. P.I. P.I. P.I. P.S. P.I.

12.95 12.99 11.65 11.49 11.08 11.07 10.65 10.50 10.55 10.78 10.33 10.30 10.37 10.17 10.09 10-06 10.00 10.04 10.06 10.06 9.96 9.88 9.52 10.50 10-51 9-88 9.79 9-86

14.74

20*13(?)

13.17

15.17

19*18(?)

12.36

14.13

15-70,

18.57(?)

12.54

14.51

15.69(9 )

19.96(?)

11.05

12-27

15-17

16-52(?)

18*8(?)

10.50

11.86

13-2(?)

15.00

16-25

11-33(?)

12.22

14.37

19.43

20.26(?)

18.1(?)

68

D. W. TURNER

This semiempirical approach has been extended to cover the effects of methyl substitution by either regarding the methyl group as contributing a pair of “pseudo T ” electrons (i.e. like a vinyl group with modified Q and values) or by considering its effect on the electronegativity (a)of the carbon atom to which it is attached (Streitwieser, 1962). These alternatives correspond to a hyperconjugative and an inductive model respectively. The two have also been combined with some success. An alternative similar to the first above is the heteroatom model envisaged by Matsen (1950) and Stevenson in which the whole methyl group is treated as a single atom X which contributes a pair of electrons to the 7r-system. The agreement with experiment is again, on the whole, quite good, with an average deviation of 0.1 1 e.v. for a range of olefins, radicals and aromatic hydrocarbons. The heteroatom model has also had considerable success in accounting for the decrease of ionization potential with increasing size in saturated hydrocarbons where there are no formal rr-electrons (Table 12). Methane has two orbital energy levels, the highest, correspondingto the I.P. 12.99 e.v., made from carbon 2p and hydrogen Is orbitals, is triply degenerate and has high p (antisymmetric) character whilst the deepest (I.P.> 21 e.v. ; carbon 2s +hydrogen Is) is largely s in character (Fig. 22). If a

2 s ( C ) +ls(H‘) +ls(H2)+Is(H3)+ls(H‘)

FIG.22. Molecular orbital energy levels for methane.

saturated hydrocarbon is built up from such units some of the highest orbitals, those not involved in C - C bonding (symmetric with respect to the carbon skeleton), will therefore be antisymmetrical with respect to the carbon skeleton and resemble in symmetry the carbon 2p orbitals used in the Hiickel M.O. approximation. Each will however contribute two electrons instead of one to the “pseudo T ” system. All the “T” orbitals will therefore be filled and the change in first ionization

IONIZATION POTENTIALS

69

potential can be related to /3, the best fit being obtained with /3 = 1.6 e.v. There should, on the simple H.M.O. basis, be a symmetrical development of the orbital energy levels as the chain length increases, and it is of interest that, at least in simple hydrocarbons (up to butane), this is reflected in the higher ionization potentials observed (Fig. 23). Ethane

20 -

I

Methane Ethane Propane Butane

FIG.23. Adiabatic ionization potentials for methane, ethane, propane, and butane arranged as an energy level diagram.

shows only two prominent values lower than 20 e.v. which differ by just the expected amount 3.25 e.v. ( = 2/3) whilst propane shows the expected three values, the middle one, 13-17 e.v., being close to that of methane, 12.99 e.v. It may be, therefore, that the first ionization potentials of saturated hydrocarbons relate to electrons in essentially C-H bonding orbitals rather than C-C orbitals, as is often assumed. REFERENCES Al-Joboury, M. I., and Turner, D. W. (1963). J . Chem. SOC. 5141. Al-Joboury, M. I., and Turner, D. W. (1964). J . Chem. SOC.4434. Al-Joboury, M. I., May, D. P., and Turner, D. W. (1965). J . Chem. SOC. 616. Basila, M. R., and Clancy, D. J. (1963). J . Phys. Chem. 67,1551. Brion, C. E. (1964). J . Chem. Phye. 40, 2995. Brown, H. C., and Okamoto, Y . (1957). J . A m . Chem. SOC.79,1913. Clementi, E.(1962). J . Chem. Phys. 36,750. Cloutier, G.G., and Schiff, H. I. (1959). J . Chem. Phys. 31, 793.

70

D. W. TURNER

Collin, J. E. (1961). IX Colloq. Spectr., Lyon, p. 596. Compton, K. T. (1916). Phye. Rev. 8,412. Cook, D. (1958). J. Am. Chem. SOC. 80,49. Crable, G. F., and Kearna, G. L. (1962). J. Phye. Chem. 66,436. Dibeler, V. H., and Reese, R. M. (1964). J. Chem. Phye. 40, 2034. El-Sayed, M. F. A., and Kasha, M. (1961). J. Chem. Phye. 34,334. Ehrenson, S. (1962). J. Phye. Chem. 66,706. Fox, R. E., Hickam, W. M., Grove, D. J., and Kjeldaas, J. (1955). Rev. Sci.Imtr. 26, 1101. Franck, J., and Hertz, G. (1913). Ber. phyaik. am. 34 (the early work is summarized in Franck, J. and Jordan, P., “Anregung von Quantenspriingen durch Stosse”, Springer-Verlag, Berlin, 1926.) Frost, D. C., and McDowell, C. A. (1955). Proc. Roy. SOC. A232, 227. Higasi, K., Omura, I., and Baba, H. (1956). Nature 178, 652. Hoyland, J. R., and Goodman, L. (1960). J. Chem. Phy8. 33, 946. Hurzeler, H., Inghram, M. G., and Morrison, J. D. (1958). J. Chem. Phy8. 28, 76. Isaacs, L. D., Price, W. C., and Ridley, R. G. (1967). “Threshold of Space”, ed. M. Zelikoff,Pergamon Press, Oxford. Kallmann, H., and Rosen, B. (1930). 8.Elektrochem. 36, 748. Kaufman, J. J., and Koski, W. S. (1960). J. Am. Chem. SOC. 82,32,3262. von Koch, H., and Lindholm, E. (1961). Arkiv Fyaik 19, 123. Krishna, V. G., and Chowdhury, M. (1963). J. Chem. Phy8. 67, 1067. Kuppermann, A., and Ruff, L. M. (1962). J. Chem.Phye.37,2497 (seealso Simpson, J. A., andMielczarek, S. K. ibid. 39,1606; andLassettre, E. N., andFrancis, S. A. ibid. 40, 1208). Lindholm, E. (1954). 8.Naturforsch. 9a, 535 and later papers. Marmet, P., and Kerwin, L. (1960). Can. J. Phy8.38, 787. Mason, S. F. (1959). J. Chem. SOC.1240. Matsen, F. A. (1950). J. Am. Chem. SOC.72, 5243. Morrison, J. D., and Nicholson, A. J. (1952). J. Chenz. Phy8. 20, 1021. Mulliken, R. S. (1935a). J. Chem. Phy8.3, 506. Mulliken, R. S. (1935b). J. Chem. Phy8.3,664. Nakajima, T., and Pullman, B. (1968). Bull. BOG. chim. France 1502 (see also Compt. rend. 246, 1047). Pettersson, E. (1963). Arkiv. Fyaik 25, 181. Pope, M. (1962). J. Chem. Phy8.37, 1001; 36, 2810. Shull, H., and Hall, G. G. (1959). Nature 184, 1539. Smith, F. T. (1961). J. Chem. Phy8.34, 793. Streitwieser, A., Jr. (1961). “Molecular Orbital Theory for Organic Chemists”, Chap. 7, Wiley, New York. See also J. Amer. Chem. SOC.82, 4123 (1960). Streitwieser, A., Jr. (1962). J.Phye. Chem. 66, 368. Streitwieser, A., Jr. (1963). “Progress in Physical Organic Chemistry”, Vol. 1, Interscience, New York, Chap. 1. Turner, D. W. (1962). “Determination of Organic Structures by Physical Methods”, Vol. 2, eds. Nachod, F. C. and Phillips, W. D., Academic Press, New York, pp. 353 ff. Turner, D. W., and Al-Joboury, M. I. (1962). J. Chem. Phy8.37,3007. Vilesov, F. I. (1960). Doklady Akad. Nauk.S.S.S.R. 132, 1332. Vileeov, F. I., Kurbatov, B. L., and Terenin, A. N. (1961). Doklady A M . Nauk. S.S.S.R. 138, 1329.

IONIZATION POTENTIALS

71

Watanabe, K. (1957). J. Chem. Phys. 26, 642. Watanabe, K.,Marmo, F., and Inn, C. Y. (1956). Pby.9. Rev. 91,1155. Watanabe, K.,Nakayama, T., and Mottl, J. (1959). Final Report on Ionization Potentials of Molecules by a Photoionization Method, Dept. Army No. 5B-99-01004, ORD TB2-0001-00R-1624. Wheland, G . W., and Mann, D. E. (1949), J . Chem. Phya. 17,264. Whittemore, I. M., Stefani, A. P., and Szwarc, M. (1962). J. Am. Chem. SOC.84, 3799.

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REACTIVITY INDICES IN CONJUGATED MOLECULES: THE PRESENT POSITION H. H. GREENWOOD and R. McWEENY Quantum Theory Group, University of Keele, Staffordshire, England

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I. Introduction A. Reactivity Indices . B. HuckelTheory C. Nature of the Methods D. Derivatives and Heterocyclics . 11. Some Applications of the Indices . . A. Heterolytic Reactions B. Homolytic Reactions . 111. Properties of the Secular Equations A. Partial Derivatives and Polarizability Coefficients . B. Energy Level Diagrams and Parameter Variations . IV. The Isolated Molecule Method A. Analytical Properties of Approximate Methods . B. Analytical Properties of Exact Methods . V. The Localization Method A. Analytical Properties of Approximate Methods . B. Analytical Properties of Exact Methods . VI. Relationship between the Indices VII. Frontier Orbital and Charge Transfer Theories VIII. The Physical Basis of Reactivity Indices . A. Polarization and Electrophilic Substitution . B. The Structure of a-Complex Intermediates . C. Some Related Topics IX. Reactivity Indices in Many-Electron Theory . A. Perturbation Methods in SCF Theory . B. P , and r,,,as Reactivity Indices . . C. Effect of Heteroatoms . D. Alternant Hydrocarbons. Finite Changes . X. Conclusions and Future Prospects . References

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73 73 76 78 80 81 82 87 88 89 90

95 97 99 102 105 106 107 112 118 119 122 125 129 130 135 138 140 141 143

I. INTRODUCTION A. Reactivity Indices MOLECULARorbital theories of the substitution reactions of conjugated molecules have been presented and reviewed on many occasions. I n general, the validity of a theory has been judged according to its performance in predicting, by reference to the numerical values of certain

74

H . H . GREENWOOD A N D R . MCWEENY

indices, the observed reactivities of different positions in the molecule. A detailed and critical study of the theoretical basis of the various indices, of their anaIytical properties and interrelationships, and, more especially, of their connection with physical situations likely to arise during a reaction, is much more difficult to find. The aim of the presentreviewis to remedy this omission by trying to rationalize the somewhat confused state of the subject and by seeking a better understanding of the principles involved in setting up reactivity indices. For this reason, a complete documentation of the literature will not be attempted and references will be confined largely to a relatively small number of key papers ; references to many varied applications of the indices, covering a vast field, may be found in other recent review articles. For the same reason, only a limited amount of strictly new material will be presented, this relating mainly to the introduction of more elaborate quantum mechanical techniques and to prospects for the future. Since the discussion will be confined entirely to the properties and significance of reactivity indices, details of the reaction process itself and its description in terms of rate equations will not be considered. This means that certain assumptions are implicit throughout, and these must be mentioned at the outset. Briefly, a reaction rate is determined by an activation energy AE, defined by reference to the variation of energy as reagent and molecule approach along some assumed reactionpath (Fig. 1). Often the configuration corresponding to the peak is assumed to be essentially that of a certain transition complex, which has only a transient existence before breaking down to give the reaction products : AE may then be calculated, in principle, by reference to this hypothetical complex. More accurately, under conditions of constant temperature and pressure, the reaction rate is determined by the free energy of activation

A @ = AH-TAS where AH and AS are enthalpies and entropies of activation. For a limited temperature range

AH

=

AU-RT

where A U is the activation energy, A U =NAE, and the Arrhenius rate equation is then k = Ae-AUIRT = Ae-AEtkT with

It is generally assumed that the entropy change AS is substantially the

R E A C T I V I T Y I N D I C E S I N C O N J U G A T E D MOLECULES

76

same for all positions of substitution, involving a similar modification of the a-bonded framework, and that the relative rates of reactions leading to a given substitution a t different positions are therefore determined purely by the factor exp ( - AE/kT). The activation energy AE is then subdivided into two parts, one (AE,) relating to changes in the n-electron energy alone and the other containing contributions associated with distortion of the a-bonded framework, steric and solvent effects and all other terms not included in AE,. Again, it is customary to assume that energy changes of the second type are substantially similar for different

Reaction co-ordinate

FIG.1. Energy variation in reaction (purely schematic).

positions of attack. With these assumptions, it is possible to discuss the relative reactivities of different positions in terms of r-electron properties alone. For comparative purposes, the energy curve to be discussed (Fig. 1) may then be regarded as that of E , against a reaction coordinate -such as the distance of approach of a reagent (charged or otherwise) along some chosen reaction path towards a given position. It must be emphasized that the form of the complete energy curve is largely hypothetical in so far as reliable calculations have not been performed expect on the simplest (and most atypical) reactions, such as H+Ha +Hz+H

In particular, there is no convincing evidence for a discrimination among active positions according to values of AE, alone, and indeed the barrier itself may arise very largely from the other terms in AE (including not only n-electron effects but also, for example, the energy required to

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H . H . GREENWOOD A N D R . MCWEENY

dissociate an attacking ion from its solvation complex). Authors frequently fail to indicate the nature of the terms included in their hypothetical energy curves; and it is by no means self-evident that these should be approximately constant for different positions of attack. I n this somewhat unsatisfactory situation, the discussion of E, alone is clearly a temporary expedient, without which little progress could be made. This limitation is accepted throughout the present review except in later Sections where the physical interpretation of the reaction mechanism is discussed and where future prospects are indicated. Two main methods of approach are used in discussing the variation of E,. These have been associated with different parts of the reaction path; the isolated molecule method is usually assumed to refer to the initial stages of the reaction, and the localization method is generally associated with a transition state in the region of the maximum of the energy curve. Each method has its own reactivity indices; these are defined in detail in later Sections, but at this point it is useful to list them, along with certain additional indices relating to models introduced more recently, and to indicate their applicability. Method Isolated molecule

Property (at atom r)

Index

charge self-polarizability free valence

qr Vr, r

p, ~

Localization method

L,+ L; Lr

Recent methods

fr

frontier charge superdelocalizability Z value

zr

} heterolytic homolytic

~~

localization energy

$r

Reaction

electrophilic nucleophilic free radical

,t

}

heterolytic and homolytic

B. Huckel Theory The indices are all defined in terms of the Huckel molecular orbital method. This has been described on many occasions, and need not be discussed in detail here, but a brief statement of the basic equations is a necessary foundation for later sections. The method utilizes a “oneelectron ” model in which each rr electron moves in a effective field due partly to the o-bonded framework and partly to its averaged interaction with the other rr electrons. This corresponds conceptually to the HartreeFock approach (Section IX) ; but at this level no attempt is made to define more precisely the one-electron Hamiltonian F, which contains the effective field. Instead, each rr-type molecular orbital (MO) is approxi-

REACTIVITY INDICES I N CONJUQATED MOLECULES

77

mated as a linear combination of (2p) atomic orbitals (LCAO approximation), one on each of the n conjugated centres,

and best approximations to the desired MO’s are then obtained by solving the secular equations

hc

=

ESC (matrix form)

78

i.e.

C h,c,

s=1

78

= E

z S,c,

(2)

(r = 1,2 ,.... n)

s=1

Here S is the overlap matrix with elements xrs =

J 4F48dT

(3)

and h has for its diagonal elements (hrr)the “coulomb integrals ” denoted by (4) E Y = 47“h4rd7

J

and off-diagonal elements (h,) the “resonance integrals ” PYS

=

J 4Fh48dT

(5)

Solutions of ( 2 ) occur for n particular values of E , namely the “orbital energies ” cl, E ~ , .. .E ~ , . .. E,, each yielding its own set of A 0 coefficients (c,$ and a corresponding MO : #j = Z C r j 4 r (6) The quantities (4)and (5) are treated, in Huckel theory, as purely empirical parameters, while S , is usually neglected for r # s. As a further approximation Pr8 is neglected unless atoms r and s are connected; and the values of E ~ pr8 , are assumed to depend only on the nature of atoms r and s (e.g. ar=ct0 if r is a carbon atom, &=/30 if r-s is a C-C bond). Both quantities are negative, larger magnitudes corresponding to more electronegative atoms and to stronger bonds, respectively. With these approximations ( 2 )takes the simpler form

hc

(7)

= EC

and the n simultaneous equations represented by (7) have non-trivial solutions only when

A ( € )=

1912

1913

1921

ff2-E

1923

1931

1932

u3-E

... ... = o

(8)

*.-

which is an nth degree equation whose roots are the n orbital energies.

78

H. H. GREENWOOD A N D R . MCWEENY

The n-electron distribution is described in terms of the q, at each atom (assuming for simplicity real orbitals

(T)

“charge”

t#r)

and the (T)“bond order” p,, for any pair of atoms s and t (Coulson, 1939) Pst =

C njcsjctj

(10)

j

where nj is the number of electrons in thejth MO. The “free valence” F, is also defined (Coulson, 1947) in terms of the bond orders: where N, is the sum of the orders of bonds between atom s and its = d3 being a theoretical maximum value of IV, neighbours, Nmax derived from trimethylenemethane (Streitwieser, 1961). The equations (9)-( 11) represent generalized definitions for any orbital occupancy nj obtained by filling the available MO’s in ascending energy order; but for the usual closed shell ground state nj = 2 for occupied MO’s and 0 otherwise. I n Huckel theory, Enis approximated as a sum of orbital energies, E say, computed just as if the electrons were independent. Coulson and Longuet-Higgins (1947a,b) showed that the total r-electron energy in the ground state is then

and that for variations subject to (8) a8

q8 =

and Pd =

(a,)

a(2)

The charges and bond orders thus indicate the response of the system to infinitesimal changes of its coulomb and resonance integrals, respectively.

C. Nature of the Methods The isolated-molecule method stems from the pioneering work of Wheland and Pauling (1935) on the orientation effects of substituents in benzene derivatives. It assumes that electrophilic and nucleophilic reagents attack preferentially at positions of high and low charge (a,) respectively, thus providing a more precise formulation of earlier

R E A C T I V I T Y I N D I C E S I N C O N J U G A T E D MOLECULES

79

electronic interpretations of heterolytic reactions due to Ingold, Lapworth and Robinson. I n discussing active positions it is convenient to use the following conventions : r = position a t which a reaction is envisaged (a carbon atom) u = position already substituted (or replaced by a hetero-atom) in the molecule considered. For the majority of simple hydrocarbons (i.e. for the “alternants” discussed in Section IV) the charge qris unity for any position of attack, and Wheland and Pauling therefore determined active positions by considering the relative magnitudes of the charges qi produced in the polarized molecules corresponding to various choices of position r, the polarization being caused by the field of the approaching reagent. The effect of the charged reagent was supposed to be a change Sa, in coulomb integral at the position r of attack, and the resultant charge qi may in this case be written (to first order)

a: = q r + n ; , , . ~ % (15) where nr,?is the “self-polarizability ” of atom r. Coulson and Longuet, for ~ the corresponding Higgins (1947b) derived expressions for T ~and changes 66 in rr-electron energy : 66 = qrSar+&,,,Sa2, and the self-polarizability T,., ,thus determines the second-order energy change. Even at this point it is worth noting the gross approximation involved in simulating the effect of the charged reagent by changing one coulomb integral only. I n fact, all a’s and /3’s are changed, many of them by amounts not much smaller than Sa,. A rough estimate (cf. Brown, 1963) gives for the change due to unit positive charge at point X =

- e2 R,

where Rx, is the distance between X and centre r.l Even at a distance of 5 A this corresponds to about 2 e.V. (for E N l),which compares with a carbon-carbon resonance integral (which is the natural energy unit in Huckel calculations) usually assumed to be of the order 1 e.V. The polarization effect must therefore be large, and because of the simple inverse-distance form of 60; must affect even more distant centres to a considerable extent. The importance of polarization will become clear 1 Sometimes a “dielectric constant” E is added in the denominator to allow empirically for solvent effects.

80

H. H. GREENWOOD AND R . MCWEENY

in Section 11, and the basis of the approximations will be re-examined in Section IX. The other isolated molecule index, the free valence F,,is used in discussing homolytic reactions, and determines the effect of reduction of resonance integrals between an atom r under attack and its two neighbours. Denoting the two neighbours by p and q, the change in resonance integral v m =

W‘J( =w

produces a change 6 6 in n-electron energy given by

66

2Nr6P = 2 ( 2 / 3 - F r ) 6 p (16) where N , is the total (generally non-integral) number of n bonds formed by r with its neighbours, and Fv is introduced as in (1 1). The change &3 is generally associated with a postulated change in hybridization from trigonal to tetrahedral due to incipient u bonding with an uncharged reagent in the neighbourhood of atom r ; and for this reason (16) is used in discussing radical reactions. The indices of the localization method will not be defined in detail at this point, but they relate to the considerably greater changes in T electron energy which occur at a more advanced stage of the reaction. I n the corresponding transition complex the reagent is supposed to be a-bonded to the molecule, and the original path of conjugation is therefore broken. The energy changes L,+,L, and L; are calculated assuming that 2, 1 or 0 electrons (respectively) are “localized” a t centre r and consequently withdrawn from the conjugated system. The remaining indices originate from somewhat more elaborate interpretations of the reaction mechanism, and have a considerably Iess clear-cut theoretical significance ;their consideration is deferred until Section VII. =

D. Derivatives and Heterocyclics The indices of the isolated molecule method are frequently used in another context; €or the presence of a substituent group, or a heteroatom, at position u formally resembles that of a charged reagent in so far as it results in a coulomb integral au which differs from that (ao,say) €or the corresponding “parent” hydrocarbon, i.e. a, = a. +&a,. Thus, for any system which differs from a parent hydrocarbon only by changes 6a, in coulomb integrals (the number of 7~ electrons and conjugated centres being the same) the charges can be obtained from those of the parent by perturbation formulae analogous to (15). I n fact, with a change $a,, (17) % % + n.9.u 6% where rrs,u is the “atom-atom polarizability” which gives the change in --f

REACTIVITY INDICES I N CONJUGATED MOLECULES

81

q8per unit increase in au (for the parent) and is a self-polarizability in the case s =u. Expressions for these coefficients were also given by Coulson and Longuet-Higgins (1947b) and a precisely similar analysis applies to , in resonance integrals. The values of q6and F6obtained for changes Sg a derivative or heterocycle in this way may then be used in discussing its active positions; and i t is because of this double use of perturbation methods that the r and u convention for reactive and substituted positions (Section IB) is useful. I n using the isolated molecule indices in this way, it is important to distinguish the two types of substituent, commonly referred to as “inductive ’’ and “mesomeric ”. An inductive substituent is adequately described by making the parameter change au+au + &xu, this change resulting essentially from the formation of a polar 0 bond which modifies the effective electronegativity of atom u without otherwise changing the v system. A mesomeric substituent, on the other hand, is generally regarded as extending the region of conjugation; in aniline, for example, the nitrogen becomes part of the conjugated system and benzene may no longer be regarded as a parent molecule in the sense that the electron distribution may be obtained from that of the parent merely by a parameter change. I n such cases the perturbation equation (17) does not apply directly, and it is necessary to consider the derivative as a new molecule with a new conjugated framework, the mesomeric group either donating or accepting T electrons. It is, however, possible to utilize the polarizabilities if these are defined with respect to a new parent hydrocarbon isoelectronic with, and having the same conjugated path as, the derivative. Thus the appropriate parent hydrocarbon for aniline would be the benzyl anion, with the same pattern of seven centres and the same number of electrons. The electron distribution in the derivative is frequently close to that in the appropriate parent, and any modifications due to the replacement of C by N, for example, may then be inferred from the change ac+aN (exactly as for a purely inductive effect). There is of course no sharp distinction between inductive and mesomeric effects ; both may occur together and the present definition of the two terms simply indicates the theoretical models appropriate to two limiting situations. 11. SOMEAPPLICATIONS OF

THE

INDICES

I n general, reactivity indices are tested by comparing a predicted sequence of active positions, deduced from the magnitudes of a given index, with that observed experimentally. I n some applications calculated localization energies have been substituted directly into relative

’

82

H . H . G R E E N W O O D A N D R. M C W E E N Y

rate equations (Dewar and Sampson, 1956a; Dewar et al., 1966b), but here the test is more severe and satisfactory results often require adjustment of empirical parameters. The aim of this sectionis not to discuss the general correlation of theory and experiment but rather to investigate a few selected molecules in some detail, in order to illustrate the relevance of various indices and to show how easily wrong conclusions may be drawn if they are used with insufficient care or in a wrong context. The emphasis will be initially on the isolated molecule approach and different types of reaction will be considered in turn.

A. Heterolytic Reactions The second-order equation for the 7-electron energy change, due to change in the coulomb integral at position r, S& = q,6ur+~7r,~,6u2,

(18)

forms the basis of the isolated molecule theory of heterolytic reactions. I t is frequently invoked only to illustrate the function of qr and rr,.,, which are then used quite separately in seeking correlations with experimental data. This procedure is certainly not justified by the form of equation (18) but appears to have been carried over from the study of alternant hydrocarbons, in which the leading term is the same for all positions, and discrimination among them depends on r,,,alone. I n other systems, however, the two terms in (18) may represent a h e balance of opposing effects, depending in a critical way upon the actual value of Su, and hence upon the position of the reagent when directing effects begin to operate. The index q, alone would adequately describe the effect of a Su, so small as to cause no appreciable polarization of the molecule ; but an order-of-magnitude estimate of Su, (Section I) shows that the polarizing effect of an ion even two or three bond lengths away from r may outweigh the effect of a heteroatom in the conjugated framework, and the terms in (18)are then of comparable importance. There are also limitations on the magnitude of Surfor which (18)is a useful approximation, depending on the rate of convergence of the infinite expansion. The finite change A& in 7-electron energy due to an arbitrary change in coulomb integral Su,, can however be calculated by direct solution of the secular equations. There is thus a distinction between the upper limit on 6u, set by the equation (18), and that which may be used in computing A& and is determined only by the validity of the model. Current theory has not established to what extent the model is over-simplified though clearly i t could be improved by, for example, changing the coulomb integrals at other atoms: this problem will be taken up in Section IX.

REACTIVITY

INDICES IN CONJUGATED MOLECULES

83

On the basis of this model, however, it is interesting to investigate one or two applications which illustrate the interplay of the two indices in (18) when Su, is fairly large. For this purpose we must consider heterocycles, substituted systems or non-alternants in which considerable charge inequalities occur, and q, becomes a significant index. The heterolytic reactions of such molecules are then almost invariably discussed in terms of the charges q, alone, one reason perhaps being that the polarizabilities T,,,are seldom available except for alternant hydrocarbons (Sandorfy et al., 1950; Sandorfy and Yvon, 1949). Discrepancies arise quite frequently when q8 is compared with experimental data, quinoline providing a good example (Ridd, 1963). The nitrogen atom will be represented by a change So(, = 0*5p, though this choice does not significantly affect the conclusions.

The charges q, at perimeter atoms in the ground state are shown in Fig. 2. Experimental data on nitration (Dewar and Maitlis, 1957) and bromination (Derbyshire and Waters, 1950) indicates that electrophilic substitution occurs exclusively, and almost equally, at positions 5 and 8, whereas Fig. 2 indicates 3 > 8 > 6 as the sequence of active positions. There is therefore a serious discrepancy in the predictions. Since this situation is by no means uncommon in heterocyclicsand other substituted systems, Ridd (1963)justifiably concludes that the charge q, is overrated as a reactivity index, and that little evidence exists to suggest that it determines orientation properties. However, the correlation is not so much with q, but with the implied finite change A 8 defined earlier, and the growing importance of the second (and higher) terms in (18) means that it is in the context of the polarized molecule that the role of q, as a reactivity index must be considered. To illustrate the situation we present in Figs. 3a and 3b the “exact” charges q: in the polarized molecules (cf. equation (15))when Scr, due to the attacking ion takes the values 0.5 Po and 1-5 Po respectively, for the atom positions r=3,5,6 and 8 (Greenwood and McWeeny, 1965). Each molecular diagram shows the results of four calculations r = 3,5,6,8) and should not be confused with the charge distribution of a single calculation such as that shown in Fig. 2. The results show

84

H . H . GREENWOOD A N D R . MCWEENY

clearly that in the polarized molecules the charge builds up more rapidly at the site of attack when this coincides with the 5 or 8 positions than when it coincides with position 3. I n the same way the energy changes Ad may be calculated.

1,522

1.205 (a).

1.544

6ar = 0.6po

(b). 6ar = 1.5P0

FIG.3. Charges p i in the polarized molecule

The changes Ad are negative, correspondingto increased stability, and are given in units of Po; each diagram corresponds to four calculations ( 6 ~ r=3,5,6,8), ~ ; and shows how, as 6ar the polarization parameter increases, positions 8 and 5 overtake 3 as the “active” positions. The predictions and results show that discrepancies between’theoretical

(a).6ar = 0.5 j30

(b). 6ar = 1.5j30 FIG.4. Energy changes dB

experimental results begin to disappear when the change in field at the position r of attack, produced by an approaching reagent, is similar in magnitude to the change 6a, at the position u occupied by a heteroatom, that is when 6 a , S~cr,. This result bears out our earlier conjecture that polarization effects may outweigh those due to a heteroatom, in this case nitrogen, and that the charges “seen” by an ion near the molecule might in fact correlate with the observed active positions. To summarize, the results can be understood qualitatively as a reduction in the influence of the nitrogen atom as the polarizing effect of an approaching positive charge begins to dominate, or alternatively as the emergence of the polarization terms in (18) as the major factor determining orientation, this exerting its greatest effect, in the case of quinoline, a t the 5 and 8 positions. It is now possible to interpret more clearly the roles of the charges qs and self-polarizabilities rr, of the unperturbed heterocycle in equation (18). Although the values of n,,r are not often available, it is permissible for qualitative discussion to invoke those of the parent hydrocarbon,

REACTIVITY

INDICES

IN CONJUGATED MOLECULES

85

and, since the absolute value of T,,,in naphthalene is greater at a than at /Ipositions, it follows that (IT5.51

3

sII >

ITS,

I T S , 31

so that when 6a, is sufficiently large the second-order terms in (18) can offset the first order terms, for which q3

>

,

k S q5>

It is interesting to note that at the inactive position 4, a large polarizability term does not apparently compensate for the low charge, q 4 = 0.932, which arises from deactivation by nitrogen in the same ring (Fig. 2). Clearly, both q, and T,,,must be taken into account. Non-alternant hydrocarbons possess uneven charge distributions in the ground state, even when no substituents are present, and again comparisons of qr and T,,,separately with experimental data may produce

0 . k

0.959

0,241

FIG.5

2.341

(b)

discrepancies. I n azulene the active positions of electrophilic attack are correctly indicated by the charge distribution. The localization theory (SectionI)is also successful in this case. On the other hand, fluoranthene, which has been discussedin some detail (Streitwieser, 1961 ;Brown, 1964 ; Fukui, 1964) shows several discrepancies. Electrophilic substitution occurs at the positions 3 and 8 (Streitwieser, 1961) with small yields at the 1 and 7 positions (Streitwieser and Fahey, 1962). The charges and self-polarizabilities are shown attached to the right and left perimeter atoms respectively in Fig. 5a. The performance of two other indices is indicated in Fig. 5b : localization energies for electrophilic attack are shown on the right perimeter atoms, and the frontier electron charges of Fukui on the left. I n addition to these, free valence (P8)and 2, values have been studied (Brown, 1964). The localization energy gives easily the best correlation with observed reaction rates, the only anomaly being the high activity predicted for the 7 position; none of the other

86

H . H . GREENWOOD A N D R . MCWEENY

indices appear to correlate with experiment. Since, in quinoline the effect of polarization compensated for the effect of the charges to give substantial agreement with experimental data, it seemed at least possible that the large self-polarizability 7r3, = 0.462 (Fig. 5a) might similarly compensate for the low charge q3 = 0.959, and the low value n2, = 0-400 nullify the higher charge q2 = 1.005, and so on. Calculations were therefore performed (Greenwood and McWeeny, 1965) to determine A 8 and the charges q: a t the position r of attack in the polarized molecule. To avoid ambiguities, a fairly large value Sa,=2*0 Po was taken, though again this is not unrealistic as a representation of the effect of an ion a few bond lengths away. Figure 6 gives the changes A 8 in n-electron

8

I.fi3li 1.648

1.363

1,366

1.335

1.632 1.623 1.655

n:

1.358 1.354

A8

FIG.6. Charges and energy changes due to polarization (6ar = 2.0 P o )

energy, in units of Po, against the perimeter atoms on the right, and charges qi in the polarized molecule against those on the left. Again, the results of all five calculations (8ar= 2.0 Po; r = 1,2,3,7,8)are shown in the same diagram. Thus, the same change Sa, at each atom produces the largest charge qh= 1.655 at position 3, and the smallest, qL= 1-623 at position 2 in the corresponding polarized molecules. Consequently, the charge distribution in the ground state (Fig. 5a) gives a poor reflection of the availability of electrons produced by the polarizing effect of the ion, as represented by the change Sa,. I n comparing the changes A& in 7r-electron energy with experimental data, a single anomaly remains for atom 7, where a large energy of stabilization A& = 1.366 is obtained. A similar anomaly appears in the localization energy L t (Fig. 5b) for atom 7, which again suggests a highly active position, contrary to experiment. It must of course be remembered that the theoretical model is still oversimplified, using the same a and P values for the five-memberedring, and that the sequence of active positions might still easily be modified by further refinement. To summarize, there is strong evidence that when qr and nr,?are considered together, in their complementary role in (1 8) for systems in which

REACTIVITY

INDICES IN CONJUGATED

MOLECULES

87

the charge distribution is uneven in the ground state, the discrepancies that may be obtained by comparing the indices separately with experimental data largely disappear. It is then possible to obtain a better performance from the indices of the isolated approximation than has generally been supposed. It is also clear (e.g. from the inactive 4 position in quinoline) that there , ~than for using qr; is in general no more justification for using 7 ~ by~ itself it is only for alternant hydrocarbons that the self-polarizability is the discriminating factor, and in all other cases rr,r should be considered only to the extent that it modifies conclusions based on the leading term qr8ur in (18). Moreover, the relative importance of the two terms depends on the value of 8ar, and this in turn upon the position of the reagent.

B. Homolytic Reactions The free valence P,was proposed by Coulson (1947,1948) as a suitable index for predicting, in the isolated molecule method, the free radical reactions of conjugated molecules. The main physical justification for the index is that it represents a measure of the available r bonding at an atom, which may be significant in reactions that are not primarily ionic in character. The free valence has received only moderate acceptance as an index for radical reactions, perhaps because its physical basis is comparatively obscure. Yet in performance i t is seldom inferior to other indices; it is in fact related mathematically both to the corresponding localizationenergy (SectionVI)and to the self-polarizability (SectionIX). Kooyman and Fahrenhorst (1953) showed that the relative reactivities towards trichloromethyl radicals correlate with the highest free valence in a variety of aromatic hydrocarbons. Since there is an empirical linear relationship between localization energiesand free valences (Streitwieser, 1961), i t follows that the correlations found by Szwarc (1955, 1957; Szwarc and Binks, 1959) between relative reactivities of conjugated molecules towards methyl radicals and localization energies (Coulson, 1955), would also hold for free valences. It is however in the reactions of substituted aromatic molecules that patterns emerge which clearly indicate the relevance of the free valence in radical reactions. The benzene derivatives provide a good example. Orientation effects in benzene derivatives operate in two ways. If the substituent is inductive there are large f i s t order charge displacements at the ortho and para positions, and these can be estimated approximately using the atom polarizabilities ns,u(which is very small at the meta position). The changes of bond order, however, and consequently of free valence, vanish in first order and hence depend on 8ar2. The charge qsat position s therefore increases or decreases from the value unity in the

88

H . H . GREENWOOD A N D R . MCWEENY

parent hydrocarbon according to the nature of the substituent ; but the change in free valence F , is always of the same sign, irrespective of electronegativity of the substituent. Similar results hold for mesomeric substituents; large changes in q, are confined to the ortho and para positions, their signs depending on whether the substituent is electron-attracting or electron-donating, while the changes in F, are independent of the nature of the substituent and arise purely from the introduction of a non-zero 8 connecting it with the ring. These properties are in accord with the experimental fact that radical reactions occur at the same atom positions, regardless of the nature of the substituent group (Wheland, 1942). More recent experimental evidence on benzene derivatives investigated by Hey et al. (Chang Shih et al., 1958; Hey et al., 1960; Hambling et al., 1960) supports these findings, even when the reagent contains strongly polar bonds which may have some small effect on the a’s; for, although these effects change the relative rates somewhat, they do not alter the occurrence of substitution in ortho-para positions. Another result of a similar character was obtained by Fahrenhorst and Kooyman (1955)on the relative reactivities of 9-substituted anthracenes ; they showed that the activity towards radical attack at the 10-positionis enhanced by 9-substitution, irrespective of the polarity of the substituent group (Greenwood, 1955b).The free valence therefore shows a correspondence with radical reactivity in situations where discrimination amongst reactivity indices is possible.

111. PROPERTIES OF THE SECULAR EQUATIONS In this section we discuss, in general terms, certain properties of the secular equations (8) which provide insight into the various methods employed in defining reactivity indices. The energy levels arise from solution of the equation

I a1-E

B12

813

* * -

I (8)

Different methods employ the same equation, but make different choices of the way in which one or two of the coulomb or resonance integrals vary as a particular region of the molecule comes under attack, these parameters being chosen to simulate the changes likely to be produced by the approaching reagent. It is a relatively straightforward matter, as illustrated in sub-section C, to trace the variation of energy levels when these few integral parameters change, and this technique serves to establish

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89

relationships between the various theoretical methods and the context in which they are defined.

A. Partial Derivatives and Polarizability Coeficients Expansion of (8) yields a polynomial, the characteristic or secular polynomial, whose roots are determined by the values of the parameters a,,, pm. The ground state energy (12) is likewise a function of the (a,/?) parameter values, as are all quantities such as A 0 coefficientsinthe MO’s, charges qs, bond orders psi, etc. It is possible, therefore, to specify the kth partial derivative with respect to any au or ?,/ at an arbitrary point defined by a set of values (a,/?)in the parameter space, and to make expansions such as

where A = ej, csj, qs, pst,F,, and so on. The first and second derivatives are the polarizability coefficients defined by Coulson and LonguetHiggins (1947a,b); for example,

are the atom-atom and atom-bond polarizabilities respectively. The coefficients are, therefore, slopes, curvatures and, in general, partial derivatives in the a,/? space, and individual terms of the expansions (19) and (20)represent contributions to the finite change AA. Now AA may be a mathematical representation of a physical quantity, but considerable care must be exercised in associating calculated values of the coefficients themselves with experimental data. It must be remembered that alternative forms of expansion about the arbitrary point (a,/?)can be found, with successive terms different from those of (19) and (20) and that the polarizability coefficients are unique only in the sense of being defined in terms of the power series. Some reference must now be made to the properties of the basic set of equations for the special case of alternant hydrocarbons. The secular polynomial A (e) acquires important analytical properties when all a’s and all /?’stake common values a. and Po, and when, in addition, the molecule is “ alternant ” in the sense of the Coulson-Rushbrooke (1940) theorem. The following results are well known : (i) Bonding and antibonding molecular orbitals are “paired”, with energy levels lying symmetrically below and above a. respectively. 4

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I€. H . G R E E N W O O D A N D R . M C W E E N Y

(ii) A non-bonding orbital with energy a. is obtained for systems with an odd number of conjugated atoms. (iii) When the MO’s are filled in ascending energy order, the rr-electron charge density qs at each conjugated atom of the neutral molecule is unity. Simplification in the discussion of spectroscopic states (Dewar and Longuet-Higgins, 1954; McLachlan, 1959) and many developments of analytical expressions (Coulson and Longuet-Higgins, 1947a,b; Fukui et al., 1957a; Greenwood, 1952b) for quantities describing the ground state, originate in these properties. Their relation to the reactivity problem, and to analytical properties of the polarizability coefficients appearing in (19) and (20) are described in some detail in Sections IV and VI.

B. Energy Level Diagrams and Parameter Variations Energy level diagrams have seldom been used to show how the disposition of levels changes with variations of the a and /3 parameters describing the system, and how such processes can be related to spectroscopic changes and postulated reaction mechanisms. Yet, they can often give a qualitative understanding of the effects of molecular modifications with a minimum of effort, and for this reason at least deserve mention. The diagrams are best understood in terms of the apparent “repulsion” between the energy levels of combining systems, which can easily be related to a perturbation treatment of the secular equations. For example, two carbon atom rr electron levels (1) and (2) with energies a. would interact to remove the degeneracy

-I-

-

a0 -

_____--_-- (1)

(2)

- --- - - --(3)

FIQ.7. Splitting of levela by interaction.

and produce two separated rr electron levels (3) as in the ethylene molecule. Working on this basis, the distribution of levels in many aromatic hydrocarbons can be constructed systematically, by reference to a few simple molecules whose levels are known. I n the case of benzene and other molecules with high symmetry, the process is sometimes obscured by additional degeneracies, but the general idea of repulsion amongst levels persists. Let us consider, for example, how the levels of styrene (c) can be synthesized from benzene (b) and ethylene (a), and

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91

those of stilbene (d) from styrene and benzene; and, finally, how the “twisting ” of stilbene about the central bond produces the levels of two benzyl systems (e).

(a)

---

-

__--

--

(b)

(d 1

(C)

FIG.8. Effect of ‘‘fusion”on energy levels: a,b-+c;b,c-*d; d-,e

(el on “twisting”.

For this purpose let the levels be labelled from the lowest in each system upwards, and let a plus sign indicate “interaction” leading to repulsion so that, for example, a1 (bz + b3) + cz, c3, c4 implies that the threefold degeneracy consisting of the level a, (cl= 1.0g) in ethylene (a)and the twofold degeneracy be, b3 ( c Z = c3 = 1.Og) in benzene (b) interact to produce the levels cz, c3, c4 ( c Z = 1.414 /I,c3 = 1-0 fl and c4= 0.662 g) of styrene (c). Note also that the “repulsion” produces a lowering from bl to cl. Next, the imaginary “fusion” of benzene and styrene to form stilbene is characterized by

+

c4

-+ a

7

d4, d6,

bZ+b3+C3

CZ

df3

+ d3

dl, dz

bl+Cl -+

On the other hand, the relationship between the levels of stilbene and the two benzyl systems (e) follows a different pattern,

dl, dz

% + e l +-

ez+ez -+d3,d4

4,dtl

e3+e3 e4+e4

--f

4,d 8

92

H . H . GREENWOOD A N D R . MCWEENY

every degenerate pair of Ievels of the two benzyls corresponding to two distinct levels of stilbene. It is clear that the construction of such diagrams requires no actual calculation, but that they may be of considerable value in discussing the effects of structural changes in a molecule. They are useful, for example, in the interpretation of the U.V. spectra of related molecules; and there are many instances, in which effects are normally discussed in terms of numerical calculations, where the diagrams can provide an immediate qualitative explanation. We turn now to the use of energy level diagrams in discussing the effect of parameter variations of the kind envisaged in defining reactivity indices.

Case (i): a,.variation The energy levels of an alternant hydrocarbon (AH),equal in number to the number of conjugated carbon atoms, are arranged symmetrically about a. (Fig. 9)

I + da,

FIG.9. Change of energy levels AH of alternant hydrocarbon with ar;limiting levels coincide with the levels RM of the residual molecule.

A “residual molecule” (RM) can be defined for every atom T of an even alternant hydrocarbon as the odd alternant hydrocarbon obtained by omitting atom r from the original system. The secular determinant for the residual molecule with atom r removed is obtained from A ( € ) in

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93

equation (8) by crossing out the rth row and column; this determinant so that will be denoted by & ( E ) , 4 , T ( 4

= 0

(22)

gives the energy levels of the residual molecule. It can be proved that for all possible residual molecules, corresponding to all atoms r of the system, the energy levels “separate” those of the parent hydrocarbon (Fig. 9), their actual positions depending upon which atom r is selected. The central level lies at the zero of energy a0 and the corresponding MO is usually termed the non-bonding orbital (NBMO). We select a particular atom r , of an even alternant hydrocarbon, and change the coulomb integral by an amount &a, so that the new value becomes a, = ao+Sa,

A change in which Sa, is negative is characterized by the foIlowing properties (Greenwood, 1955a). (1) All energy levels are lowered. The lowering of the deepest bonding level is limited only by the magnitude of 6a,. The remaining levels are lowered towards those of the residual molecule as limiting values (Fig. 9). (2) The molecular orbitals are changed so that correspondingto the deepest level q,becomes increasingly localised a t the atom r , and all others tend towards the MO’s of the residual molecule. This condition is achieved by the migration of a node of each orbital until it cuts the bonds which connect atom r with the residual molecule. Alternatively, 6a, may become positive, in which case the pattern of energy levels is the mirror image in the zero of energy (ao)of that obtained for the case when Sa, is negative (Fig. 9). It is not difficult to show that, in this case, the levels of the residual molecule are now the limiting values of the lowest levels, and the uppermost antibonding level is now limited only by the magnitude of &a,. I n the same way, the orbital corresponding to the uppermost level tends to become localized in the region r , all other orbitals changing towards those of the residual molecule.

Case ( i i ): pr8variation A second important type of change involves variation of a selected resonance integral : A 8

= Bo+SPm

where &Pr8represents an arbitrary finite change. Remembering that ,!I is a negative quantity, Sp,, is first taken positive so that a limiting choice sp= - p will make pr8= 0 ; this corresponds formally to a condition of no interaction between atoms r and s. This case is easy to understand and

94

H. H . GREENWOOD AND R . MCWEENY

has in fact already been described for the stilbene molecule, in which putting Spx = -Po for the X bond of Fig. (10) changes the energy levels of stilbene to those of benzene and styrene, while putting S/3, = -Po for the Y bond changes the levels to degenerate pair of benzyl levels. No further comments are necessary.

FIG.10

Case (iii): &,, /Irp variation The next case is that in which the resonance integrals between a perimeter atom r and its two neighbours, r, and q, are reduced equally to final values /Irp =prU= 0.

AH

RM

FIQ.11. Change of energy levels AH of alternant hydrocarbons as p( =pIp=&,)+O.

I n this case (Greenwood, 1957) the energy levels change towards those of the residual molecule, but by a general " contraction " of levels towards the zero of energy a. as shown in Fig. (1 1). The innermost pair produces, in the limit, a degenerate pair with energy ao. The molecular orbitals also change in general towards those of the residual molecule, with the exception of those of the innermost pair, which retain a uniform distribution over the complete parent hydrocarbon. I n the limit Sp = -Po, when the

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95

innermost pair becomes degenerate, an alternative solution may be obtained by taking orthogonal combinations of the degenerate orbitals. I n this way it is possible to transform these two orbitals into the n--electron atomic orbital localized a t atom r , and the non-bonding orbital of the residual molecule (i.e. to the solutions physically appropriate to the “separated” system).

Case (iv): Pr8large and negative Finally, we consider the case in which SP,, is negative, and makes /3,8 large and negative. The lowest and uppermost levels then break away from below and above the others respectively, the corresponding MO’s becoming formally equivalent to bonding and antibonding orbitals associated with the bond r-s. The remaining levels tend towards those of a molecule with centres T and s missing, which is thus a residual molecule The “bond ” r-s obtained in the defined with respect to the bond r-s. limiting configuration is not to be confused with an ethylenic double bond, since, although the M O ’ s are formally similar in the limit as PIS becomes more negative, the bond described by this artificial /3 value would be much stronger. By the same token, the process should be distinguished from that defining the bond localization energy (Brown, 1949), in which localization is introduced by putting Pa =/38u= 0, where t and u are neighbours of r and s respectively. The present case is, in fact, similar to that discussed by Muller et al. (1954) in considering the structure of a transition state complex with hyperconjugation, and will be discussed in some detail in Section VIII.

IV. THEISOLATED MOLECULEMETHOD This section deals with analytical properties of the Huckel molecular orbital theory and the associated isolated molecule method of predicting the active positions in a conjugated molecule. We shall deal with polarizability coefficients defined as certain partial derivatives with respect to the coulomb and resonance integrals described in Section 111. The important derivatives are those relating to the total nelectron energy 8,and to the charges q8,free valencesB’*,and bond orders pst, which derive from the ground state electron density. To limit the amount of information to be presented, attention will be focused on derivatives with respect to the 12sonly, ignoring for the most part those which relate to the p’s. The treatment of effects arising from /3 variation proceeds along completely similar lines. We must, at the outset, distinguish between the two kinds of change in coulomb integral that are applied in practice.

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H . H . GREENWOOD A N D R . MCWEENY

( 1 ) The change Scr, may represent the effect of a substituent or heteroatom at the uth position. I n this case the T electron energy levels, charges q,, free valences F, and bond orders patcan be obtained by direct solution of the secular equations (8) using

a, = ao+Sa,

(23)

Alternatively, perturbation formulae may be employed to derive the same results approximately, starting from the parent alternant hydrocarbons and using the polarizability coefficients. Thus, for example, =

TS,U%L

(24)

gives the approximate change in charge density at the sth atom in passing from the parent hydrocarbon to the derivative, where

is the atom-atom polarizability associated with atoms s and u in the hydrocarbon. Corresponding atom-bond polarizabilities =,t,u

= __

8%

and free valence polarizabilities

are both zero, and second derivatives are needed to obtain Sp,, and SF,. From (24) the charge q, in the derivative is q 8

=

1+T8,UScrU

(28)

since qs= 1 in the parent hydrocarbon. These approximate values will not, in general, coincide with the “exact” values obtained by direct solution of the secular equations, since SLY, is seldom small in practice. Usually changes in coulomb integral are expressed in units of Po so that

k/3o (29) where k is positive or negative for substituent groups or atoms that are respectively more or less electronegative than a conjugated carbon atom. Values for nitrogen substitution, for example, have been selected from the range k = 0.2 to 1.0, and for oxygen substitution from the range k = 1.0 to 2.0 (Streitwieser, 1961). (2) The change Sa, at the position r of attack may be employed in discussing the ionic reactions of conjugated molecules, through the equation Sau =

6 8 = q,Sar as described in earlier Sections. I

+

4Tr,,8a:

(18)

REACTIVITY INDICES I N CONJUGATED MOLECULES

97

The charges q8 of equation (28) may be used as reactivity indices, either intuitively as relative measures of coulombic attraction or electron availability, or through equation (18), bearing in mind that in this case 6 6 approximates the “exact” change A&, as discussed in Section 11. Since the leading term in (28) is unity, predictions of the active positions in derivatives can be made in terms of computed values of the r8,u coefficients for the parent hydrocarbons. Moreover, changes with the same sign of 6au necessarily yield the same active positions, which, in practice, provides a theoretical explanation of orientation in benzene derivatives. Now the polarizability coefficients for alternant hydrocarbons have interesting analytical properties, like the secular equations themselves (Section 111).These properties arise as special cases from a more general analysis which applies to theJinite changes dq,, q 8 = +’ q 8 (30) obtained by exact solution of the secular problem with au= a,, +actu. The two developments, approximate and exact, will be presented in turn. Fortunately, the results must be closely parallel, and this gives some justification for the qualitative description offered by the polarizability method. A. Analytical Properties of Approximate Methods Expressions for polarizability coefficientswere first developed (Coulson and Longuet-Higgins, 1947a,b)in two forms, on the one hand as contour integrals in which the integrands are functions of the determinant (8)and its minors, and on the other hand by perturbation methods in terms of the energy levels ej and the corresponding molecular orbitals t,hj of the parent molecule. The first method will be consideredin some detail, for although it involves the mathematical device of integration in the complex plane, the procedure is ultimately straightforward for alternant hydrocarbons and will be used later to determine the finite changes. I n contrast, the terms of the perturbation method beyond the second order are too unwieldy for general analysis, though the definitions of some polarizability coefficients will be given in the perturbation form for completeness. We select without proof, from the theory of Coulson and LonguetHiggins (1947a,b), those formulae which relate to quantities used in the description of chemical reactivity, as follows :

4*

98

H . H. G R E E N W O O D A N D R. M C W E E N Y

Integration is along the y axis of the complex plane between - co and + 00 and ( i y ) is the argument in all secular determinants or minors; the same limits of integration apply to all formulae in this section, and will therefore be omitted. Aa,b is the determinant obtained by crossing out the ath row and bth column of A in equation (8) and A' is the derivative of A with respect to the argument (iy). The discussion will now be specialized to parent molecules which are even alternant hydrocarbons. All the analytical properties to be referred to originate from the basic properties of these molecules. Thus, for an even alternant hydrocarbon, with n = 2m conjugated atoms, A ( € ) is a polynomial with even powers of E in which successive non-zero terms alternate in sign, so that

A ( € ) = (a,r"-aa,,En-2+an-4E"-4.. .+a,) (35) The polynomials of the minors A , that arise contain either odd or even powers of E only ;when odd, ( 6 ) can be taken out as a factor multiplying a polynomial with even powers only. The substitution r-.(iy) then gives polynomials in which all terms carry the same sign and are real functions of y multiplied by the factors unity or ( i y ) . I n practice the factors (iy) either cancel between numerator and denominator in the integrals, or yield integrands that are odd functions of y and therefore integrate to zero. Integration is then straightforward, though numerical methods are usually required for the larger molecules which give rise to high-order polynomials (Coulson and Jacobs, 1949). The polarizability coefficients can now be derived by differentiation of the forms (31) to (34), to give first order derivatives

Coulson and Longuet-Higgins made an extensive study of the properties of these expressions and showed, for example, that the coefficients

REACTIVITY I N D I C E S I N CONJUGATED MOLECULES

99

(37) and (38) are zero. The alternative forms obtained by perturbation methods involve the coefficients csj of A 0 q5s in the j t h MO :for example, r8,u

=4

22

j=1 k = m + l

c8jcujc8kcuk Ej EL

-

(39)

The fact that certain coefficients are identically zero for alternants, also exhibit characteristic properties, is clearly of great and that the rssu importance. It means that the properties of all molecules which derive from a given alternant hydrocarbon parent, as estimated using the polarizabilities, will have many features in common. The most important general properties of the atom-atom polarizabilities are (i)that in passing along the perimeter of the molecule from the position of substitution, successive r 8 ,alternate , in sign (Coulson and Daudel(l955); (ii)that if s belongs to the same (starred) set as u, then ther,,values aresmall, as for meta positions; whereas if s and u belong to opposite sets the rs,u are large, as for ortho and para positions, though diminishing with distance from the site u. These features reflect the orienting effects of substituents in heterolytic reactions, as embodied in the " law of alternating polarity" (Coulson and Longuet-Higgins, 1947a,b). A further conclusion, useful in the case of free radical reactions arises from the fact that F , , in equation (38) is analytically zero, and that consequently, to second order,

This shows that the change 6F, is independent of the sign of the electronegativity change produced by the substituent group, a result in accord with the experimental findings mentioned in Section IIB, and lends support to the notion that F , is a useful index for free radical attack. The general features of the theory, expressed in analytical properties which are largely parameter-independent, are thus in accordance with observation, and there seems to be a good case for further investigation of the q and F indices.

B. Analytical Properties of Exact Methods As noted in Section 11, truncated series may give misleading results, depending upon the magnitude of the parameter, 6u, say, used in the expansion ; and certainly the values currently used in the representation

100

H. H. GREENWOOD A N D R . MCWEENY

of substituents (Streitwieser, 1961) cast some doubts on the numerical values and predicted properties derived from polarizability coefficients. It is possible, however, to find analytical properties of theJinite changes due to an arbitrary 6a,. For this reason, and because it applies equally not only to the effect of substituents but also to the large changes 6a, at an attacked atomand hence to the reactivity indices used in the isolated molecule method, the theory of finite changes will be briefly outlined. A finite change in any quantity A can be written as the Taylor series

where A r q , , F,, p,, and, as usual, we consider the one parameter, 6a,. Then, starting from the integral formulae (31) to (34), successive differentiations under the integral sign give for the general derivative of q, (Greenwood, 1952b)

with similar expressions for the derivatives of F, and p,,. Consequently from (42).

m

AF,

=

2

k=l

(-

7r

1

(iy)

(SCL,)~ ( T )(7dy)

A,,

A,,

k-l

(45)

The properties of the minors of the secular determinant of an alternant hydrocarbon may again be used to show that the integrals for which the index k is even in (44)and odd in (45) and (46)are zero. It follows that the finite change Aq, is an odd function, of 6au, while AF, and Ap,, are even. Any inequalities between values of any index for two different positions (u),as defined in equations (31) to (34) which arise as first terms of the corresponding infinite series in (44) to (46)) persist term-by-term in the expression for the exact finite changes (Baba, 1957). I n consequence, the broad agreement with experiment found earlier in the description of ionic and radical reactions by the approximate method carries over to the exact form.

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101

Since alternate terms of the expansions (44) to (46) are zero, it follows that the integrands of successive terms differ only by the factor ( A u , U / A ) 2 . This shows how the expansion can be summed to give expressions in closed form, and forms the basis of the formulae given by Fukui et al. (1957a). I n fact Fukui prefers to introduce

which is real, since AU.Ucan be factored into the product of (iy) and a polynomial containing even powers of ( i y ) only. With this notation, equations (44) to (46) take the form (47)

(48) (49) to which may be added the change in energy A&, given by Fukui et al. (1957a)

A& = Su, - In (1 + (SCL,)~y 2 G:] d y

(50)

Corresponding formulae can be deduced for the finite changes obtained by variation of an arbitrary resonance integral Bw (Fukui et al., 1957a). The formulae (47) to (50) provide a means for calculating the exact changes Aq, etc. for any prescribed values of &au,changes which should form the basis of comparisons with experimental data. The correlation between exact and approximate results, already referred to, follows directly from these formulae and was originally emphasized by Fukui et al. (1957a): for a given position u of substitution the term ( A , . / A ) determines the relative magnitudes of changes in q, at different atoms s of a conjugated system in the expressions for both the approximate (36) and exact finite (47) changes, thus ensuring that the same inequalities hold in both cases. Similar properties hold for changes in free valences F,, and bond orders pst. The same formulae may be applied, with the replacement u+r to determine the finite change in rr electron energy due to polarization by an approaching charged reagent. As described earlier, the change Su, is then assumed to be due to the presence of the reagent in the neighbourhood of the atom position r under attack.

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H . H . GREENWOOD A N D R . MCWEENY

V. THELOCALIZATION METHOD The context in which the localization method is defined has already been explained in the introductory Section I, but although the method itself is well known the physical basis of its premises remains in many ways obscure. I n particular, the concept of “localization of n electrons’’ requires clarification, and the validity of theoretical relationships between reactivity indices of the isolated molecule and localization methods needs further discussion. I n this Section we recall the original statement of the method in some detail, and then review some subsequent developments; the relationship between the two methods is discussed in Section VI. The localization method was originally described by Wheland (1942) with reference to resonance theory, the activated complex being considered as a resonance hybrid consisting of a variable mixture of structures including (I)and (11).

Type (I)describes the substrate with the ionic reagent R close to the carbon atom under attack, but not joined to it by a covalent bond. The structure was assumed to correspond to a “polarized ground state” as considered in the earlier work of Wheland and Pauling (1935), and therefore to the situation envisaged in the isolated molecule approximation. If structure (I) largely determines the form of the activated complex, then the charge distribution and polarizability indices of the substrate would determine the ease of reaction and the preferred positions of attack as in the isolated molecule approach. I n structure (11),on the other hand, the reagent R is joined to the substrate by a covalent bond; this defines a so-called “residual molecule” (RM) as the conjugated system obtained by excluding the position of attack (cf. Section 111).It is supposed that electrophilic attack will occur at positions where a pair of electrons can be easily localized, and nucleophilic a t positions where a (r vacancy” is easily formed. A label z is used in structure (11)to indicate the net charge ( + or - ) which appears within the residual molecule as a result of the corresponding charge displacements. To obtain a practical method, Wheland considered the extreme situation in which structure (11)would outweigh all others in describing the activated complex, and

R E A C T I V I T Y I N D I C E S IN C O N J U G A T E D M O L E C U L E S

103 assumed that the carbon atom under attack would a t this stage be essentially tetrahedral. He then defined the localization energy as the difference in energy of the T electrons in the unperturbed ground state, and the Same number of electrons in structure (11). Thus, for example, Wheland gave for the energy of the six T electrons in the ground state of benzene 6ao + 5.8667 /I and for the energy of the six electrons in structure (11), 6a0+ 4.0174 /I in the three cases corresponding to the localization of 2 , O or 1electrons (cf. Fig. 13, which refers to the general case). The localization energy in each case was then d W = - 1.8493 /I. A fundamental difficulty in Wheland’s approach is that the number of T electrons in I1 may be essentially different from the number in I, for any electrons localized leave the T system to engage in u bonding. Wheland’s procedure therefore amounts to formally assigning an energy a. to each localized electron, corresponding to removal of its contribution to T bonding, without enquiring too closely into the physical nature of the localization; and it is already clear (Fig. 13) that for an alternant molecule the localization energies so defined will be the same for electrophilic or radical attack. Of course, the localized electrons do not really occupy a 2p atomic orbital with energy ao, but any changes arise essentially from u bonding effects and may plausibly be assumed the same for different positions of attack. With this assumption, the localization energy as estimated by Wheland (1942) should properly reflect the differences of activation energies between different positions for any one type of reaction. An alternative prescription for calculating the localization energy has also been widely used, the energy of the 0 , l or 2 localized electrons simply being omitted; and again failure to allocate a realistic energy to the excluded electrons is irrelevant so long as only diflerences of activation energy are being considered. The crux of the argument, in each case, is simply that the whole of the a-bonding rearrangement energy is a “local ” quantity not depending on position of the attacked atom in the framework. At a slightly deeper level, the difficulty of this approach lies in its acceptance of a transition complex in which the original classification into u and 7r electrons has been broken; consequently pure T electron theory is inadequate for the prediction of energy changes, and a complete analysis must await the inclusion of the u bond modifications at the point of attack. Preliminary attempts to include such effects have invoked hyperconjugation (Muller et al., 1954; Fukui et al., 1954a) and other factors (Dewar et al., 1956), but little progress has yet been made towards a more detailed theoretical interpretation based on more complete calculations.

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H . H . GREENWOOD A N D R . MCWEENY

Here, therefore, we return to the localization theory in its simple form and investigate the utility of localization energies as reactivity indices. Energy level diagrams have frequently been used to indicate occupancy of the orbitals in type I1 structures as follows :

I

-

I

I

I

I

I I I

-

-

i

& RM

(E)

FIG.13. Occupation of energy levels in Wheland structures I1 for (E) electrophilic, (N) nucleophilic, and (R) radical reactions.

I n these diagrams the energy level schemes denoted by RM refer to the residual molecule of an even alternant hydrocarbon, while urdenotes the level associated with an electron localized at position r of attack, this quantity taking thc value uoin Wheland’s formulation. These features of the energy level scheme for residual molecules indicate why, for an even alternant hydrocarbon, there is in general no distinction between Wheland’s localization energies for electrophilic ( E ) , nucleophilic ( N ) and attack, the localized electron(s)and the NBMO of the residual radical (R) molecule having the same energy. Since, however, the assumption u,= uo amounts to little more than an arbitrary fixing of the zero of activation energy, different in the different types of attack, no absolute significance can be attached to the apparent equality of E , N and R localization energies. Only differences for the different positions of attack in areaction of given type are likely to be significant; and the use of localization energies in trying to estimate a given barrier height must be doomed to failure in view of the many energy terms which have been omitted on the grounds that they are likely to be about the same for different positions. We therefore concentrate on the possibility of estimating activation

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105

energy differences for substitution a t different positions in, say, heterocyclics or hydrocarbon derivatives, and to the effects of the heteroatoms or existing substituents in determining their differences. The description is parallel to that for other indices (SectionIV), the alternative procedures involving (A) perturbation theory using a parent hydrocarbon as a starting point and (B) exact solution of the secular problem for the derivative or heterocyclic and for the residual molecules for various positions of attack. The broader questions of the physical interpretation of localization, of its connection with the formal processes introduced in Section 111,and of the mathematical relationship between localization energies and other indices will be taken up in Sections V I and VIII.

A. Analytical Properties of Approximate Methods I n this subsection we consider analytical properties of first- and second-order approximations to the change in localization energies produced by a change Sa, in coulomb integral at a position u of substitution. This change indicates the influence of substituent groups or atoms by determining differences between localization energies in derivatives and in the parent hydrocarbon. Longuet-Higgins (1950a) developed a simple and elegant method for calculating the change in localization energy L, with change in coulomb integral Sa, at any position u, to the first order in Sa,. Let &’ be the r electron energy in an even alternant hydrocarbon and bRM the energy of the electrons in the residual molecule corresponding to localization at the rth atom position. This atom position is denoted by r, since a position of localization is to be identified as a position of attack. Strictly the label r should be added to localization energies throughout the following analysis, but is omitted for simplicity. Let 8’and BkM be the corresponding values when a change Sa, is made in coulomb integral at the uth position, where u is not the position of attack. Then &” = &‘+q,Sau+O(Sa~) and SiM = b R M q,”” Sa, O(Sa3

+

+

by equation (13), where q,, qEMare the charges at atom u in the even alternant hydrocarbon and its residual molecule respectively, and the symbol 0 denotes “order of”. The localization energy L for the alternant is

L

= &‘RY-&‘

and for the derivative

L’

=

biM--b’

106

H . H . GREENWOOD A N D R . MCWEENY

The change 6L in localization energy is then obtained to the first order in &a, as 6L = L ' - L = (qE'-

1)6au

since q, = 1 for the alternant. It is well known (e.g. Coulson and Rushbrooke, 1940) that 9,"" differs from unity by the contribution at the uth atom due to electrons occupying the NBMO ; and that this term may be obtained (Longuet-Higgins, 1950b) by inspection, using only simple arithmetic. We now use the symbols L:, L; and L, to represent the localization energies for electrophilic, nucleophilic and radical attack respectively, at the same atom position r, reintroducing the appropriate label. Thus 6L: = c ~ , S a , (51)

SL, = -c~,Sa, (52) where c,, is the coefficient of $, a t the position of substitution, in the NBMO ($m,say) of the residual molecule. Longuet-Higgins did not treat specifically the case for radical attack, but it is interesting to note that the non-bonding orbital in this situation is singly occupied so that ":9 = 1 at all atoms u of the residual molecule, which shows that SL, (86,) is zero to the first order in 6a,. The second order term is non-zero, so that SL,(6a,) is, like 6F, in the isolated molecule approximation, an even function of 8a,, and therefore independent of the sign of the electronegativity of the substituent relative to carbon.

B. Analytical Properties of Exact Methods The analytical properties of the exact changes in localization energies, of which ( 5 1 ) and ( 5 2 ) represent the first order terms in 6a,, can be obtained by a direct method depending upon the properties of the secular equations (Greenwood, 1952a). The results may be summarized as follows. The changes AL)- and AL; ( A denoting exact changes) in the localization energies for ionic reactions are odd functions of the parameter change &,, and the relationship

dL,+(&xu) = AL; ( - Sa,)

(53)

holds for localization at any atom r defining a residual molecule. I n contrast, the change AL, in the localization energy for radical reactions has the property dL,(Ga,) = dL,( -6aJ (54)

REACTIVITY INDICES I N CONJUQATED MOLECULES

107

so that AL, is independent of the sign of the electronegativity change relative to carbon. The predictions of the perturbation analysis are therefore confirmed by the exact theory; furthermore, the analytical dependence of indices used in the localization method upon the sign of the change in electronegativity relative to carbon, is analogous to that of corresponding indices used in the isolated molecule method (Section IV). VI. RELATIONSHIP BETWEEN

THE

INDICES

The general agreement obtained between the two basic methods of approach in predicting the active positions of alternant hydrocarbons was originally interpreted as a confirmation of the validity of the theoretical models on which they were based (Wheland, 1942). However, the results of numerical calculations on large numbers of different molecules suggested that the various indices were mathematically related and therefore bound to be in agreement. Later, other reactivity indices, such as the “superdelocalizability ” (Fukui et al., 1954a) and “2 values ” (Brown, 1969)-which arise from variants of the two basic methods and are discussed in Section VII-were also found to show essentially the same pattern of agreement. These similarities between the predictions of different methods have been noted on many occasions by various authors and are summarized in detail in Streitwieser (1961). I n the case of the alternant hydrocarbons it is therefore seldom possible to say that agreement between predictions and observed reaction rates, based on a given index, points unambiguously towards a particular reaction mechanism. On the other hand, it is clear from previous sections (11,I V and V) that such ambiguities may often be partially resolved by considering how the indices are changed by the effect of heteroatoms or inductive substituents. For example, in Section IIB it became evident that the theoretical interpretation of the roles played by the various indices was in harmony with experimental evidence based on the reactions of benzene derivatives, We now show that for even alternant hydrocarbons the observed correlations among reactivity indices can in fact be ascribed to analytical properties of the equations from which they are determined. The existence of mathematical relationships among the indices follows essentially from the contour integral methods referred to in Section IV, but before sketching the theory it is useful to make some preliminary qualifications concerning the method of approach. At this stage we shall in fact consider the relationships from a purely mathematical standpoint, regardless of whether the limiting processes used in establishing them are physically realistic. This does not appear to inhibit the usefulness of the

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H . H . GREENWOOD A N D R . MCWEENY

approach, because here the aim is merely to trace the relationships between numerical quantities calculated using different prescriptions. It has already been remarked that the problem of interpreting the localization processes, and in particular of allocating an appropriate energy to the localized electrons is a difficult one. I n developing the theory, therefore, it is important to remember that the physical plausibility of any of the processes envisaged is not a t this stage an issue. The analytical relationships depend for proof upon expressions for the finite changes in n electron energy developed in Section 111,which will be considered in the compact form given by Fukui et al. (1957a). I n the treatment of heterolytic reactions of alternant hydrocarbons, a change Sa,in coulomb integral is assumed to occur at the position r of attack and the replacement u+r must therefore be made in the formulae of Sections I V and V, which refer to the change Sa, due to a substituent or heteroatom. The corresponding finite changedbis then given by (equation(50))

and the corresponding approximate form is, by equation (18),

where q, = 1for an even alternant hydrocarbon, and the self-polarizability

from equation (36),with s and u replaced by r. The first point to note is the appearance of the function G, in the integrands in (55) and (56). This permits the comparison of magnitudes for different positions r and s of attack in the same molecule. Thus if nr,r

r

=8,8

(57)

we have, for a given change Sa,=Sa,=Su, db,(Sa,) 5 db,(Sa,)

(58)

the inequalities being taken algebraically. The inequalities given here disagree with those given by Fukui et al. (1957a) which seem to need rather more careful consideration. For example, the self-polarizabilities T , , ~are negative quantities so that (57) implies ln,,,l 2 1n8,,1. Since the second term on the right hand side of (55) depends on Sa2, and carries a negative sign, its contribution is always negative. Thus when SCL(= Sa, = Sa,) is negative, corresponding to electrophilic attack, the

REACTIVITY INDICES I N CONJUGATED MOLECULES

109

negative contribution is increased, and the total change A 8 is negative. Then (58) implies IAd,(W I L I A & S ( W I (59) which means the lowering of n electron energy is greatest at the position of absolute largest self-polarizability. When Sarispositive, corresponding to nucleophilic attack, the first term on the right hand side of ( 5 5 ) , which dominates, is diminished by the negative second term. Then (58)implies that IA8r(Sa)I 5 I d ~ s ( W l

(60)

which means that the raising of n electron energy is least at the position of absolute largest self-polarizability. These results are not altogether clear from the original formulation (Fukui et al., 1957a). We can now consider the theoretical relationships between reactivity indices of the isolated molecule and localization methods. First we quote a generalized definition of the localization energy at atom r given by Fukui et al. (1957a)

L, (Fukui)

m

= 2 j=1

(6: - ej)

+ ( 2 - v ) ( a ,- EL)

(61)

Here 6; are the energy levels of the residual molecule defined by isolating atom r, and ej those of the parent alternant hydrocarbon; j = m indicates the non-bonding orbital which contains v electrons ( v = 0 , 1 , 2 for electrophilic, radical and nucleophilic attack) ; and a, is the coulomb integral for a localized electron on atom r. This quantity differs from the localizof Wheland in allowing the localized electrons to take ation energy (L,) an energy ar#ao. Its meaning is clear from Fig. 14 from which the formula is easily derived. To obtain L,it is necessary only to subtract ( 2 - v )a, (i.e. to remove the localized electrons with energy a,) and to add ( 2 - v ) a. (i.e. to give them energy a. instead). Thus the Wheland localization energy is

L,

=

L,(Fukui)+ ( 2 - v ) (ao- a,)

It is now possible to obtain L,as the result of an actual limiting process of the kind considered in Section 11; for the orbitals which result on letting a,-+ k co are identical with those of the residual molecule by itself, with energies depicted in Fig. 14, while the energy of the electrons removed from conjugation is given the standard value a. after completing the limiting process. To allow for a,-+ k co, the equation may be written more cautiously

L, = ar-trt 2t

{~d,(~,)+(2-v)(ao-~r)} 4)

(62)

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H . H . G R E E N W O O D A N D R. M C W E E N Y

where A&,(a,) is the actual energy change defined by ( 5 5 ) for the hypothetical perturbation ao+ar and is thus a continuous function of a,. We note also that L, (Fukui), allowing a finite ar # a,,,may be written in the form (62) using a in place of the variable ar, and then putting a, in place of uo.

-

I

I

I

I

I

I I I

-

UO-_

I

ek RM

(El

FIQ.14. Occupation of energy levels after localization. The position of a, is purely schematic; in general a7 # ao.

It is also possible to correlate differences of localization energy with differences of atom polarizability. For suppose we consider electrophilic attack on two alternative positions r, s with a,, as-+- co ; then from(62)

L:-L$ =

9t m

a+-

(db,(a)-db,(a)}

(63)

but if nT,,> ns,8the right hand side will be positive for all values and L f > L $ . A similar treatment may be applied in the case u,,a,++a, hence rr,? > n,,, implies

Lf > L$ L; > L,

(64)

The existence of these inequalities is less surprising when it is remembered that the early stages of the localization process described above correspond precisely to polarization of the isolated molecule, and that the subsequent changes in levels and orbitals, as discussed in Section 111,follow essentially by an analytic continuation. It follows that predictions of the sequence of active centres, in an even alternant hydrocarbon, based on localization energies must agree with those based on polarizabilities. This

R E A C T I V I T Y I N D I C E S I N C O N J U G A T E D MOLECULES

111

is not the case for other types of system and it is therefore extremely valuable to be able to estimate the effect of heteroatoms and substituents by the methods of Section I V (for T,,,) and Section V (for L,). It must be stressed that the precise nature of the limiting process u,+ f 03 is not in question; it is sufficient that this leads in the limit to the localized orbitals envisaged in the Wheland-Fukui definition (61), as described in Section 111. Fukui et al. (1957a) also derived a further important relationship connecting the free valence and the localization energy L,. I n this case the changes imposed were not in coulomb integrals, but in the two resonance integrals pTPand /Ir4 connecting the atom position r under attack with its two carbon neighbours p and q. The proof follows a similar pattern to that which applied in the case of a change Su, in coulomb integral. The free valence enters the expression for the approximate change Sb in T electron energy due to changes Sp,=Sp,, (=Sp) in the resonance integrals /Irp =pPg=/I involving the position of attack r through equation (16)

6 6 = 2 (<3 -F,)

Sp

(16)

The formula for the corresponding finite change d b was given by Fukui et al. in the closed form

Now the free valencep, can be expressed in the integral form (Fukui et al. 1957s)

which, as before, provides a basis for establishing a relationship between F,, F , on the one hand and db,, on the other, according to the magnitudes of G, and G,. This correlation is independent of the magnitudes which makes of S/3 and therefore holds for the limiting case a/? = -#I /I=p,,=&=O. It is clear that this condition corresponds to isolating atom r from the rest of the conjugated system, so that db,(p)-+L,as /I-+O. The correlation between the free valences and localization energies at any two atoms r and s can then be expressed in the form

F , > F , implies L, < L,

(66)

During the corresponding localization process, in which p+O for the two bonds connecting atom r to the rest of the molecule, the MO's for the innermost pair of orbitals change as described in Section I11 (Fig. 11).

112

H. H . G R E E N W O O D A N D R. M C W E E N Y

There are no charge shifts in this process, q8remaining equal to unity at all atoms. The limiting n electron distribution therefore indicates localization of a single n electron at the position of attack as required for the case of a radical reaction. The inequalities (64) and (66)thus cover all three cases envisaged in the localization theory.

VII. FRONTIER ORBITALAND CHARGETRANSFER THEORIES The frontier orbital approach (Fukui et al., 1952,1954b) has met with considerable success in so far as frontier orbital charges correlate well with experimental data. The performance of these indices is often superior to that of others, with the possible exception of localization energies. It is, however, difficult to give meaning to the correlation since physical interpretations of the role of the frontier electrons in reaction mechanisms are often obscure, and attempts to give substance to Fukui’s hypothesis have frequently embodied questionable procedures or models. For electrophilic reactions, the “frontier orbital ” is the highest occupied orbital of the unperturbed ground state of the molecular system under attack, and the frontier electron “density” f,. (or, more properly, “charge”) is the contribution to q,. arising from the pair of electrons occupying this orbital. The frontier orbital for nucleophilic attack is defined as the lowest empty orbital of the same system, and the frontier electron charge f,.is the contribution to qr that would result from double occupancy of this vacant orbital. For radical attack both orbitals are taken into account, and the frontier electron charge is that which would result from one electron in each. The frontier electron charge f r is then used as an index to predict the active positions in a given molecule. Unlike other indices, however, the frontier charge cannot be used for comparative purposes amongst different molecules, forfr clearly becomes smaller as the frontier orbital becomes more delocalized-as in a large molecule. Whereas the isolated molecule and localization methods were based on fairly well defined physical models, the basis for the conception of frontier electrons was slight. Originally they were conceived as participating in active triplet states (Fukui et al., 1952),then as being intimately concerned in the formation of u bonds at the position of attack (Fukui et al., 195413). Later (Fukui et al., 1954a, 1957a) a formal theoretical development associated the frontier electron density with T electron energy changes similar to those used in conventional isolated molecule approximations, but now embodying the notion of hyperconjugation at the position of attack. We sketch briefly Fukui’s analysis. The atomic orbital basis of the n electron system is assumed to be increased by the

R E A C T I V I T Y I N D I C E S I N C O N J U G A T E D MOLECULES

113

addition of a pseudo rr type orbital +* associated with the attacking reagent X and the hydrogen atom H at the position r of attack.

FIQ.15

A roughly symmetrical disposition of the centres X and H about the plane of the molecule is assumed, and the pseudo (or “group”) orbital has the form 4; where 4: = ( 4 X - $ H ) / & (67) and 4x and tjH are valence orbitals associated with atoms X and H . The trigonal arorbital of the carbon atom is assumed to be concerned with a-bonding with the symmetrical combination

4:

= (4X

+$ H ) / d 2

(68)

The coulomb integral associated with 4: is a* and the resonance integral between 4; and dr is 8*. The secular determinant defining the augmented system takes the form 0 0

0

0

a*-€

a11-e

p12

821

aZ2-E

. . .p* ... ...

= o

(69)

8* a r r -E where the leading minor refers to the molecule under attack. Fukui used perturbation methods, assuming 8* to be small, to derive an approximate expression for the change 8 6 due to hyperconjugation, or augmentation of the T electron system :

86=

2 j=l

(vj-v)c;j ej - a*

j?*2 + v(a* - a x )

The index jis taken over all MO’s of the molecule under attack, and vj is the occupancy; v is 0, 1 or 2 according as the reagent is electrophilic, radical or nucleophilic. The coefficient of /3*2in (70) is itself independent of 8*,and is thus merely an expansion coefficient, analogous to those of

114

H . H . GREENWOOD A N D R . MCWEENY

the isolated-moleculemethod. The coefficient depends, however, through a*,upon the nature of the attacking reagent. At this point, Fukui et al. (1954a) define a quantity, the superdelocalizability S,, by the expression 8, =

2

j=1

(vj-v)c?j Ej

- uo

(71)

which differs from the coefficient in (70) in replacing a* by the standard coulomb integral ao. The index S,, like those of the isolated-molecule approximation, is then independent both of the perturbation ,8* and of intrinsic properties of the attacking reagent ; that is, it can be defined, like other indices, in terms of the properties of the substrate alone. It is then argued that since Iej- aol is least for the levels of the two frontier orbitals, which are nearest to the zero of energy ao,the summation S, is dominated by the corresponding terms, which (from the properties of alternants) yield :f where Af = )ef - a o / Si = 2 c(72) hf and f indicates a frontier orbital. It is claimed that this equation then gives a theoretical foundation for the frontier orbital hypothesis. It is clear that there are a number of questionable steps in the treatment. I n particular the replacement of a* by a0 is wholly responsible for the special significance given to the frontier electrons; for equation (70) shows that if a* is close to any ej ofthe substrate, the correspondingorbital term would tend to dominate the sum. Yet, even if we grant that the determinant (69)with p* small could represent a model for the transition state complex, it is not difficult to show that the sum of terms neglected in passing from equation (71) to (72)is often larger than#: itself. Clearly, the significanceof the frontier electrons cannot be established unequivocally on this basis. Fukui et al. (1957b)have developed further the idea of charge transfer through hyperconjugation a t the position of attack. Noting that, for electrophilic attack, this mechanism would result in the transfer of two electrons from the substrate to the reactant, they propose that the coulomb integral of the pseudo T orbital should vary, to prevent a large effect of this kind, from the value u* to Ef, the energy of the frontier orbital, at which stage normal conjugation may begin to operate. It is not clear how the assumed change in a* to ef is to be made compatible with the adjustment of a* to a,,employed in the definition of the superdelocalizctbility. Although an analysis is constructed on these ideas, the approach seems to be empirical and speculative. Further comment will be reserved for the general discussion of Section VIII.

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115

Brown (1959) has presented a charge transfer model of the transition state for electrophilic reactions which differs appreciably from that proposed by Fukui and his collaborators and leads to the definition of a new reactivity index termed the “ 2 value ”. The model is based on a more conventional formulation of the charge transfer mechanism, which avoids the complete transfer of electrons associated with v=O,1,2 in Fukui’s model. There is no dependence on the formation of a pseudo 7~ orbital in the transition state, nor is hyperconjugation invoked. A wave function @c.t. for a charge transfer complex is written as a linear combination of a wave function@odescribingthe unperturbed ground state of the molecule under attack, and a function Q 1 which differsfrom@oin the replacement of one of its orbitals by the valence orbital of the reagent. Thus the wave function Qc.t. = a@,+b@,

(73)

describes a condition of partial transfer of one electron from the substrate to the reagent. The method used bears a close resemblance to that introduced by Dewar (1949) in consideringthe “ connection’’ of two 7~ electron systems; but this is purely formal, since the Q0, are here molecular wave functions rather than orbitals. Let be the ground state of the molecule under attack, and represent the configuration obtained by transfer of an electron from the ith occupied MO to the vacant orbital of an attacking electrophilic reagent. Then a general wave function @c.t. for describing one-electron charge transfers can be written as the linear combination of configurations @c.t.

=

ao@o+al@i,+a~@,+...

(74)

which gives rise to a configuration interaction problem, with eigenstates given by

Hoo Hoo-EE H10 H10 H20 H20

HOl H11-E H 11-E

HO2

HO2

HOl

... ...

Hoj Hoj

==oo

H22-E H 22-E

Hjo Hjo

... ...

Hjj--EE

Hjj

(75)

where Hij is the matrix element between @i and Ojof a Hamiltonian operator #* representing the charge transfer complex. I n the oneelectron scheme, this operator is regarded as a sum of terms, one for each electron, X‘* = h ( l ) +h(2) . . . . The approximations of Huckel theory

+

116

H . H . GREENWOOD A N D R . MCWEENY

(e.g. neglect of overlap)then ensure that the matrix elements H,(i #j# 0 ) are all zero, and with the substitutions

w = H0,-E Hoo-Hjj

Aj =

(76)

equation (75) then leads to

The remaining matrix elements are

Hoj = inwhich @,

=

I

dSjd7

dSO&'+

(78)

{ $ ~ ( 1 ) ~ ~. .( .2 ~) j ( ~ ) ~1)j ... ( ~~+ ~ ( ~ - l ) ~ , ( ~ ) }

and

+ {. .

.y$(U)$j(U+

1).

.

where t,hi is an occupied MO of the molecule under attack $i

=

2 c,i+a

the bar denoting j? spin, and its absence u spin, and c $ ~ is the vacant orbital of the electrophilic reagent. With the Huckel approximations already introduced, H o jreduces to the single term Hoj =

d/5~,.j+ei@*#,dr

= &crjPer

(79)

where peris the resonance integral associated with +e and the r orbital 4, a t the position r of attack. This quantity relates to some characteristic separation of molecule and reagent, corresponding to the postulated transition state and per may thus be written in terms of the standard integral Po in the form Per =

gbP0

(80)

where g$ is a multiplying factor characterizing the type of transition complex. On substitution, equation (77) takes the form

The diagonal elements dj=Roo- H j jrelate to the formal transfer of an electron from the j t h MO of the molecule under attack to the vacant

REACTIVITY I N D I C E S IN CONJUGATED MOLECULES

117

orbital of the electrophile, which can be approximated, in the usual way, by comparing the ionization energy Ij of the j t h MO with the electron affinity A * of the electrophile

Aj

A*-Ij Now Ij can be expressed in terms of Po as ,w

(82)

Ij = ao-kjpo (83) and for convenience A* can be written in similar units, and with respect to the same origin, as Therefore where

is a pure number. If W is also written in the same units as

W = -2po equation (81)becomes

(87)

and the most positive value of 2 then corresponds to the most stable charge transfer complex derived by mixing the configurationsof equation (74). I n principle this defines the 2 value for a given position r of attack, but Brown has found that configurations arising from replacements of orbitals other than the highest occupied, that is the frontier orbital, make a small, and virtually negligible contribution to the lowest charge transfer state. Therefore all terms except the frontier orbital (j =f) term in (88) are dropped, and the 8,value is then obtained from the resulting simple expression 2, = Yf+ 2 g t (c%/ Yf) (89) Brown concludes, therefore, that the frontier orbital density distribution c,: determines the position of attack. The concept is in many ways attractive, and is based upon less speculative applications of quantum mechanical ideas than those described earlier in this section, but it does not result in any form of chemical bonding in the usual sense either by partial or complete u bonds or v bonds. It would seem to be, in fact, more appropriate in describing stable v complexes as visualized by Mulliken (1950) and Dewar (1951). The role of the frontier orbitals in providing the configuration that

118

H . H . GREENWOOD AND R . MCWEENY

contributes the greatest weight to the most stable charge transfer state is fairly obvious from the equations : but, although the mechanism of charge transfer complexing has long been associated with the idea of an ionization, it must be stressed that an actual ionization process is not involved.

VIII. THEPHYSICAL BASISOF REACTMTYINDICES The previous sections have been concerned mainly with the definition and analytical properties of reactivity indices relating to various simplified theoretical models and with relationships amongst them. Effects such as polarization and localization, which undoubtedly occur, have been discussed in terms of the indices, but difficulties in relating these effects to the various stages of a real reaction process have also become apparent (e.g. localization as discussed in Section V ) ; and when the physical significance of the indices is investigated more closely, it appears that there are comparatively few criteria upon which an evaluation can be made. The correlations between numerical values of the indices and experimental data provide the most satisfactory criterion, a t the lowest level, but the introduction of new indices, based on rather different physical models, that invariably correlate equally well, frequently obscures earlier hypotheses. Nevertheless a good deal can be learned about the role of reactivity indices from the theoretical background already discussed, especially by reference to recent experimental work. A good correlation between theoretically predicted sequences of active centres and observed sequences is, of course, the ultimate test of success, but ignorance of the reaction mechanism involved, and the consequent use of a variety of hypothetical models, has been seen to lead to some ambiguity. To obtain more detailed information about the role of the various indices, it is necessary to refer to experimental work, particularly that of recent years. The following sources of information and methods of analysing postulated reaction mechanisms seem to be particularly relevant : (i) experimental work revealing the existence of .Ir-complexes and a-complexes as reaction intermediates. This stems mainly from work on reaction kinetics, but spectroscopic evidence is also important; (ii) theoretical considerations of the plausibility of proposed mechanisms.

It will not be possible to describe the extensive and stimulating experimental work that has done much to clarify the role of r-complexes

R E A C T I V I T Y I N D I C E S I N C O N J U G A T E D MOLECULES

119

and a-complexes as possible intermediates in reaction mechanisms (Dewar, 1951; Dewar et al., 1956b; Brown et al., 1952, 1953; Stock and Brown, 1963; Melander, 1950; Olah, 1958,1961 ;Berliner, 1964), but it is important that theoretical methods of approach should take cognizance of these significant developments. First, it is necessary to distinguish the two types of complex envisaged. A a-complex structure (Stock and Brown, 1963) for substitution by the electrophile X+takes the form

FIQ.16

and is essentially similar to the Wheland structure (Fig. 12) used in the localization method, except that i t receives a more literal interpretation as an actual system, rather than a structure in the sense of resonance theory; it involves formation of a a-type bond with X a t the position of attack by means of two electrons withdrawn from the 7-electron system, with the remaining 7-electrons confined to the residual molecule. In the general definition of n-complexes (Dewar, 1951) the electrophile X+ forms a loose addition complex

tx+ FIQ.17

with the whole n-electron charge cloud, and is not associated with a particular carbon atom. Similar complexes are well known involving aromatic molecules and various electron acceptors, such as halogens, silver ions and larger systems such as picrates, trinitrobenzenes and so on. I n general, n-complexes are conceived as low-energy intermediates, that precede the formation of high-energy a-complex intermediates ;these are associated with the transition state configuration which then “decomposes” to give products (Stock and Brown; 1963).

A. Polarization and Electrophilic Xubstitution From the various accounts that have been given of the role of n-complexes and a-complexes as possible intermediates in reaction mechanisms, that described by Olah et al. (1961)is selectedfor special attention, since it

120

H . H . GREENWOOD A N D R . MCWEENY

embodies most of the currently accepted interpretations (see Stock and Brown, 1963;Berliner, 1964),and, more particularly because it includes the notion of localized .rr-complexes,which appear to find a natural place in the theory. Several descriptions of the process of addition of the electrophile X+ to aromatic substrates, based on kinetic and other evidence have been given and most versions agree that the potential energy surface does not consist of a simple barrier, but involves details relating to metastable intermediates.

Reocfion co-ordinofe

FIQ.18. Energy variation in electrophilic reactiom following Olah.

The form of potential energy curve deduced by Olah from kinetic evidence on the nitration of benzene, and some alkyl- and halo-benzenes, by nitronium ions derived from NO; B F r is shown in Fig. 18. I n this diagram, position D is associated with a localized structure analogous to that of Fig. 16 and 19b.

The electronic configurations in the transition states C and E, through which D is formed and destroyed, are also assumed to resemble D in electron configuration, in accordance with Hammond’s hypothesis (1955). Position B is associated with r-complexing between NO; BF4and aromatic substrate, but a particular feature of Olah’s interpretation is the recognition of localized wcomplexing at particular atoms with high r-electron charges. The reactions concerned are fast, and show little

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121

substrate selectivity, since the rates of nitration are almost the same for various derivatives. Nevertheless, there is orientation, and the isomer distributions are substantially the same as for conventional nitrations. Olah interpreted the low substrate selectivity as due to a form of rcomplexing involving the complete rr-electron cloud, but differing from Dewar’s model (1951)in that the r-complexing is assumed to be localized at atoms of high rr-electron charge. This interpretation appears to be necessary in order to explain the observed orientations. Now this idea should clearly find a place in the isolated molecule picture where, if Olah’s , ~ indicate the interpretation is to be followed, the charge qr and T ~would energy of attraction, including polarization, according to (18) 66 = qr6ar + &rr,r8a; with which the reagent X+ would adhere at position r . The physical

nature of the problem suggests, as emphasized previously, that the polarization effect must be appreciable in this r-complexing process. The structure used by Olah to describe the r-complexing is that of Fig. 19a; the r-electron charge distribution cannot be uniform over the molecule in the presence of the NO: ion, and therefore charge displacements have been included to represent polarization in the figures. The inclusion of polarization simply extends Olah’sinterpretation which assumed that the charge qr would determine favourable positions of rr-complexing. The interpretation gives a new significance to the basic equation (18) used in the isolated molecule method, and a more satisfactory explanation of the role of the reactivity indices qr and rrr9r . The localized wcomplex is thus associated with the partial localization of an electron pair at the position of attack, and a charge distribution in the residual molecule already resembling that of the a-complex. Olah et a.2. (1962a,b)include in the barrier leading from A to the localized r-complex represented by B in Fig. 18, anactivation energy required to break the NO: BF,--solvent complex, the potential energy referring to the complete system of “ion pair plus molecule”, with solvent effects to some extent included. Thus theessentialdepression of r-electron energy (equation (18))due to polarization leads to a metastable r-complex in Olah’s scheme, when balanced against the energy required to detach X+ from the solvent. The main barrier can be associated with separation of the ion pair and changes of hybridization that involve the orbital partially localized at the position of attack, and lead to the formation of the a-bonded transition state complex ;it is the energy changes during this phase of the reaction which, in the localization theory (Section V), are assumed to be substantially similar for different positions of attack. It is important to recognize that the description given above goes 6

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H . H . GREENWOOD A N D R . MCWEENY

somewhat further than that of Section I1A, though both are based upon equation (18),which provides a fair description of thepolarization process. It also gives substance to the part actually played by the qr and T?,?,a desirable feature of any theoretical description. Obviously they can provide no more than an approximate measure that is useful for purposes of prediction in comparative studies. What is important from the interpretive point of view is that the simple theory provides a general guide through which it is possible to recognize that energy changes and charge shifts due to a normal physical polarization process provide a realistic account of localized .rr-complexesas deduced experimentally, in which appropriate valence conditions are provided in the molecular substrate at the position of attack.

B. The Structure of a-Complex Intermediates The formation of o-complexes as metastable intermediates is essentially linked to the idea of a change from trigonal towards a tetrahedral form of hybridization at the position r of attack; the change is formally translated in the theory into reductions in the resonance integrals between r andits two neighbouring atomsp and q ; this leads to an “interruption” in the path of conjugation that isolates atom r from its corresponding residual molecule. I n heterolytic reactions, this process follows polarization, represented approximately by equation (1S), which occurs a t distances of separation larger than those at which hybridization changes become operative. I n the case of homolytic reactions, polarization is either non-existent or small, and orbital localization is supposed to arise purely from changes in hybridization initiated by a neighbouring reagent; the localization of orbitals associated with this process was described by case (iii)in Section I11and developed in Section VI. According to equation (16) of the isolated molecule method, the .rr-electron energy increases by an amount given approximately by (8s = sg, = Sg), which suggests that localized .rr-complexes are unlikely in homolytic reactions. Thus the same energy levels and orbitals of the residual molecule in the a-complexes are obtained as the limits of three distinct physical processes ; for electrophilic reactions the energy levels are lowered towards those of the residual molecule, and the level associated with the localized orbital emerges, before hybridization changes become operative, from below the “band” of energy levels; for nucleophilic reactions the levels are raised, and the localized level emerges similarly from above the “band” ;and for radical reactions the occupied levels are raised, the unoccupied lowered, as a consequence of hybridization 6 6 = 2(d3-P,)sg

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changes, and the localized orbital is associated with a level at the centre of the “band ”. The remaining distinction resides in the occupancy of the localized orbital which participates in changes of hybridization at the position of attack, and which automatically satisfies the valency requirements of the attacking reagent in the three types of reaction. I n contrast, these conditions are imposed in the formulation of the localization method when defining Wheland structures. The localization energies L,f,L; and L,obviously apply to corresponding a-complexesin which the energies of localized electrons involved ultimately in a-bonding are formally set equal to (Section VI). Thus reactivity indices of the two basic methods, the isolated molecule (sub-section A) and the localization method, fit naturally into the physical pattern described in terms of n- and a-complexing. A case for the frontier orbital hypothesis is more difficult to establish on similar physical grounds. For both electrophilic and nucleophilic attack the frontier orbitals are amongst those which are “repelled ” from the position under attack and become increasingly associated with the residual molecule. It appears therefore that no physical significance can be attached to the fact that the numerical values of frontier orbitals in the molecule under attack predict the active positions successfully. On the other hand, when no polarization occurs, as in free radical reactions, the frontier orbitals are precisely those that combine to form a localized orbital at the position of attack. It seems logical, therefore, to bestow some significance on the frontier orbitals in the case of free radical reactions only. It will be noted that the remaining reactivity indices, the superdelocalizability S, and the 2, value, that have been specially identified with frontier orbitals, are defined within a context which ignores polarization. Charge shifts are derived from these forms of definition, but these do not result from appropriate representations of the field of approaching charged reagents. Apart from difficulties, previously discussed, concerning the definition of the superdelocalizability, the validity of the models upon which these indices are based is, therefore, open to question. Both the “hyperconjugation” effect that forms the basis of the definition ofS,, and the charge transfer basis for Z, apply at distances of separation of the order of one to two bond lengths whereas polarization, which is ignored, is already appreciable at several bond lengths. Mulliken’s model of the transition state (Pickett et al., 1953; Muller et al., 1954) is related indirectly to the structure of a-complexes. It is based on the idea of hyperconjugation effects stabilizing the transition state, and, although not directly invoking reactivity indices, must be mentioned as perhaps the most satisfactory description given so far.

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H . H . GREENWOOD A N D R . MCWEENY

Mulliken draws on the equivalence between two descriptions of a localized double bond, as (a) a 7 and u bond superposed and (b) two “bent” u bonds, as applied, for example, to the case of bonding in ethylene (Hall and Lennard-Jones, 1951). I n the present case a pseudo-double bond is visualized involving the rr orbital c $ ~ on the atom r under attack and a pseudo-rr orbital 4; formed by combining the valence orbitals of the reagent X+ and the hydrogen atom attached to atom r , as described in Section VII. The equivalent structures are then

(a)

FIG.20

in which (A)represents a CJ and pseudo-7 bond superposed and (B) corresponds to the a-complexversion of the transition state. Mulliken emphasized that the equivalence holds only for a high degree of double bond character in the superposed u and pseudo-7 bond of structure (A) and imposed a large negative value (in fact ,3*=2P0) on the resonance integral connecting bTand 4: to ensure that this condition was fulfilled. It was also pointed out that hyperconjugation itself, in the transition state, is meaningful only when the interacting 7-electron systems largely preserve their identity, and this again is ensured by taking a large neg!,* which preserves 7 character in the pseudo-doublebond. ative value of 3 A number of interesting refinements were introduced, notably a degree of self-consistency, but only the more general properties of the model, relevant to our present discussion, can be considered here. By imposing a large negative value /?*= 2p0, solutions are obtained analogous to that described in case (iv) in Section I11; the lowest and uppermost levels break away from below and above the other levels, the corresponding MO’s becoming roughly equivalent to bonding and antibonding orbitals associated with the pseudo-double bond. This is, in fact, obvious from the alternative interpretation (in Hiickel approximation, rather than Mulliken’s refined treatment) of hyperconjugation introduced between a pseudo-double bond with energy levels f 2.000,3,, and the residual molecule for benzene with levels & 1.732,3,,, & 1.000,30 and 0.0,3,; a simple energy level diagram shows that when hyperconjugation is included the

REACTIVITY

INDICES IN CONJUGATED MOLECULES

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pseudo-double bond is largely associated with the lowest bonding level with an energy lower than 28,. Mulliken’s model is entirely compatible with the descriptions given previously in this Section, since charge shifts that result from polarization are already taken into account in forming the a-complex by subsequent changesin hybridization. Fukui’s model, upon which the definition of the superdelocalizability is based, resembles Mulliken’s only in the use of a pseudo-.rr orbital cj:, and the formulation of the “ hyperconjugation” problem is quite different, since P* is taken by Fukui to be small, so that S, can be defined by perturbation formulae. I n particular, the bonding of the pseudo-.rr orbital cj: in Fukui’s model primarily involves the least bound, or frontier orbitals, whereas in Mulliken’s model the most bound MO is involved.

C . Some Related Topics 1. Spectroscopic evidence for o-complexes Important information has been obtained on the possible structure of reaction intermediates from spectroscopic studies of protonated aromatic molecules (Gold and Tye, 1952; Reid, 1954). Gold and Tye (1952) measured the U.V. absorption spectrum of anthracene in concentrated sulphuric acid under reversible conditions, and showed that the spectrum differs from that in inert solvents, resembling that of diphenylethylene (Fig. 2lb) in concentrated sulphuric acid. The similarities were attributed to proton addition a t a mesoanthrenic position which by “extracting ” this position from conjugation gives a residual molecule analogous to that of the cation formed by protonation of diphenylethylene as shown.

@p& H H

Descriptions of the changes in spectroscopicproperties show important differences according as the process leading to localization of electrons required for bond formation with the added proton is attributed to polarization or to “interruption” of the path of conjugation. Figures 228 and b represent part of the energy level diagram for the two cases respectively, and the relevant excitation, in the simple Hiickel approximation, from the highest occupied to the lowest unoccupied orbital is

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H . H . GREENWOOD AND R . MCWEENY

illustrated (i) for the molecule under attack, (ii) at a stage of partial localization, and (iii) for complete localization where the excitation refers to transitions between .rr-levelsof the residual molecule. An interpretation based upon “interruption” of the path of conjugation would lead to singly occupied degenerate orbitals, one on the residual molecule and one at the point of localization. The latter would not suffice for formation of an incipient a-bond, and the spectrum would correspond to a neutral residual molecule. The a-complexing usually

(0)

(b)

FIG.22. Changes in spectrum due to (a) polarization (b) “interruption” of path of conjugation.

assumed, however, corresponding to a point near the maximum of the potential barrier (D in Fig. 18), would follow the polarization process described in Section VIIIA and is consistent with the observed spectral changes. Whether or not the attached proton does actually form a acomplex is debatable : the reversibility observed in the dilution experiments of Gold and Tye might in fact lend more support to the idea of a localized .rr-complex,for which the potential barrier involved (A to B in Fig. 18) would be much smaller. On the other hand, provided two electrons have been localized at the point of attack, the further change towards tetrahedral hybridization (i.e. a-complexing) is not ruled out, and there is some evidence from the NMR experiments of MacLean et al. (1958) that the two hydrogen atoms are indeed equivalent. Further experimental work could throw light on this important question.* *See the Chapter by Perkampue in the present Volume,

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IN CONJUGATED MOLECULES

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2. flurface states in solids

Surface states in solids have been intuitively associated with mechanisms of catalysis in chemical reactions and are, therefore, relevant to the subject of this review. Moreover, the formal treatment of surface states by the tight-binding approximation (Goodwin, 1939 ; Baldock, 1952 ; Grimley, 1958) corresponds closely to the techniques used in the isolated molecule method for conjugated molecules, and many of the qualitative ideas described previously can be carried over to the theory of surface states. Such ideas form a useful background that should assist the development of suitable models for catalytic mechanisms, which are still in the earliest stages of formulation (Grimley, 1958). It is possible to use energy level diagrams and corresponding orbital properties, as described in Section 111, to obtain a simple and direct understanding of the results obtained by more complete methods of analysis; these concern, in the main, the origin, enumeration and classification of surface states. A brief indication of the method of application, and the form of results will be given. Coulomb integrals a. and resonance integrals are employed for all atoms and nearest neighbours in the bulk of the solid, and surface potentials are introduced by changes in the parameters, usually confined to coulomb integrals

so

ar = ao+Sar

(90)

where r is an atom in a surface layer. Consider, as a simple model, a linear chain of N atoms, each with one valence atomic orbital, such that all coulomb integrals and resonance integrals are initially equal to a. and Po respectively. Then a band of N energy levels with N corresponding “molecular ’’ orbitals is obtained from the equations of the tight binding approximation, which are completely equivalent to the secular equations of (8) when the values a. and are inserted. Let the coulomb integral of the end atom, r = 1 , now be changed according to (go), where 6a, increases or decreases from zero. At a particular threshold value for 6 q , a single level emerges from below or above the band according aa 6al is negative or positive; the remaining levels, according to the rules mentioned in Section 111, tend towards those of the “residual molecule’’ which is the linear chain excluding the end atom r = 1, These levels remain, therefore, within the band, as originally defined. The lowest, or uppermost, orbital (according as Sal is negative or positive) becomes increasingly localized at the position r = 1, and this orbital describes the single surface state that can be generated by the change in one coulomb integral. Nodes of the remaining orbitals move towards the atom r = 1 until, in the limit, one node coincides with the bond joining atoms 1 and 2.

so

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H . H . GREENWOOD A N D R . MCWEENY

I n this way nodal properties of the orbitals of the “residual ” molecule are preserved. Suppose now the coulomb integral a t the other end atom, r =N , is modified by changing Sa, from zero to the value S q . Then a second level emerges from above or below the band to near coincidence with the first emerging level, and the corresponding orbital becomes increasingly localized at the Nth atom. The remaining levels are approximately those of a new “residual ” molecule formed by excluding r = 1 and N from the original linear chain and these, therefore, lie within the original band; the nodal properties of orbitals are again correctly preserved. Alternatively, both coulomb integrals can be changed simultaneously by Sal=&a, and both levels emerge from the band nearly together but the

r = 1 2 3 4 ....

.... N

FIG.23. “Surface” states of linear chain.

orbitals are no longer localized separately atoms r = 1 and N . Suppose, for example, Sal= Sa, is negative under these circumstances ; then the two lowest levels emerge from below the band and the orbitals that emerge are, successively, the nodeless orbital and the next orbital with one node. These are “localized” in both atoms, r = 1 and N , as indicated in Fig. 23, and, since they correspond to a twofold degeneracy, can be combined in sum and difference forms to give two alternative forms that are substantially localized on each atom separately ; these new orbitals are then equivalent to the two “surface ” state orbitals extracted separately, as described previously. I n real crystals the potential rises as the surface is approached from inside, so that Sa, is positive, and surface states emerge from above the band, from corresponding orbitals having the largest number of nodes; these are difficult to sketch, and for this reason only the case with Sa, negative is considered above. The extension of these ideas to a two-dimensional model is straightforward. Consider a regular rectangular lattice with edges, parallel to x and y axes, containing respectively N and M atoms, and suppose all N

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129

atoms in one edge parallel to z are modified by 6a, (positive). At some threshold value of 8ar,N surface state levels emerge from above the band; the remaining levels are approximately equal to those of the corresponding two-dimensional residual molecule, and necessarily remain within the band. The surface states emerge in the sequence given by the number of nodes ( N - 1)) (N- 2), (N- 3 ) . .. 2 , 1, 0 in the z coordinate of the corresponding orbitals, each orbital having the maximum number ( M - 1) of nodes in the y coordinate. When two parallel edges are modified, 2 N surface states emerge from above the band, and this case can be treated as an extension of the linear chain with two modified end atoms. The development for four modified edges in a two-dimensional model follows the same pattern. Clearly the description of surface states in threedimensional systems becomes increasingly difficult to describe, but not too difficult to visualize, since substantially the same principles hold. IX. REACTIVITY INDICES IN MANY-ELECTRON THEORY The discussion so far has turned entirely on Huckel theory. Indeed, almost all the work on reactivity theory during the past twenty years or more has been built on the somewhat insecure foundation of a oneelectron model which is known to possess many defects, perhaps the most serious being the complete neglect of interaction among the electrons (often amounting to many hundreds of electron volts), except in so far as this can be absorbed into the empirical parameters. This is a particularly disturbing situation when it is remembered that chemical significance is frequently attached to indices which differ by one or two units in the second decimal place-corresponding perhaps to energy differences of the order of 1/10 e.v. On the other hand, there have been significant advances in many-electron theory, including for example the development (Pople, 1953 ;McWeeny, 1956) of semi-empiricalversions of Roothaan’s approximate self-consistent field (SCF) theory (Roothaan, 1951). Most of these developments may be applied most directly within the framework of the isolated molecule method, in which the reactivity indices are the charges and self-polarizabilitiesof the unperturbed ground state of a given molecule; calculations based on the localization model (e.g. Nesbet, 1962) have made less progress, and will not be considered. It is therefore natural to enquire whether indices similar to qr and T,,? in Huckel theory can still be defined, and calculated more precisely, in self-consistent field theory. The obvious questions are

(i) Is it possible to find indices with properties similar to those of the charges, bond orders and polarizabilities of Huckel theory, using 6*

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H . H . GREENWOOD A N D R. MCWEENY

a complete many-electron theory which properly includes electron interaction effects? (ii) How far is it possible to characterize the actual effects of an approaching reagent (e.g. charged or uncharged ion) in terms of these indices? (iii) Is it possible, as it is in Huckel theory, to use the same polarizability indices to estimate the effect of heteroatoms upon the electronic structure and properties of a given parent hydrocarbon?

It will appear that there is, in fact, a strong correspondence between Huckel and SCF methods in which the SCF charge qr and self-polarizability rr?,). at a position r of attack are related to the change in rr-electron energy 6E produced by variation of parameters associated with the rth atom (see Section IXB) as in equation (18). Similarly, the charges q8 in a molecule substituted at position u can be calculated approximately from the SCF atom-atom polarizabilities rr8,u of the parent (see Section IXC), and used subsequently as indicators of the active positions in the derivative. The results are completely general but again alternant hydrocarbons have specially interesting properties. The notation used previously in discussing the isolated-molecule method distinguished carefully between the change Suu in coulomb integral due to a substituent at any atom u of the conjugated system, and a similar change 6ur in coulomb integral at the position r of attack due to the proximity of a charged reagent. The distinction was made to avoid the confusion which often arises when the polarizabilities are used for the two purposes just indicated. I n view of the slightly greater complexity of the SCF formulation, however, we shall now use r,8,t,u, as general indices, distinguishing a particular choice by explicit reference to, for example, “the position r of attack”. I n practice, the context is usually sufficient to eliminate risk of ambiguity. A. Perturbation Methods in SCF Theory It would be out of place to give a detailed review of the approximate SCF theory, as developed for rr-electron systems, at this point. It is, however, necessary to explain the basic equations, and convenient to use a form in which only the charges and bond orders appear (McWeeny, 1956, 1964). The total rr-electron energy E may then be written where and

fr8,

Gr8 are elements of the framework Hamiltonian matrix (i.e.

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131

referring to an electron in the field of the o-bonded framework) and the “ electron interaction matrix ”, respectively. This is a completely rigorous expression for the energy, on the basis of the one-determinant wave function of Hartree-Fock theory with MO’s expressed in LCAO form. The coefficients P,,may be collected into a matrix P which also defines the electron density function P in terms of the basic AO’s

The elements of P are thus identical with the charges (diagonal elements

P,,=p,) and bond orders (off-diagonalelements, P,,), used by Coulson and

Longuet-Higgins (1947a,b), though (93) provides a more general definition extending even beyond the Hartree-Fock approximation. P is the (one-electron) “ density matrix ” (e.g. McWeeny, 1960) or “ charge-andbond-order matrix”. It is assumed here that the AO’s are mutually orthogonal, as is necessary for the validity of the approximations usually made (Pariser and Parr, 1953a,b; Pople, 1953);this may be ensured by a preliminary mixing of the “ordinary” AO’s to form an accurately orthogonal set with similar localization (McWeeny, 1956, 1964). Integration of the density (93) then shows that P,,is the amount of charge (in while the “overlap terms ” Po+,+: electrons) associated with orbital contain zero net charge though modifying the density in the bond regions. Before defining the Hamiltonian more precisely we note that if the diagonal elements are denoted by a: and pi8then (91) becomes

+,,

which compares closely with ( 1 2 ) except that E now includes electron interaction. At first sight, then, P,,and P, might appear to have the significance attributed to them in Huckel theory, being expressible as energy derivatives, though now E is the true total energy and the significance of a: and pi8 has yet to be discussed. Unfortunately, the situation is not so simple; for the essence of Hartree-Fock theory is that the interaction of the electrons, embodied in the matrix G ,depends upon the forms of the MO’s they occupy (i.e. upon the solutions themselves, defined as the orbitals which make E a minimum in the sense of variation theory). Determination of the SCF MO’s thus requires a tedious iterative procedure, which we sketch only for the case of a closed-shellground state, though generalization is possible (McWeeny, 1964). When all MO’s are doubly occupied, the stationary conditions yield the familiar secular equations

h,,c, 8

=

EC,

(r,s = 1,2, ...)

(95)

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H. H. GREENWOOD A N D R. MCWEENY

for orbital energies and A 0 coefficients. These equations compare with ( 7 ) but now h,, is an element of the Hartree-Fock Hamiltonian in which G,, supplies the effective potential field on an electron provided by all the other electrons :the reason for the factor in (92) is simply that in the total energy the interaction between any two electrons must be counted only once. Hiickel theory thus makes the error of using the same Hamiltonian in both the energy expression and the secular equations, a practice which is theoretically inconsistent. The MO’s determine the P,, exactly as in Section I With suitable approximations it turns out that h,, is linked (through G?,) to the charge density and the basic parameters by ‘TT

=

+ iP?, + c +

wI

YTt

(‘88

-’ 8 )

Y78

(98)

S(#T)

hT8

=

flT8

- 4’?8

YT8

(99)

Here 2, is the number of 7r electrons provided by atom s; w, is essentially an “ionization potential” for an electron extracted from 4, in the presence of the part of the framework associated with atom T alone (a somewhat hypothetical quantity), p,, is a framework resonance integral, and yrsis the coulomb interaction between electrons in orbitals 4, and 4,. The essential parameters, in the semi-empirical form of the theory, are w,, pr8and y,, and from their definition these quantities are expected to be characteristic of atom r or bond r-s, not of the particular molecule in which they occur (for a discussion see McWeeny, 1964). I n the SCF calculation, solution of (95) leads to MO’s from which charges and bond orders are calculated using (97); these are used in setting up a revised Hamiltonian according to (98) and (99); and this is put back into (95) which is solved again to get new MO’s, the process being continued until self-consistencyis achieved. It is now clear that prediction of the variation of the self-consistent E with respect to the parameters is a matter of considerable difficulty. This problem may be solved in various ways. In particular the firstorder change may be obtained easily from general principles (McWeeny, 1955) and yields

equations formally similar to (13) and (14). It should be remembered, however, that E is the total r-electron energy (electron interaction

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133

included) and that wr and& are the framework parameters; it is generally assumed that the a, and firs in equations (13) and (14) approximate to Hartree-Fock quantities (hrr,hr8),but clearly great care is necessary in setting up the correct differential relationships. I n the description of the reactivity problem it is, in fact, the quantities wr and prS which are changed by the electrostatic field of an approaching reagent (which is a perturbation of one-electron terms in the Hamiltonian) and it is therefore proper that they should appear in (100). On the other hand, insertion of a heteroatom (which represents a form of substitution) is accompanied not only by a change of wr but also by a change of yrr;the establishment of differential relationships in this case will be taken up in Section IXC. The second-order changes, in terms of which polarizability coefficients may be defined, are much more difficult to discuss because they involve essentially a change in the wave function (made in such a way as to preserve self-consistency)-unlike the first-order changes, which involve the unperturbed wave function only. Approximate formulae for the polarizabilities were first obtained (McWeeny, 1956) using a " steepest descent" method to minimize the energy, a useful result being the establishment of a connection between rr,,, and F,,valid for systems of any kind (non-alternant or heteroaromatic included) and applicable either in Hiickel theory or in a more complete theory. According to this method T r , r 1: Prr(2-Prr)

~ 8 . 21 r

- T r , r P 2 (8

+

T)

2(vr - Yr)

where *r =

C

hrapar

a(#?)

and y, which may amount to as much as half of w,, is a complicated expression which arises from the need to maintain approximate selfconsistency. At the level of the Huckel approximation, vr would reduce to the sum of the orders of the rr bonds connecting r with its neighbours and grwould be absent. The generalization to the more complete theory is thus particularly simple, and although absolute values may be changed considerably in admitting self-consistency,the ratios of different atomatom polarizabilities depend essentially on the pattern of charges and bond orders. I n Huckel approximation the self-polarizability of an atom is seen to be inversely proportional to the number (v,) of rr bonds it is forming-a satisfactory result which links rrr9,directly with Fr. The approximate polarizabilities calculated by the steepest descent method are useful mainly because they are easily calculated from the charge-and-bond-order matrix of the unperturbed molecule ; but their

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H . H . UREENWOOD A N D R . MCWEENY

theoretical foundation is insecure, and their accuracy uncertain, in the sense that they give only part of the second-order energy, plus parts of all other orders. A more rigorous way of separating the orders, based on a power series development in the perturbation parameter, must therefore be sought. One way of proceeding, due to Greenwood and Hayward (1960), involves direct numerical solution of the SCF equations for a series of values of the parameter of interest, w, say. The slope of the E curve at the origin is then P,, while the polarizabilities nr,, may be obtained either as slopes or curvatures,

determined numerically at the origin (Sw, = 60, = 0). The numerical values obtained for several systems were found to follow a general pattern similar to that derived by Huckel theory, though significant differences did occur. It is, of course, difficult to compare absolute values, provided by the SCF theory, with the much more empirical values of HuckeI theory which are usually expressed in units of K1.One way of effecting the comparison is to write the SCF quantities in units of (/3scF)--’ where Pzrn =he, (for the “standard” carbon-carbon bond in benzene), which appears to be the nearest SCF equivalent of the empirical Huckel /lo. Another practice would be to express all polarizabilities in units of the self-polarizability of a carbon atom in benzene. A recent re-examination of the perturbation problem (McWeeny, 1961 ;Diercksen and McWeeny, 1965), leads to a method of determining, to any prescribed order, the perturbation of an electronic system due to any applied field. This method involves the direct calculation of the first-, second-, third-order corrections to the charge-and-bond-order matrix

P = Po+hP‘1’+X2P‘2’+...

(102)

corresponding to a perturbed wave function which remains self-consistent to any prescribed order in the perturbation parameter (which might be, say, the change Sw, at centre T ) . We state briefly the conclusions of this analysis. The Hartree-Pock Hamiltonian, with elements given in (98) and (99) is written h = f+G (103) where f for the perturbed system differs from f, before the perturbation :

f

=

f,+Xf‘l’

(104)

The problem is then to find the matrices in (102) which give the changes

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135

in all the charges and bond orders due to the perturbation, where the procedure must be iterative because G depends on the P being calculated and must therefore be revised to achieve self-consistency. The total electronic energy may also be developed in powers of h :

E

=

E + M(') +A2 E(') + ...

(105)

and it turns out that determination of P (l)is sufficient to determine the energy E even to the third order. The prescription for calculating P ( l ) need not concern us here (see McWeeny, 1961 ; Diercksen and McWeeny, 1965). The resultant energy changes are extremely simple :

E(') = C f$;)P8, 1, 8

E(2) =

4 C f$;)p$

(106)

r. I

(where the zero subscript is now discarded, Pr8referring to the unperturbed system), The atom-polarizabilities are easily introduced by considering a one-element change in fo, of amount awl: in this case, using Sw, in the place of the perturbation parameter A, f(') has only one non-zero element, f$:)= 1. The elements of P(l)then determine all the atom-atom Thus, from (106) and atom-bond polarizabilities of the form r8,r, E(')=P,, and E(2)=iP$:).The treatment of bond perturbations is entirely similar, except that two elements, parand pr8are changed, and the most important results are

are obtained in a similar way, and The other polarizabilities T , , ~and rr8,tu the third order term in (105)is also easily obtained (Diercksen and McWeeny, 1965). Again it should be noted that it is the framework parameters, w, and &, which occur most naturally in the perturbation theory. Numerical values of the indices are now in course of calculation, for both aromatic hydrocarbons and heteroaromatic systems, and it will be of great interest to make a more detailed and systematic comparison with Hiickel theory.

B. P, and r,,?as Reactivity Indices To make a preliminary assessment of the significance of P,, and r,,,in discussions of heterolytic reactions, we use the usual point charge model

136

H . 11. G R E E N W O O D A N D R . M C W E E N Y

in which the perturbing field acting on an electron is (using atomic units, e = 1 ) ) = -qlrQ (109) where rQ is the distance of the electron from charge q at point Q. The magnitude of the charge may be used as the perturbation parameter ( A = - q ) )and the perturbation matrix f(l)then has elements

v

It was anticipated in Section I that many elements of this matrix would have comparable values, whereas in the simple treatment used previously all were neglected except for the single element f::) for the atom r to which Q was closest. Now if (as we have supposed) 4rand are suitably orthogonalized AO's, the values of fit) for r # s are very small, and in good approximation f ( l )becomes the diagonal matrix with elements

f:?

=

YQr

(111)

where yo, corresponds to the coulomb interaction between an electron in 4, and an electron at point Q . Every centre in the molecule is therefore perturbed by the point charge, with 6wr = - qyQrfalling off roughly as the inverse distance of Q from centre r : this is hardly fast enough to justify the neglect of all terms but one. On inserting (1 11) in (106)i t follows that

It(') E ( 2 )=

=

x Prr

3 c YQrP!r)

(112)

YQr

T

=

4 r,

(113)

YQrTr,8YQ8 8

where the first-order change of P has been eliminated by introducing T,,8 . Thus the self-polarizabilitiesalone are not sufficient to characterize the effect of a charged reagent-all atom-atom polarizabilities may be significant. Before writing down the total perturbation energy, to second order, it should be noted that the actual interaction energy will include that between the charge q and the a-bonded framework-which has been ignored in computing the T electronic energy, but which is very large and almost exactly cancels the energy of the T electrons in the field of the charge q. It is therefore important to make consistent approximations in evaluating the net interaction energy: the most obvious procedure (though refinements are possible; see Diercksen and McWeeny, 1965) is to take Energy of framework ion in field of q

(

)( +

energy of Z, electrons in orbital 4,

T

energy of

) (nrk?:F:) =

'

REACTIVITY INDICES IN CONJUGATED MOLECULES

i.e.

Energy of part of framework associated with centre T in field of charge q

137 (114)

The interaction energy between molecule and charge q is then, to second order, Ei, = 2 q Y Q r ( Z r -prr) + 4 2 q2Y Q r Y Q s rr, 8 (115) r, 8

This may be compared with the much cruder approximation, adopted previously, in which only one atom ( T , say) is supposed to be perturbed, and = q ? / Q r ( z r -prr)

+ $azY Q r rr, r

(116)

d (C-C bond lengths) I

1

2

1

I

3

h

r .C

a u

*$

-0.05

r Y

x

c c

W

.-us .-NL

0

n

-0.10

FIG.24. Curve A based on equation (116); B on equation (116). Results obtained for benzene and for approach towards a fl carbon atom in naphthalene nearly coincide,and a single curve haa been used to represent both cases; in reality, the curve for benzene always lies slightly above the other.

138

H . R . GREENWOOD A N D R . MCWEENY

A satisfactory feature of (116) is that the first-order term, which describes the interaction between the external charge and the unperturbed molecule, continues to disappear if the electron distribution is highly uniform as in an alternant hydrocarbon; in such cases the propensities for reaction are still dominated by the polarization term, but this now has a less simple form, depending upon all atom-atom polarizabilities and on the position of the attacking ion with respect to all conjugated centres. To indicate the possibilities of energy surface calculations along these lines, we show in Fig. 24 the results of calculation of the polarization energy for a charge q approaching various centres in the naphthalene molecule along the direction normal to the molecular plane (Diercksen and McWeeny, 1965). An immediate conclusion is that the perturbation of all centres by an approaching ion must be taken into account. Extensions of the theory can be made by substituting a dipole or quadrupole for the point charge q ; in such cases localization of the influence of the external reagent may be more complete, for the perturbations then fall off more rapidly as a higher inverse power of the distance.

C. Eflect of Heteroatoma As in the case of Huckel theory, it is possible to use the perturbation method outlined in Section IXA to obtain the P matrix for a substituted or heterocyclic molecule from that of the parent hydrocarbon by regarding the latter as the unperturbed system. Diagonal elements of the P matrix for the derivative then give the reactivity indices (Prrof Section IXB) which may be used in predicting the active positions in the molecule towards ionic reagents. The perturbation then differs from that due to an external charge in that the orbital for the heteroatom may differ from the corresponding orbital in the parent molecule; it is therefore necessary to consider the variation of two-electron integrals containing that orbital in addition to the change (104). I n general, we may write similarly G = G+hG(l) (117) and the analysis is then almost unchanged, up to second order, I n place of (106) we find E(') = C (j(1)+$G(1))r8P8r (a) (118) r, 8

=

4 C (f(')+G(1))r8P$:) r.8

(b)

where the perturbation P(l) of the charge-and-bond-order matrix is calculated exactly as before but with the replacement fcl)

+ (f(l)+G(l))= h('), say

(119)

REACTIVITY

INDICES I N CONJUGATED MOLECULES

139

I n other words, the variations used in place of Sw, and SFr8in discussing the effect of a heteroatom are obtained by taking the elements of the SCF Hamiltonian and simply changing the one- and two-electron integrals to the values appropriate to the heteroatom. I n calculating the changes of charges and bond orders, it is immaterial how the matrix h(') is divided into two parts f(l)and G(l),and for unit change of any element, h,, say, the resultant P(l)matrix will determine a unique set of polarizabilities. For example, a given change a t atom r of ah, =

+ +PwSy;

(120) will give exactly the same first-order change of charges and bond orders, irrespective of how the change is apportioned between its one and twoelectron parts. This is a particularly interesting result for it means that a heteroatom with given Sw, and SPr8(relative to carbon), will disturb the uniform charge distribution in an alternant hydrocarbon only if 8h,=(Swr+@y,)#0 and that when the inequality is satisfied the modification of charge density is proportional to h,. I n other words, (0, + bw) is a convenient measure of the electronegativity of any conjugated atom. This quantity (used also by McWeeny and Peacock (1967) in comparing Hiickel and SCF calculations on heterobenzenes) formally agrees with Mulliken's (1934) index, provided w , is interpreted as an ionization potential (I,)and y, is approximated in the manner suggested by Pariser and Parr (1963a,b); for then Ur+brr

Sw,

= -Ir+Wr-4)

= -+(Ir+Ar)

(121)

The main differential relationships for the polarizabilities are

but the appearance of the 8 in equation (118a)should be noted ;it corresponds, as in (92),to the fact that, in averaging over the unperturbed wave function to get the changes in the two-electron integrals must be counted once only. To summarize : exactly the same self-consistent polarizabilities may be used in discussing the effect of heteroatoms as in discussing framework perturbations, but the perturbation parameter Sw, is replaced by ah, given in (120). The changes in charges and bond orders are given by

6P.w = 78,rShrr SP8t = r&,rShrr (123) and the total change in r electron energy due, in this case, to replacement at position r is E = lPw(% + + +r,r 8% (124)

140

H . H . QREENWOOD A N D R . MCWEENY

The new charge-and-bond-order matrix may be used as a basis for discussion of the reactivity of the heterocyclic system.

D. Alternant Hydrocarbons. Finite Changes In the case of alternant hydrocarbons it is possible to show that the finite changes in SCF charges, bond orders, and free valences due to changes in the parameters w,. and yrr(Greenwood and Hayward, 1960), have properties which are completely analogous to those of the corresponding quantities used in the Huckel approach of Section IVB. The SCF results incorporate those of the Huckel method as a special case, in which electron repulsion terms can be dropped from the non-linear equations without invalidating the derivations. The theoretical techniques used to obtain the analytical properties are essentially different from those described previously for Huckel theory, but the result can be stated briefly in similar terms, and this will suffice for present purposes. I n Section IXC the effect of a heteroatom at atom position r was represented by the change %r

= awr+P’rrSyrr

(126)

in the corresponding diagonal element of the SCF Hamiltonian. The changes in charges, bond orders and energy levels due to changes + Sh,, and -ah,, denoted by + and - respectively, possess the following properties : (i) SPrA + ) = SPrA - 1 (ii) P r A + 1 = - P r A - ) = +Prs(-)

(iii)

.i(+)

=

-€,-$+I(

(r,s same starred set) (r,s different starred sets)

-)

I n (iii) is the energy level corresponding to the ith ( i = 1,2,...n) SCF molecular orbital, and is measured from the “zero ” level (wo++yo) for carbon atoms (Pople, 1953 ; Greenwood and Hayward, 1960). Since for alternant hydrocarbons the charge P,.,is unity (Pople, 1953) the result (i)means that the change in the derivative is an odd function of the perturbation ah,,. The results listed in (ii) refer to all elements of the bond-order matrix; for neighbouring atoms, the second of these results applies (r and s in different sets), and hence bond orders in the derivative are independent of the sign of Sh,. Consequently, the change in free valence must also be independent of the sign of hrr,and the analytical properties obtained for SCF quantities are analogous to those that apply to corresponding quantities used in the Huckel method. The results (iii) also have their counterpart in Huckel theory; and (i), (ii)

R E A C T I V I T Y I N D I C E S I N C O N J U G A T E D MOLECULES

141

and (iii) together therefore provide a more convincing foundation for the regularities predicted by the simple theory, as described in Section IV.

X. CONCLUSIONS AND FUTURE PROSPECTS Most of this review has been concerned with a detailed analysis of the meaning and inter-relationship of a number of reactivity indices associated with two extreme “models” of the reaction process. These models, whose validity has not been fully discussed, involve on the one hand a perturbation calculation of part of the energy surface and, on the other hand, a direct calculation of a 7-electron energy change when molecule and reactant come together to form a transition complex. Variants on these models, involving some form of “ charge transfer ”, might apply in intermediate situations where molecule and reagent are in close proximity but an actual transition complex has not yet been formed. All such models have a limited usefulness, their function being essentially to provide a certain minimal basis on which quantum mechanical calculations can be carried out, and each has its own disadvantages. The transition state theory, for example, though attractive because it postulates a perfectly definite complex which in principle is amenable to precise calculation, entails making a plausible guess at the crucial rate-determining step in the reaction. This difficultyis not quantum-mechanical in origin, however severe may be the further difficulties of a quantum mechanical energy calculation. Further obscurities in the model itself become apparent when solvent effects are considered ; in acid solution, for example, it is likely that a heterocyclic molecule (with lone pairs) would be protonated before reaction, and that the indices for the protonated species would therefore be relevant rather than those of the isolated molecule itself; and generally a charged reagent is a solvated ion rather than a “free” point charge, and a solvation energy term should be included in the discussion. It is largely obscurities of this kind which inhibit the application of more advanced quantum-mechanical methods, and it is clearly a prerequisite of such calculations that much more information must be available about the reaction mechanism and any intermediates involved. With these limitations in mind, it is nevertheless worth considering briefly the basic quantum mechanical ideas involved in describing the approach of a reagent R to a molecule M. The isolated molecule model is clearly satisfactory a t large distances and in Section IX it has been shown that absolute calculations of v-electron energy changes can then be made, within the framework of a reasonably realistic many-electron theory. The model is satisfactory so long as the reagent can be regarded as a point

142

H . H . GREENWOOD A N D R . MCWEENY

charge, or as an agency which simply changes some of the isolated pmameters. It must break down at shorter range where repulsions are encountered corresponding to approach to the main “hump ” in the energy curve (Fig. 18). I n the localization theory (SectionV)the hump has been associated partly with an interruption of the path of conjugation and partly with a change of a-electron energy (not calculated, but assumed constant for different positions of substitution). I n the isolated-molecule approach, failure to account for the hump is due partly to neglect of overlap between the orbitals of M and R (which can give strong repulsions), and partly to neglect of distortion of the a-bonded framework as an incipient bond with the reagent begins to form. We now formulate the problem in quantum-mechanical terms. So long as the electron distributions of M and R do not overlap appreciably, the system M + R is well-represented by a wave function of the form

+

y&fR(1,2,.* . N ) = d[pM(1,2, ...NS) Y / , ( N , 1,

.-??)I

(126)

in which ?PM is a wave function for the isolated molecule, YR for the isolated reagent and d produces a normalized and fully antisymmetrical wave function. We may then write the total electronic energy (McWeeny, 1961)

E = E‘+ER+EMR = EfK+ER (127) where EZ,= EM+ ZMR contains the whole of the interaction energy EMR, and may be represented as the energy of M with an “effective Hamiltonian” %‘Zf: this latter contains as a “perturbing potential’’ the field produced by R, regarded as a static charge distribution. The wave function YMwill be perturbed by this field, and the resultant reduction in energy is the “polarization energy ”. The basis of the isolated molecule approximation is now clearer : it involves the supposition that R is not itself polarized, the whole of the interaction energy arising from electrostatic effects plus polarization of M in the field of the unmodified radical R; and also the approximation of this latter by the field of one or more point charges. These approximations may have some validity at moderate distances, provided M has an easily polarized T system and R has not ; and in this case the indices such as P,.,and T,,,should be of some value in predicting the energy changes. At short range, however, the approximations are certainly invalid; and since the usual interpretation of Pa, for example, involves incipient bonding and therefore a fair degree of overlap, such quantities must be viewed with suspicion. Consideration of short-range effects,in which the repulsive terms which lead to the hump in the energy curve are called into play, is an extremely 1 We neglect the weaker “dispersion” interactions responsible for van der Waals forces.

REACTIVITY I N D I C E S I N CONJUGATED MOLECULES

143

difficult matter. The factorization may be retained down to shorter distances provided the overlap between YR and ?PM is properly allowed for; this does lead to strong repulsive terms in the interaction energy, but also to very cumbersome energy expressions. As the distance decreases it then becomes necessary to mix (126) with “ charge-transfer ” states involving products such as Y$Yz as invoked in a descriptive way by Fukui, Brown and others; and finally the factorization of the wave function ceases to be useful-there is only a single system, this being the system (probably with only a transient significance) which the transition state theory tries to crystallize into a specific transition complex. During these latter stages of reaction the 0-n- separation, which is valid only for the unperturbed system M, must of course break down. The difficulties of direct calculation of a complete energy curve along these lines are all too obvious, and it is clear that the isolated-molecule approximation, with its simple indices, and the transition state theory, with its various localization energies, will continue to be used in practical applications. But it is also evident that there is scope for very considerable refinements :in particular, advances in many-electron theory should now be used in putting the various indices on a surer footing, and in calculating more reliable values, and also in attempting a more realistic estimation, with due regard for the u electrons, of the localization energies. It seems clear that much progress in this direction may be expected during the next few years, thanks largely to the rapid development of computational techniques; it must be hoped that this progress will be matched in experimental studies leading to a clarification of reaction mechanisms and of the various models used to represent the successive stages of a reaction. REFERENCES Baba, H.(1957). Bull. Chem. SOC. Japan 30, 147. Baldock, G.R.(1952). Proc. Cambridge Phil. SOC.48,457. Berliner, E.(1964). “Progressin Physical Organic Chemistry”Vol. 2, John Wiley, New York, p. 253. Binks, J. H., and Szwarc, M. (1959). J . Chem. Phys. 30,1494. Brown, H.C., and Brady, J. D. (1952).J . Am. Chem. SOC.74,3570. Brown, H.C., and Nelson, K. L. (1953). J . Am. Chem. SOC.75, 6292. Brown, R. D.(1949). Arntralian J . Sci. Res. A2,564. Brown, R.D.(1959). J . Chem. SOC. pp. 2224,2232. Brown, R. D.(1963). Tetrahedron 19,SuppZ. 2, 337. Brown, R. D.(1964) in ‘‘MolecularOrbitals in Chemistry, Physics and Biology Academic Press, New York, p. 486. Chang Shih, Hey, D. H., and Williams, G.H.(1958). J . Chem. SOC. 4403. Coulson, C. A. (1939). Proc. Roy. SOC.(London) 169A,413. Coulson, C. A. (1947). DiscuseiOmr, Faraday SOC. 2,9.

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Coulson, C. A. (1948). J . chim. Phys. 45, 243. Coulson, C. A. (1955). J . Chem. SOC.1435. Coulson, C. A., and Daudel, R. (1955). “Dictionary of Molecular Constants”. Coulson, C. A., and Jacobs, J. (1949). J . Chem. SOC.2805. Coulson, C. A., and Longuet-Higgins, H. C. (1947a). Proc. Roy. SOC. (London)191A, 39. Coulson, C. A., andLonguet-Higgins, H. C. (1947b). Proc. Roy.Soc. (London)192A, 16. Coulson, C. A., and Rushbrooke, G. S. (1940). Proc. Cambridge Phil. SOC. 36, 193. Derbyshire, D. H., and Waters, W. A. (1950). J . Chem. SOC. 673. Dewar, M. J. S. (1949). Proc. Cambridge Phil. SOC.45, 638. Dewar, M. J. S. (1951). Bull. SOC.Chim. France 18, C71. Dewar, M. J. S., andLonguet-Higgins, H. C. (1954). Proc. Phy8.soc. (London)67A, 795. Dewar, M. J. S., and Maitlis, P. M. (1957). J . Chem. SOC.2521. Dewar, M. J. S., and Sampson, R. J. (1956a). J . Chem. SOC.2789,2946. Dewar, M. J. S., Mole, T., and Warford, E. W. T. (1956b). J . Chem. SOC.3581. Diercksen, C., and McWeeny, R., (1965). in press (J. Chem. Phys.). Fahrenhorst, E., and Kooyman, E. C. (1955). Nature 175, 598. Fukui, K., (1964) in “Molecular Orbitals in Chemistry, Physics and Biology”, (Academic Press). Fukui, K., Yonezawa, T., and Shingu, N. (1952). J . Chem. Phys. 20, 722. Fukui, K., Yonezawa, T., and Nagata, C. (1954a) Bull. Chem. SOC. Japan 27,423. Fukui, K., Yonezawa, T., Nagata, C., and Shingu, H. (1954b). J . Chem. Phy8.22, 1433. Fukui, K., Yonezawa, T., and Nagata, C. (1967a). J . Chem. Phy8.26,831. Fukui, K., Yonezawa, T., and Nagata, C. (1957b). J . Chem. Phy8.27, 1247. Fukui,K., Morokuma, K., Yonezawa, T., and Nagata, C. (1960). J . Chem.Phys. 32, 1743 Gold, V., and Tye, F. L. (1952). J . Chem. SOC.2172. Goodwin, E. T. (1939). Proc. Cambridge Phil. SOC.35, 221, 233. Grimley, T. B. (1958). Proc. phys. SOC.72, 103. Greenwood, H. H. (19524. Trans. Faraday SOC.48, 585. Greenwood, H. H. (1952b). J . Chem. Phys. 20, 1333. Greenwood, H. H. 1955a). J . Am. Chem. SOC.77, 2055. Greenwood, H. H. (1955b). Nature 176, 1024. Greenwood, H. H. (1957). J . Am. Chem. SOC.79, 5365. Greenwood, H. H. (1959). J . Chem. Phys. 31,553. Greenwood, H. H., and Hayward, T. H. J. (1960). MoZ. Phys. 3, 495. Hall, G. G., and Lennard-Jones, J. E. (1951). Proc. Roy. SOC.(London) 205A, 357. Hambling, J. K., Hey, D. H., and Williams, G. H. (1960). J . Chem.SOC.3782. Hammond, G. S. (1955). J . Am. Chem.SOC.77,334. Hey, D. H., and Williams, G. H. (1953). Di8cu88ions Faraday SOC.14,216. Hey, D. H., Moulden, H. N., and Williams, G. H. (1960). J . Chem. SOC. 3769. Kooyman, E. C., and Fahrenhorst, E. (1953). Trans. Faraday Soc. 49, 58. Koutecky, J., Zahradnik, R., and Cizek, J. (1961). Trans. Faraday SOC.57, 169. Levy, M., and Szwarc, M. (1955). J . Am. Chem. SOC. 77, 1949. Longuet-Higgins, H. C. (1950a). Nature 166, 139. Longuet-Higgins, H. C. (1950b). J . Chem.Phy8. 18,283.

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MacLachlan, A. D. (1959). Mol. Phys. 2, 271. MacLean, C., van der Waals, J. H., and Mackor, E. L. (1958). MoZ. Phys. 1, 247. McWeeny, R. (1955). Proc. Roy. SOC.(London) 232A, 114. McWeeny, R. (1956). Proc. Roy. SOC. (London)237A, 355. McWeeny, R. (1960). Rev. Mod. phys. 32, 335. McWeeny, R. (1961). Phys. Rev. 126, 1028. McWeeny, R. (1964). in “Molecular Orbitals in Physics, Chemistry and Biology Academic Press, New York, p. 305. McWeeny, R., and Greenwood, H. H. (1965). Unpublished calculations. McWeeny, R., and Peacock, T. E. (1957). Proc. Phys. SOC.(London) A70, 41. Melander, L. (1950). Arkiv. Kemi 2, 211. Muller, N., Pickett, L. W., andMulliken, R. S. (1954). J. Am. Chem.Soc. 76,4770. Mulliken, R. S. (1934). J. Chem. Phys. 2, 782. Mulliken, R. S. (1950). J. Am. Chem. SOC.72,600. Neebet, R. K. (1962). J. chim. Phys. 59, 750. Olah, G . A,, and Kuhn, S. J. (1958). J. Am. Chem. SOC.80, 6535. Olah, G. A., and Kuhn, S. J. (1962e). J. Am. Chem. SOC.84,3684. Olah, G. A., Kuhn, S. J., and Flood, S. H. (1961). J. Am. Chem. SOC. 83, 4571. Olah, G. A., Kuhn, S. J., Flood, S. H., and Evans, J. C. (1962b). J. Am. Chem. SOC. 04, 3687. Pariser, R., and Parr, R. (1953a). J. Chem. Phys. 21, 466. Pariser, R., and Parr,R. (1953b). J. Chem. Phy8.21, 767. Pickett, L. W., Muller, N., and Mulliken, R. S. (1953). J. Chem.Phys. 21, 1400. Pople, J. A. (1953). Trans. Faraday SOC. 49, 1375. Ridd, J. H. (1963). “Physical Methods in Heterocyclic Chemistry” 1, 109. Reid, C. (1954). J . Am. Chem. SOC. 76, 3264. Roothaan, C. C. J. (1951). Rev. Mod. Phys. 23,69. Sandorfy, C . and Yvan, P. (1949). Comptee Rendw, 229, 715. Sandorfy, C., Yvan, P., Chalvet, O., and Daudel, R. (1950). Bull. SOC. chim.France 151, 304. Stock, L. M., and Brown, H. C. (1963) in “Advances in Physical Organic Chemistry,” Volume 1, ed. V. Gold, Academic Press, London and New York, p. 35. Streitwieser, A. Jr., (1961). “Molecular Orbital Theory for Organic Chemists”, John Wiley, New York. Streitwieser, A. Jr., and Fahey, R. C. (1962). J. Org. Chem. 27, 2532. Szwarc, M. (1955). J. Polymer Sci.16, 367. Szwerc, M. (1957). J. Phy8. Chem. 61,40. Swam, M., and Binks, J. H. (1959). “Theoretical Organic Chemistry” Special Publication no. 12, The Chemical Society, p. 262. Wheland, G . W. (1942). J. Am. Chem. SOC. 64, 900. Wheland, G. W., and Pauling, L. (1935). J. Am. Chem. SOC.57, 2086.

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THE GAS PHASE PYROLYSES OF SOME SMALL RING HYDROCARBONS H. M. PREY Chemistry Department, Southampton University, England I. Introduction . 11. Cyclopropane . III. Alkylcyclopropanes . IV. Unsaturated Cyclopropanes . A. Vinylcyclopropanes . B. 1-Methyl-2-vinylcyclopropanes . C. 1,2-Divinylcyclopropanes . D. Methylenecyclopropanes . V. Bicyclopropyl . VI. Bicyclic Systems Containing Cyclopropane Rings . A. Bicyclobutane . B. 1,3-Dimethylbicyclo[l,l,O~utane . . C. Bicyclo[2,1,OJpentane D. 2-Methylbicyclo[2,1,O]pentane . E. Bicyclo[3,1,0fiexane . F. Spiro-pentane G. 3,4-Homotropilidene . VII. Tricyclic Systems Containing Two Cyclopropane Rings VIII. Cyclopropene A. Tetrfunethylcyclopropene . IX. Systems Containing Four-membered Rings . A. Cyclobutsne B. Alkylcyclobutanee . C. Dialkylcyclobutanes . X. Unsaturated Cyclobutanes . A. Isopropenylcyclobutane . B. 1.2-Divinylcyclobutanes C. trans-l,2-Dimethyl- l,2-divinylcyclobutane . D. tram-1-Isopropenyl-2-methy1-2vinylcyclobutane E. Methylenecyclobutane XI. Bicyclic Compounds Containing Cyclobutane Rings A. Bicyclo[2,l,Ofiexane . B. Bicyclo[2,l,l$exane . C. Bicyclo[B,B,O$eptane XII. Tricyclic Systems Containing a Cyclobutane Ring . XIII. Cyclobutene A. Alkylcyclobutenes . XIV. Bicyclobutenes A. Bicyclo[4,2,O]octene . B. Bicyclo[3,2,0fieptene . C. Bicyclo[2,2,0~exadiene . XV. Tricyclic Systems Containing Cyclobutene Rings . XVI. Conclusion . Referenwe .

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148 148 151 155 156 161 163 164 166 166 166 168 166 168 168 168 169 169 170 170 170 170 172 173 176 176 176 178 179 179 180

180 181 181 183 183 185 188 188 188 189 189 190 191

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H . M . FREY

I. INTRODUCTION INthe past decade the pyrolyses of small ring hydrocarbons have been very extensively investigated. Probably more work has been reported in this period than in the preceding hundred years. This development has resulted from several distinct causes. First, the discovery of many new synthetic procedures has made numerous strained ring systems relatively easily available. Second, the advent of gas chromatography has allowed the analysis of the reaction products (often of some complexity) to be carried out with ease and high precision. Third, many of the pyrolyses appear to involve truly unimolecular reactions and have been studied in order to test the well-developed theories of such transformations. As well as the major causes listed above, a number of more specific reasons have resulted in much work in some special cases. These include studies resulting directly or indirectly from an interest in the kinetics and thermochemistry of the reactions of methylene. I n some cases, interest in reaction mechanisms of some alicyclic compounds in the liquid phase has led to gas phase work. Finally in some instances the pyrolytic studies have allowed estimates of resonance energy and strain energy to be made. I n this chapter we will restrict our attention in the main to hydrocarbons containing three- and four-membered rings, and to reactions that have been investigated in the gas phase. Heterogeneous reactions will not be discussed. Liquid-phase reactions and pyrolyses of aliphatic hydrocarbons, or of alicyclic hydrocarbons not containing small rings, will be mentioned only when they help in the understanding of the results obtained in the small-ring alicyclic gas-phase reactions. Similarly, compounds containing elements other than carbon and hydrogen will be mentioned only when they throw light on the mechanisms of the reactions of the hydrocarbons being considered. 11. CYCLOPROPANE The thermal isomerization of cyclopropane to propylene is perhaps the most important single example of a unimolecular reaction. This system has been studied by numerous workers. Following the work of Trautz and Winkler (1922), who showed that the reaction was first order and had an energy of activation of about 63,900 cal mole-l measured in the temperature range 550-650" C, Chambers and Kistiakowsky (1934) studied the reaction in greater detail and with higher precision from 469-519OC. They confirmed that it was first order and, for the reaction at its highpressure limit, obtained the Arrhenius equation

k

= 1016*17 exp (- 65,OOO/RT) s0c-l

PYROLYSES O F SMALL RING HYDROCARBONS

149

From 700 to 10 mm the rate constant decreased to around 60% of the high-pressure value. Chambers and Kistiakowsky concluded that the isomerization was unimolecular and suggested two possible reaction paths. One involved the rupture of a carbon-carbon bond in the cyclopropane ring to yield trimethylene, followed by hydrogen migration to yield propylene. The other path involved hydrogen migration and carbon-carbon bond rupture occurring simultaneously, without the immediate formation of trimethylene. Much of the recent work on the cyclopropane-propyleneisomerization has had one of two objectives, either to try and determine which of the two reaction paths suggested by the early workers is involved, or to test the various theories of unimolecular reactions. Corner and Pease (1945), using catalytic hydrogenation to analyse their reaction product, but otherwise working under similar conditions to Chambers and Kistiakowsky, suggested that all the results obtained could be represented just as well by the reaction scheme CHz-

+

CH2

CH2-CH2-CH2.

.CHa-CHa-CHz

.CHz---CHo--CHz.

+

. + CH2------\

CH2

(1)

CHs--GH=CH2

(24

CH2 + 2CH3-CHdHa

(2b)

/

as by the simple unimolecular path suggested earlier. Since they found that “inert” gases did not increase the rate of reactions in the region where the rate constant was pressure-dependent, they argued against the reaction being unimolecular. However, i t is now apparent that their choice of experimental parameters was rather unfortunate, and within their analytical accuracy no appreciable increase in rate would have been observed. Pritchard et al. (1953), using an improved analytical technique, were able to study the reaction down to a pressure of less than 0.1 mm (where the rate constant is only 10 % of the high-pressure value). Their results indicated quite clearly that the reaction was unimolecular, and in the pressure region, where the rate constant had decreased appreciably addition of inert gases did lead to an increase in rate. At the same time, Slater (1 953) applied his theory of unimolecular reactions to this isomerization. The Slater theory starts initially from the earlier treatments of Hinshelwood and Lindemann. It provides a dynamic representation of how a molecule with sufficient energy reaches the “configuration” of the activated complex. The model treats a11 oscillators as simple harmonic,

160

H. M. FREY

no intramolecular energy transfer between oscillators occurring between collisions. A critical co-ordinate is selected in the molecule undergoing reaction (equivalent to the reaction co-ordinate in transition state theory) and reaction occurs when this co-ordinate exceeds a definite magnitude. Large changes in the magnitude of this co-ordinate occur owing to the fortuitous coming into phase of the various oscillators. The application of the Slater theory requires a complete vibrational description of the reactant, but the only kinetic information required is the energy of activation. By selection of the carbon-hydrogen distance between atoms not bonded in the cyclopropane molecule as the critical co-ordinate, Slater computed the fall-& curve for the isomerization reaction. The agreement between theory and experiment was remarkably good. This is equivalent to the second reaction path mentioned earlier. Slater further showed that if a reaction co-ordinate depending solely on carbon-carbon bond rupture was used (corresponding to the formation of trimethylene intermediate), no agreement between theory and experiment was possible. On the basis of these calculations the hydrogen migration mechanism was for some time accepted as the most probable reaction path. More recently the situation has changed considerably. Much evidence has accumulated which indicates that intramolecular energy transfer is a rapid process, and hence this casts doubt on the validity of the simple Slater model. (It should also be noted that in unimolecular reactions where there is a large entropy change, owing to large differences in vibrational frequencies between the activated complex and the ground state molecule, the simple model must fail.) It may well be that the apparent agreement between theory and experiment is largely fortuitous. I n addition Golike and Schlag (1963) have shown that the experimental results do not rule out a carbon-carbon rupture mechanism, provided that a sufficiently complex reaction co-ordinate is chosen. Attempts to defke the reaction path more precisely have resulted in work with deuterium- and tritium-labelled cyclopropanes (Blades, 1961; Rabinovitch et al., 1961; Weston, 1957; Linquist and Rollefson, 1956). This work has received considerable theoretical discussion (Benson and Nangia, 1963). Much of it is beyond the scope of this review and will not be considered further. However, one investigation of particular interest involving the 1,2-dideuterio-cyclopropanesrequires some discussion. Rabinovitch et al. (1958) observed that trans- and cis-1,2-dideuteriocyclopropanes undergo a reversible geometrical isomerization at around 400" C. This geometrical isomerization appeared to be unimolecular, and was faster than the structural isomerization to propylene. I n a more detailed investigation of this reaction, Schlag and Rabinovitch (1960)

PYROLYSES O F SMALL RINQ HYDROCARBONS

151

confirmed its unimolecular nature, and determined the high-pressure Arrhenius constants, viz. :

k

=

1018.4exp(- 65,10O/RT)sec-I

The rate constants were determined at a series of pressures in the fall-off region, and the fall-off curve was very similar to that obtained for the structural isomerization to propylene. The similarity of the two sets of data suggests that both reactions may proceed through similar reaction paths. One obvious possibility is that once again the trimethylene biradical is formed, which can undergo internal rotation followed by recyclization. An alternative transition state has been suggested which invoIves, as an activated complex, a much expanded cyclopropane ring in which hindered internal rotation occurs (see also Smith, 1958). 111. ALKYLCYCLOPROPANES The cis-trans isomerization of cyclopropanes is not restricted to the deuterium-substituted molecules. cis- and trans-1,2-Dimethylcyclopropane have been shown to undergo reversible geometrical isomerization as well as slower structural isomerization. All the processes are homogeneous and kinetically first order, and almost certainly unimolecular. The reaction scheme is shown below.

&[

]-

CH3.CH2. C H = CH .CHI cisandtrans (CHs)& = CH. CH3

Ckrr

CHI.CHi(CH3)C = CHz The Arrhenius equations for the various reactions are shown in Table 1. The geometrical isomerizations of 1,2,3-trimethylcyclopropaneand 1-ethyl-2-methylcyclopropanehave also been studied. I n both cases geometrical isomerization is faster than the structural isomerization reactions to yield olehs. The Arrhenius equations obtained were :

k,,

-,trans

k&# -,

(trimethylcyclopropane) = (Frey and Marshall, l963),

exp ( - 60,95O/RT) sec-l

(ethylmethylcyclopropane) = 10l6'O8 exp ( - 58,87O/RT)sec-l (Elliott and Frey, 1964).

H. M. FREY

152

TABLE1 Arrhenius Parameters for the Isomerizations of 1,2-Dimethylcyclopropanes~

E (kcal logloA mole-')

Product

Reactant

cis- 1,2-dimethylcyclopropane trans-1,2-dimethylcyclopropane cis-l,2-dimethylcyclopropane 2-methylbutene-1 2-methylbutene-2 cis-1,2-dimethylcyclopropane c~s-l,2-dimethylcyclopropane cis-pentene-2 trans-pentene-2 cis-1,2-dimethylcyclopropane trans-1,2-dimethylcyclopropane 2-methylbutene-1 trans- 1,2-dimethylcyclopropane 2-methylbutene-2 trans- 1,2-dimethylcyclopropane cis-pentene-2 trans-1,2-dimethylcyclopropane trans-pentene-2 4

15.25 13.93 14.08

13-92 13.96 13.93 14.08 14.40 14.30

59.42 61.90 62.30 61.40 61.20 61-90 62.30 63.60 62.90

Flowers and Frey (1960, 1961a).

The structural isomerization of a number of alkyl substituted cyclopropanes has been investigated. I n all cases the reaction is probably unimolecular. I n general several olefins are formed. The results obtained are shown in Table 2. It is to be expected (especiallyif a diradical is an TABLE2 Arrhenius Parameters for the Structural Isomerization of Alkylcyclopropanes

Reactant

-

methylcyclopropane

1,2-dideuterio-3-methylcyclopropane ethylcyclopropane 1,l-dimethylcyclopropane 1,l -diethylcyclopropane 1,1,2,2 -tetramethylcyclopropane

logioA

E(kca1 mole-1)

15.45

GB.0

14.43

62.3

'1

14.40

61.6

}

15.06

6243

14-95 14.84 15.83

63.8 63.4 64.4

Product ~

butene- 1 cis- and trans-butene-2 isobutene As above pentene-1 cis- and trans-pentene-2 2-methylbutene-1 2-methylbutene-2 3-methylbutene-1 3-ethylpentene-1 3-ethylpentene-2 2,4-dimethylpentene-2

1 J

i

intermediate) that the more highly substituted alkylcyclopropanes will isomerize with a lower energy of activation than cyclopropane itself, owing to the higher stability of a tertiary or secondary radical than a

153

PYROLYSES O F SMALL RING HYDROCARBONS

primary one. This effect may be somewhat masked by experimental may be compensated by errors (where apparently high values of EaCt high A values). We prefer therefore to look at the rates of isomerization of a number of alkylcyclopropanes at one particular temperature, somewhere in the middle of the temperature range of these studies, where the experimental errors are at a minimum. The results are shown in Table 3. From the table it can be seen that substitution of each methyl or ethyl TABLE 3 Rate Constants for Structural Isomerization at 730"A

Reactant

lO5k (sec-1)

cyclopropane methylcyolopropane ethylcyclopropane 1,l -dimethylcyclopropane 1,l -diethylcyclopropane 1,1,2,2-tetrarnethylcyclopropane

6.46 9.60 11.7 20.0 20.0

34.8

Path degeneracy

12 10 10 8 8 4

Corrected 10% (sec-1)

6.46 11.5

14.0 30.0 30.0 104

group results in approximately doubling the rate. I n the cases of methylcyclopropane (Chesick, I960), ethylcyclopropane (Halberstadt and Chesick, 1965),and 1,l-dimethylcyclopropane(Flowersand Frey, 1962a) the reactions have been studied a t sufficiently low pressures to observe a decrease in rate constant with pressure. As is to be expected from unimolecular reaction theory, the pressure a t which this occurs decreases as the complexity of the molecule increases. On pyrolysis, in addition to the expected C5olefins, ethylcyclopropane also yields butadiene and methane (this constitutes an important reaction path, the yield of butadiene being about 20% of the total products). This type of decomposition is probably general for ethylsubstituted cyclopropanes, since 1 , l -diethylcyclopropane yields 2ethylbutadiene and methane as well as C, olefins (Frey and Marshall, 1965). It is possible that the decomposition to the butadiene is also a simple unimolecular process via a transition state such as shown below.

A similar transition complex can be written for the decomposition of the 1 , l diethylcyclopropane. However, since the pre-exponential factor for 6

H. M. FREY

154

the decomposition path in the case of the diethyl compound is 1016.44 (indicating a very large positive entropy of activation), it seems Unlikely that this mechanism, with its fairly rigid geometrical requirements for the transition complex, can be correct. (With this complex it is unlikely that the A factor would be greater than lo1'.) The alternative possibility is that the decomposition proceeds by a radical chain mechanism. For ethylcyclopropane Halberstadt and Chesick (1965) have suggested the following scheme : I'

-

J

fast

~H~-TH-CH-=CHZ I

kH3---H

\

CH4 + C4Hs

A similar mechanism could be operative in the case of the diethyl compound. An alternative scheme, which we outline for the case of 1 , l diethylcyclopropane, is

followed by abstraction of a hydrogen atom by the methyl radical from the Cs olefins formed by the normal cyclopropane isomerization Et

Et

\

CH-CH==CHz

/

+ .CHa

+

CH4

+

\.CCH=CHa /

(6)

Et

Et or

Et

Et

\

\

/

Et

CH=CH--CHs+ .CHs

-+

CHI+

C==CH-6Ha

/

Et

(6)

P Y R O L Y S E S OF S M A L L R I N G H Y D R O C A R B O N S

155

Both these reactions would be very fast at 400' C and lead to the same resonance-stabilized radical. CH2

Et

\.C=CH=CH2

/

Et

\\

+

CCH=CHs

/

+ .CHa

(7)

Et

These processes constitute a chain reaction. There are many possible chain-ending steps, which could account for some of the minor products observed in the pyrolysis. Certainly the pyrolyses of 3-ethylpent-1-ene and 3-ethylpent-2-ene do yield ethylbutadiene, but the rate of production of the diene is considerably slower than in the pyrolysis of the cyclopropane. Thus reaction (4) represents a sensitization of these latter processes. Further, unlike Chesick, we envisage the formation of the methyl radical from the cyclopropane to involve the rupture of the cyclopropane ring, and believe that this concerted process should be energetically favoured over the two-step mechanism. There are several simple experimental tests that could be used to decide between these mechanisms. IV. UNSATURATED CYCLOPROPANES

A. Vinylcyclopropanm Overberger and Borchert (1960) were the first to report that the pyrolysis of vinylcyclopropane yielded cyclopentene as the major product. Independently Flowers and Frey (196lb) studied this isomerization and found that it was homogeneous and kinetically first order and almost certainly unimolecular. The Arrhenius equation for the isomerization was found to be

k

= 1013'6 exp (-

49,6001RT) sec-I

I n a more detailed investigation Wellington (1962) determined the Arrhenius parameters for the isomerization to the minor products as well as those for the reaction leading to cyclopentene. The results are shown below.

k (cyclopentene) = 61 exp ( - 49,70O/RT) sec-' k (penta-l,4-&ene) = 1014'43exp(-57,30O/RT) sec-l k (tram-penta-l,3-&ene) = 1013'00exp( - 53,6OO/RT)sec-l k (cis-penta-1,3-diene) = 1013.90 exp ( - 56,20O/RT)sec-l I n none of the work was any isoprene detected.

H . M. FREY

156

It will be noted that the isomerization to cyclopentene proceeds with a considerably lower energy of activation than the other cyclopropane isomerizations so far discussed. As a result these reactions have been investigated kinetically at temperatures about 100’ lower than those not having a vinyl substituent. A number of substituted vinylcyclopropanes have been studied and the Arrhenius parameters for their isomerizations to substituted cyclopentenes determined. The results are shown in Table 4. From the results in Table 4 it can be seen that the isomerizations TABLE4 Arrhenius Parameters for the Isomerizations of Vinylcyclopropanes to Cyclopentenes

Reactant vinylcy clopropane isopropenylcyclopropane 1 -methyl-1-vinylcyclopropane trans-1-cyclopropyl-butene-1 1 -methyl-1-isopropenylcyclopropane

loglo A

E(kca1 mole-’)

cyclopentene 1-methylcyclopentene 1 -methylcyclopentene 3-ethylcyclopentene

13.61 13.89 14.11 13.79

49.7 50.9 49.35 49.98

1,2-dimethylcyclopentene

14.14

50.5

Product

all have energies of activation of around 50 kcal mole-l and “A” factors nearly two orders of magnitude lower than for the &-trans isomerization of cyclopropanes. These results can be explained by the formation of an allylically stabilized biradical as the intermediate :

We picture the energy diagram for this mechanism as that shown in Fig. 1. The biradical when formed will have sufficient energy to recyclize to the cyclopropane and, if the energy barrier is no higher than pictured, it will also be energized with respect to isomerization to the cyclopentene. If the energy barrier for isomerization is lower than shown, isomerization to the cyclopentene will be faster than recyclization to the cyclopropane. (Experimental data are not yet available about this possibility.) Essentially the same potential-energy diagram would be required for the biradical mechanism for the cis-trans isomerization of cyclopropanes. Under these circumstances, we may equate the difference between the

PYROLYSES OF SMALL RING HYDROCARBONS

167

energy of activation of the two processes for analogous compounds with the allylic resonance energy. A treatment of this kind for a number of pairs of compounds yields a value of 13 & 1 kcal mole-l. The most recent estimate for the allylic resonance energy comes from the studies of Benson and his co-workers on iodine-catalysed isomerization reactions. They obtained a value of 12.6 f 1 kcal mole-l (Eggar et al., 1964) which is in excellent agreement with the value quoted here. It is of course possible that the isomerizations of vinylcyclopropanes to cyclopentenes occur by a one-step concerted process, and that the agreement noted in the allylic resonance energy values results from a fortuitous cancellation of two

T

w

Reaction Co-ordinote

FIQ.1.

effects. Further evidence on this point will be presented later, but at this stage we note that the agreement strengthens the case not only for the biradical intermediate in the unsaturated cyclopropanes but also for the saturated compounds. It will also be noted from the results in Table 4 that, unlike the saturated cyclopropanes, the vinylcyclopropanes isomerize with normal preexponential factors. Consideration of the postulated transition complex and the reactant molecule makes it clear why this is so. I n the reactant the vinyl group can undergo essentially free rotation. I n the transition complex the allylic part of the biradical is rigid and cannot rotate. Thus the entropy contribution of this free rotation in the reactant is lost on forming the transition complex. As a result of ring rupture one new centre of free rotation is produced which is not present in the reactant. The result of these effects is that on passing from the reactant to the

H. M. FREY

158

transition complex there is almost no entropy change, and the isomerization proceeds with a normal A factor. The formation of dienes in the isomerization of vinylcyclopropanes is analogous to the formation of olefins in the isomerization of saturated cyclopropanes. Again we envisage the mechanism as involving an allylically stabilized biradical as the first step. Hydrogen atom transfer can now occur to yield the dienes as the second step. Since these reactions have a higher energy of activation than the ring-closure reaction we picture the energy diagram as that shown in Fig. 2. One of the steric requirements for complete allylic resonance is that all the seven atoms involved (three carbon and four hydrogen) should be in a plane. If the

1

Reaction Co-ordinate

FIQ.2.

vinyl group is substituted in the cis position, then this steric requirement will result in some interference in the cyclization to the cyclopentene. Ring closure can only occur after some rotation about the terminal bond in the allylic system has taken place, and such rotation decreases the overlap of the r electrons, which in turn means that full allylic resonance energy is not available. This implies that in such cis-substituted compounds the reaction path is analogous to that for the isomerization to dienes, i.e., the barrier to ring closure to a cyclopentene is greater than that to the initial formation of the biradical. It is therefore to be expected that cis-substituted vinylcyclopropanes will isomerize with higher energies of activation than tram-compounds. This expectation has been realized in the case of cis- and tram-I-cyclopropyl-1-(p-methoxypheny1)prop-1-ene. Berlin et al. (1965) have reported that in the temperature range 332-371' the trans-compound readily rearranges to the cyclo-

159 pentene. However, the cis-compound shows no measurable isomerization in the time required for complete conversion of the trans-compound to the cyclopentene. Exactly the same argument will hold for a &substituted vinyl group. This haa been verified experimentally in the case of l-cyclopropyl-2methylpropene (Elliot and Frey, 1965a). The Arrhenius equation for the isomerization to 3,3-dimethylcyclopenteneis P Y R O L Y S E S O F SMALL R I N G H Y D R O C A R B O N S

k

=

1014’00exp (-54,60O/RT) 8ec-l

Thus the rotation of the allylic system out of the plane (required before ring closure can occur) results in the reduction of the “available allylic

resonance energy” by about 5 kcal mole-l. This particular steric requirement does not apply to the isomerizations to the dienes, and these have much the same values as for vinylcyclopropane itself, viz. : k(5-methylhexa-l,4-diene) = 1014’61 exp ( - 56,65O/RT)sec-l k(cis-2-methylhexa-2,4-diene) = 33 exp ( - 53,00O/RT)sec-l k(trans-2-methylhexa-2,4-diene) = 1013’26exp ( - 52,10O/RT) sec-l

Since the isomerization to the cyclopentene is made more difficult by the substitution, but the isomerizations to the dienes are unaffected, the result is that (unlike the case of vinylcyclopropane itself) the dienes now constitute major products of the reaction. The rearrangements of a series of I-p-substituted phenyl-l-cyclo-

1

1

I

T

w

I

D-0 T

160

H . Ed. F R E Y

propylethylenes have been studied (Ketley and McClanahan, 19654. With the exception of the fluorine substituted compound, they all isomerize at virtually the same rate (whichis close to the extrapolated value for isopropenylcyclopropane). The p-fluoro compound isomerizes at about half this rate at 350". The cause of this rather small effect is not clear and needs further experimental work. A number of other vinylcyclopropanes have been studied qualitatively. Some of them are shown on p. 159. I n all cases the isomerizations occur at 300" C which indicates that their energies of activation are probably close to that for vinylcyclopropane (Doering and Roth, 1963).

A particularly interesting exampleisthat of 1,2-dicyclopropylethylene. I n this case, the rearrangement of one of the cyclopropyl rings leads to a product which still contains a vinylcyclopropane system, and hence

Time ( m i d FIa. 3. The thermal isomerization of 1,l-dicyclopropylethylene.(X) axis Time in minutes; (Y) axis Percentage yield; 0 , 1,l-dicyclopropylethylene;0 , l-cyclopropylcyclopentene; 0,bicyclo[3,3,0]octene-1.

P Y R O L Y S E S O F SMALL RING HYDROCARBONS

161

there is the possibility of further isomerization. An alternative is a concerted attack leading directly to the bicyclo-octene, (See equation 9) Preliminary experiments by Ketley and McClanahan ( 1965b)indicated that the reaction proceeds predominantly or entirely by the two-stage process, the direct process (k3) being insignificant under their experimental conditions. A more detailed study of this reaction (Branton and Frey, 1965)confirms these findings and the results at 372.4" C are shown in the figure. The curves are exactly those expected for two consecutive first-order processes and the rate constants kl and kz are found to be sec-l and 4.30 x sec-l. 9.72 x

B. 1-Methyl-2-vinylcyc1opropane.s cis- 1-Methyl-2-vinylcyclopropane undergoes yet another type of isomerization. At temperatures around 200°C it rearranges by a unimolecular process to yield cis-hexa-1,4-diene as the sole product (Ellis and Frey, 1964a). A detailed study of this reaction yielded the Arrhenius equation k = 1011'03exp( - 31,24O/RT)sec-l Both the frequency factor and the energy of activation are far smaller than for the other cyclopropane isomerizations discussed so far. The small frequency factor suggests a very rigid transition complex, in which the free rotation of the methyl and vinyl groups has been lost. The postulated complex is shown below.

The ring complex shown would account for the low A factor, and further explains the formation of only cis-diene. This 1,5-hydrogenshift mechanism has also been postulated to account for the thermal isomerization of a number of 1,3-dienes (Wolinsky et al. 1962). This type of isomerization has been studied in detail as applied to the reversible interconversion of cis-Z-methylpenta-l,3-diene and 4-methylpenta-l,3-&ene, CH3 HzC\\,

c-c

.H3C'

>CH H '

e

H3C

CH2 )XI

\c=c

H3C'

'H

The Arrhenius equation for the cis-%methyl to the 4-methyl compound is

k = 1011'43exp( - 32,76O/RT) sec-l 6*

162

11. M . P R E Y

(Frey and Ellis, 1965). The Arrhenius parameters are very close to those obtained for the cis-1-methyl-2-vinylcyclopropaneand support the postulated similarity of the two transition states. Further evidence that the low A factor arises mainly from the loss of internal rotations in the transition complex, comes from the work of Grimme (1965)on the thermal isomerization of bicyclo[5,1,0]octene-2 to cyclo-octa-l,4-diene.

The Arrhenius equation was found to be

(k,+ k,)

=

exp ( - 38,600 & 600/RT) sec-I

Since the equilibrium is largely in favour of the octadiene, k, k2,and hence these Arrhenius parameters must be very close to the values for the forward reaction. The “normal” value for the A factor is to be expected in this case since the reactant has a rigid structure with no possibility of free internal rotations, and hence there is little entropy change on going to the transition complex. trans-1-Methyl-2-vinylcyclopropane undergoes isomerization only at temperatures over 100” higher than are required for the cis compound. The major product is however the same, viz. cis-hexa-l,Cdiene, but 3-methylcyclopentene is also formed as a minor product ( N 8 %). The Arrhenius equations for these two isomerizations are given below :

k (cis-diene) =

7 4 exp (

- 48,64O/RT) sec-l

k (cyclopentene) = 1013*67exp ( - 48,64O/R27) sec-l (Ellis and Frey, 1964b). The minor path of the reaction is of the type already discussed for other vinylcyclopropanes, and within experimental error the Arrhenius parameters are identical with them. The Arrhenius parameters for the isomerization to the cis-diene differ markedly from those for the analogous process starting from the ciscyclopropane. However, in the case of the trans-1-methyl-2-vinylcyclopropane stereochemical reasons prevent this reaction occurring directly by the transition state postulated for the cis-cyclopropane. To reach such a transition state, the cyclopropane ring must first break and rotation must occur. Once rotation occurs then the reaction path leading to the cis-dienebecomes easy, and this reaction will occur rapidly. Thus, accepting this mechanism, we associate the energy of activation of the process with that required for ring rupture. Again a comparison of this energy of activation with that for the trans-cis isomerization of

P Y R O L Y S E S O F SMALL R I N Q HYDRO CARBO NS

163

1-methyl-2-ethylcyclopropaneyields a value for the allylic resonance energy of 11.5 k 1.5 kcal mole-l, in good agreement with the other estimates previously discussed. The “high” frequency factor is also to be expected for this mechanism.

C. 1,2-Divinylcyclopropanes cis-l,2-Divinylcyclopropane does not yet seem to have been isolated. I n reactions where it would be the expected product the compound actually isolated has always been 1,4-~ycloheptadiene.Thus pyrolysis of the di-quaternary hydroxide shown below at 80°C yields only this diene :

Even the reaction of diazomethane in the presence of cuprous chloride with cis-hexatriene at -40°C yields this cyclic diene rather than the cyclopropane :

C-[C]--O (Vogel, 1962; Vogel et al., 1961.) It would thus appear that the isomerization of the cis-1,2-divinylcyclopropane occurs with a very low energy of activation. trans-l,2-Divinylcyclopropane has been prepared and isolated. As is to be expected, it is far more stable than the cis-compound and its thermal isomerization may be readily studied (Vogel and Sunderman, 1965). The major product ( > 99 %) is again 1,4-cycloheptadiene with less than 1% of 4-vinylcyclopentene, and the rate data fit the Arrhenius equation

k

=

1012.09exp( - 32,10O/RT) sec-l

The simplest explanation of these results is that the reaction involves the cleavage of the cyclopropane ring to give a biradical, which is doubly stabilized by allylic resonance. Rotation of the biradical allows ring

164

H. M. FREY

closure to yield the cyclic diene. The rather low A factor may appear surprising for a reaction involving ring cleavage, but it must be remembered that in the reactant the two vinyl groups can undergo internal rotation, whereas in the biradical the resulting two allylic groups cannot. If the suggested transition state is correct, then a comparison of the energy of activation for this isomerization with that for the trans-cis isomerization of trans- 1,2-diethylcyclopropane should yield a value for the allylic resonance energy. Unfortunately data are not available for the diethylcyclopropane. However the corresponding value for 1-ethyl2-methylcyclopropane is 60.1 kcal mole-l. We may estimate that the value for the diethyl compound is likely to be slightly lower than this. Using this figure we find the allylic resonance energy to be a little less than 14 kcal rnole-l, in fair agreement with other estimates. It is interesting to note that the epoxides

undergo analogous isomerizations.

D. Methylenecyclopropana The thermal rearrangement of Feist's acid has been known for a long time, and Ettlinger (1952) suggested the current accepted structure of the product, viz., CO.OEt

210"

CO.OEt

EtO.OC.CH CO. O E t

More recently this reaction has been investigated by Ullmann (1959, 1960). While the presence of a carboxyl group attached to the cyclopropane ring facilities the reaction, it is by no means essential. Thus at 250' the followingrearrangement occurs (Ullmann and Fanshawe, 1961):

4

CH2.CO.OCH3

-

[)ECH.CHz.CO.

OCH3

Chesick (1963) has studied the thermal reversible isomerization of ethylidenecyclopropane in the gas phase

PYROLYSES O F SMALL R I N G HYDROCARBONS

165

for which

(k,+k,) = 1014'26exp( -40,45O/RT) sec-' At 210°C the equilibrium constant is 1-3. This isomerization may take place by a concerted mechanism or via the intermediate formation of an allylically stabilized species as shown below :

For maximum stabilization this intermediate must be planar, and this means that some twisting must take place in the cyclopropane before the ring ruptures. This process is greatly helped energetically by the resulting overlap of the T electrons of the double bond with the vacant orbitals which result from the incipient carbon-carbon bond rupture. We will consider this process further in a later section.

V. BICYCLOPROPYL The decompositionof this compound has been studied between 408 and 474°C (Flowers and Frey, 1962b). The overall rate of decomposition is given by k = 1016'S6exp(-60,71O/RT) sec-' The primary decompositions occurring by parallel first-order processes yield cyclohexene, butadiene plus ethylene, and four cyclopropylpropenes. The cyclopropylpropenes formed initially decompose to yield various c6 dienes at rates comparable with those of the primary reactions, and this leads to a complex reaction mixture that contains at least seventeen products.

VI. BICYCLIC SYSTEMS CONTAININGCYCLOPROPANE Rwas A. Bicyclobutane The recent syntheses of this compound have made it available for thermal studies (Wiberg and Lampman, 1963; Frey and Stevens, 1964; Srinivasan, 1963). Above 190"C, bicyclobutane isomerizes to butadiene. The reaction is predominantly homogeneous but there is some evidence for a small heterogeneous component of the reaction. The results of Srinivasan et al. (1965) yield the Arrhenius equation

k

=

1014'62exp(-41,4OO/RT) seC1

166

H. M. F R E Y

and those of Frey and Stevens (1965) yield

k

=

1014'02exp( - 40,58O/RT) sec-I

Since Frey and Stevens did not observe an appreciable surface effect, the small differences between the Arrhenius parameters may well depend on the differences in conditions. At first sight the relatively high value for the energy of activation for this isomerization is surprising. Cyclobutene isomerizesto butadiene more readily than does bicyclobutane and yet the strain energy of bicyclobutane of ca.69 kcal moled1 is likely to be about 16 kcal molew1 more than that for cyclobutene. It has been suggested that the isomerization of bicyclobutane occurs by a concerted process, and that the relatively high energy of activation is to be ascribed to the great differences in geometry between reactant and product, leading to a highly strained transition state.

B. 1,3-Dirnethylbicyclo[l,1,O]butane Chesick (1964) has reported the thermal isomerization of this compound for which there are now thermochemical data (Turner et al., 1965). The only product was 2,3-dimethylbutadiene. Once again the results suggest a concerted process for the reaction. Above 260' the reaction appears to be entirely homogeneous, and using these data one obtains

k

=

1014*45exp (-43,3OO/RT) sec-l C. Bicyclo[2,1,0-Jpentane

The thermal isomerization of this compound was first studied in detail by Halberstadt and Chesick (1962)in the temperature range 288-310OC and in the pressure range 67 to 0.04 111111, and was found to be homogeneous and kinetically first order. Cyclopentenewas the major product ( > 99 yo)and the high-pressure Arrhenius equation obtained was

k

=

1014*68exp ( - 46,60O/RT) sec-l

A minor product (correspondingto about 0.5 %of the cyclopentene peak) was detected which had the same retention time as methylenecyclobutane. At pressures below 3 mm the rate constant decreased with pressure and fell to approximately one half of the high-pressure value at 0.07 mm. The results obtained could be fitted by the Kassel equation by assuming that the reactant had eighteen effective oscillators. The data are thus consistent with the isomerization being a truly unimolecular transformation. On the basis both of the observed energy of activation and thermochemical data and of estimates of bond strengths, these

P Y R O L Y S E S O F SMALL R I N G H Y D R O C A R B O N S

167

authors argue that the process does not take place via the intermediate formation of a cyclic biradical, viz.

but rather via,

rJ --H

Steel et al. (1964) reject these arguments and do not consider that the reaction path represented by equation (11)can be eliminated :indeed they favour this scheme. Their own work on this isomerization, carried out over a somewhat wider temperature range, yielded the Arrhenius equation for the formation of cyclopentene

k

=

1014'10exp(-45,60O/RT) sec-l

I n addition they noted the formation of some penta-l,4-diene. This appears to be a primary product formed by a parallel isomerization of the bicyclopentane. The Arrhenius equation for this reaction path is

k

=

1014'36exp(-52,30O/RT) sec-'

Steel et al. therefore suggest this modification of equation (1l ) ,

It appears likely that the peak reported by the earlier workers as having the same retention time as methylenecyclobutane, was in fact penta-l,4diene. Some support for this comes from the observation that highly energetic bicyclopentane (produced by the addition of methylene to cyclobutene) isomerizes to cyclopentene and to penta-l,.l-diene at almost equal rates, but no methylenecyclobutane is formed (Elliott and Frey, 1965b).

168

H . M. FREY

D. 2-Methylbicyclo[2,1,O]pentune Chesick (1962) investigated the kinetics of the cis-trans isomerizatioii of 2-methylbicyclopentane from 203 to 232' C. The data indicate that the reaction is unimolecular with (k&,

+ kt,,,,)

=

1014'45 exp ( - 38,90O/RT) sec-l

By similar arguments to those used earlier he concludes that the isomerization does not involve the cyclic biradical. However, the objections of Steel et al. (1964) mentioned earlier in the case of the unsubstituted bicyclopentane isomerization are just as relevant in this case. It appears therefore that there is as yet no conclusive evidence against a biradical intermediate (though this in itself does not imply that such an intermediate must be involved), and the situation in respect of the probable transition state is remarkably similar to that of the simple cyclopropane isomerizations.

E. Bicycle[3,1,Olhezane The thermal isomerization of this compound in the temperature range 420-490" C gives rise to two major products, cyclohexene and l-methylcyclopentene: kcyclohexene = kmethylcyclopentene

1013'29exp (-57,40O/RT) sec-I - 1013'89exp( - 61,1701RT) sec-l

When these results are compared with those obtained for the isomerization of cis-l,2-dimethylcyclopropaneit is seen that the presence of the second ring system results in a more rigid transition state (Frey and Smith, 1962).

F. Spiro-pentune This compound undergoes a first-order thermal isomerization to give methylenecyclobutane in the temperature range 360-410' C (Flowersand Frey, 1961~).The rates of isomerization fit the Arrhenius equation

k

= 1015'86exp(-57,57O/RT) sec-l

The very large value of the pre-exponential factor indicates a transition complex which is very "loose" compared with the highly strained spiro-pentane structure. Inspection of the "models " of the reactant and product makes it clear that considerable distortion of the reactant must occur on going to the transition complex. A minor reaction path results in the formation of allene and ethylene. These products are primary,

169 since at these reaction temperatures methylenecyclobutane itself is relatively stable. PYROLYSES O F SMALL R I N G HYDROCARBONS

G. 3,4-Homotropilidene I n this compound the Cope rearrangement, which occurs with cis-1,2divinylcyclopropane, will not produce a new compound, viz.,

The occurrence of the reaction can however be detected by N.M.R. spectroscopy (for a detailed discussion of the observed spectra, see Doering and Roth, 1963). It is estimated that 3,4-homotropilidene undergoes this rearrangement about 1000 times per second a t 180"C and about once per second at - 50' C. These data require further verification since they lead to highly improbable values for the A factor and for the energy of activation of the reaction. At much higher temperatures the compound isomerizes irreversibly to tetrahydropentalene :

VII. TRICYCLIC SYSTEMS CONTAINING Two CYCLOPROPANE RINGS No complete kinetic experiments have yet been described for the isomerization reactions of tricyclic systems containing two cyclopropane rings. A number of preliminary observations have been reported and some of the isomerizations noted are given below.

170

H. M. FREY

While activation energies for these reactions have not yet been obtained, i t is clear from the temperatures at which the isomerizations have been found to occur that they must have significantly smaller energies of activations (perhapsby as much as 10to 15 kcal mole-l) than those for the cis-tram isomerizations of dialkylcyclopropanes. This suggests that the two cyclopropane rings can co-operate, especially if the geometric arrangement is favourable.

VIII. CYCLOPROPENE If stored as a liquid, even at - 78', cyclopropene undergoes a fairly rapid polymerization reaction. However, in the gas phase, at temperatures above 325' (in a stream of helium), it isomerizes smoothly to yield methylacetylene. This is clearly analogous to the isomerization of cyclopropane to propylene. A. Tetramethylcyclopropene

The pyrolysis of this compound at around 490' in a stream of nitrogen yields 1,2,3-trimethylbuta-l,3-diene.Unlike the parent compound, it does not yield a substituted acetylene (Stechl, 1964). It is thus apparent that the movement of a hydrogen atom is much easier than that of a methyl group. It is possible that the isomerization involves a fivemembered ring, viz. :

y

__f

J = = J+ Ha

g'

(13)

Since the diene readily forms an adduct with maleic anhydride it probably has the stereochemistry demanded by the reaction path shown in equation (13).

IX. SYSTEMS CONTAINING FOUR-MEMBERED RINGS

A . Cyclobutane The thermal decomposition of cyclobutane to yield ethylene has been very extensively investigated (Genaux and Walters, 1961; Kern and Walters, 1952, 1953). The reaction is homogeneous and kinetically first order. Addition of inhibitors to the reactant does not affect the rate, and

P Y R O L Y S E S O F SMALL R I N G H Y D R O C A R B O N S

171

it is concluded that no chain processes are involved. At pressures below about 100 mm the rate constant falls with decreasing pressure, but the high-pressure value may be regained by the addition of inert gases (Pritchard et al., 1953). All the evidence indicates that the decomposition is of a unimolecular nature, with the high-pressure rate constant given by k = 1016'6exp( - 62,50O/RT)sec-l

At very low pressures (below 0.001 mm) the rate constant again becomes independent of pressure. The exact pressure at which this occurs depends on the dimensions of the reaction vessel (Butler and Ogawa, 1963; Vreeland and Swinehart, 1963). The simplest explanation of this effect is that activation and deactivation by the walls of the reaction vessel are now playing a major part in the reaction; however, more experimental work is required before definite conclusions can be drawn. The pyrolysis of 1,1,2,2-tetradeuteriocyclobutanegives rise to CZH4, C2H2Dzand CzD4 in ratios close to 1:2 :1. Thus the direction of cleavage of the cyclobutane ring is hardly affected by the substitution. Copyrolysis of a mixture of cyclobutane and cyclobutane-d, at a number of temperatures showed that the deuteriated compound decomposes with an energy of activation about 500 cal greater than the undeuteriated molecule (Srinivasan and Kellner, 1959). The decomposition of completely deuteriated cyclobutane has also been studied (Langrish and Pritchard, 1958). The decomposition of cyclobutane can be discussed in terms of two quite distinct types of transition complex. I n the &st we imagine the simultaneous lengthening of two of the carbon-carbon bonds and the contraction of the other two to yield a complex very like the product molecules, viz. : 'H~C-CHZ ( I H&-CHZ

-

+

:

HzC--CH? I 1 I I 1 HaC-CHz

CZH4

+

--f

CsHi

I n order to account for the large positive entropy of activation for the reaction, it is necessary to assume that there is virtually free rotation of the incipient ethylene molecules in the complex. The second possible transition complex involves the complete rupture of one carbon-carbon bond to give the tetramethylene biradical, and the reaction path may be envisaged as shown below : TI?('-

C'Ha

H2C-CH2

H?C---(;'Hr &Hz

/ j e&C.' .CH2 ' - -H!(2 7

H2C-CHa

-

2CeH4

172

H. M. FREY

Calculations based on this second model give the observed value for the entropy of activation. I n addition, this model may be used to account for the observed isotope effect (Benson and Nangia, 1963). If the tetramethylene biradical is involved then it is to be expected that appropriately substituted cyclobutanes might undergo cis-trans isomerization reactions. This will be referred to again later. One final point should be mentioned in connection with biradical intermediates in both cyclopropane and cyclobutane reactions. This concerns the absence of any effect of radical inhibitors on these systems, when it might be expected that they would interact with the biradicals. I n fact calculations show that, under the conditions of formation, the biradicals have extremely ~ and hence, unless radical inhibitors are short lifetimes ( ~ 1 0 - lsec) present at pressures of the order of several atmospheres and react on almost every collision, no effect is to be expected. B. Alkylcyc1obutane.s Walters and his co-workers have investigated the decomposition of a number of alkylcyclobutanes. Substitution of alkyl groups was found to have only relatively minor effects on the rates of decomposition. The results obtained are shown in Table 5. I n the case of methylcyclobutane TABLE 5 Arrhenius Parameters for the Decomposition of Alkylcyclobutanes

Product

logloA

E(kca1 mole-1)

propylene + ethylene butene-1 +ethylene pentene-1 ethylene 3-methylbutene-1 +ethylene

15.38 15.56 15.53 15.63

61.2 62.0 61.6 62.6

Reactant methylcyclobutane" ethylcyclobutaneb n-propylcyclobutanec iso-propylcyclobutaned

Das and Walters (1958). Wellman and Walters (1957).

+

c

Kellner and Walters (1961). Zupan and Walters (1963).

the reaction has been investigated at pressures down to 0.003 mm (Pataracchia and Walters, 1964). Below 1 mm the rate constant decreases with decreasing pressure and a t the lowest pressure has fallen to less than one third of the high pressure value. The "fall-off'' curve can be fitted using the classical Kassel equation by assuming that the molecule contains 23 effective oscillators. I n the case of cyclobutane itself the fall-off curve can be fitted with 18 effective oscillators. This increase in the number of effective oscillators with increasing complexity of the molecule is in complete accordance with current views of unimolecular reaction theory.

P Y R O L Y S E S O F SMALL R I N G HYDROCARBONS

173

C. Dialkylcyclobutanes The decompositions of both cis- and trans-1,2dimethylcyclobutane have been reported (Gerberich and Walters, 1961). The overall scheme for the reactions may be represented as follows :

+ C4Hs cis and trans

Unlike the case of cis- and trans-l,2-dimethylcyclopropane, the cis-transisomerization of the dimethylcyclobutanes is considerably slower than their decomposition reactions. The Arrhenius equations for all these processes have been measured and are given below :

For cis-1,2-dimethylcyclobutane : k 1 -- 1015.48 exp ( - 60,40O/RT) sec-l k 2 -- 1015'57exp(-63,000/RT)sec-l k 3 -- 1014'81 exp ( - 60,10O/RT) sec-l For trans-l,2-dimethylcyclobutane :

k 4 -- 1015'45exp( - 61,6001RT) sec-l k, = 1015'46 exp (- 63,40O/RT) sec-l k6 = 1014'57exp(-61,30O/RT) sec-l We fist consider the decomposition reactions leading to olefins in terms of an intermediate biradical. The cleavage of the cyclobutane can take place in two ways, to give two distinct biradicals, viz. : (14)

H . M . FREY

174

which can then form the products as shown. The biradical formed according to equation (14) will be relatively more stable than that formed according to equation (15), since the free electrons are both located on secondary carbons, rather than on one secondary and one primary carbon atom. Thus pathway (14) should have a lower energy of activation than (15). The difference in the energy of activation for the formation of propylene compared with that for ethylene plus butene-2 from trans-dimethylcyclobutane amounts to 1.8 kcal. This is ameasure of the difference in stability of the two biradicals. The difference is even larger in the case of the cis-dimethylcyclobutane (2.6 kcal) owing to the repulsion between the methyl groups in the cyclobutane.

t

W

Reaction Co-ordi note

FIG.4

Both cis- and trans-butene-2 are formed from each of the dimethylcyclobutanes. They are not however formed in equilibrium amounts. Further, more cis-butene-2 than the equilibrium amount is formed in the decomposition of cis-l,2-dimethylcyclobutane. The fact that the cis- and trans-butene-2 are not formed in their equilibrium amounts would not conflict with the free biradical being an intermediate. However, since different ratios are produced from the cis- and trans-cyclobutanes, this does imply that either the lifetime of the free biradical is of the same magnitude as the time for one rotation of the groups in the biradical, or that the biradical is never strictly a “free biradical”. I n either case the configuration of the reactant will, to some extent, determine the stereochemistry of the products. Since cis-trans isomerization of the dimethylcyclobutanes is observed, the same arguments about expanded ring versus biradical transition

I'YROLYSES O F SMALL R I N G H Y D R O C A R B O N S

175

complexes which were used in the case of cyclopropanes are applicable to cyclobutanes. Since, however, the cis-trans isomerization is slower than the decomposition reactions in the case of the cyclobutanes, if we are to use a similar potential energy diagram to that suggested for cyclopropane isomerization, then it follows that the reaction path must be envisaged as shown in Fig. 4. Thus the energy barrier for the recyclization of the biradical is higher than that for the decomposition to olefins.

X. UNSATURATED CYCLOBUTANES A. Isopropenylcyclobutane

No results have yet been reported for the kinetics of the pyrolysis of vinylcyclobutane though there is some indirect evidence that one of the reaction paths would yield cyclohexene. Kinetic results are available for isopropenylcyclobutane and by analogy with cyclopropane systems the behaviour of this compound should be very similar to vinylcyclobutane. It has been reported (Ellis and Frey, 1963) that the pyrolysis of isopropenylcyclobutane gives rise to ethylene, isoprene and 1-methylcyclohexene. These products arise by two simultaneous first-order processes which are both homogeneous :

The Arrhenius equations for the two processes are

The similarity of the reaction leading to 1-methylcyclohexeneto that of the isomerization of isopropenylcyclopropane to 1-methylcyclopentene suggests that analogous transition complexes are involved, i.e. an allylically stabilized biradical. Ring closure of the biradical yields the

176

H. M. FREY

cyclohexene. I n this case the cleavage of the biradical to yield isoprene (and ethylene) competes favourably with this process, viz. :

On the basis of this mechanism the difference in the energy of activation for the decomposition to isoprene and that for the decomposition of isopropylcyclobutane to 3-methylbutene-1 should equal the ally1 radical resonance energy. The value obtained in this fashion is 11-6f 1 kcal mole-l in close agreement with the values obtained by other methods. A number of other cyclobutanes have been studied in which this effect, i.e. stabilization of the biradical intermediate, results in a lowering in the energy of activation of the reaction. These include

(Roquitte and Walters, 1964) and in all these cases the energy of activation is between 7 and 9 kcal mole-I, less than for the corresponding alkylcyclobutane. B. 1,2-Divinylcyclo6utanes The relatively easy rearrangement of cis-l,2-divinylcyclobutanewas first reported by Vogel (1958) who found that at 120" cis,cis-1,5-cyclooctadiene was the only product.

More recently, kinetic data have become available for the isomerization of this compound and also for the trans- 1,2-divinylcyclobutane (Hammond and DeBoer, 1964). From determinations of the rate of formation from the cis- 1,2-divinylcyclobutane at of the cis-cis-l,5-cyclo-octadiene four temperatures between 65 and 108"C, an enthalpy of activation of

P Y R O L Y S E S O F SMALL R I N G HYDROCARBONS

177

23.1 kcal mole-1 was obtained. The entropy of activation was found to be - 11.7 e.u. The very low value for AH* and the relatively large negative entropy of activation are both consistent with a reaction path as shown below :

(Another product, which may be the cis-trans-cyclo-octadiene, is also formed in a small-percentage yield). This is exactly analogous to the transition complex postulated for the isomerization of cis 1,2-divinylcyclopropane. trans-l,2-Divinylcyclopropane decomposes only at temperatures appreciably higher than those used for the studies on the cis compound. The major products formed in the ratio of about 3 :1 are 4-vinylcyclohexene and cis-cis-l,5-cyclo-octadiene respectively, together with a few per cent of butadiene. From kinetic studies between 139 and 210' C the enthalpy of activation was calculated as 34.0 kcal moleF1,and the entropy of activation as - 1.2 e.u. Hence the slower reaction of the trans-compound is entirely due to its much higher enthalpy of activation. The measured enthalpy of activation corresponds to an energy of activation of about 34-8 kcal mole-l and comparison of this result with that for the trans-cis isomerization of 1,2-dimethylcyclobutane (61.3 kcal mole-l) gives a value for the allylic resonance energy of 13-2kcal. This value supports the idea that the transition complex involved is the double allylically stabilized biradical. Hammond and DeBoer (1964) have also reported work with optically active trans-l,2-divinylcyclobutane.They found that the loss of optical activity of the starting material was greater than the loss of starting material. This suggests that after the initial cleavage some of the biradical recyclizes to the cyclobutane to give an enantiomer of the starting material. The enthalpy and entropy of activation for the loss of optical activity were found to be 36.5 kcal mole-l and + 4-6 e.u. respectively. Finally, the vinylcyclohexene formed in the isomerization of the optically active trans-1,2-divinylcyclobutanewas found to have a small optical rotation. Since neither the absolute rotation of the starting material nor that of the vinylcyclohexene is known, the extent of the sterospecificity of the reaction cannot be determined. The authors however believe it to be small. Perhaps the simplest explanation of all the results which encompasses the fact that allylic units are believed to be stereochemically stable (Walling and Thaler, 1961)is that, while ring

178

H. M. FREY

rupture does occur, the rates of ring closure are only slightly slower than the rates of internal rotation of the biradical (the energy barrier for ring closure being about 1 kcal higher than that for rotation). The suggested scheme is shown diagramatically below :

*d

enantioilier of starting material.

T

7 1

__t

11

C . trans- 1,2 -Dimethyl-1,2-divinylcycclobutane The decomposition of this compound has been studied by Hammond and DeBoer (1964)and Trecker and Henry (1964) with similar results. Trecker and Henry find that the rate of reaction is given by

k

=

1014'3eexp( - 32,20O/RT) sec-l

together with The major product is 1,4-dimethyl-4-vinylcyclohexene smaller amounts of 1,6-dimethylcyclo-octa-l,5-diene, isoprene and 4isopropenyl-1 -methylcyclohexene.

P Y R O L Y S E S O F SMALL R I N G H YDRO CARBO NS

179

D. trans-l-~ao~openy~-2-methy,?-2-viny~cycbbutane The decomposition of this compound is shown schematically below :

A/+$+++&+(sl A

B

C

D

E

The relative percentage yields of products at 135~7°Care (A) 11.1, (B) 1.3, (C)45.7, (D) 32.1, (E)9.8. The yield of isoprene has been scaled down by a factor of 2 since the decomposition of one molecule of the cyclobutane yields two molecules of isoprene. The products and rates of reaction of this cyclobutane and the previous one discussed are both consistent with the reaction paths already mentioned.

E. Methylenecyclobute The pyrolysis of methylenecyclobutane has been studied independently by Chesick (1961)and Brandaur et al. (1961). The decompositionis first order and appears to be unimolecular, the products being allene and ethylene. Chesick, working in the temperature range 430-470' C, found: k, = 1016'6sexp( - 63,30O/RT) 8ec-l The rate constant decreases with pressure below about 10 mm and at 0.1 mm has fallen to about a half of the high-pressurevalue. Brandaur et al. working between 410-470' C,found: k = 101s'oQexp( - 61,50O/RT) sec-1 While there is a small discrepancy between the two determinations of the energy of activation, it is clear that the value cannot be far from that for the decomposition of methylcyclobutane. Thus the presence of the double bond has little significant effect on the energetics of the process. It might have been expected that, since an intermediate biradical could be allylically stabilized, the decomposition should proceed through a relatively low-energy path, viz. :

El-

H2C-\,C/H~

H&=C=CHz __f

H2L;--L!H2

+

Cz&

However, as has been mentioned earlier when considering the isomerization of ethylidene cyclopropane, in methylenecyclobutane, the four

180

H. M. F R E Y

hydrogen atoms involved in the allylic resonance structure are in a pIane at right angles to that required. Thus we have steric inhibition of resonance. Twisting of the double bond, to give some overlap of the .rr-electrons with the forming orbitals due to rupture of the appropriate carboncarbon bond in the cyclobutane ring, is not favoured in this case as it is in the corresponding cyclopropane analogue (unless a CH2 were expelled from the ring and this is not energetically feasible). An alternative transition state has been suggested for this reaction involving a semi-ion pair (Benson, 1964). With such a transition complex the high energy of activation arises from the difficulty of the second step (splitting-out of the ethylene) rather than the primary ring rupture.

XI. BICYCLIC COMPOUNDS CONTAINING CYCLOBUTANE RINGS

A. Bicyclo[2,lY0]hexane Relatively few bicyclic compounds containing a cyclobutane ring have been studied kinetically. Bicyclo[2,1,O]hexane has been investigated by Steel et al. (1964) in the temperature range 130-21OoC, when the only product is diallyl. The results obtained are fitted by the Arrhenius equation k = 1013.4exp ( - 36,00O/RT) sec-l The authors suggest the isomerization proceeds via the rupture of the weak bridgehead bond, viz. :

If this is the reaction path, then the biradical is probabIy not to be thought of as the “flat” strain-free cyclohexane biradical

0 but rather a biradical in which there is considerable distortion of the molecule so that it closely resembles the reactant. Certainly, the normal value of the A factor for the isomerization appears to rule out a transition state where a carbon-carbon bond other than the bridgehead one is ruptured.

P Y R O L Y S E S O F SMALL R I N G H YDRO CARBO NS

181

B. BicycZo[2,1 ,I]hexune The thermal isomerization of this compound (a valency bond isomer of bicyclo[2,2,0]hexane) is of particular interest. Between 327 and 366" C and at pressures from 0.2 to 20 mm, Srinivasan and Levi (1963)found that this compound isomerized cleanly by a first-order process to give diallyl.

Addition of nitric oxide and propylene, or increase in the surface-tovolume ratio of the reaction vessel, did not affect the rate of reaction. The data were fitted by the Arrhenius equation

k

=

1016'17exp(- 5 5 , O O O / R T ) sec-l

The values of these Arrhenius parameters contrast dramatically with those obtained for the bicyclo[2,2,0]hexane isomerization. I n this compound there is no weak bridgehead bond, and hence the reaction path is more closely akin to that for cyclobutane itself. The similarity of the A factors for this reaction and that for other simple cyclobutanes supports this contention. If this is so, then the lowering of the energy of activation in this bicyclic compound by some 7 kcal mole-l from that observed in the alkylcyclobutanes is to be attributed to extra strain energy in this molecule.

C. BicycZo[3,2,0]hepturte The decomposition of this compound occurs between 426 and 464' C by two concurrent paths to yield as initial products cyclopentene plus ethylene and hepta-l,6-&ene.

CH~=CH(CH~)&H=CHB

-+

C4Hs C3He

The decomposition is homogeneous and probably unimolecular, with rate constants given by kcyclopentene =

10'4'84exp ( - 60,74O/RZ') sec-I

kheptadiene= 1015'40exp( - 63,97O/RT)sec-l (Ellis and Frey, 1964~).

182

H. M. FREY

The two reaction paths may involve two different biradicals :

Biradical I would yield cyclopentene plus ethylene, biradical I1 the hepta-1,6-diene. Process I may have a lower energy of activation because of the stabilization of the free electron by the secondary carbon atom and also because less energy is required to compress the appropriate carbon-carbon bond, in the cyclopentane ring to yield the cyclopentene, than to rupture the ring to give the diene. At the temperatures where the decomposition of this bicyclic compound occurs a t a reasonable rate there is some decomposition of the primary products. Cyclopentene decomposes by a molecular path to yield cyclopentadiene plus hydrogen. This decomposition has been studied in detail by Vanus and Walters (1948). The decomposition of the hepta-l,6-&ene is also important and appears to be predominantly a non-chain homogeneous process, and may occur by the cyclic transition state shown below :

The thermal isomerizations of other bicyclic systems containing a cyclobutane ring appear not to have been investigated kinetically in detail, with the exception of wand B-pinene. These isomerizations all probably proceed through allylically stabilized biradicals, but the systems are complex and the studies were carried out well before the advent of modern analytical techniques of gas analysis. It is doubtful therefore whether a detailed discussion is worth while before more precise data are available (see Trotman-Dickenson, 1955). One case of some interest for which kinetic data are not available, but for which equilibrium data are, is that of cyclo-octa-l,3,5-triene. At 100" there is a rapid equilibration between the triene and bicyclo[4,2,0] octadiene :

PYROLYSES O F SMALL RING HYDROCARBONS

183

-

with the equilibrium mixture containing 85 yoof the triene. The freeenergy difference between the two forms is very small ( 1.5 kcal mole-l) and the presence of substituents can drastically alter the equilibrium proportions (Cope et al., 1952).

XII. TRICYCLIC SYSTEMS CONTAININGA CYCLOBUTANE RING The only system of this kind which appears to have been investigated kinetically in detail is tricyclo[3,3,0,02~6]octane(Srinivasan and Levi, 1964). At temperatures in the range 327 to 366" C the isomerization is a homogeneous first-order reaction. The observed products were 4-vinylcyclohexene, butadiene and 1,5-cyclo-octadiene.However, from separate studies on the cyclo-octadiene, it is concluded that the tricyclo-octane first isomerizes to the cyclo-octadiene which then undergoes secondary reactions to yield the other observed products. The observed rate is then the rate of this primary reaction, viz. :

a-0

for which k: = 1016'61exp( - 55,90O/RT) sec-'. Within experimental error, the energy of activation of this isomerization is the same as that for the isomerization of bicyclo[2,l,l]hexane to diallyl. It would thus appear that the presence of the third ring does not appreciably increase the strain in the cyclobutane ring. The remarkable tricyclo-octanes shown below have recently been synthesized (Avram et al., 1964). They both yield 1,5-cyclo-octadieneon pyrolysis at 150"C which suggests that the kinetic parameters for these isomerizations cannot be two dissimilar to those for the isomerization of bicycle[2,2,0]hexane,

XIII. CYCLOBUTENE The thermal isomerization of cyclobutene to butadiene is one of the best known examples of a thermal unimolecular isomerization. Cooper

184

H . M . FREY

and Walters (1958)first investigated this reaction in detail and found the reaction to be homogeneous, fist-order, and unaffected by the presence of radical inhibitors. Their results were fitted by the Arrhenius equation

k

-

= 1013'oBexp ( 32,50O/RT)sec-'

A more recent study of this isomerization has been carried out over a very extended pressure range (Hauser and Walters, 1963). The high-pressure rate constants were obtained by extrapolation, whence

ka

-

10'3'26exp( - 32,70O/RT)sec-l

At 5 mm the rate constant has already begun to decrease from the highpressure value, and at 0.15 mm it is only about 13% of the high-pressure value. Addition of inert gases in the "fall-off" region increases the value of the rate constant towards the high pressure limiting value. The very low value of the energy of activation for this isomerization is of considerable interest. Comparison with the decomposition of cyclobutane shows a reduction of 30 kcal mole-' caused by the presence of the double bond. If a similar transition state were involved in both reactions, then this difference would be a measure of the extra strain energy of the cyclobutene. This is quite unrealistically high. Thus we eliminate the possibility that the reaction path is as shown below :

(See, however, the arguments of Benson, 1964.) A transition complex which is consistent with the low energy of activation of the isomerization involves the simultaneous deformation (twisting) of the cyclobutene ring with the stretching of the carboncarbon bond opposite the double bond :

This twisting allows overlap between the electrons of the double bond and the vacant orbitals forming as a result of the rupture of the carbon-carbon bond, and thus considerably reduces the energy required to break this bond. With this transition state no free (or slightly hindered) internal

186

PYROLYSES O F SMALL RING HYDROCARBONS

rotations are possible and hence a normal A factor is to be expected for the isomerization, again in striking contrast to the very high values found for cyclobutane decompositions.

A. Alkylcyclobutenes The thermal isomerizations of a number of alkyl substituted cyclobutenes have been investigated in the gas phase. I n all cases the reactions have been shown to be first order homogeneous reactions with no radical-chain component. The results obtained are shown in Table 6. TABLE6 Arrhenius Parameters for the Isomerization of Cyclobutenes

Reactant

1-methylcyclobutene" 3-methylcyclobuteneb 1-ethylcyclobutenec 1,2-dimethylcyclobutne~ 1,3-dimethylcyclobutenee 1,4-dimethylcyclobutenee

trans-1,2,3,4-tetramethylcyclobutenef

cis-1,2,3,4-tetramethylcyclobutenef

a

Frey (1962).

* Frey (1964). c

Frey and Skinner (1965a).

Product

isoprene trans-pentadiene-1,3 2-ethylbutadiene 2,3-dimethylbutadiene trans-2 -methylpentadiene-1,3 trans-3-methylpentadiene-1,3 3,4-dimethyl-trans,trans-hexadiene-2,4 3,4-dimethyl-cis,trans-hexadiene2,4

d

e

f

logloA

E(kca1 mole-1)

13-79 13.53 13.76 13.84 13.65 13.52

35.10 31.55 34.83 36.04 33.00 33.39

13.85

33.59

14.20

37.7

Frey (1963). Frey et al. (1965). Frey and Skinner (196513).

Close examination of Table 6 reveals several points of interest. The isomerization of 3-methylcyclobutene yields only trans-penta-l,3-&ene with none of the cis-isomer. With the transition state suggested for the isomerization of cyclobutene, either isomer could be formed. However, the trans-isomer will clearly be favoured since it involves a rotation of the methyl group away from the ring rather than towards it, with less steric repulsion. Cyclobutenes with substituents on both C3 and C4 carbon atoms may exist in cis and trans forms. The isomerizations of such compounds involve another problem of some interest. The simplest cases for which 7

186

IT. 31. F R E Y

data are available are the cis- and trans-3,4-diniethylcyclobutenes (Winter, 1965). Two possible reactions may be considered for each of these isomers, viz. :

These processes may be designated conrotatory (16) and disrotatory (17). In practice the isomerization of the appropriately substituted cyclobutenes follow a conrotatory pathway. Thus cis-3,4-dimethylcyclobutene yields only cis-trans-2,4 hexadiene, and trans-3,4-dimethylcyclobutene yields only trans-trans-2,4-hexadiene. On the basis of the twisted transition state suggested previously, the conrotatory process is in fact the one to be expected. However, the situation is not quite as simple as here implied. By similar arguments the thermal cyclization of hexatrienes would also be expected to be conrotatory, whereas in fact it is disrotatory, viz. :

The stereochemistry of the cyclobutene isomerizations and the reverse processes of this type, involving the formation of a bond between the ends of a linear system containing a number of rr-electrons, has been discussed by Woodward and Hoffmann (1965). They term such processes electrocyclic and consider that their steric course is determined by the symmetry of the highest occupied molecular orbital of the open-chain isomer. I n an open-chain system containing 4n rr-electrons (such as butadiene), the symmetry of the highest occupied ground-state orbital is such that bonding interaction between the ends of the chain must involve overlap between orbital envelopeson opposite faces of the system, and this can only occur in a conrotatory process :

PYROLY S E S O F SMALL R I N G H YDRO CARBO NS

187

For an open chain system with (4n + 2) .rr-electrons,the reverse is true and hence cyclization and ring rupture are in this case disrotatory. This description of the process shows why the conrotatory process is favoured in the cyclobutene isomerization. It does not rule out the reverse process where the conrotatory process is energetically very unfavourable. Finally, inspection of the results given, Table 6, shows that substitution of an alkyl group on C1 or C2 results in an increase in the energy of activation of the reaction, whereas substitution of an alkylgroup on the 3-or 4position results in a lowering of the energy of activation. These two effects are about equal in magnitude and hence the energies of activation for the isomerizations of cyclobutene, and 1,3- and 1,4-dimethylcyclobutenes are all very close to one another. Similarly, the energy of are activation for cyclobutene and traw-1,2,3,4-tetramethylcyclobutene equal. The cis-l,2,3,4-tetramethylcyclobutene has an appreciably higher energy of activation,owing to the steric repulsion between the two methyl groups in the transition complex. The reduction in the energy of activation of isomerization by substituents in the 3- and 4-positions may be a simple steric effect. Thus there is a greater repulsion between the alkyl substituent in these positions and the hydrogen atoms on the adjacent carbon atoms in the reactant than in the transition complex. The increase in energy of activation by substitution on the 1-or 2-position (whichis of the same magnitude for CHSand C,H,) may be due to the stabilization of the reactant cyclobutene by such substituents. There is also a minor effect (in the same direction) due to the greater steric repulsion of the alkyl group and a hydrogen on the adjacent methylene group in the product diene than in the reactant. The thermal isomerizations of a number of cyclobutenes have also been studied in the liquid phase (Criegeeet al., 1965). The rates of isomerization of cis- and trans-l,2,3,4-tetramethylcyclobutene in a number of solvents (toluene, mesitylene, diphenylether, o-dichlorobenzene, nitrobenzene, quinoline) have been measured. Within experimental e r r ~ r the , same rates are obtained, irrespective of solvent. This is to be expected for a

188

H. M. F R E Y

unimolecular reaction of this type. Further, the energies of activation for these isomerizations are the same, within experimental error, in the gas and liquid phase.

XIV. BICYCLOBUTENES

A. Bicyclo[4,2,O]octene

Bicyclo[4,2,O]octene isomerizes smoothly to yield 1,3-cyclo-octadiene only at temperatures appreciably higher than are necessary for the monocyclic cyclobutenes. A study of this reaction in the gas phase in the temperature range 235 to 285"C yielded the Arrhenius equation

k

= 1014'13exp(-43,18O/RT) sec-I

(Branton and Frey, 1965b). I n this case the conrotatory process is energetically unfavourable because of the strain energy in cis-tram1,3-cyclo-octadiene,and hence the reaction must occur by a disrotatory process. The possibility that the isomerization occurs by a non-concerted process involving first the complete rupture of the bridgehead bond can probably be ruled out on the basis of a comparisonof both the A factor and energy of activation of this reaction with those obtained for bicyclo[3,2,0]heptane .

B. Bicyclo[3,2,Olheptene The thermal isomerization of this compound has been studied in both gas and liquid phases (Branton et al., 1965). The compound is more stable than the corresponding bicyclo-octene but does isomerize to 173-cycloheptadienein the gas phase in the temperature range 274 to 327" C. The rates obtained are fitted by the Arrhenius equation

k

= 1014'31exp(-45,51O/RT) sec-I

Isomerizations carried out in the liquid phase, using dimethyl phthalate as the solvent, yielded the Arrhenius equation

E

=

1014.65exp (-45,86O/RT)sec-l

As in the case of the bicyclo-octane the isomerizations must occur by a disrotatory process. It is clear that, owing to the rigid nature of these bicyclobutenes, considerable stretching of the bridgehead bond is necessary before appreciable twisting of the cyclobutene ring can

PYROLYSES O F SMALL R I N G HYDROCARBONS

189

occur. Hence this stretching takes place before appreciable energy is recovered by overlap of the .rr-electrons. This is reflected in the appreciably higher energy of activation in the bicyclobutenes. As is to be expected, the compounds are even more stable than the corres-

ponding unsubstituted bicyclobutenes (Criegee and Furrer, 1964; Askani, 1965).

C. Bicyclo[2,2,O]hexadiene

m4

This compound has recently been prepared by the following route : 0

6

ml

P ~ ~ O A C ) ~ ~ 20%

Yield

0

(van Tamelen and Pappas, 1963). The bicyclohexadiene isomerizes to benzene with a half-life of 2 days at 20' C. Ilf this reaction proceeds with a normal A factor, it must have an energy of activation of m. 24 kcal mole-l. Bearing in mind the strain energy of this system, and the resonance energy of benzene, this does not appear an unreasonable value. It is interesting to note that 1,3,4-tri-t-butylbicyclo[2,2,0]hexadiene, which is readily formed by the photolysis of 1,2,5-tri-t-butylbenzene, reverts to its precursor only on heating to around 150°,

(van Tamelen and Pappas, 1962) which probably reflects the strain energy in the substituted benzene.

XV. TRICYCLIC SYSTEMS CONTAINING CYCLOBUTENE RINGS A a a m et al. (1964)have reported the preparation of the tricyclic systems shown below and their thermal isomerizations. Both isomers yield cyclo-octatetraene at temperatures above 100' C. Compound I isomerizes to cyclo-octatetraene with a half life of about 20 minutes

H . M. P R E Y

190

%\ ? (I)

8/

at 140°C. Assuming a normal A factor for this reaction leads to an energy of activation of about 29 kcal mole-l. The octamethylderivatives of these tricyclic compounds have also been prepared (Criegee, 1962). They isomerize on heating to yield the octamethylbicyclo-octatriene shown below :

That this compound is formed rather than octamethylcyclo-octatetraene probably merely reflects the relative stabilities of these compounds.

XVI. CONCLUSION We have discussed in this chapter the thermal pyrolyses of anumber of strained ring compounds. I n most of the cases considered there is good evidence that the processes are unimolecular. Where possible we have tried to suggest plausible transition complexes, and reaction paths, based on a consideration of such factors as the kinetic parameters, stereochemistry of the reaction and effect of substituents. I n reactions of this type, the description of the transition complex is fraught with difficulties, since the absence of such things as solvent effects (which can be so helpful in bimolecular reactions) limit the criteria on which such descriptions may be baaed. Often two types of transition complex may be equally good at accounting for the observed data. Sometimes one complex will explain some of the data while another is better able to account for the remainder. It is probable that in many cmes our representation

P Y R O L Y S E S O F SMALL R I N G HYDRO CARBO NS

191

of the transition complex is too simple-biradical compared with expanded ring in the cyclopropane isomerizations-and that the true situation lies between the extremes, in exactly the same way as the simple Kekul6 formulae do not represent all the properties of benzene. Finally i t should be noted that the description of the reaction path by which the reactant reaches the transition complex is even more =cult, and poses problems of energetics which have as yet hardly been touched. REPERENOES Askani, R. (1965). Chem. Ber. 98,2322. Avram, M.,Dinulescu, I. G., Marica, E., Mateescu, G., Sliam, E., and Nenitzescu, C. D. (1964). Chem. Ber. 97,382. Benson, S. W. (1964). “Advances in Photochemistry”, Vol. 2. Interscience,New York, 1. Benson, 5.W., and Nangia, P. S. (1963). J . Chem. Phy8.38, 18. Berlin, A. J., Fisher, L. P., and Ketley, A. D. (1965). Chem. (e: I d . (London)509. Bledes, A. T. (1961). Can. J . Chem. 39, 1401. Brandaur, R. L., Short, B., and Kellner, S. M.E. (1961). J . Phy8. Chem. 65,2269. Branton, G. R., and Frey, H. M.(1965). To be published. Branton, G. R., Frey, H. M., and Montague, D. C. (1966). To be published. Butler, J. N., and Ogawa, R. B. (1963). J . Am. Chem.SOC.85, 3346. Chambers, T. S., and Kistiakowsky, G. B. (1934). J. Am. Chem. SOC. 59,399. Chesick, J. P. (1960). J . Am. Chem. SOC.82,3277. Chesick, J. P. (1961). J . Phy8. Chem. 65, 2170. Chesick, J. P. (1962). J . Am. Chem. SOC.84, 3250. Chesick, J. P. (1963). J . Am. Chem. SOC.85, 2720. Chesick, J. P. (1964). J . Phy8. Chem. 68, 2033. Cope, A. C., Haven, A. C. Jr., Ramp, F. L., and Trumbull, E. R. (1952). J . Am. Chem. SOC. 74,4867. Cooper, W.. and Walters, W. D. (1958). J . Am. Chem. SOC.80,4220. Corner, E. S., and Pease, R. N. (1945). J . Am. Chem. SOC. 67,2067. Criegee, R. (1962). Angew. C h . (Int. Ed.) 1,519. Criegee, R., and Furrer, H. (1964). Chem. Ber. 97, 2949. Criegee, R., Seebach. D., Winter, R. E., Borretzen, B., and Brune H-A. (1966). Chem. Ber. 98, 2339. Das, M.N., and Walters, W. D. (1958). 2.phy8ik. Chem. (Neue Folge) 15, 22. Doering, W. von E., and Roth, W. R. (1963). Angew. Chem. (Int. Ed.) 2,116. Egger, K. W., Golden, A. S., and Benson, S. W. (1964). J . Am. Chem.SOC. 86,6421. Elliott, C. S., and Frey, H. M. (1964). J . Chem. Soo. 900. Elliott, C. S., and Frey, H. M. (1965a). J . Chem. SOC.346. Elliott, C. S., and Frey, H. M. (1965b). To be published. Ellis, R. J., and Frey, H. M.(1963). Trum. Furaduy SOC.59, 2076 Ellis, R. J., and Frey, H. M. (1964a). Proc. Chem. SOC.221. Ellis, R. J., and Frey, H. M. (1964b). J . Chem. SOC.5678. Ellis, R. J., and Frey, H. M. (19640). J. Chem. SOC. 4184. Ettlinger, M. G. (1962). J . Am. Chem. SOC. 74, 5806. Flowers, M. C., and Frey, H. M.(1960). Proc. Roy.Soc. A257,122. Flowers, M. C., and Frey, H. M.(1961). J . Chem. SOC.6660.

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Flowers, M. C., and Frey, H. M. (1961a). Proc. Roy.SOC.A260,424. Flowers, M. C., and Frey, H. M. (1961b). J. Chem. SOC. 3547. Flowers, M. C., and Frey, H. M. (1962a). J. Chem. SOC.1157. Flowers, M. C., and Frey, H. M. (1962b). J. Chem. SOC.1689. Frey, H. M. (1962). Trans. Faraday Soc. 58, 957. Frey, H. M. (1963). Trans. Faraday SOC.59, 1619. Frey, H. M. (1964). Trans. Faraday SOC. 60, 83. Frey, H. M., and Ellis, R. J. (1965). J. Chem. SOC.4770. Frey, H. M., and Marshall, D. C. (1963). J . Chem. SOC.5717. Frey, H. M., and Marshall, D. C. (1965). J . Chem. SOC.191. Frey, H. M., and Skinner, R. F. (1965a). Trana. Faraday SOC. 61, 1918. Frey, H. M., and Skinner, R. F. (1965b). To be published. Frey, H. M., and Smith, R. C. (1962). Trans. Paraday Soc. 58, 697. Frey, H. M., and Stevens, I. D. R. (1964). Proc. Chem. SOC.144. Frey, H. M., and Stevens, I. D. R. (1965). Trans.Faraday Soc. 61,QO. Frey, H. M.,Marshall, D. C., and Skinner, R. F. (1965). Trans.Famduy Soc. 61,861. Genaux, G. T., and Walters, W. D. (1951). J. Am. Chem. SOC.73,4497. Gerberich, H. R., and Walters, W. D. (1961). J. Am. Chem. SOC.83, 4884. Golike, R. G., and Schlag, E. W. (1963). J. Chem.Phys. 38, 1886. Grimme, W. (1965). Chem. Ber. 98, 756. Halberstadt, M. L., and Chesick, J. P. (1962). J. Am. Chem. SOC. 84, 2688. Halberstadt, M. L., and Chesick, J. P. (1965). J . Phye. Chem. 69,429. Hammond, G. S., and DeBoer, C. D. (1964). J. Am. Chem. SOC.86, 899. Hauser, W. P., and Walters, W. D. (1963). J. Phya. Chem. 67, 1328. Kellner, S. M. E., and Walters, W. D. (1961). J. Phys. Chem. 65,466. Kern, F., and Walters, W. D. (1952). Proc. Nat. A d . Sci. U.S., 39, 937. Kern, F., and Walters, W. D. (1953). J . Am. Chem. SOC.75, 6196. Ketley, A. D., and McClanahan, J. L. (1965a). J. Org. Chem. 30, 942. Ketley, A. D., and McClanahan, J. L. (1965b). J. Org. Chem. 30, 940. Langrish, J., and Pritchard, H. 0. (1958). J. Phys. Chem. 62,761. Linquist, R. H., and Rollefson, G. K. (1956). J. Chem. Phys. 24,725. Overberger, C. O., and Borchert, A. E. (1960). J. Am. Chem. SOC.82, 1007; 4896. Pataracchia, A. F., and Walters, W. D. (1964). J. Phys. Chem. 68, 3894. Pritchard, H. O., Sowden, R. G., andTrotman-Dickenson,A. F. (1953). Proc. Roy. SOC.A217, 563. Rabinovitch, B. S., Schlag, E. W., and Wiberg, K. B. (1958),J. Chem.Phys. 28,604. Rabinovitch, B. S., Setser, D. W., and Schneider, F. W. (1961). Can. J. Chern. 30, 2609. Roquitte, B. C., and Walters, W. D. (1964). J. Phya. Chem. 68, 1606. Schlag, E. W., and Rabinovitch, B. S. (1960). J. Am. Chem. SOC.82, 5996. Slater, N. B. (1953). Proc. Roy. SOC.A218, 224. Smith, F. T. (1958). J. Chem. Phys. 29, 235. 85, 4045. Srinivasan, R. (1963). J. Am. Chem. SOC. Srinivasan, R., and Kellner, S. M. E. (1959). J. Am. Chem. SOC. 81, 5891. Srinivasan, R., and Levi, A. A. (1963). J . Am. Chem. SOC.85, 3363. Srinivasan, R., and Levi, A. A. (1964). J . Am. Chem. SOC.86, 3756. Srinivasan, R., Levi, A. A., and Haller, I. (1965). J . Phys. Chem. 69, 1775. Stechl, H.-H., (1964). Chem. Ber. 97, 2681. Steel, C., Zand, R., Hurwitz, P., and Cohen, S. G. (1964). J. Am. Chem. SOC.86, 679.

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Trautz, M., and Winkler, K. (1922). J. prakt. Chem. 104, 53. Trecker, D. J. and Henry, J. P. (1964). J . Am. Chem. SOC. 86, 902. Trotman-Dickenson, A. F. (1955). “Gas Kinetics”, Butterworths Scientific Publications, London, p. 140. Turner, R. B., Goebel, P., Doering, W. von E., and Woburn, J. F. (1965). Tetrahedron Letters, 997. Ullmann, E. F. (1959). J . Am. Chem. SOC.81, 5386. Ullmann, E. F. (1960). J . Am. Chem. SOC. 82,505. Ullman, E. F., and Fanshawe, W. J. (1961). J . Am. Chem. SOC. 83, 2379. van Tamelen, E. E., and Pappas, S. P. (1962). J. Am. Chem. SOC.84,3789. van Tamelen, E. E., and Pappas, S. P. (1963). J . Am. Chem. SOC. 85,3297. Vanus, D. W., and Walters, W. D. (1948). J. Am. Chem. SOC.70,4053. Vogel, E. (1959). Ann. 615, 1. Vogel, E. (1962). Angew. Chem. 74,829. Vogel, E., and Sunderman, R. (1965). Personal communication. Vogel, E., Ott, K.-H., and Gajek, K. (1961). Ann. 644, 172. Vreeland, R. W., and Swinehart, D. F. (1963). J . Am. Chem.Soc. 85,3349. Walling, C., and Thaler, W. (1961). J. Am. Chem. SOC.83, 3877. Wellington, C. A. (1962). J . Phys. Chem. 66, 1671. Wellman, R. E., and Walters, W. D. (1957). J. Am. Chem. SOC.79,1542. Weston, R. E. (1957). J . Chem. Phys. 26, 975. Wiberg, K. B., and Bartley. W. J. (1960). J. Am. Chem. SOC.82, 6375. Wiberg, K. W., and Lampman, G. M. (1963). Tetrahedron letter^, 2173. Winter, R. E. K. (1965). Tetrahedron Letters, 1207. Wolinsky, J . , Chollar, B., and Baird, M. D. (1962). J . Am. Chem. SOC. 84, 2776. Woodward, R. B., and Hoffmann, R. (1965). J . Am. Chem. SOC.87,395. Zupan, M., and Walters, W. D. (1963). J. Phys. Chem. 67, 1845.

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THE BASICITY OF UNSATURATED COMPOUNDS H.-H. PERKAMPUS DepartmeJ of Molecular Spectroscopy of the Imtitute for Organic Chemistry, Technische Hochschule, Braumchweig, Germany I. Definition of Basicity . A. General Comments on the Acid-bese Concept . B. Basicity of n-Electron Bond Systems 11. The Structure of the Proton Addition Complexes . A. SurveyofMethods B. N.M.R. Spectra of Proton Addition Complexes . C. The I.R. Spectra of Proton Addition Complexes . D. T h e Electron Excitation Spectra of Proton Addition Complexes . III. Methods for Determining the Basicity of Unsaturated Hydrocarbons . A. D e t e d a t i o n of the Basicity from Partition Equilibria B. Determination of the Baaicity from Vapour Pressure Meaaurements C. Determination of the Besicity by Means of Conductivity Meaaurements D. OtherMethods IV. Basicity Scale and Basicity Constants of Unssturated Compounds . A. Notes on the Establishment of Basicity Scales . B. Basicity Gradation of Unsaturated Compounds . C. Basicity Constants of Aromatic Compounds D. BasicityofAzulenes V. Theoretical Treatment of Proton Addition Complexes . A. Localization Energies and Basicity B. Considerationof the Influence of Substituents . VI. Supplementary Remarks . References .

.

.

.

.

.

.

.

.

.

196 196 197 200 200 201 214 222 232 232 238 244 264 202 202 203 271 281 284 284 289 297 300

I. DEFINITION OF BASICITY A. General Comments on the Acid-base Concept THEcurrent general definition of the acid-base concept is based on the definitions by Bronsted and Lewis. According to Bronsted’s theory (1923) an acid-base interaction can be described by the general relation (1): (1) acid + base+proton According to (1) acids and bases can be interconverted. They are also said to be conjugates of each other. The equilibrium constant of the reaction (1)is the so-called acidity constant (which is not measurable).

K A = aH+--abase aacid

196

H.-H. PERKAMPUS

Its reciprocal is the basicity constant K,

1 = =-

---

%cid

(2b) KA aH+ abase If two conjugate acid-base pairs are coupled with one another, then, depending on the magnitude of the constants (2a, b) a proton exchange can take place and this is described as a protolytic reaction. I n general, the solvent itself is one acid-base pair. acid I +base I1 + acid I1+ base I AI+BII

(3)

+ AII+BI

Hence the equilibrium constant of the protolytic reaction (3) is:

K thus represents the quotient of two acidity constants. If water is the solvent the protolytic reaction is described as the dissociation of an acid or base. The coupling of two acid-base pairs according to (3) is universally applicable and, in particular, includes organic solvents. Thus Bronsted’s theory explains the acidity and basicity of organic solvents and of the substances dissolved therein, with the free electron pair of the solvent molecules here fulfilling the basic function, as e.g. in the case of acetone (a) and ether (b): H3C

‘C=g + HCI + [H9C\C=6,H] + C1-

H3C/ CH3-G-CH3 (b)

H3C/

+ HCI +

[ = I CHa-G-CHs

+ C1-

These and similar solvents are distinguished by the fact that they themselves cannot eliminate any protons. On the other hand one is still dealing with “water-like” solvents in the case of alcohols, since the selfdissociation of the alcohols resembles that of water in order of magnitude (see Gurney, 1953). The ability of free electron pairs to function prompted Lewis (1923) to a more general definition of the acid-base concept, According to Lewis, acids are substances which can take up a lone electron pair from another atom or group of atoms with the formation of a covalent bond; buses on the other hand are substances which can make a free electron pair available. The definition given by Lewis is

THE BASICITY O F UNSATURATED COMPOUNDS

197

more embracing than that of Bronsted, since it also includes as acids molecules which are incapable of donating protons. One therefore distinguishes between proton acids (so-calledBronsted acids) and Lewis acids, and understands by the latter term molecules having electron gaps, e.g. BF,; AlCI,; AIBr,; GaCI,; SbCI,, as well as cations generally. The interaction between Lewis acids and bases can thus also be thought of as an electron donor-acceptor (E-D-A) interaction. This means that for these reactions it is already necessary to discuss a transition to the field of molecular compounds. The difference from pure EDA complexes can however be recognized by the magnitude of the intermolecular bond length (Briegleb, 1961). I n the case of pure EDA complexes, the so-called CT-complexes(chargetransfer complexes)there is no localized bonding of the two components, and their mutual spacing is of the order of approximately 3 A. I n the case of the interaction between Lewis acids and bases having free electron pairs, on the other hand, a o-bond is often formed, the bond length of which is clearly less. A large number of compounds having free electron pairs yield such complexes with Lewis acids, for which a a-bond may be assumed and can also be demonstrated in many cases. Examples of this are :

(a)

E

+ BF3

GQ BF3

An interaction of the type (a) can be proved both by means of electron excitation spectra (Perkampus and Kortiim, 1965) as well (ts by I.R. spectra (Luther et al., 1958; Perkampus and Hoffmann, 1965). The addition of a Lewis acid to a C=O double bond, as in example (b),permits a clear effect on the -0 valency vibration in the I.R. spectrum to be observed as a consequence of the demands of the Lewis acid on the C==O double bond (Terenin et al., 1958; Perkampus and Baumgarten, 1964d). B. Basicity of r-Electron Bond Systems I n addition to those compounds which contain hetero-atoms having lone electron pairs and which are therefore characterized as “ bases ”, there exist analogous interactions with molecules which do not possess any lone pairs. It is however known from the chemistry of unsaturated compounds, particularly of aromatics, that solutions of such compounds,

198

H.-H. PERKAMPUS

e.g. in concentrated sulphuric acid, show an intense colour even if the pure compound is colourless (Gabriel and Leupold, 1898; cf. Clar, 1952). Investigations as to the dependence of these colour phenomena on the acid concentration show without doubt that protons are involved (Gold et al., 1952; Gold and Tye, 1952). The nature of this interaction was for a long time described as a so-called r-complex (Dewar, 1946) and was interpreted as an interaction of the r-electrons with the proton. The consistent application of the Lewis acid-base definition means that this interaction demands a “basic character” of the unsaturated compound. The easily mobile r-electrons must be regarded as the carriers of the basic property. Since r-electron energy and .rr-electron density depend strongly on the constitution of the unsaturated compounds, it is to be expected that the basicity of unsaturated compounds will also depend on their constitution. More exact investigations have now shown that an interaction in the nature of a complex cannot by itself be used to interpret the colour phenomena. On the contrary, i t is necessary to distinguish between a weak interaction, which only causes a deformation of the r-electron cloud, and a strong interaction, which causes a change of r-electron distribution (Brown and Brady, 1952). The first type applies in solutions of hydrogen halide in benzene and methylbenzenes, where thermodynamic measurements force one to the conclusion of an intermolecular interaction between the solvent molecules and the dissolved hydrogen halide molecules (Brown and Brady, 1952).

The interaction in strong acids, such as concentrated sulphuric acid and hydrofluoric acid, in which strong colour changes may be observed, clearly differs from this. These colour effectsfurthermore resemble those which had also been observed long ago in the ternary system aromatic substance-Lewis acid-hydrogen halide (Gustavson, 1878, 1890, 1903, 1905). After Norris and Rubinstein (1939) had postulated the existence of carbonium ions in systems of this type, Gold and Tye (1952a, b, c) suggested for the formation of a proton addition complex by the following equation :

Comparison with the general equation (3)for aprotolyticreactionshows that this equation corresponds to Bronsted’s definition if the aromatic substance is accorded a basic character. The “proton addition complex ”

T H E B A S I C I T Y O F U N S A T U R A T E D COMPOUNDS

199

produced by the addition of the proton represents a cation acid, and is also described as the conjugate acid of the hydrocarbon. I n the ternary systems aromatic substance (A)-Lewis acid (MXJhydrogen halide (HX) the formation of a proton addition complex can be formulated analogously. A+HX+MX,

+ AH+MX,

(6)

The equilibrium constant of reaction (6) is

Since the acid HX acts as a solvent, its activity may be regarded as constant and included in the equilibrium constant. f* is the mean activity coefficientof the cation acid and the stabilizing anion X-. The way in which equations (6) and (6) are written define the corresponding equilibrium constants a0 basicity constants KB. Their reciprocal corresponds to the acidity constant K A and gives the acid strength of the conjugate acid AH+. From equation (6) the basicity constant, again for the cme in which HX acts as the solvent, is found to be

where f * denotes the mean activity coefficient of the cation acid and of the MXh-ion, fA denotes the activity coefficient of the aromatic substance, andf- denotes the activity coefficient of the Lewis acid in the HX solution. The fact that equations (7) and (8) are related to the solvent, and indeed to the acid itself aa the solvent, means that KB or KB-values apply to a particular solvent. It must therefore not be expected apriori that a basicity scale of unsaturated hydrocarbons formed by these values can immediately be transferred to another system. The relation between the constants KB and Kb is given by the equilibrium (9) MXs+X- + MX, (9) with the equilibrium constant

200

H . -H. P E R K A M P U S

which is the ratio of the constants KB and Kg,

It is therefore possible, knowing K , to convert the constant Kk obtained from (8) into K,. Equations (7), (8), (9a) thus permit the basicity constants to be determined if the concentrations and activity coefficients of the ions and neutral molecules present in the solution are known. 11. THESTRUCTURE OF THE PROTON ADDITION COMPLEXES

A. Survey of Xethods The use of thermodynamic relationships to determine the basicity constants and their temperature dependence presupposes that the existence and structure of a proton addition complex of this type has been proved. If one considers the structure suggested by Gold and Tye (1952a, b, c) it is obvious which physico-chemical methods can be used to prove the existence of this complex. We shall take benzene as an example:

(i) The addition of the proton destroys the sp2-hybridized valency state of a C-atom, and converts it into an sp3-hybridized tetragonal valency state. In the proton addition complex one thus finds, as a new structure, a -CH2-group adjacent to a conjugated system. Since hydrogen atoms are bonded to trigonal and tetragonal C-atoms, i.e. to C-atoms of differing electron density, this effect can be demonstrated by means of the N.M.R. spectrum. (ii) I n addition to a change in the valency state of one of the C-atoms, the addition of the proton produces in many cases a lowering of the symmetry of the basic molecule. I n the case of benzene, the symmetry is lowered from D6,, to C2v. As a result forbidden transitions for 1.R.inactive normal vibrations become allowed, so that the I.R. spectrum of a proton addition complex shows great changes compared to that of the free aromatic substance. Furthermore the number of normal vibrations is increased by three as a result of the additional proton.

THE BASICITY O F UNSATURATED COMPOUNDS

201

(iii) The third effect is the influence of the proton addition on the electron distribution. The visible effect caused by this is the deepening of the colour which takes place on addition of the proton. To interpret this effect, quantum-chemical calculations can be coupled with the experimental determination of the electron excitation spectra. (iv) The positive charge which arises can be regarded as the fourth characteristic of the formation of a proton addition complex. However, methods which can be applied to this are directly connected with the thermodynamic relationships and therefore serve for the analysis of the systems present in the solution. Like all thermodynamic quantities, they can therefore not give any information as to the structure of an individual ion and should be distinguished as “macroscopic quantities ” from those quoted under (i)-(iii), which may be described as “microscopic quantities ”.

B . N.M.R. Spectra of Proton Addition Complexes 1. Cfhemicaldisplacement in proton addition complexes As has already been stated, the possibility of demonstrating a proton addition complex by means of N.M.R.-spectroscopy depends on the formation of an aliphatic CH2-group on the addition of a proton. Since the position of the proton signals relative to a standard is strongly influenced by the chemical environment of the protons, changes in bonding can be recognized by the “chemical shift ”, i.e. by the position of the proton resonance signals. If, for example, a proton is added to benzene, a methyl derivative of benzene, or a polynuclear aromatic hydrocarbon, then the occurrence of a new signal in the range between T = 4 and 7 p.p.m. (i.e. between - 6 and - 3 p.p.m. from tetramethylsilane) may be expected. MacLean and collaborators (1968) have indeed been able to demonstrate an additional N.M.R.-signal in this range for the proton addition complexes of several benzene derivatives and of some simple condensed aromatic substances. Figure 1 shows, by way of example, the proton magnetic resonance spectra of 7,12-dimethylbenz[a]anthraceneand of its proton addition complex. Figure la shows two bands for the CH3protons of this aromatic substance. This means that the two CH,-groups are not equivalent. As soon as the proton addition complex with the configuration CH-CH, is produced in a strongly acid solution one of these two signals is strongly displaced (Fig. lb). The two CH,-groups can be emily differentiated, since in the case of one CH,-group the adjacent single proton causes the CH,-signal to appear as a doublet and, conversely, the free protons of the methyl

202

H.-H. PERKAMPUS

I

I

0

I

I

I

1

I

200

266t/S

I

0

(d)

C( , ,

I.

t

I

-

2601

CIS

H

0

1

200

*H

*

F;:h I

I

I

I

I

200

I

I ,

260 CIS

FIU.1. PMR-spectraat 40 c/s and 298OI2,according to MacLean et aZ. (1968). (a) 7,12dimethylbenz[a]anthacene in CC4, (b)proton addition complex of (a)in CFs. COsH 22 mole % HzO-BFs, (c) deuteron addition complex of (a) in CFs.COzD+24 mole % of DzO .BFs, (d) 9,10-dih~dro-9,10-dimethylanthacene in CCl4. (B=benzene as a standard.)

+

T H E B A S I C I T Y O F U N S A T U R A T E D COMPOUNDS

203

group cauae the signal of the single proton to appem as a quartet. At the same time it is possible to identify the CH,-signal which belongs to the methyl group in the 7-position. In the corresponding deuteron addition complex (cf. Fig. lo) the quartet disappems, since the resonance fiequency of the deuteron lies in a different range. Finally, Fig. l d shows, an example of an in the case of 9,10-dihydro-9,1O-dimethylanthracene, configuration. Here both CH,-groups are unequivocal CH-CH, equivalent so that only one doublet for the CH,-protons and one quartet for the CH-protons are found. Similar results were obtained for mesitylem, pentamethylbenzene, hexamethylbenzene, hexaethylbenzene, 9,IOdimethylanthacene, pyrene and benzo[a]pyrene. Table 1 summarizes the results of MacLean and collaborators (1968) converted to T-VaheS. TABLE1 Chemical shift of the aliphatic CHI- or CH-groups efter proton addition to some mmatic compounds (MacLeen et al., 1968)

Compound

H3Ch

C

H

HF +BFa

6.88

HF +BF3

6.28

HF + BF3

8.01

3

6-73

0

The T-value is the chemical shiR in p.p.m. expressed on a scale in which a + 10 p.p.m. is aasigned to tetramethylsilene.

value of

204

H . - H . PERKAMPUS

TABLE1-continued Aliphatic proton peake Compound

Solvent

74H1

Or 70H-0Hi“

.

~

CF3. CO. OHfHzO.BF3 ( 17 mole yo)

6.28

CH3

HF

+ BF3

.

. +

.

.

5.78

.

CF3 CO OH Ha0 BFs (19 mole yo)

CFs CO OH+HzO.BFs (22 mole Yo)

6.73

4-46

The “aliphatic character” of the CH-bond may be particularly clearly recognized from the signals of the CHs protons. The signal of a methyl group bonded to a benzene nucleus is displaced towards lower fields and lower 7-values relative to an aliphatic methyl group. Thus the aliphatic character achieved through the addition of the proton causes a displacement of this methyl group signal to higher fields. Of the compounds quoted in Table 1, these effects are shown very clearly by the methylanthracene derivatives, as is seen in Table 2.

T H E BASICITY O F UNSATURATED COMPOUNDS

205

TABLE 2 Chemical shift of the CHs-protons in the proton addition complex Compound

I

Solvent

70x1

cc14

{ CFs(17.COmole.OH%)+Ha0 .BFs

(P.P*m.)

8-88 6.43

8.30 8.60

6-88

7.00

6.28

8.13 8.30

I

CH3

cc14

{ CFs;127COmole.OH%)+Ha0 .BF3

8.31 8.66

Comparison with the 9,lO-dihydro-9,10-dimethylanthracenealso listed clearly shows the aliphatic character of the proton-carrying Catom. Whereas one of the methyl group signals practically remains at 6.3-6-6 p.p.m., the second methyl group is displaced to higher fields and thus approaches the position of an aliphatic methyl group. The methylene groups present after proton addition can also be clearly recognized in the N.M.R. spectra of azulene and some of its derivatives (Schulze and Long, 1964). 2. N.M.R. Spectra and exchange processes

The fact that aromatic substances are relatively weak bases always requires the use of strong acids. However, proton exchange processes take place in such media, and these can interfere to an extraordinary extent with this particular method of measurement. A very similar situation exists for proton addition complexes as in the case of alcohols and other systems involving hydrogen bonds. I n the present case the situation is in part even more complicated, since both an intermolecular and an intramolecular proton exchange has been

206

H.-H. PERKAMPUS

demonstrated (MacLean and Mackor, 196lb). It is therefore necessary to consider the following: (a) Intermolecular proton exchange with the solvent:

AH+X-

--f

A+HX

(b) Intramolecular proton exchange :

Here the proton has migrated from the 2-position to the 3-position or from the l-position to the 4-position. (c) Intermolecular proton exchange :

a. Intermolecular proton exchange with th solvent. I n cases (a) and (c) conditions can be chosen such that only one of the two exchange processes remains. According to the investigations of Mackor and collaborators (1958b), reaction (a) is endothermic for the case of a strong base and a strong acid, so that the exchange speed depends on two factors: Grstly, it will decrease as the proton concentration of the solvent is increased, and secondly it will decrease on changing to a more basic hydrocarbon. The N.M.R. spectrum of the 7,12-dimethylbenz[a]anthracene shown in Fig. 1 illustrates the example of a basic hydrocarbon. The signal of the CH3group of the C-atom to which the proton has been added shows a sharply defined doublet, with a splitting of J = 7 c/s. This means that no significant exchange takes place in this system and that the exchange reaction is therefore certainly slower than 7 c/s. In order to study the dependence of the exchange reaction (a) on the proton concentration alone, i.e. on the acidity of the solvent, MacLean et al. (1968) chose the system pentamethylbenzene-CFS, CO .OHHzO. BF3.

T H E BASICITY O F UNSATURATED COMPOUNDS

207

After addition of a proton to pentamethylbenzene, three different methyl groups are present :

I

CH3

(P)

In strongly acid solutions (HF+ BFS)in which the exchange reaction (a) has been largely suppressed, one therefore observes, as shown in Fig. 2, three proton signals, the intensities of which are in the ratio of

FIG. 2. PMR-spectrum of the proton addition complex of pentamethylbenzene in HF + B F s ; benzene used as internal standard (MacLean et aZ., 1968) 298’K.

1;”IG. 3. PMR-spectra of the CHs-protons of pentamethylbenzene ea s funotion of acidity; scale 8 c/s; 298°K. (a) CFsCOOH, (b) CFsCOOH+12 mole % HzO.BFs, (c) CFsCOOH 20 mole % HzO. BFs, (d)CFsCOOH 30 mole % HzO BFs.

+

+

.

1:2 :2, corresponding to the positions p :0 : m. On the other hand only a single signal is found in weakly acid solutions (Fig. 3a). If the acidity of the solution is increased one first notes a broadening of the signal (Figs. 3b, 3c),until one finally obtains, in the solution of CFsCOOH+ 30 mole yo H20.BFs, an N.M.R.-spectrum which agrees with that depicted in Fig. 2, as can be seen in Fig. 3d. The example chosen is particularly well suited to a study of the exchange reaction (a) since in pentamethylbenzene there is a single

208

1E.-H. P E R K A M P U S

position of high proton afIinity and “intramolecular exchange ” is impossible. If this prerequisite is not met, then the exchange reactions (b) and (c) increasingly assume importance. I n strongly acid solutions, in which reaction (a)is practically completely suppressed, these exchange reactions therefore cause broadened signals in the N.M.R. spectra of the proton addition complexes.

I

6

7

8

9 1 ;

(4

(b) FIG. 4. PMR-spectrum of the proton addition complex of hexamethylbenzene. (a) HF+BFa at 188°K (Brouwer et al., 1965a), (b) at 243”K, rapid exchange (MacLean and Mackor, 1962). (CH multiplet, CHs doublet).

b. Intramolecular proton exchange. MacLean and Mackor (1961c, 1962) thoroughly investigated the proton addition complex of hexamethylbenzene between - 110°C and - 30°C as an example of an intramolecular exchange reaction (b). At - 110°C the reaction takes place very slowly. At that temperature one observes an N.M.R. spectrum which consists of four signals for different methyl groups in the proton addition complex of the hexamethylbenzene, the assignment of which is shown in Fig. 4a (MacLean and Mackor, 1961b). The splitting is J , = 6.8 c/s, as a result of coupling between the protons of this CH-CHs group, and J 2= 3.5 c/s for the long-range coupling between the added proton and the methyl group in thepara-position. The coupling constant between the methyl group in the ortho-positionand the added proton is

T E E B A S I C I T Y O F U N S A T U R A T E D COMPOUNDS

209

J g =1 CIS. The coupling between the methyl groups in the meta-position and the added proton is negligible. As the temperature is increased, so the proton can successively occupy different positions in the ring since all ring atoms have the same proton afhity, so that we are dealing with the intramolecular exchange described under (b). I n these temperature ranges the N.M.R. spectra show broad and diffuse signals. If the temperature is sufficiently high, then this exchange reaction takes place extremely quickly. The N.M.R. spectrum resulting from this at - 30"C, given in Fig. 4b, shows a doublet for the methyl groups and a multiplet structure for the CH-group. The doublet of the methyl group signals corresponds to the two spin states of the added proton, and the splitting J = 2-1 CIScan be additively compounded from the three coupling constants quoted above, on the assumption that they all have the same sign : J = +[J1+J 2

+

2J3]

Thus all methyl groups become equivalent because of the very rapidly occurring exchange. As a result, however, all spin states of the six methyl group protons affect the added proton in the same way, so that the multiplet of the CH-proton has to be interpreted in terms of the 19 spin states of the 18 methyl group protons. This type of temperature dependence, and in particular the N.M.R. spectrum in Fig. 4b, is a convincing proof of the intramolecular exchange reaction (b) in this system. Similar situations apply in the case of durene (1,2,4,5-) and prehnitene (1,2,3,4-tetramethylbenzene)(MacLean and Mackor, 1962; Brouwer et al., 1965a). c. Intermolecular proton exchange withut participation of the solvent. Whereas the intramolecular exchange reaction (b) is practically independent of the concentration of the reaction partners, and is therefore of zero order, an intermolecular exchange reaction according to (c) has to depend on the concentration. It is indeed found that for mesitylene, m-xylene and anisole the exchange speed is of fist order relative to the concentration of these molecules (MacLean et al., 1962). I n the case of mesitylene an exact investigation of the N.M.R. spectra as a function of temperature shows that the exchange reaction (a) also has to be taken into account. Figure 5 gives a schematic survey of the temperature dependence of the N.M.R. spectrum of mesitylene and of its proton addition complex in H F + B F 3 as the solvent (MacLean and Mackor, 1962). The spectrum at - 100°Cshows that in addition t o the proton addition complex free mesitylene is also still present, as can be seen from the assignments in Fig. 5. On increasing the temperature it is found that the

210

H.-H. PERKAMPUS

signals of the ring protons become superimposed on the signal of the protons of the “aliphatic” CH2-group and the methyl group signals coalesce to give a single relatively sharp signal. From - 3OoC onwards

II

I TIi I I

/

t

111

? -98OC

0

200

100 c/sec

FIG.6. PMR-spectra (60 c / s ) of mesitylene and of its proton addition complex in HF + BFa at various temperatures according to MacLean and Mackor (1962). Sea text.

to higher temperatures the lines of the ring protons and the line of the HF-proton begin to broaden (MacLean and Mackor, 196lb), until they merge into a single broad signal at + 50°C. This means that within this latter temperature range the exchange reaction (a) takes place a t a measurable speed.

TABLE3 Chemical shifts of proton addition complexes of some methylbenzenes (according to Brouwer et aZ., 1965a) The references 0 - , m- and p- in each case refer to the position of the ring protons or the methyl groups relative t o the added proton

rj

x

Y

Proton addition complex

W

WE,(Methyl GOUPS)

TC-E

k-

ca U

t"C

Solvent

P-

0-

m-

TCRI

-125

HF+BFa

-

1-2

1.82

5.04

1.94

5.08

2.17 2.07

6.23

P-

0-

m-

2Y

*

CHJ I

-

7.4

-

7-0

7.40

7.0

7.12

-

6.9

CH2 I H

CH3

.

CH3 -45

H

CH:i

HF+SbFa

-

1.32

tr

il)

212

00

2

n

2 ?

l-

I

I

dl 00

I

l-

I

z W

X

n 0

x x

W

H.-H. PERKAMPUS

g

x

q-$ x

n

x 16

2

16

0

v)

t-

m I

I l l

I

n

'9

t-

0

2

*

2 m

x

I

m 0 I

2 -?

t-

2

n

W

I

I I rz

i

F9

&

n

m I

m 0

+

+

-?

Gu

THE BASIUITY O F UNSATURATED COMPOUNDS

+ I

8:88

213

214

H.-H. PERKAMPUS

The temperature-dependence of these spectra can therefore be explained if one assumes an intermolecular proton exchange according to (c)for the range of - 100°Cto - 30"C, and a proton exchange with the acid according to (a) above - 30°C. Similar situations prevail in the system m-xylene-HF-BF,, which has been investigated in the range of -101°C to -49°C (MacLean and Mackor, 1962). According to these explanations, the N.M.R. spectra of proton addition complexes can unambiguously be observed only if the rapid intramolecular or intermolecular exchange processes have been eliminated. I n order to achieve this, two factors can be varied, the temperature, and the strength of the acid. Brouwer et al. (1965b, c) have collected the chemical shifts of the proton addition complexes of a substantial number of methylbenzenes, taking these two possibilities into account (Table 3). 3. Summary

N.M.R. spectroscopy furnishes a proof for the presence of proton addition complexes. The possibility of recognizing proton exchange processes is inherent in the method. Of the three exchange reactions discussed, the intermolecular exchange processes are particularly relevant to the question of the bmicity of aromatic systems. The discussion of N.M.R. spectra given so far thus already provides information as to the positions of particularly high proton afKnity within a molecule, and, in conjunction with the dependence of the N.M.R. spectra on the acid concentration, also provides information as to the proton affinity of different molecules. A quantitative analysis of the N.M.R. spectra and of their temperature dependence permits the life of the proton addition complexes and hence of the exchange speeds of the various reactions, as well as the corresponding activation energies, to be determined (MacLean and Mackor, 1962; Brouwer et al., 1965a, b). The use of N.M.R. spectroscopy further requires that the proton afiinity of the aromatic substances should not be too low. Benzene and toluene, for instance, have such a low proton affinity that no proton addition complex has so far been demonstrated by means of N.M.R. spectroscopy, even at - 100°C. A combination with other methods is therefore required in order to demonstrate proton addition complexes in these cases.

C. The I.R. Spectra of Proton Addition Complexes Compared to the N.M.R. spectra of proton addition complexes discussed in Section 11,B, and the electron excitation spectra to be discussed in Section 11, D, the I.R. spectra of these complexes have hitherto been

THE BASICITY OF UNSATURATED COMPOUNDS

215

very little investigated. The reason for this lies probably mainly in the cell technique which does not always sufficiently meet the requirements for absolute absence of water. I n order to circumvent these difficulties, Perkampus and Baumgarten (1963,1964a) measured the I.R. spectra of these and similar complexes in the solid state at temperatures down to 60°K (Perkampus and Baumgarten, 1961). Using this technique, it is possible to investigate thin films of substances which can be sublimed and easily evaporated in a high vacuum and, in particular, to eliminate the effect of the solvent, which is a disturbing factor in many cases. This technique further permits one to allow a second and third component to act on these films, so that interactions in the solid state can be followed. The system aromatic substanc+HX-MX,, which leads to the formation of a proton addition complex according to the formulation given in the introductory section, was chosen for investigation. It is therefore to be expected that the formation of this complex should be accompanied by a pronounced change of the I.R. spectrum of the aromatic component, since the addition of a proton causes a change in the symmetry of the aromatic compound in many cases. I n addition to the normal vibrations being increased by three by the added proton, bands which are forbidden in the case of benzene itself should manifest themselves. Though the formation of the proton addition complex of benzene thus requires a pronounced change of the molecular skeleton, it has only recently proved possible to demonstrate the existence of this complex (Perkampus and Baumgarten, 1963). Figure 6 schematically shows the I.R. spectra in the solid state at 77'K for the ternary systems benzene-HC1-AlCl,, benzene-HBr-AlBr, and benzene-HC1-GaC18 (Perkampus and Baumgarten, 1964b). Several new bands are seen to arise as a result of the interaction, and the nature of the ansolvo-acid has no significant influence on the I.R. spectrum of the ternary complex. This is very simply explained if one msumes the formation of a proton addition complex in which the stabilizing counterion has only a slight effect. However, a pronounced change of symmetry simultaneously accompanies the proton addition. Benzene, having a symmetry DBh,gives rise to a complex belonging to the symmetry group C2". As a result vibrations which are 1.R.-inactive in benzene can become 1.R.-active in the complex. This undoubtedly explains the new band at 6.27 p, corresponding to 1595 cm-l, which also occurs in substituted benzene and which is attributable to a C = C skeletal vibration. Thus similar relationships exist to those in the compaxison between benzene and toluene. The isotope effect of perdeuteriated benzene may be used to distinguish between C=C and C-H vibrations. The interaction in the ternary

216

H.-H. PERKAMPUS

complex benzene-d6-GaC1,-DC1 also leads to characteristic changes in the I.R. spectrum (Fig. 7). A simple comparison of the spectra (Fig. 7a and Fig. 7b) shows that some bands practically retain their position whereas others are strongly shifted to longer wavelengths. This fact permits a relatively easy assignment in the case of some bands. Thus the bands at 6.27 and 6.92 p, corresponding to 1595 and 1445 cm-l, in the benzene complex, are skeletal vibrations, since the isotope effect of the corresponding bands in the d6-complexis very small. The new band at 16.62 p

1.a.

1.0.

I!

crystalline

solid

!.a.

!.a.

I II

Tp i.a.

I

solid

solid

1.0. II 1I

I

I

I

I II

II

I II 1 I I 1 I 1500 1000 500 cm-' FIO. 6. Summary of the I.R. spectra of the solid proton addition complexes of benzene with different Lewis acids at 77'K (1.R.-inactive vibrations of benzene are shown with broken lines). (Perkampusand Baumgarten, 1964b.) I

(640 cm-l) (Table 4) in the benzene complex corresponds to a band at 20.4 p (490 cm-l) in the d6-complex. The relatively great isotope effect thus identifies it as a C-H vibration. The basis for the further assignment of the bands to specific vibrations is the assignment of the benzene bands given by Whiffen (1955) on the basis of an exact molecular model calculation. Accordingly the ratio vH/vDis a criterion for the nature of the vibrations. I n the attempted interpretation given in Table 4, the procedure was f i s t to look for the various possible assignments on the basis of the expected spectral regions, and then to select from these those assignments in which the intensity of the bands of benzene and of the d g -

THE BASICITY O F UNSATURATED COMPOUNDS

217

complex were approximately similar and for which the ratio vH/vD corresponded as nearly as possible to that for benzene. The transfer of the expected ranges from benzene to the proton addition complex is justified by the fact that an analogous procedure also proved possible for other benzene derivatives and for pyridine (Wachsmann and Schmid, 1961 ;Baumgarten, 1962).

0

5

I

I

I

I

I

I

I

I

I

6

7

8

9

10

II

12

13

14

15

P

0. 5

1

6

I

7

I

I

1

8

9

10

I

I

I

I1

12

13

I

15

14

P

FIG.7. I.R. spectra in the solid state, at 77"K, of (a) (C&+) (CfaC14-).

(GaC14-), (b) (CaD?+)

The transfer of the expected ranges is particularly satisfactory for skeletal vibrations, whereas it is probably less precise in the case of C-H vibrations, since the vibrations of the H-atoms are more strongly influenced by the added proton, and since three additional fundamental vibrations can also arise. For this reason the assignment of the C-H vibrations in the intermediate frequency range is less reliable than for the other bands. Furthermore, as these investigations showed, the proton addition complex of benzene is stable only up to about 220°K. This is probably the main reason why the existence of this complex has only now been demonstrated. This instability, coupled with the exchange processes 8

218

H.-H. PERKAMPUS

requiring consideration in solution (see 2b) is probably also the reason why it is not possible to demonstrate this complex by means of N.M.R. spectroscopy. On going to methyl-substituted benzene derivatives the effects observed with benzene become more pronounced (Perkampus and Baumgarten, 19648). Already with toluene it is found that the stability of the ternary complex has increased, since the latter decomposes into its components only above 250°K. From xylene onwards all complexes are stable, even at room temperature. This is already a manifestation TABLE 4 Assignments for the ternary complex benzene-Lewis acid-hydrogen halide (Perkampusand Baumgarten, 1963a) Vibration H-Complex D-Complex Y (cm-1) I v (cm-1) I 1595 s 15801 vw 1445 vs 1328 vw 1205 m 1178 s 983 v w 953 w 901 m 814 m 690 vs 640 vs 881 w

vH/vD

VE/b

Complex

1541 s 1527 w 1425 vs 1047 vw 818 s 856 s 822 vw 768 vw 872 m

1,035 1.035 1.015 1.270 1.314 1.376 1-195 1.243 1-034

510 m 490 8 553 w

1.352 1.306 1-052

Benzene

}

1.028

Type

W

No.

}

8a, b

1.110 1.228 1.358 1.389 1.203 1.224 1.053

W

19 3 9 15 5 17 1

1.352

Y

11

-

1a 0 5 1

W

6 6 6

Y Y

Y W

6

of the increasing basicity of the benzene derivatives with increasing number of methyl groups. On the other hand, the rate of complex formation in the solid state seems to depend greatly on steric circumstances. It is particularly low for those methylbenzenes, such as mesitylene or durene, which contain only isolated unsubstituted hydrogen atoms, or which are completely methylated (hexamethylbenzene). On complex formation the bands of the Lewis acid change in the same way as observed for benzene (Perkampus and Baumgarten, 1963). Figures 8 and 9 show, by way of examples, the I.R. spectra of the ternary systems toluene-HC1-GaCls and m-xylen+HCl-GaCl,. The pronounced changes can be interpreted if the formation of a proton addition complex is assumed. A detailed discussion of the I.R. spectra

219

THE BASICITY O F UNSATURATED COMPOUNDS

of the complexes of toluene, 0 - , m-, p-xylene, mesitylene, hemimellitene, pseudocumene, durene, and hexamethylbenzene shows that the numerous new bands which occur can be correlated with bands which are inactive in the basic methylbenzene (Perkampus and Baumgarten, 19648). 2000

5

1200

1500

6

7

8

700

800

1000

9

10

12

II

500

600

cml

13

cm-1

15

14

*.._... -*. I

I

I

4

-

', I

,

-

I I

-

!

0

13

I

14

I

I

I

I

15

16

17

18

I

19

20

I

21

22

23

24

I"

FIG.8. I.R. spectra of toluene (broken line) and of its proton addition complex (solid line) in the system toluene-GaCl3-HCl at 77'K. (Perkampus and Baumgarten, 1964a.)

Pronounced changes which are characteristic for the structure of the complexes occur particularly in the range of 670-900 cm-l. It is known that in this range the number and position of the bands depend on the number of mutually adjacent H-atoms of the ring. Table 5 surveys the most intense bands of the proton addition complexes and their assignment to the expected ranges summarized by Bellamy (1960).

220

H.-H. PERKAMPUS

It is found that the bands can be relatively successfully assigned to these expected ranges if the two H-atoms which are bonded to a single C-atom after proton addition are regarded aa substituents and are not taken into account when counting the adjacent H-atoms. 2000 ~~

1200

1500

~

cm-'

800

1000

too D %

50

Ol

I

6

5

100

0

700 1

13

1

1

I

I

7

8

'

I

9

I

t

10

II

600 I

I

I

I2

1

I

13

14

I

15

'mc

500

I '

I

I

I

I

I

I

I

14

15

16

17

IS

19

20

I

21

22

24

23

P FIG.9. I.R. spectra of m-xylene (brokenline)and of its proton addition complex (solid line) in the system m-xylene-GaCl~-HCI at 77°K. (Perkampusand Barngarten, 1964a.)

The various aromatic ions which are summarized in Fig. 10 can be determined relatively easily on the basis of these considerations. The discussion of this field supports the theoretically required isomeric proton addition complexes in which proton addition can take place both in the o-position and in thep-position relative to the methyl group. Thus a reaction in the m-position or at the carbon atom carrying the methyl group is less favoured compared to the other possibilities. This accords

T H E BASICITY O F UNSATURATED COMPOUNDS

221

well with the results of Mackor and collaborators (1957),who studied the D-H-exchange of methylbenzenes in detail. Baumgarten (1964) carried out analogous 1.R.-spectroscopic investigations with naphthalene and anthracene. Here again the pronounced changes in the I.R. spectrum can be interpreted by the formation of a TABLE6 Correlation of the bands which occur in the range 670-900 cm-1 to the number of mutually adjacent H-atoms in the ternary complex aromatic substance-GaCl3-HC1 Adjacent H-atoms

6

4

3

2

730-770

736-770

760-810

800-860

860-900

VS

VS

VS

m

660-726

700-760

m

m

Aromatic substance Benzene 690 vs Toluene o-Xylene m-Xylene p-Xylene

742 vs

848 vs (709 vs)

829 8 (732 8 ) 857 vs (720 8 )

Hemimellitene (1~3)

Pseudocumene (1,2,4) Durene (1,2,4,6)

Not assigned

898 vs (893 m)

797 m (710 s) 876 s 873 m

697 m 779 s 830 m

867 m

Mesitylene (1,3,5)

1

784 vs (729 8) 824 s (734 8 )

712 m 876 m 888 m 889 m

743 m

proton addition complex. However, the assignment is more difficult for polynucleax aromatic compounds than for methylbenzenes. In principle the investigation of ternary systems in the solid state thus presents the opportunity of measuring the I.R. spectra of proton addition complexes. I n the cme of strongly basic aromatic substances it is furthermore also possible to demonstrate the existence of a-complexes in the binary system aromatic substance-Lewis acid without the participation of protons (Perkampus et al., 1964~).

222

H.-H. P E R K A M P U S

Benzene

I

Toluene

p-Xylene

I

0-Xylene

(5HS

Mesitylene ~~

!+: CHI Hemimellitene

H3C Pseudocumene

Durene

Fm. 10. Position of proton addition for various methylbenzenes. (Perkampus and Baumgarten, 1964a.)

D. The Electron Excitation Spectra of Proton Addition Complex.es The complex formation of aromatic hydrocarbons with Lewis acids in the presence of hydrogen halide and the colour of the so-called “red oils” associated with this is the oldest observation which indicates that the interaction is connected with a pronounced effect on the electronic structure of the aromatic hydrocarbons (Gustavson, 1878, 1890, 1903, 1906). The observation that aromatic substances dissolve in concentrated sulphuric acid with a deepening of colour is almost equally old (Gabriel and Leupold, 1898). Though the most striking physical property has thus been known for a very long time, an explanation of these effects could only be given very much later. Norris and collaborators (Norris and Rubinstein, 1939;Norris and Ingraham, 1940) first established that this colour change in concentrated sulphuric acid is associated with the formation of carbonium ions. Subsequently it proved possible to show that the formation of the coloured species depends on the acid concentration (Gold et al., 1962; Gold and Tye, 1962a). The aromatic substances could be recovered unchanged, with a normal spectrum, by dilution of

T H E BASICITY O F UNSATURATED COMPOUNDS

223

the solutions whose absorption spectra differed very greatly from the absorption spectra of the aromatic substances in normal solvents. Gold and Tye investigated, inter alia, the following aromatic substances : 1,ldiphenylethylene, triphenylethylene and anthracene, and found similar spectra in concentrated sulphuric acid despite the great differences of the absorption spectra of these aromatic substances in organic

222

I

"

mP

300

2 50 1

1

l

1

'

400

500

I 1 " ' I

'

1000

' " I

FIG.11. Electron excitation spectrum of 1,l-diphenylethylenein concentrated HzS04 according to Cold and Tye (1962a).

solvents. As may be seen from Fig. 11, a solution of 1,1-diphenylethylene in concentrated sulphuric acid gives an intense maximum at 23,200 cm-l (431 mp). The position of this maximum coincides with that of the triphenylcarbonium ion (Evans, 1961). Gold and Tye concluded that the light absorption of the compounds referred to is attributable to a carbonium ion the electronic structure of which corresponds to that of the diphenylmethyl cation. A carbonium ion of this type can be e a d y obtained from these compounds by addition of tb proton :

H.-H. PERKAMPUS

224

A proton addition complex of this type can also be formulated for triphenylethylene and numerous other aromatic carbons. It is a characteristic of all these conjugate acids that the positive charge is distributed over the whole molecule by a charge resonance. The electron excitation spectra of the ternary systems aromatic substance-HX-MX, were investigated at the same time (Eley and King, mP 182

200 I

'

-

250 I

'

8

l " " 1

300

500

400 "

8

l

a

'

'

FIG.12. Electron excitation spectra (a)of mesitylene in n-heptane, (b) of its proton addition complex in HF + BF8, and (c) of the proton addition complex of pentamethylbenzene in HF. (Dallingaet al., 196%; Brouwer et al., 19668.)

THE BASICITY O F UNSATURATED COMPOUNDS

225

1952; Reid, 1954). I n these ternary systems the formation of proton addition complexes also takes place, as is shown by a comparison with the electron excitation spectra of aromatic substances in concentrated showed that in acids. Detailed investigations by Dallinga et al. (1968~) 182

200

300

250

400

500

-

cni'

FIG.13. Electron excitationspectra (a)of anthracene in n-hexane,(c) of anthracene in HF, and (b) of the proton addition complex of 2-methylanthracenein HF (Dallinga et QZ., 1958a).

HF as the solvent the addition of BF, (ternary system) in the presence of weakly basic aromatic hydrocarbons only serves to increase the acidity of the acid. Thus the interaction of the aromatic substance always involves a proton acid. Figures 12 and 13 show examples of the electron excitation spectra of proton addition complexes. For the two methylbenzenes the light absorption of the proton 8*

226

€1.-H. P E R K A M P U S

addition complex is strongly shifted to the red end of the spectrum, compared with the absorption of mesitylene in n-heptane (Fig. 12). I n addition to the strong red displacement, the high intensity of the long wavelength band ( € 2 :10,000) should be mentioned. The situation is also similar for anthracene and 2-methylanthracene (Fig. 13). The intensity of the long wavelength band here rises to E = 40,000. Table 6 gives a summary of the maxima and corresponding extinction coefficients of some proton addition complexes. TABLE6 The long wavelength absorption bands of some proton addition complexes in solution

Reference

vmax.

Solvent

(cm-1)

Benzene +AlzBre+HBr Toluene + 4 B r e HBr HF BFs HF BFs

30,100

332

3800

a

30,700

326

-

a

28,200 27,400

355 365

11,000 7600

b b

26,660 27,600 25,650 24,400 26,250 26,250 28,200 19,600 19,600 22,760 28,300 21,760

377 362 390 410 381 381 354 510 510 440 363 460

b b b

24,600 23,700 23,600 25,200 19,000 19,250

408 422 423 397 527 520

9800 5800 10,900 (shoulder) 18,700 11,200 12,200 13,000 6300 9000 7500 3000 (shoulder) 37,000 31,000 43,000 42,000 18,000 33,000

19.050 22,500 22,300 21,600 19.200 20,600 16,600 23,200

625 444 448 464 621 487 603 431

8560 21,560 60,000 18,000 27,000 9500 13,600 32,800

e

Substance Benzene Toluene Mesitylene 1,2,3,5-Tetremethylbenzene Pentamethylbenzene Dimesityl Naphthalene

+ +

+

HF HF HF +BFs (3 atm.) 1,4-Dimethylnaphthalene HF BFs 2,3-Dimethylnaphthalene HF + BFs Acenaphthene HF HF + BFa Phenanthrene 9-Methylphenanthrene HF +BFs Biphenyl HF + BFa Fluorene HF + BFs

+

Anthracene 2-Methylanthracene 9-Methylanthracene Benz[a]anthracene 5-Methylbenz[a]anthracene 7-Methylbenz[a]anthracene Tetrace~ne Pyrene Benzo[a]ppne Benzo[e]p yrene Perylene 1,l -Diphenylethylene

HF HaS04, conc. HF HF HF HF

HF HF HF HF HF HF HzS04, conc.

b b b c

b b b b d b

e e e

f b b b b d

T H E B A S I C I T Y OF U N S A T U R A T E D C O M P O U N D S

Triphenylethylene 1-Phenyl-1-a-naphthylethylene 1,6-Diphenylhexatriene 1,8-Diphenylocta~tr~ne Azulene 2-Methylezulene 1-Methylezulene 1-Cyenoezulene 1-Chloroezulene a

Luther and Pockele (1966).

c

Reid (1964). Gold and Tye (1962e). Mackor et al. (1966).

* Dalling8 et al. (19688). d

*

23,200 18,200

434 660

21,200 18,600 27,600 24,400 27,400 29,600 27,800

473 638 362 369 366 337.6 360.0

27,000 18,600

227

d d

-

22,400 19,600 12,400 9260 10,200

I Adbersberg et al. (1969). 0 Plattner et al. (1962). A Long end Schulze (1964). Stagemeyer (1966).

'

I n addition to the purely experimental proof of the proton addition complex by comparison of the electron excitation spectre of caxbonium ions obtained in different ways, which in any case is restricted to a few examples, a general proof is possible by a theoretical interpretation of the electron excitation spectra with the aid of the basic model. I n the case of anthracene three isomeric proton addition complexes have to be taken into account :

The treatment of these r-electron systems, which have two welectrons and one skeleton C-atom fewer than anthracene, was carried out by Venijn Stuart and Kruizinga (1968) by means of the HMO end SCF method. Figure 14 shows the result of these calculations for the three isomeric proton addition complexes of anthracene compared to the measured electron excitation spectra (Dallinga et al., 1958a). It can be clearly seen that the measured spectrum agrees with that calculated for the isomeric

228

H.-H. PERKAMPUS

complex (a) as regards the position of the maxima and the intensity of the bands. The authors carried out the calculation for a considerable number of aromatic hydrocarbons by this method, in part also including configuration interaction (CI). As in the cme of anthracene, the possibility of isomeric carbonium ions was taken into account for biphenyl, naphthalene, phenanthrene, pyrene, and perylene. Comparison with the measured spectra permitted a distinction between the isomeric carbonium ions in some cases. The possibility of this differentiation only

n

50 x IO%m''

V-

FIG.14. Comparison of the calculated spectre of the three isomeric proton addition complexes of anthracene with experimental results.

exists where the proton affinity of one C-atom greatly differs from that of the other ring C-atoms. According to this investigation, addition to the a C-atom is favoured for naphthalene, and addition to the C-atom 5 is favoured for phenanthrene (Dallinga et al., 1958a).l I n the case of benz[u]anthracene the positions 7 and 12 are approximately equivalent. Mackor and collaborators therefore discussed the effect of the position of methyl groups on the spectrum of the proton addition complex benz[u]anthracene in connection with the investigation of the basicity of methyl-benz[a]anthracenes (Mackor et al., 1956). The carbonium ions A and B are present in solution : 1 For numbering see

Table 26.

T H E BASICITY O F UNSATURATED COMPOUNDS

229

13

A

The results show that a long wavelength intense band at 6300 A (18,900 cm-l) has to be amribed to the ion A and a band at 4600 A (21,700 cm-l) to ion B. This assignment was supported by calculations (Verrijn Stuart and Mackor, 1957). The proton addition complexes of isomeric methylbenz[a]anthracenes may be regarded as examples of ions A and B (Table 6). Table 7 summarizes the theoretically calculated and experimental absorption maxima. Agreement between theory and experiment is very good. TABLE 7 Comparison of theoretical end experimentally determined electron excitation energies of some proton addition complexes ( D d h g a et aL, 19688; Verrijn Stuart and Mackor, 1957) %ax.

Compound

Theoretical

(cm-1) Experimental

26,000 s 39,400 60,260

30,100 s 40,000

22,300 w 24,700 s 38,700 44,900

24,400 sh 25,600 s 36,700 39,400

18,700 21,700 26,100 33,900

19,600 s

(5) s (6) (1) B (6)

24,400

H

H@ -‘LA’. ’

22,300 w 24,700 s 38,700 44,900

23,800 sh 28,300 B 37,900 39,200

230

H.-IT. P E R K A M P U S

TABLE 7-conDinued VIM=.

Compound

Theoretical

(cm-1)

Experimental

21,400 s 24,200 33,700 m 40,200 s

22,500 m 36.000 s 40,500 m

24,960 26,160 s 38,400

24,600 s 39,000 43,000

17.800 w 24,100 B 26,260

19,000 w 22,600 s 24,600

20,200 B 24,600 26,800

19,300 s

18,200 24,300 s 25,200

19,000 22,300 B 23,600

More recent calculations which take into account the effect of doubly excited configurations in the configuration interactions (CI) (Colpa et ul., 1963 ;De Boer et ul., 1964) show that for mesitylene and cycloheptatriene the inclusion of doubly excited structures improves the agreement between calculated and experimenhl excitation energies (Table 8 ) . However, comparisonof theoretical and experimental oscillator strengths shows that as regards the intensity of the second band the CI calculations which take doubly excited c o r d p a t i o n s into account give worse agreement. I n these calculations the effect of the C2H4-bridgein cycloheptatriene was taken into account by means of suitable inductive parameters (Colpa et d.,1963).

THE BASICITY O F UNSATURATED COMPOUNDS

231

TABLE 8 MO calculations of spectra, including configuretion intermtion (Colpa et oL,1963; De Boer et at.. 1964) Without doubly excited codgurations

With doubly excited configurations

H 3 27,400 c v 0.24 28,200 ---/

Experimental values

43,800 64,100

0-13 0.96

36,700 62,600

0.24 0.01 044

28,300 39,000 49,800

28,200 44,600 63,300

0.46 0.17 0.79

29,600 36,100 62,000

0.46 0.01 0.87

28,400 36,400 46.400

0.16

0.16 0.46

CH3

a The oscillator strengths were estimated from the spectrum given by Brouwer and collaborators (1965a) using the relationshipf =4.32 x em=. Av,,.

In this context attention must be drawn to investigationsof the binary system of aromatic substance-MX,. The interaction can lead either to a r-complex (a)or a a-complex (b):

Investigations of this type were first carried out by Eley and King (1952) and by Reid (1954). Subsequent critical investigations by Luther and Pockels (1 955) of the light absorption of such systems in solution could not confirm the originally formulated a-complexes. The investigations have to be carried out with very careful exclusion of moisture: even small amounts of moisture adsorbed on the walls of the cell suffice to furnish protons for the formation of a proton addition complex. Perkampus and Kranz (1962, 1963) therefore carried out investigations of the absorption spectra of the binary systemsaromatic substanc+.Lewis acid in the solid state in a high vacuum. The spectra so obtainedreaemble

232

H.-H.P E R K A M P U S

the spectra of the proton addition complexes in their position and structure. Similar results were obtained byAalbersberg et al. (1959a,b) for the system anthracene-BF, and tetracene-BF, in 1,2-dichlorethane as the solvent. Since the authors exclude the presence of protons, the identity of the spectra can only be explained by a a-complex according to (b) of which the n-electronic states correspond to those of a proton addition complex. This finding admittedly means that the extremely interesting question as to the existence of a a-complex between the aromatic substance and the Lewis acid cannot be unambiguously answered by means of electron excitation spectra. On the other hand I.R. investigations in the solid state are appropriate for clarifying this question. Perkampus and Baumgarten ( 1964c) could thus demonstrate the formation of such a-complexes of methylbenzenes with some Lewis acids, and these complexes could be converted to the proton addition complexes by subsequent addition of hydrogen halide. Other methods must therefore additionally be used to distinguish between a proton addition complex and a a-complex according to (b). On the other hand n-complexes between m-xylene and Lewis acids can be demonstrated by U.V.-spectroscopy for extremely dry systems (Staats, 1962).

111. METHODS FOR DETERMINING THE BASICITY OF UNSATURATED HYDROCARBONS The formation of a proton addition complex can take place either in a binary system (equation ( 5 ) ) or in a ternary system (equation (6)). Correspondingly, one obtains the basicity constants K B and K i respectively, according to (7)and (8),and these are related to one another through the equilibrium (9) and the relationship (10). It is in the nature of these strongly acid systems that conventional methods for analysing the equilibrium composition can only be used with difficulty. Three main methods have proved of value for the analysis of such systems, viz. : A. determination of the basicity by means of partition equilibria, B. determination of the basicity by means of vapour pressure measurements, and C. determination of the basicity by means of conductivity measurements. A. Determination of the Basicity from Partition Equilibria If an aromatic hydrocarbon (A) is dissolved in a strong acid, and a proton addition complex is formed according to equation (5), the equilibrium constant of this reaction is given by equation (7).

THE BASICITY OF UNSATURATED COMPOUNDS

233

Since the acid itself serves as the solvent, a,, is practically constant and can be included in KB. This only applies as long as the autoprotolysis of the concentrated acid is very slight. If HF is used as the acid then this condition is probably fulfilled since, according to Fredenhagen (1939; Fredenhagen and Cadenbach, 1930), anhydrous HF does not dissociate significantly. On the other hand, in the case of sulphuric acid the dissociation of the acid itself has to be taken into account so that we here have to deal with two interrelated equilibria. The equilibrium (5) then has to be formulated as

and the constant KB defined as

.

AH+ logK, = -logaH+ f-+log--+

CAH

f A

CA

Assuming the Hammett acid function

Ho

=

-logaH+---f A fAH+

to apply to this equilibrium, one has

If a solution of this type is now brought into contact with &norganic phase, a partition equilibrium is set up in which, for practical purposes, only the pure aromatic hydrocarbon dissolves in the organic phase. If the organic phase is denoted by a prime, one then finds the partition coefficient to be :

P = CAH+ + CA ci

CA = -CAH+ +I

ca

cA

The ratio c A / c a represents the partition coefficient PA of the free aromatic substance between the two phases. Since it may be assumed that cAH+ cA, equation (11) simplifies to

234

H.-H. P E R K A M P U S

If cAH+from equation (1la) is introduced into (7), one obtains :

or, expressing it logarithmically, with PA= cA/ca

If the concentration of free aromatic substance in the acid phase is approximately expressed by the partition coefficient PA= cA/ca one analogously obtains the relationship (Gold and Tye, 1952b): Ho = pKB + logPA -log---CHA+ ca

(12c)

When using relation (12c) it was found that the determination of PAis subject to large errors, as a result of which the pKB values naturally became very inaccurate (Gold and Tye, 195213). Plattner and collaborators (1949) also drew attention to this source of error when evaluating partition equilibria of azulene derivatives. Mackor and collaborators (1958s) therefore elaborated the relationship (128) and introduced the partition coefficient Po, related to zero concentration, for the distribution of the free aromatic substance between the acid and organic phases. Po = lim ea’-+O

Using Po one then finds, for the distribution of the free aromatic substance between the two phases at any desired concentration, taking the activity coefficients into account :

When the concentration of the aromatic hydrocarbon in both phases is low, the activity coefficient fi in the organic phase may be assumed to be equal to 1. Equation (12) then becomes

and (12a) can more exactly be written as :

THE BASICITY O F UNSATURATED COMPOUNDS

235

According to (12b) a determination of the partition coefficient P presents the opportunity of determining the quantity log[KB .Po]. If anhydrous hydrofluoric acid is used as the acid phase, a further fact about one variable in (12b) can easily be introduced. It is known from the investigations of Fredenhagen (1939; Fredenhagen and Cadenbach, 1930) that alkali fluorides are practically completely dissociated in anhydrous HF. The acidity of HF can therefore be varied over a wide range by the addition of alkali fluoride or BF,, with the acidity being reduced by the addition of alkali fluoride but increased by the addition of BF, as a result of the reaction : BF,+F-

+ BF,

Depending on the basicity of the aromatic substance, the partition experiment is therefore either carried out in a solution of HF + NaF (or KF) or in HF + BF,. Because of the complete dissociation of NaF in HF the concentration cx-, i.e. the concentration of fluoride ions in the present instance, may be expressed by the stoicheiometric concentration of the alkali fluoride. Hence ( 12a’)

and log [ K B .Po]= lOgP +log cNnF + 2 logf *

(12b’)

The formulae (12a’, 12b’) apply to strongly basic aromatic hydrocarbons. I n the case of weakly basic aromatic hydrocarbons one has to use the system HF + BF,, since the acidity of the HF is greatly increased by the formation of the B K ion. Here again the acidity can be affected by the addition of NaBF,. I n this system the basicity constant K&is given by equation (8). As regards the distribution equilibrium of the free aromatic substances between the acid and organic phases, one again finds, from (13):

The activity of the BF, in a solution of NaBF, in HF is given by the partial pressure of BF, according to Henry’s law : PBF3

= k.fBF3.CBFs

(15)

where k is the proportionality constant of Henry’s law. If one again assumes complete dissociation of the NaBF, in H F + BF, solution, then

236

H.-H. PERKAMPUS

cNaBF, may be substituted for cBF4-, Using (lla), (14a) and (15), equation (8) may therefore be written logarithmically as :

The product [FB. Po.fi]can be determined at a given concentration of NaBF4, with a corresponding partial pressure of BFs, and the experimentally determined partition coefficient P according to (11). The basicity constant is obtained as the product [ R B . P o ] . I n order to determine K Bit is necessary to know Po,particularly since this partition coefficient of the free aromatic substance is strongly dependent on the structure of the aromatic substance (Gold and Tye, 1952b; Plattner et al., 1949). For weakly basic aromatic substances Pocan be directly determined from the distribution equilibrium between KIF and an organic solvent, since the proton addition complex is formed in significant amounts in HF only if the acidity is increased by addition of BFs. Mackor and collaborators (19584 therefore determined Po for benzene, naphthalene, biphenyl and phenanthrene directly. It was found that the Povalues were, to a good approximation, directly proportional to the molar volume of the aromatic substance in the liquid phase. This presented the possibility of determining graphically the Po values for other aromatic substances which could not be determined directly because of their greater basicity. Similar determinations of P o were carried out for methyl derivatives of benzene (Mackor et al., 1958b). I n these it was found that logPo decreases by 0.2 for each methyl group substituted in the benzene nucleus, and by 0.40 for an ethyl group. I n order to solve the equations completely, the mean activity coefficients f+ of the ions are required. If one assumes the extended DebyeHuckel relationship for the concentration-dependence of the mean activity coefficients lOgf, = equation (12b') may be written as : log [ p .CNaF] - 1.06.2/=

B . CF= log [ K B . P o ] - 2 . B . C N a F

(17)

(18)

If this law applies in the present instance, then plotting the left-hand side of (18) against the concentration of NaF should give a straight line with slope B and an intercept on the ordinate which corresponds to log[KB.Po]. Figure 15 shows that according to the measurements of Mackor and collaborators (1958a) the requisite linearity is very well fulfilled.

T H E BASICITY O F UNSATURATED COMPOUNDS

237

Using the B-value obtained from the graphical evaluation, one thus obtains the relationship logf * =

- 0.53. G+ 0.24. cNaF

(19)

Equation (19) is valid for a large number of aromatic substances investigated in the system HF + NaF. A higher alkali fluoride concentration was necessary for aromatic substances of high basicity. For solubility

- -1.3

- -2.0 0,

2

0-

-0.10

-

0

05 ~ N O F

FIG.15. Text of the Debye-Huckel law end evaluation of K, for the partition measurements on pyrene end enthrecene according to equation (18) (Mackor et al., 19688).

reasons, KF was used in these cases. I n the system HF + KF, an equation which has been extended by one further term applies, logf* = - 0.53 6

-

+

k 0.165. c g ~ 0.1 i 5 G ~

(20)

Analogous investigations of the HF + BF, +NaBF4 system showed that in this case B has to be taken as equal to zero, so that the mean activity coefficient is approximately given by the Debye limiting law (21)

When carrying out these measurements in practice it proved convenient to use molalities instead of molarities. Accordingly, c is to be replaced by m in the formulae.

238

H.-H. PERKAMPUS

Mackor and collaborators (1956, 1958a, b) carried out investigations of this type for the systems aromatic substance-[HF + NaF (or KF)]n-heptane and aromatic substance-[HF + BF8 +NaBF4]-CC14. As is clear from equations (9) and (lo), the formation equilibrium of the tetrafluoroborate ion has to be taken into account for the ternary system. The relation (10) applies between the equilibria (5) (6) and (9) and the equilibrium constants (7), (8) and (9a). On the basis of the measurements of Mackor et al. (1958b)one finds, for equation (10): log K = log-K;, = 6.6 & 0.2 KB log KB = log K&- 6.6 f 0.2

(224

The K & values determined can be converted into K , values by means of this relation. B. Determination of the Basicity from Vapour Pressure Mmurements Vapour pressure investigations of the systems here under discussion have frequently been carried out (cf. Olah, 1963). However, many of these studies are concerned with the question of the composition of the complexes formed in binary or ternary systems (Van Dyke, 1950; Brown and Pearsall, 1952; Brown and Brady, 1949, 1952; Brown and Wallace, 1953a, b ; Lieser and Pfluger, 1960a, b). To answer this question, the vapour pressure diagrams were recorded as a function of the compositionof the binary or ternary system. The direct evaluation of the Henry’s law constant, however, also permits the basicity of the unsaturated hydrocarbons to be determined. According to Henry’s law, the vapour pressure of a gas above its solution is directly proportional to the concentration c, or the mole fraction xu of this gas in solution. It applies if the solutions are sufficiently ideal. P , = k . c , or P , = k1.5, (23) If ideality cannot be assumed, then the activity has to be used in the calculation instead of the concentration or mole fraction :

P,

=

k.c,.f,

=

k.a,

(234 Brown and Brady (1949) have investigated the solubility of HCl in solutions of benzene derivatives in toluene at -78.5”C. The authors were able to establish that Henry’s law is obeyed over a wide range of concentrations and that the solubility of HC1 depends on the aromatic substance. The constant k of Henry’s law decreases corresponding to the increase in solubility. This is already a manifestation of the effect of

239

THE BASICITY O F UNSATURATED COMPOUNDS

the basicity of the aromatic substance, since the increasing solubility of the HC1 is to be interpreted in terms of complex formation with the aromatic substance. I n a subsequent study, Brown and Brady (1952) carried out analogous investigations for solutions of aromatic substances inn-heptane at - 78.51OC. Figure 16 shows thevapourpressuremeasurements as a function of the mole fraction of the HC1 for some solutions of aromatic substances in n-heptane. The deviations from the slope of the Henry's law straight line in n-heptane are attributable to complex SO(

I

I

I

1

I

XHCl-

FIG. 18. Henry's law lines in the system aromatic substance-HC1-n-heptane, at 196"K,according to Brown and Brady (1962).

formation of HCl with the dissolved aromatic substance, which explains the increasing solubility of HC1. The equilibrium constant of the reaction A+HCl

+ (A.HC1)

expressed in mole fractions is found to be : XC K, = xA .xHC1

(24)

xc, xAand xHa are the mole fractions of the complex [A. HCI], of the free aromatic substance and of HCl in the solution. The mole fractions

240

€1.-H. PERKAMPUS

may be determined from the measured vapour pressure data in n-heptane and in the solutions : xHCl

=

P

k0

This corresponds to the mole fraction of the dissolved HC1 if there were no complex formation. Lo is the Henry’s law constant for HCl in n-heptane.

This mole fraction indicates the proportion of HCl which is additionally dissolved as a result of complex formation. XA = x 0 A - x ~

This is the mole fraction of the free aromatic substance present in the solution; i.e. amount weighed out minus complex concentration. This evaluation assumes an ideal solution and the formation of a 1 :1 complex. Table 9 gives the results of this calculation. I n order to achieve a consistent formulation of the equilibrium we use the reciprocal of the dissociation constant given by Brown and Brady (1952) multiplied by ko. Since the measurements show that Henry’s law is very well obeyed, the equilibrium mole fractions in Table 9 were given as above, computed with the aid of the Henry’s law constants ko and kA. As may be seen from the equilibrium constants in the last column of the table, the stability of the complexes increases with the number of methyl groups in the benzene nucleus, which implies that the basicity of the aromatic substances also increases in the same sense. The extension of these measurements to other methylbenzenes is rendered difficult by the low solubility in n-heptane.l For this reason toluene was used as the solvent (Brown and Wallace, 1953b). If the association constants determined from these experiments are related to the value for p-xylene, one obtains a relative basicity scale which is summarized in Table 10. Comparison with the relative reactivity of benzene towards halogenation (de la Mare and Robertson, 1943; Condon, 1948), for which the basicity of the aromatic substances is a determining factor, shows that the same reactivity sequence can be deduced from the vapour pressure measurements. However, in the case 1 Brown and Melchiore (1 966) have recently determined the temperature-dependence of complex formation of aromatic hydrocarbons with HCI and HBr in n-heptase solution. Dissociation constants and thermodynamic data were calculated.

THE BASICITY O F UNSATURATED COMPOUNDS

24 1

TABLE9 Calculation of K from vapour pressure curves in Fig. 15 according to equation (24). (System: aromatic substance-HC1-n-heptane at - 78-5'C; measurements by Brown and Brady, 1952) Aromatic substance

k, (mm)

103x0,,

x = ~ lP =ko 103x0

P (=)

~~~~~~~

Benzene (ko=4520)

3500

Toluene (ko=4520)

3170

na-Xylem (ko= 4520)

2980

Mesitylene (ko=4520)

2550 3510

3910

47.2 47.0 46.6 47.2 46.2 46.6 47.2 46.9 46.8 47.00 46-80 46.60 19.50 19-45 19-40 19.23 9-86 9.81 9.80 9.75

35.1 47.4 72.5 31.45 49.05 61.10 25.00 39.99 45-95 30.25 41.46 49-92 20.50 30.79 40-55 65.19 12.11 34.64 44.79 62.83

7.77 2.26 10.50 3.07 16.05 4.72 6.97 2.97 10.90 4.65 13-50 5.77 5.54 2.85 8.75 4.55 10.15 5.23 6.70 5.17 9-19 7-07 11.05 8.55 4-55 1.31 6.81 1.97 8.99 2.60 14.45 4.17 2.68 0.42 7-67 1-20 9.95 1-56 13-90 2.18

lOsx,

K

R

~~~~

44.94 6.50 43.93 6.65 41.88 7.03 44-23 9.65 42.25 10.10 40.83 10.50 44.35 11.6 42.35 12.3 41.57 12.4 41.83 18.1 39.73 19.4 38.05 19.6 18.19 16.2 17-48 16.6 16-80 17.2 15-06 19.2 9.44 16.6 8.61 18.2 8-24 19.1 7.57 20.7

TABLE 10 Comparison of relative basicity with relative reactivity for the halogenation of some methylbenzenes (Brown and Brccdy, 1952) Aromatic substance

Relative basicity

Relative reactivity

Benzene Toluene Ethylbenzene Isopropylbenzene t-Butylbenzene p-Xylene o-Xylene rn-Xylene Pseudocumene Hemimellitene Mesitylene Prehnitene iso-Durene

0.61 0.92 1.OG 1.24 1.36 1 .oo 1.13 1.26 1.36 1-46 1.59 1.63 1-67

5.0 x 10-4 1.6 x 10-1 1.3 x 10-1 8.0 x 10-2 5.0 x 10-2 1.00 2.10 2.0 x 102 3.4 x 108 4.0 x 10% 8.0 x 104 2.0 x 103 2.4 x 108

6.7 10.1 12.1

18-3

242

H . -H. PERKAMPUS

of the reactivity, the ratios vary by several powers of 10. A comparison of this gradation with the results from distribution equilibria shows that the complex formation is here of a radically different type. I n the systems discussed above, one is only dealing with the formation of a loose n-complex, since the systems are of insufficient acidity. Similar unstable n-complexes were observed by Brown and Wallace (1953a)also for the system aromatic substanct+A12Br6. As the stability of these complexes increases for a series of methylbenzenes, so the colour simultaneously deepens. However, this colour is probably attributable to traces of moisture which allow the formation of a proton addition complex. Because of the high extinction coefficient of the proton addition complexes (cf. Table 6) very small amounts of water sufiice to produce a colour. This was confirmed by investigations by Stmts (1962). Staats showed at the same time that one must assign to the n-complex in the m-xylene-A12Br6system a band which is slightly displaced to the red from the absorption of m-xylene and which is to be regarded as a charge transfer band. The results of vapour pressure measurements, which indicate a loose interaction, appear to be in good agreement with this spectroscopic result. It follows from the above considerations that it is necessary to use systems of greater acidity in order to study the formation of proton addition complexes by means of vapour pressure measurements. As with the partition equilibria discussed under IIIA, the systems HF + NaF (or KF) and HF + BF, + NaBF, have again to be considered. Measurements of this type were carried out for the methylbenzene(HF+ BF,) system at 0°C by MacCaulay and Lien (1951). However, the authors used the method only in order to demonstrate the formation of the proton addition complex. They used partition measurements to determine the basicity. I n the case of the aromatic substancc+HBr-A12Br6system Brown and Wallace (1953b) also demonstrated only the formation of the proton addition complex and discussed its composition. I n addition, qualitative statements were made as to the stability of the complexes. Again, the stability clearly depends on the number of substituent methyl groups. Detailed quantitative vapour pressure measurements for the systems referred to above have been published by Mackor et al. (1958a, b). For the systems containing an aromatic substance, HF and BF,, the equilibrium constant is found to be given by equation (8) (p. 199). As BF, is added to HF, HBF4is formed and this can dissociate into H+and B C . As a result, the total amount of BF, dissolved in the acid phase is given by Co

= C B F ~+ CBFC

(25)

T H E BASICITY OF UNSATURATED COMPOUNDS

243

The activity of the dissolved BF, is related to the pctrtial pressure of the BF, above the solution by Henry's law :

Since the experiments are generally carried out at low concentrations of BF,, fBF8 can to a good approximation be regarded as 1. One thus obtains from (26) and (26) PBF~ C B F ~ - = Co--

k

(27)

If no further electrolytes are added to the solution and if only weakly basic aromatic substances are being investigated for which it has been ascertainedthat no proton addition complexes are formedwith HF alone, then it is possible to equate the concentration of BF;; ions with that of the proton addition complex formed. CAH+ = CBF.-

(28)

If (26), (27) and (28) are inserted into (€9, one obtains:

( -); .(co-;)*f: Co

K& = C,

.f

According to Mackor et al. (1958a) it is necessary to apply a correction to (28) to correct for interference from impuritiesin the HF which cannot be excluded. One then obtains for (28) CAE+

=

~BF~--0'01

and hence :

Figure 17 shows the vapour pressure measurements of Mackor et al. (1968s) for the system of naphthalene-(EW + BF,) at 0°C. The broken straight line shows the BF, pressure above a pure solution of BF, in HF. The continuous curve represents the total vapour pressure of the system referred to. The BF, pressure is obtained as the difference between the

244

H.-H. PERKAMPUS

curve of the partial pressure of HF and the continuous curve. I n order to determine the constant KL, equation (29a) can be rearranged :

If the right-hand side is plotted against plk one should obtain a straight line, the slope of which is given by K i . c A . Figure 18 shows that the linearity is very well obeyed in the case of the experiment of Fig. 17. K;3can then be obtained with the aid of the concentration of the aromatic substance. Since the concentration of the aromatic substance in the solution of HF + BF3is low, the corresponding activity coefficientfA may be taken as equal to 1. This method was used to determine the K;3 values of naphthalene, phenanthrene, p-xylene and toluene, and the values converted to K Bby the use of equation (22a) (Mackor et al., 1958a, b).

C . Determination of the Basicity by Means of Conductivity Measurements According to equation ( 5 ) the addition of a proton to an aromatic hydrocarbon produces the protonated aromatic substance and the counter-ion stabilizing the addition complex. I n those cases where the solvent itself furnishes the protons and has a sufficiently dielectric constant, it is assumed that the complex dissociates into its ions. This condition is fulfilled in the case of HF, since the dielectric constant of anhydrous HF is 83.6 a t 0°C (Fredenhagen and Dahmlos, 1928). The extrapolation of the values measured by these authors in the range of - 73" to 0°C gives a value of E = 59 at 20°C. This value is high enough for dissociation to occur, even at room temperature. HF itself is only very slightly dissociated, but alkali fluorides dissolved in HF are practically completely dissociated into their ions, as could be shown by means of conductivity measurements (Fredenhagen et al., 1930). The addition of water and alcohols also increases the conductivity of HF. Fredenhagen and Cadenbach (1930) attributed this to the addition of a proton to the OH group of the alcohol. It is interesting that methyl alcohol, ethyl alcohol and water give the same limiting conductance ( A , = 360). Since the fluoride anion is always involved, this means that the oxonium ions of these alcohols have the same mobility. I n the case of the aromatic substances, the aromatic cation and the fluoride anion are present in anhydrous hydrofluoric acid. If we use equation (5), then the known laws for weak electrolytes may be used for this formation equilibrium. If the degree of formation of the aromatic

THE BASICITY O F UNSATURATED COMPOUNDS

+

246

+

FIG.17. Vapour pressure of the system naphthalene HF BFa at 273OK. aa a function of the amount of BFa added (continuous curve). Vapour pressure of the system HF+BFs (broken curve) (Mackor et aL, 19588).

FIG. 18. Graphical determination of the product K;.m, according to (29b) for the measurements of Fig. 17; (Mackor et aL, 1958a).

246

H.-H. PERKAMPUS

cations is denoted by 8, and if co is the stoicheiometric concentration of the aromatic substance, then the equilibrium concentrations are given bY CAE+

=

~ 0 . 6= cF-

and CA

= cO.(l-p)

Hence equation ( 5 ) becomes

if activity coefficients are neglected. Since /3 can be regarded as having the same significance as the degree of dissociation, it is also possible in this instance to express this quantity in terms of the equivalent conductances :

Since HF serves as the solvent, the concentration cHF may be regarded as constant and may be included in the constant K , or taken into account as a constant factor. If measurements are related to 1000 g of solvent, as is desirable for practical reasons, then this factor for HF is found to be cHF = 50. If (31) is introduced into (30), one obtains an expression analogous to the Ostwald Dilution Law :

or

Conductivity measurements aimed at determining K B from equation (30) were carried out by Kilpatrick and Luborsky (1953) for a considerable number of methylbenzenes. The results of these measurements are given in Table 11. As shown by the measurements for the various methylbenzenes, the equivalent conductance for the same concentration of aromatic substance strongly increases with increasing number of methyl groups. This already shows qualitatively that the basicity increases in the same sense, i.e. that the formation of the aromatic cations is favoured. One further notes for the individual methylbenzenes that the equivalent conductance is very dependent on the total concentration of the aromatic substance

247

T H E BASICITY OF UNSATURATED COMPOUNDS

TABLE 11 Equivalent conductances of some methylbenzenes in anhydrous HF at 20°C. (Kilpatriok and Luborsky, 1953)

Molality Aromatic substance Benzene Toluene p-Xylene

0-Xylene m-Xylene Pseudocumene (1,2,4) Hemimellitene (1,2,3) Mesitylene (1,3,5)

Durene (1,2,4,5)

Prehnitene (1,2,3,4)

Isodurene (1,2,3,5)

m A

(i,

0.0868 0.216 0.442 0.072 0.181 0-3035 0.0585 0.0833 0.134 0.167 0.0596 0.148 0.292 0-0524 0.172 0.364 0.0532 0.1105 0.207 0.0541 0.117 0.238 0.0545 0.0857 0.156 0.204 0.275 0.0147 0,0147 0.0209 0.0324 0.0595 0.0640 0.0920 0,132 0.1995 0.0491 0.0568 0.0580 0.0880 0.1 113 0.162 0.1905 0.206

2-3 0.65 0.32 6.3 2.8 0.5 9.1 6.7 5.2 4.55 7.9 5.4 3.7 40.9 18-3 7-0 54.5 41.4 27.8 65.3 38.3 23.2 299 297 218 223 194 245 398 194 61.7 129 117 102 78.0 55.5 322 314 290 259 252 264 250 221

K , according to (30) 4.2 x 10-8 0.82 x 10-8 0.41 x 10-8 2.6 ~ 1 0 - 7 1-97 x 10-7 0.07 x 10-7 4-60 x 10-7 3.55 x 10-7 3.4 x 10-7 3.3 x 10-7 3-5 x 10-7 4.1 x 10-7 3.9 ~ 1 0 - 7 9.5 x 10-6 6.2 x 10-6 1.8 x 10-6 1-85 x 10-5 2.2 x 10-5 1.9 x 10-5 2.8 x 10-5 2.0 x 10-5 1.5 x 10-5 2.9 x 10-3 4.4 x 10-3 3.8 x 10-3 8.4 x 10-3 8.6 x 10-3 2.1 x 10-4 1.5 x 10-4 0.14 x 10-4 1.7 x 10-4 1.4 x 10-4 1.5 x 10-4 1.2 ~ 1 0 - 4 0.88 x 10-5 4.1 x 10-3 4.4 x 10-3 2.7 x 10-3 3.0 x 10-3 4.1 x 10-3 16.0 ~ 1 0 - 3 17.0 ~ 1 0 - 3 8.2 x 10-3

&in

presence of excess BFs

245 182 166 266 209 205 225 267 219.5 185.5 294.5 235.5 205 271.0 234.0 197.0 278.0 221.0 208.5 272.0 254.0 204.5 218-0 202.0

-

273.0 272.0

-

250 238.5 197 280 276 243

-

224 212.5

-

248

11.-H. P E R K A M P U S

TABLE11-conlinued

Molality Aromatic substance

Pentamethylbenzene

Hexamethylbenzene

A"

m A ~~~

~

0.0141 0.0413 0.0789 0.148 0.0069 0.0181 0.0304 0.0725 0-1374

K B according to (30)

Atin presence of excess BFs _ _ ~ _ _

~~~

362 340 312 284

1.3 4.8 9.4 28

412 397 3496 297

2.7 8.6 6.3 4.3

-

x 10-3

x 10-3 x 10-9 ~10-3

x 10-2 x 10-2 x 10-2 x 10-2

in the solution, in a manner resembling weak electrolytes. This means that it is possible from the concentration dependence to obtain the limiting value of the equivalent conductance a t infinite dilution by extrapolation, since this value is, according to (31), needed for the calculation of K B according to (30). This is possible if the equivalent conductivity is proportional to the square root of the concentration co, i.e. if the Debye-Huckel-Onsager law is obeyed. It is known that this square-root law is also obeyed for non-aqueous solvents as a good approximation, as long as the dielectric constant of the solvent is not less than E = 30. Figure 19 shows the equivalent conductivities as a function of dm for three examples. If one bears in mind that, because of experimental difficulties, the accuracy of measurements in aqueous solutions is not attained, then the square root law is obeyed to a good approximation. Using the Debye-Huckel-Onsager law, Kilpatrick and Luborsky in addition calculated the theoretical curve which, however, is obeyed by the measured values only at the lowest concentrations. These were experimentally accessible in the case of hexamethylbenzene. The values for €(HE')and rlHF for the calculation of the constants were taken from the literature (Fredenhagen and Dahmlos, 1928 ; Simons and Dresdner, 1944) ( E = 59 ~ ;rlzoOc ~ =~ 0*00210 ~ poise). One thus finds the constant A at 20°C of the Debye-Huckel-Onsager law to be given by the equation :

A = 0.356.(10+299 1 Kilpatrick

(33)

et al. (1965) haa recently re-examined the viscosity data of liquid HF.

THE BASICITY O F UNSATURATED COMPOUNDS

249

Knowing A , it is therefore possible to calculate the theoretical straight line. The limit of concentration above which deviations from the theoretical straight line are to be expected can be estimated to be (cf. Kortiim, 1957) :

The required values can be found approximately. Taking A , 1:380 and A = 435 (according to (33)), this limit is found to be c,,. < The 500

FIO.19. Equivalent conductance A,,, aa a function of z/m in HF at 293°K; according to Kilpatrick and Luborsky (1953). -m-wHexamethylbenzene, -0-0Pentamethylbenzene, -0-0Mesitylene.

lowest concentrations listed in Table 14 are a power of ten higher than this limiting concentration, so that the deviations from the straight line and the differing slopes are entirely intelligible. For this reason, the extrapolation of a value for A , is also subject to an error which is transferred to the constant K B determined by means of (31) and (30). Kilpatrick and Luborsky (1953) used a single value of A . for all aromatic ions in the evaluation of the measurements summarized in Table 11. A direct test of this assumption is not possible for most methyl9

250

H.-H. PERKAMPUS

derivatives of benzene, since they are converted to the proton addition complex only to a slight extent because of their low basicity. If, however, the formation equilibrium is displaced to the right by the addition of BF,, complete formation of the aromatic cations can be achieved. The conductivity of this system is then determined by the mobility of the aromatic cation and of the tetrafluoroborate anion. The difference between the equivalent conductance of this solution and that of the aromatic substances in HF is then determined, according to Kohlrausch’s law, by the difference of the mobilities of the anions F- and B K . Table 11 includes these values of equivalent conductances for aromatic substances in the system (HF+ BFs). Merely from the values for different methylbenzenes at comparable concentrations i t is possible to see that the equivalent conductances so obtained agree relatively well. At a concentration of 0.05 m, the mean value is found to be A = 276 with a mean deviation of k 6 %. Examination of the equivalent conductances measured as a function of the concentration of aromatic substance shows that, leaving aside the deviations occasioned by the technique of measurement, the values for all methylbenzenes scatter around a curve obtained from the Debye-Hiickel-Onsager law. For this reason, Kilpatrick and Luborsky (1953) used a A-value interpolated from the straight line for hexamethylbenzene, i.e. they did not use the limiting value for d%=0. The K Bvalues listed in Table 11 were determined by means of this value, with successive approximations being carried out in the calculation of B according to (31). The K Bvalues so obtained show a pronounced concentration-dependence, which is unusual for weak electrolytes. The uncertainty of these values is in practice determined by three factors : (1) the use of concentrations beyond the validity of the Onsager law; (2) uncertainty of the extrapolated Ao-value; (3) neglect of activity coefficients. N

Of these three factors, the effect of the second one can be tested by means of another method of evaluation which is independent of the choice of a A-value. Equation (32) can be recast to give : K;.A;--K;.A,A, (35) It should therefore be possible to calculate K ; and A , from the slope and intercept of the straight line obtained by plotting A i .m, against A,. &.mo

=

Figure 20 shows this evaluation using the equivalent conductances given by Kilpatrick and Luborsky. The expected linearity is approximately obeyed for pentamethylbenzene, mesityIene and hexamethylbenzene.

T H E BASICITY O F UNSATURATED COMPOUNDS

251

I n the case of isodurene, the values scatter badly, as was to be expected from the equivalent conductances above 0.1 molal in Table 11. It is, however, interesting to note that the straight lines for pentamethylbenzene and mesitylene intersect very nearly on the abscissa. This means that the A,-values of these aromatic substances are the same and that the assumption of Kilpatrick and Luborsky ( 1 953) is supported by

-

fh

FIQ.20. Analysis of conductance measurements according to equation (35), me text. -m-mHexamethylbenzene, -0-0Pentamethylbenzene, -0-0Mesitylene, -x -x - Isodurene.

this evaluation. The value of the limiting conductance obtained from this evaluation is A,= 375, which agrees very well with the A,-value obtained by Fredenhagen and Cadenbach (1930) for straight-chain alcohols in HF as the solvent. For hexamethylbenzene, however, this evaluation yields a value of A , = 445 which is considerably higher than for the other methylbenzenes. The same result is already recognizable in Fig. 19. The values for hexamethylbenzene always differ clearly from those for the other methylbenzenes. It therefore seems desirable to recalculate the KB values using the value (lo= 375. As may be seen in Table 12, the order of magnitude of the values is maintained but the concentration-dependence is now significantly reduced and appears more as a random scatter. For this reason it is no doubt justifiable to

H.-H. PERKAMPUS

252

TABLE12 Treatment of conductance measurements according to equation (30), using A0 values from equation (35) Compound

Benzene Ao= 375 Toluene A0 = 375 p-Xylene do =375 o-Xylene A0 = 375 m-Xylene no= 375 Pseudocumene A0 = 375 Hemimellitene do=375 Mesitylene Ao=375

Prehnitene A0=375

Isodurene do = 375

Pentamethylbenzene = 375

no

Hexamethylbenzene A0 = 445

m

0.0868 0.2 16 0.442 0.0702 0.181 0.304 0.0585 0.0833 0.134 0.167 0.0595 0.148 0.292 0.0524 0-172 0.364 0.0532 0.1105 0-207 0.0541 0.117 0.238 0.0545 0-0857 0-156 0.204 0.275 0.0595 0.0640 0.0920 0.132 0.1995 0.0491 0.0568 0.0580 0.0880 0.1113 0.0141 0.0413 0.0789 1.48 0.0181 0.0304 0.0725 0.1374

2.3 0.65 0.32 6.3 2.8 0.5 9.1 6.7 5.2 4.6 7.9 5.4 3.7 40.9 18.3 7.0 54.5 41.4 27-8 65.3 38.3 23.2 299.0 279.0 218.0 223.0 194.0 129.0 117.0 102.0 78.0 55.5 322.0 314.0 290.0 259.0 252.0 362.0 340.0 312.0 284.0 412.0 397.0 349.5 297.0

0.00614 0.00173 0.00118 0.0168 0.0075 0.00133 0.0243 0.0179 0-0139 0.0123 0.0210 0.0144 0.0099 0.109 0.0488 0.0187 0.145 0.110 0.0743 0.175 0-102 0.062 0.797 0.745 0.580 0.595 0.517 0.344 0.312 0.272 0.208 0.148 0.86 0.838 0.773 0.692 0.672 0.967 0.908 0.833 0.758 0.928 0.893 0.785 0.667

0-65x 10-8 1.30 x 10-8 1-20x 10-8 4.02 x 10-7 2.0 x 10-7 1.1 x10-8 7.1 x 10-7 5.4 x 10-7 5.3 x 10-7 5.1 x 10-7 5.4 x 10-7 6.2 x 10-7 5.7 x 10-7 1.4 x 10-5 0.9 x 10-5 0.3 x 10-5 2.63 x 10-5 3.0 x 10-5 2.5 x 10-5 4.0 x 10-5 2.7 x 10-5 1.7 ~ 1 0 - 5 3.4 x 10-3 3.7 ~ 1 0 - 3 2-5 x 10-3 3.6 x 10-3 3.0 x 10-3 2.14 x 10-4 1.8 ~ 1 0 - 4 1.9 x 10-4 1.45 x 10-4 1.06 x 10-4 5.2 x 10-3 4.9 x 10-3 3.06 x 10-3 2.7 x 10-3 3.1 x 10-3 8.0 x 10-3 7.4 x 10-3 6.6 x 10-3 7.0 XIO-3 2.4 x 10-3 4.5 x 10-3 4.2 x 10-3 3.7 x 10-3

1.05 x 10-8 2.0 x 10-7 5.7 x 10-7

5.8 x 10-7 0.87 x 10-5 2.7 x 10-5 2.8 x 10-5 3.2 x 10-3

1.7 x 10-4

3.8 x 10-3

7.3 x 10-3

3.7 x 10-3

THE BASICITY OF UNSATURATED COMPOUNDS

253

take a mean value. However, compared to the KB values in Table 11, the values so determined are in the case of hexamethylbenzene lower by a power of ten. This leads to the assumption that there must be a systematic error in the case of hexamethylbenzene, which causes the equivalent conductances to be too high. This assumption is also supported by the comparison of these values with the values obtained by Mackor and collaborators (1958b) from partition measurements. For mesitylene, these authors find a value of KB=0.39 and for hexamethylbenzene K,=27-0 at 0°C. I n these values, c H F = 5 0 has been included in the constants. Allowing for this factor, the following values and hexamethylbenzene, are obtained : mesitylene, KB = 7-8. KB = 5.4. 10-1 For mesitylene, this result agrees with the Kilpatrick and Luborsky’s (1953) values and the value in Table 12. If the KBvalue of mesitylene at 2OoC is recalculated with the thermodynamic data of Mackor et a,?. (1958b), one obtains excellent agreement of the constants obtained by the two methods. Equally good agreement is also found for m-xylene. However, in the case of hexamethylbenzene the deviations are of the order of magnitude of 1-2 powers of ten. There is also no agreement for the weakly basic aromatic substances benzene, toluene andp-xylene. I n the case of these aromatic substances, Mackor and collaborators (1958a, b) were able to show that in H F solution only an extremely low conversion to the aromatic cations took place because of the low acidity of the solvent. This means that the concentrations on which the calculation of KB from conductance measurements is based have to be corrected. If the reaction of equation ( 5 ) is formulated in two steps, A+HF

1

2

+ [AH+.F-] + AH++F-

the constant K, is described as the product of two equilibrium constants :

=

[AH+].[F-] [AH+. F-]

K2K; =

[AH+]. [F-] [AH1

K2

= KB

(37)

The analysis of the conductance measurements took place according to equation (37). Step 1may be formulated as the primary formation of an ion pair and stage 2 as the dissociation of a weak electrolyte. The correct

254

H.-H. PERKAMPUS

K,-value is therefore obtained only if the supposition that [AH+.F-] may be taken as equal to [A] is correct. This assumption probably does not apply in the cases of the more weakly basic methylbenzenes and of benzene, so that the values for K , are uncertain to the extent of K;. The discussion of conductance measurements shows that it is desirable to combine other methods for the determination of the concentration with the conductivity investigations. D. Other Methods 1. Investigations of electron-donor-acceptor (EDA)complexes

The methods for the determination of the basicity of aromatic compounds discussed hitherto have as their starting point the formation of a proton addition complex in an acid solution. I n addition to this interaction, numerous intermolecular interactions are known which are also directly connected with the basicity of unsaturated compounds but which do not lead to the formation of a true covalent bond. This interaction was already mentioned in connection with the vapour pressure measurements of the system of aromatic substance-HC1, and leads to a .rr-complex (Dewar, 1946). This is a case of electron donor-acceptor interaction, the electron donor being the basic component. It may therefore be expected that for a given electron acceptor gradations of donor strength should be recognizable as gradations of basicity. One of the most frequently investigated electron acceptors is the I,-molecule, the EDA-complexes of which with a large number of unsaturated compounds have been spectroscopically investigated in the ultraviolet and visible spectral region (Briegleb, 1961). Benesi and Hildebrand (1949) investigated the absorption spectra of iodine in various solvents. On going to benzene and methylbenzenes, these authors found a new intense band in the region of between 270 and 400 mp, which is not present in non-polar and saturated solvents (Kortum and Friedhelm, 1947). These bands are bathochromically displaced as the number of methyl groups increases, whilst the absorption band in the visible region is simultaneously displaced hypsochromically. This effect was interpreted as complex formation of iodine with the aromatic substance. I n n-heptane and carbon tetrachloride, Benesi and Hildebrand (1949) determined the constants for the formation of this complex in benzene and mesitylene. The formation of a 1 :1 complex as assumed and the concentration of the complex formed was determined spectrophotometrically. The K-values determined by

T H E BASICITY O F UNSATURATED COMPOUNDS

255

Benesi and Hildebrand (1949) for various concentrations of iodine and aromatic substance agreed very well. The values found were :

cc14 n-heptane

Benzene + I, 1.72 1.15

Mesitylene +I, 7.2 5.3

KM/KBZ 4.2 4.6

The differences between the two solvents are attributable to the differing activity of the aromatic substance and iodine in these solvents, particularly since it is known that these solvents show appreciable solubility differences for aromatic substances. The K-values show clearly that the mesitylene-iodine complex is more stable than the benzene-iodine complex. The ratio of the K-values of the two complexes corresponds roughly to the ratio of the K-values obtained from an evaluation of vapour pressure measurements (Table 9). It must, however, be borne in mind that these measurements were carried out at very different temperatures, so that this comparison is only a qualitative one. The determination of these K-values supports the observation that the position of the new near-U.V. bands represents a measure of the basicity of the aromatic substances. Figure 21 shows the maxima of these absorption bands for several iodine-aromatic compound complexes plotted against the relative basicity from Table 10. The position of the bands is roughly proportional to this relative basicity. The formation constant of the iodine complexes in CCl, at 25OC was spectroscopically determined by Andrews and Keefer (1952) for a large number of aromatic substances. The constants show a clear gradation of the basicity of the aromatic hydrocarbons. Similar results were obtained in investigations of the IC1 complexes (Ogimachi et al., 1955) and of the SO2 complexes (Andrews and Keefer, 1951) of aromatic compounds. Thermodynamic quantities for the formation of iodine complexes were determined from the temperature dependence of the formation constants (Keefer and Andrews, 1955). Kortiim and Vogel(l955) drew attention to the fact that the spectroscopic determination of the K-values suffered from a degree of uncertainty because of the unknown extinction coefficients of the complexes. For this reason, the authors preferred to determine the constant by means of a solubility method which had already proved of value in analogous investigations of the systems dioxan-iodine and methyl butyl ether-iodine (Kortiim and Kortiim-Seiler, 1950). In this method the solubility of iodine is determined as a function of the composition of solvent mixtures. K,-values obtained by this method are summarized in Table 13.

256

H.-H. PERKAMPUS

These results are important because the measurements are of greater accuracy than optical measurements of these systems. The effect of the solvent on these constants was also discussed in detail (Kortum and Vogel, 1955). Analogous results were obtained from investigations as to the solubility of aromatic hydrocarbons in aqueous silver nitrate solution

0.5

1.0

2.0 Relative Basicity

--t

FIG.21. v,,,. of the complex bands of iodine complexes as a function of the relative basicity (Table 10).

(Andrews et al., 1949). The solubility of the aromatic substances is attributed to the following complex formation : Ag++A

+ (Ag+.A)

having the constant (38) I n addition, a second simultaneous equilibrium has to be taken into account : Ag+ (Ag+A) (Agg+.A)

+

+

K -

[M+. A1 [Ag+].[Ag+.A]

THE BASICITY O F UNSATURATED COMPOUNDS

257

It is furthermore possible to deduce a quantity K which is dependent on the silver ion concentration : The concentration dependence of K gives the association constants K 1 and K z (Table 14). The constant K 1 shows the expected variation with the number of methyl groups. K z furthermore shows very clearly that TABLE13 K,-values of some iodine complexes obtained by the solubility method (in cyclohexane at 25°C) (Kortiim and Vogel, 1955) Aromatic substance

Ks

Benzene" Toluene Naphthalene Biphenyl Fluorene Acenaphthene 2,6-Dimethylnaphthalene Phenanthrene 2,3-Dimethylnaphthalene Pyrene 2,3,6-Trimethylnaphthalene

3.12 4-40 6.58 8.00 10.64 10.88 11.11 11.23 11.63 13.17 15.40

Kortiim and Walz (1953). TABLE14 Constants for the formation of some Ag+ complexes in water at 25°C (Andrews and Keefer, 1949) Aromatic substance Benzene Toluene o-Xylene m-Xylene p-Xylene Naphthalene Biphenyl Diphenylmethane Phenanthrene 9*

K1

Ka

2.41 2-95 2.89 3.03 2.63 3.08 3.94 3.46 3.67

0.212 0.214 0.315 0.320 0.331 0.909 1.01 1.04 1.80

258

H.-H. P E R K A M P U S

the complex formation with a second Ag+-ion is very greatly favoured in the case of polynuclear aromatic substances. These investigations were subsequently extended to a larger number of aromatic substances in order to study steric effects in this complex formation. The system water-methanol (1 : 1) was used because of the low solubility of the aromatic substances in water (Ogimachiet al., 1956). The constants determined in the two systems do not agree, and this is in the first place attributable to the different solvent systems. The polysubstituted methylbenzenes do not fit into the series of relative basicity gradation, so that the measurements give only a rough comparison. The authors attribute this to steric hindrance in complex formation, though the figure for pentamethylbenzene does not agree with this argument. If it were a case of steric hindrance, the value for this aromatic hydrocarbon should be equal to or smaller than the value for mesitylene or 1,2,4,5-tetramethylbenzene(cf. the relative values in Table 16). The basicity gradation which may be obtained from the EDAcomplexes quoted as examples completely corresponds to the gradation of donor strength in the discussion of these complexes. For this reason, such gradations can in practice be deduced from numerous other EDAcomplexes, i.e. for other electron acceptors. As examples of acceptors which have been investigated, one may mention : Tetracyanoethylene Tetranitromethane Picric acid Chloranil Trinitrobenzene

(Merrifield and Phillips, 1958; Briegleb et al., 1961) (Hammick and Young, 1936) (Anderson and Hammick, 1950; Briegleb et al., 1959s) (Foster et al., 1956) (Briegleb et al., 1959b, 1961; Briegleb and Czekalla, 1955)

Briegleb (1961)gives an extensive summary of the stability constants of EDA-complexes in connection with the donor strength of aromatic systems. 2. Association phenomena and basicity The methods hitherto quoted are all based on the pronounced changes which can be observed on interaction of electron donors and acceptors, and which can be quantitatively analysed. I n the case of weak interactions, which do not always lead to a stoichiometric complex, it is also possible to study the effect of the aromatic substances on the acceptor components, e.g. the solvent itself,

THE BASICITY O F UNSATURATED COMPOUNDS

259

in order to see to what extent the property under investigation varies within a homologous series of compounds. Methods which permit the effect on specific molecular properties to be measured are suited to this purpose. Thus, spectroscopic methods are primarily to be considered. It is known from investigations as to the position of the OH-valency vibration in various solvents that a relatively strong solvent effect occurs (Davies, 1940). This is also recognizable from the differences of the association constants of the alcohols in various solvents (Mecke, 1944, 1948). Luttke and Mecke (1949) investigated e.g. the position of the second overtone OH vibration of phenol in 18 solvents and found that, on changing from an inert solvent to a solvent which has a strong interaction with the phenol, the OH-band is displaced to longer wavelengths and broadened. I n some cases a splitting of the OH-band into two components was also observed. A resolution into two or more components always occurs if the solvent has a high proton affinity, so that a solvent molecule can form a particularly stable association with a phenol molecule as a result of an energetically favourable mutual orientation. This is the case, for example, if benzene and toluene are used as the solvents. However, this effect is even more pronounced in the case of cyclohexene. Dielectric constant measurements for phenol in various solvents agree with this observation. I n particular, the dipole moments in benzene and cyclohexene (1.45 and 1.79 D respectively), are considerably greater than the value of 1.32 in cyclohexane. Luttke and Mecke (1949) attributed this effect to the ability of this unsaturated solvent to act as a proton acceptor, i.e. to form .rr-complexes. Analogous investigations of deuteriated methanol were carried out on the OD-valency vibration vOD=2689 cm-l in CC1, as the standard solvent (Tamres, 1952, Searless and Tamres, 1951). Altogether 12 aromatic compounds, including halogen-substituted ones, were used as solvents. I n the series of solvents, carbon tetrachloride, benzene, toluene, 0-, m-, p-xylene and mesitylene, vOD shifted from 2689 to 2670 in benzene and to 2655 cm-l in mesitylene. I n the case of halogen substitution the values of vOD lie between those for benzene and carbon tetrachloride, i.e. the basicity of the aromatic substances, which is to be regarded as responsible for the formation of this .rr-complex, decreases with halogen-substitution. These conclusions had already been deduced by Liittke and Mecke (1949) from their measurements. Tsmres (1952) also reported results on the heat of mixing of the

360

H.-H. PERKAMPUS

systems aromatic substance-chloroform and aromatic substance-carbon tetrachloride. I n the first case the heat of mixing increases with the number of methyl substituents, which again leads to the conclusion of an interaction between the mobile H-atom of the chloroform and the aromatic substance as the proton acceptor. Admittedly these effects are only very slight so that a basicity sequence of aromatic substances based on such measurements is uncertain.

Ei

-

FIG.22. Dependence of HCl valency vibration on the ionization potential of methylbenzenes, according to measurements of Cook (1956).

1.R.-spectroscopicinvestigations were also carried out for the system aromatic substance -HCl, in the course of which the position of vHClwas determined as a function of the solvent (Cook, 1956). From benzene to pentamethylbenzene vHCl moves to smaller frequencies with increasing number of methyl groups. The decrease in frequency varies almost linearly with the ionization potential. Since the ionization potential may be regarded as a measure of the donor strength, the influence of the aromatic substances on vHCldepends on their donor strength, i.e. on their basicity. Figure 22 represents the dependence of vHCl on the ionization potential of aromatic substances (Cook, 1956). These measurements however probably do not suffice for a detailed discussion, particularly

261

THE BASICITY O F UNSATURATED COMPOUNDS

since some pronounced deviations from the linear dependence were observed. Dorr and Buttgereit (1963), using U.V. measurements of solutions of mesitylene and hexamethylbenzene in chloroform, bromoform, carbon tetrachloride and carbon tetrabromide, were able to demonstrate a weak “electron transfer ” complex formation with these solvents. These investigations show that hexamethylbenzene is a more powerful electron donor than mesitylene. A similar influence on an acceptor property

0’3r

2c6cn3 n3c

t5

cn3

o’2-

Q

h

P

0.1-

I

0.0 €j

-

0 0 I

9.0eV

1

FIG.23. Chemical shifts of quinone proton resonance signals (AT) in EDA complexes a function of the donor strength (ionizationpotential). ( A T relative to the position of the quinone proton signals in CCl4.) 88

which, though slight, depends clearly on the dbnor strength, was recently reported by Perkampus and Kriiger (1966). The exact position of the proton signals of the quinone protons in the charge-transfer complexes aromatic substance-p-benzoquinone was determined in connection with N.M.R. studies of intermolecular interactions, since it had been found that in these complexes only the position of the quinone proton signals, and not that of the aromatic protons, undergoes a change. If the AT-values relative to free p-benzoquinone in CC14are plotted against the ionization energy, one admittedly does not obtain a linear dependence, but rather a curve which indicates a relationship between the &values and the donor strength (Fig. 23). Thus it is here once again possible to deduce a relative gradation of basicity which does not contradict results obtained by other methods.

262

H.-H. PERKAMPUS

A comprehensive summary of the methods for the determination of basicity was undertaken by Strohmeier and Echte (1957). These authors also list further methods which have been used e.g. in the determination of the basicity of oxygen-containing organic compounds.

SCALEAND BASICITY CONSTANTSOF UNSATURATED IV. BASICITY COMPOUNDS A. Notes on the Establishment of Basicity Xcales From the methods discussed in the preceding section it will be seen that conclusions as to the basicity can be deduced from two totally different interactions. I n one case one is dealing with a conjugated acid, in which the “electron acceptor”, i.e. the proton, is fixed in the form of a covalent bond. I n the second case we are dealing with a genuine intermolecular interaction, which leads to the formation of a rr-complex or a CT-complex. I n view of these different interactions one would not apriori expect quantitative agreement amongst the basicity gradations deduced by different methods. The factors which have to be considered when assessing the results obtained with molecular compounds, are very complex so that they can only be discussed for a certain donor or acceptor at a time, and are not always convincingly transferable to another system. I n addition to questions of energy, the steric circumstances of the two components also play an important role. Furthermore, in many cases the effect of the third component, namely the solvent, is decisive. For example, the measured Henry’s law constant for the system aromatic substance-HC1, only reflects the difference between the chemical potential of HC1 in solution, p.L,, and in the vapour phase, &, (Kortum and Vogel, 1955). The values obtained therefore do not permit a quantitative interpretation and only give qualitatively the relative order of the basicity of unsaturated compounds. This is also true for partition measurements between an acid and an organic phase, if in such a case the necessary thermodynamic assumptions have not been tested or established by separate investigations. On comparing results obtained in various solvents, it is practically only thermodynamic effects which can be explained and taken into account, whereas specific solvent effects which depend on the structure of the solvent molecule can only be dealt with empirically. Furthermore the dielectric constant changes with the solvent, and this affects the existence of ion pairs. This effect will always be troublesome for complexes in which a positively charged donor molecule is stabilized by a counter-ion. I n the case of such systems, where the formation of ions is t o be

T H E BASICITY O F UNSATURATED COMPOUNDS

263

expected, the effect of the activity coefficients has to be taken into account even at relatively low concentrations. However, even where ions are not formed, one has to bear in mind that the activities of the dissolved substances in different organic solvents may differ greatly. In some cases this factor can be thermodynamically interpreted, as has been shown by Kortum and Vogel (1955) for the case of the dioxaneiodine complex in the solvents heptane and carbon tetrachloride. As regards our considerations, however, this means that the K-values obtained in different solvents will be different for the formation of the same complex. A detailed summary and discussion of the effect of the solvent on the formation constant of EDA-complexes is given by Briegleb (1961). I n all cases it is necessary to consider entropy effects, which may be caused both by the complex components themselves and by the solvent. According to the Gibbs-Helmholtz equation

AG = A H - T A S = -RT.lnKB

(40)

it is possible for the term TAS to compensate for an increase in the enthalpy of formation A H for a series of homologous compounds. This may, for example, be caused by steric effects and may already be of significance in the series of methylbenzenes, as is suggested by the thermodynamic data for the iodine complexes (Keefer and Andrews, 1955) and the Ag+ complexes (Ogimachi et al., 1956) of aromatic compounds. However, carbon tetrachloride was used in the first case and water-methanol(1: 1)in the second case. I n polar solvents the solvation components of the entropy are in particular not inconsiderable. I n general the experimental data are however insufficient to allow the various effects to be described unambiguously and systematically. The only exceptions are the proton addition complexes with which we shall deal in more detail in Section IVC. B. Basicity Gradation of Unsaturated Compounds 1. Benzene derivatives Taking into account the limitations discussed in the preceding section, the constants determined by various methods for a series of homologous compounds may be compared with one another and, if related to a reference substance, may be represented in the form of a basicity scale. I n general, p-xylene has been chosen as the reference substance within the series of benzene derivatives (Andrews, 1964). I n Table 15 benzene is taken as equal to 1, since this aromatic substance has been measured

H.-H. P E R K A M P U S

264

TABLE 15

Method Vapour pressure measurements: n-heptane-aromatic compound-HCl

1.00

1.51

-

1.81

-

toluene-aromatic compound-HC1

1.00

1-51

1.85

2.06

1-64

1.00

1.22

1.20

1-26

1-09

1.00

1.08

1.30

1-23

1.04

1.00 1.00

1.06

1.81

2.06

-

2.08 2.1

1.00

1.41

-

-

-

1.00

1.80

2.30

2.57

2.80

Complex formation with Ag+: in water in water

+ CHIOH ( 1:1)

1 2 complex

in cc14 spectroscopic

-

-

I z complex in cyclohexane : Solubility, dielectric constant measurements ICI complex in CCl4

-

-

-

-

240*

Brz complex in cc14

1.00

1.40

2.20

2.08

2.17

SO2 complex in CC14

1.00

1.68

3.5

3.17

2.85

EDA complex with (NC)z==C==C=(CN)z: in CHzClz in cc14

1.00 1.00

1-85

3.5

3.0

3-8

Heat of mixing: with CHC13 with CHBr3

1.00 1.00

1.75 2.75

2-22

-

2.26 3.12

2.30

AT-quinone protons in the EDAcomplex with p-benzoquinone in CCl4

1.00

1.16

1.66

1-5

1.5

Aromatic/Iz complex CT-band (mp)

297

306

319

-

-

-

-

-

-

315

* The values of Ogimachi et aZ.(1955) were related t o the measurements of Andrews and Keefer (1952) through p-xylene, since benzene itself was not measured by Ogimachi et a,?.

265

THE BASICITY O F UNSATURATED COMPOUNDS Summary of the basicity values of methylbenzenesdetermined by various methods

(For explanation, see text)

Reference 2.74

a

2.61

a

-

-

-

b

0.73

1.04

0.67

C

3.96 3.90

6.3

-

10.0

d

10.1

e

-

f

8.60 5-60

11.9

-

42-0 20.0

-

B h

4.6

8.65

61.6

-

-

d 6

131.0 143.0

i j

k

2.4 3.18

b c

d C

-

1

333

?n

BrownandBrady (1949,1962). Andrews and Keefer ( 1949). Ogimachi et al. (1966). Andrews and Keefer (1962). Keefer and Andrew8 (1966). Kortiim and W d z (1963); Kortiim and vogel (1956).

Keefer and Andrews (1950).

h

Andrews and Keefer

1

Briegleb et al. (1961). Tamres (1962). Perkampus end Kriiger

m

Benesi and Hildebrand

k

(1961).

Merrifield end Phillips (1968).

(1966).

(1949).

266

H.-H. PERKAMPUS

by practically every method and the various series can therefore be better compared with one another. Table 15 summarizes the values obtained for all methylbenzenes by various methods. As has already been repeatedly mentioned, the basicity increases with the number of methyl groups. The differing increase in basicity obtained by different methods is particularly clear if one compares the values for hexamethylbenzene, which vary between 4 and 140. The best agreement between the various methods is found for the first members of this series, including the trimethyl-substituted benzene derivatives. If one ignores the discussion in Section IVA, then the relative values for the same compound show a clear dependence on the type of acceptor. Admittedly the effect of the acceptor cannot be described in terms of a constant factor, since in that case the relative values in Table 15, obtained by the methods quoted, should approximately agree for individual methyl derivatives of benzene. One thus sees that in addition to thermodynamic factors the physical properties of the donor and acceptor molecule and purely geometrical problems of the relative orientation of the molecules, are of importance. For this reason a comparative discussion of the differences observed is very difficult (cf. Briegleb, 1961). If a halogen atom is substituted into the benzene nucleus in place of a methyl group, then the basicity decreases and falls below the value for benzene. O’Brien and collaborators (1939; O’Brien and Kenny, 1940; O’Brien and Byrne, 1940;O’Brien, 1942)found the following order from vapour pressure measurements : Benzene > Bromo- b Chloro-

=- Iodo-benzene

The difference between bromine and chlorine as the substituents is slight. I.R.measurements (Tamres, 1952) of the displacement of the OD-valency vibration of CH,OD dissolved in benzene derivatives also show only a slight difference between bromobenzene and chlorobenzene. The reduction of basicity of benzene by halogen substitution similarly applies to the case of toluene, as deduced by Tamres (1952)from I.R. measurements and by Ogimachi et al. (1955)from complex formation with ICl. The basicity decreases even more for multiple halogen substitution (Tamres, 1952). Ogimachi et al. (1955)also investigated in more detail the steric effect on the equilibrium constants of the complex formation of IC1 with various benzene derivatives. The basicity decreases greatly on substitution of bulky groups, e.g. the t-butyl group. This effect is particularly pronounced for 1,3,5-tri-t-butylbenzene.

THE BASICITY O F UNSATURATED COMPOUNDS

267

I n this context it is interesting that for sterically hindered iodine and IC1 complexes the maximum of the characteristic U.V.-absorption is not hypsochromically displaced compared to the position in the corresponding methyl derivative. The U.V. maximum is in the same position for hexamethylbenzene and hexaethylbenzene, and similarly for 1,3,5-tri-tbutylbenzene compared to mesitylene. The position of the maximum thus evidently depends only on the number of alkyl substituent groups and not on their size (Keefer and Andrews, 1955; Ogimachi et al., 1955). However, changes in extinction coefficients occur in some cases, though these do not show any clear trend. Steric hindrance may therefore only be recognized from equilibrium constants and from thermodynamic data, where these have been determined. An indication that the basestrengthening effect of methyl groups is connected with their effect as weak electron donors towards the ring, is given by the increase in basicity which Ogimachi et al. (1955) observed for p-methoxytoluene. 2. Olefins

Compared to benzene derivatives, the basicity of olefinic compounds has been little investigated, though the metal complexes of olefins are of great importance in preparative organic chemistry (Wilke, 1963). The bonding in these complexes largely resembles the metal complexes which have already been known for a long time. The olefinic double bond may act as a ligand by means of its 7-electron pair to form a u- and 7-bond with a transition element. Because of the participation of this 7-bond these complexes are also described as metal-7-complexes. Fischer and Werner (1963) give a survey of metal-7-complexes with diolefinic and oligoolefinic ligands. The change in the C=C valency vibration, which moves to lower frequencies in the complex compared to its position in the olefin, may be regarded as an obvious characteristic of the involvement of the olefinic double bond in complex formation. The displacement increases further on going from ethylene to butadiene, which agrees well with the clear increase in the stability of the metal complex (Fischer and Werner, 1963). To determine the basicity order, complexes with SO2 (Booth et al., 1959) and with I2 (Ketelaar, 1954; Ketelaar et al., 1952; Traynham and Olechowski, 1959) as acceptors have been investigated. Tables 16 and 17 give a survey of the K , values determined, and of the relative basicity of various monoolefins, again relative to benzene. Here again the base-strengthening effect of methyl groups is clearly marked, as may be seen by comparing 2-methyl-butene-2 and 2,3dimethylbutene-2 in Table 16. A comparison of cis- and trans-butene-2 with isobutene shows that a

268

H . - H . PERKAMPUS

TABLE16 K,-values of some ole6n-SO2 complexes in n-hexane at 25°C (Booth et al., 1959) Compound Benzene o-Xylene Octene-1 Isobutene cis-Butene-2 tram-Butene-2 Cyclohexene Cyclopentene 2-Methylbutene-2 2,3-Dimethylbutene..2

K,

KJKZ (benzene)

0.36 1.06 0.33 1.29 0.58 0.62 0.40 0.28 1.03 1.43

(1.00) 2.96 0.92 3.60 1.62 1.72 1.11 0.78 2-86 4.00

TABLE17 K,-values of some olek-iodine complexes, and relative basicity Compound

K,

KJK,(benzene)

Benzenea Di-isobutylenea 1-Bromopropene-1a cis-Dichloroethylenea trana-Dichloroethylenea Trichloroethylene" Tetrachloroethylene Cyclohexane

1.20 3.20 0.53 0.25 0.24 0.19 0.11 3.40

1.00 2.66 0.44 0.21 0.20 0.16 0.09 2.84

Cyclopenteneb Cyclohexeneb Cyclohepteneb Cycloocteneb Methylene-cyclobutaneb Methylene-cyclopentaeb Methylene-cyclohexaneb Methylene-cycloheptaneb Norborneneb

2.80 3.30 3.05 1.09 2.78 2-61 3.65 2.67 4.33

2.33 2-74 2.54 0.91 2-31 2.17 3.05 2.23 4.11

a

b

n-hexane, 25OC; Ketelmr (1954); Ketelaar et al. (1952). 2,2,4-trimethylpentane, 25°C. Traynham and Olechowski (1959).

THE BASICITY O F UNSATURATED COMPOUNDS

269

terminal double bond is more basic than the double bond in the centre. This is also shown by the data in Table 17 for the exocyclic double bond in methylene-cyclobutane, methylenecyclopentane, methylenecyclohexane and methylene-cycloheptane, with a dependence on ring size simultaneously also being recognizable. I n the cases quoted here the 6-membered ring appears to be the most basic. I n the case of mono-olefins halogen substituents again reduce the basicity, as in the case of benzene. Unfortunately no information is available which would permit a comment as to whether the halogen atom causes this effect only if it is directly linked to the C=C double bond or whether an effect is also still exerted by an adjacent saturated halogen-substituted C-atom. With multiple halogen substitution the basicity falls even more as may be seen from the examples of chlorinesubstituted ethylene5 in Table 17. 3. Condensed aromatic systems

I n going from benzene to polynuclear aromatic hydrocarbons there is in general a considerably more pronounced increase in basicity than is caused by methyl substitution in benzene. If the ionization potential is regarded as the specific index for the donor strength and hence the basicity of a molecule, then i t is to be expected that anellation should cause an increase in basicity. The examples gathered for some EDAcomplexes in Table 18 show that linear anellation has a greater effect. The basicity, i.e. the donor strength, increases along with a decrease of the ionization potential. For the examples of angular ring fusion which are quoted, one is struck by the lower basicity of these condensed aromatic substances compared to the linear fused systems with the same number of rings. This behaviour shows a clear parallel to the electron excitation spectra. Aromatic compounds with angular anellation always have a higher excitation energy than their isomers with linear ring fusion (Clar, 1952). According to a rule discovered by Scheibe the interval between the first allowed excited state and the ionization limit of a molecule is constant (Scheibe and Briick, 1950; Scheibe, 1961). An increased excitation energy therefore also always denotes an increased ionization energy. This rule is here obeyed by the aromatic substances, so that the ionization potential is probably the most specific measure of the donor strength, i.e. of the basicity. The ionization potential furthermore has the advantage of being completely independent of the properties of the acceptors. The methyl derivatives of naphthalene included in Table 18 again clearly show the effect of the methyl groups in increasing the basicity.

270

H.-H. PERKAMPUS

A clear dependence on the position of the methyl group in the naphthalene ring may be recognized : this is directly connected with the electron distribution in naphthalene. It is known that the I-position of naphthalene is the point of greatest electron density (cf. Pullmann and Pullmann, 1952; Coulson, 1961). Substituting a methyl group into the TABLE 18 Formation constants of some aromatic EDA complexes, relative to benzene

Acceptor

1 Aromatic compound Benzene Biphenyl Naphthalene Fluorene Acenaphthene Phenanthrene Triphenylene Benz[a]anthracene Anthracene Pyrene 1-Methylnaphthalene 2-Methylnaphthalene 2,6-Dimethylnaphthalene 2,3-Dimethylnaphthalene 2,3,6-Trimethylnaphthalene a b c

a

b

1.00 2.56 2.1 1 3.42 3.50 3.60

1.00 1.90 4.10

4.20

-

-

14.3 17.8 17.7 21.6 14.1

1.00

-

20.8

-

29.6 47.0

-

48.5

-

23-0 31.5

3.55 3.74 4.95

Kortiim and Vogel(l955). Briegleb et al. (1961). Bier (195G).

2-position thus increases the electron density at C-atom 1. The effect of a methyl group in the I-position is, by comparison, considerably smaller though still base-strengthening. I n the case of disubstitution one has to bear in mind that several points of increased electron density are present if the methyl groups are considered to have equal effects. The examples of iodine complexes quoted in Table 18 clearly show an increase in basicity corresponding to the increase in the number of points of equally

THE BASICITY O F UNSATURATED COMPOUNDS

27 1

high electron density. I n the case of naphthalene (a) four equally favoured positions exist at C-atoms 1, 4, 6 and 8. I n the case of monosubstitution at C-atom 2 (b) only one point is favoured, in the case of

di-substitution (c) and (d) two points in each case, in the case of trisubstitution (e) three points, and in the case of tetra-substitution (f) again four points. It may therefore be expected that 2,3,6,7-tetramethylnaphthalene (f ) will be the most basic methylnaphthalene derivative. As may be seen from the summaries, all basicity gradations quoted here have predominantly been obtained from 7r-complexes or EDAcomplexes. If the pronounced differences in the nature of the acceptors are considered, it is nevertheless possible to recognize a satisfactory, even though only qualitative, agreement of gradations. I n particular, the effect of substitution of methyl groups and halogen atom in benzene, olefins and condensed aromatic substances may be observed to be similar. C. Basicity Constants of Aromatic Compounds The preceding section summarized basicity results obtained from the stability constants of 7r-complexes and EDA-complexes. These results can only reflect a qualitative gradation of the basicity. If one moves from these complexes to a-complexes, then exact values for the basicity of unsaturated compounds can be obtained by measuring the formation equilibria of the proton addition complexes in strongly acid solutions. The experimental methods and the calculations have been described in Sections 111,A-C. The results of these investigations for forty-five aromatic compounds are collected in Tables 19, 22 and 23. All figures for basicity constants were obtained in anhydrous hydrofluoric acid as the solvent. This means that these values only apply to this solvent ; they are, however, precise.

272

H.-H. P E R K A M P U S

The relative values obtained treating p-xylene a8 the standard can, however, in good approximation be translated to other solvents, as may be seen from Table 20. This is justified by the relatively good agreement between the values in column 2 in Table 20 and the relative reactivities for halogenation. TABLE19 pKB-valuesfor methylbenzenes

C'

pKga

(OOC)

z

(0°C)

PKBb (20°C)

ApKB

Benzene Toluene

9.2 6.3

6.28 5.00

-2.92 - 1.30

5.3

6 1 2 2 2

10.0

o-Xylene

4.54

-0.76

p-Xylene m-XyIene

5.7 3.2

1 4 2 4 3 2

Aromatic substance

PKB

a

6.7

4

2 1 1 1

2

6.9 5.8 6-0 6-3 3.6 3.8 3-1 3.3 3.1

4

4.55 3-40

- 1.15 -0.20

1,2,4-Trimethylbenzene

2.9

1,2,3-Trimethylbenzene 1,2,4,5-Tetramethylbenzene 1.2,3,4-Tetramethylbenzene 1,3,5-Trimethylbenzene 1,2,3,5-Tetramethylbenzene Pentamethylbenzene Hexamethylbenzene Hexasthylbenzene

2.8

2 5 3 4

2.2

3

2

2.5

1.83

-0.37

1.9 0.4

5 2

2 3

2-2 0.9

2.10 0.80

4 6 1

2 1 6 6

0.2 -0.8 -0.6 1.2

+ 0.20 +0.40 +0.80 $. 1.24 + 2.10

-0.1

-0.w

- 1.4 -2.0

1

-

2.90

0.00

2.90

+0*10

0.70 0.44 +0*70

-

-

Mackor et al. (1958b); Brouwer et al. (1965a, b). Recalculated from the measurements of Kilpatrick and Luborsky (1953),cf. Table 12. c From an empirical formula (Perkampusand Baumgarten 1964~). C, =C-atom to which the proton has been added. a

b

1. Benzene derivatives

Table 19 first of all summarizes the pKBand pKg values for all methyl derivatives of benzene (Mackor et al., 1958b). The recalculated conductivity results (Table 12) of Kilpatrick and Luborsky (1953) are also included. The agreement of these values with the values determined by Mackor et al. (1958b) is very good for some methylbenzenes, but pronounced deviations occur for benzene, toluene, pentamethylbenzene and hexamethylbenzene, and these cannot be explained merely by the different temperature. The last column of

273

T H E BASICITY O F UNSATURATED COMPOUNDS

Table 19 shows the deviation between these two groups of investigations. Similar deviations are of course also noticeable in the relative basicities summarized in Table 20, but here the results given by Kilpatrick and Luborsky (1953) have been entered directly. Qualitatively, both series of experiments show that methyl substitution is connected with an extremely strong increase in basicity which, in the case of the values given by Mackor and collaborators, extends over TABLE20 Relative basicity of methylbenzenes Relative basicity Aromatic substence

a

b

C

d

Benzene Toluene 0-Xylene p-Xylene m-Xylene 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene 1,2,3,4-Tetramethylbenzene 1,2,4,6-Tetramethylbenzene 1,3,6-Trimethylbenzene 1,2,3,6-Tetramethylbenzene Pentamethylbenzene Hexamethylbenzene

2.0 x 10-4 2.6 x 10-1 1.0 x 100 (1.0 x 100) 3.6 x 102 1.26 x 103 1.26 x 103 6.0 x 103 6-0 x 102 2.0 x 105 1.8 x 106 6.2 x 106 1-26x 107

1.0 x 10-2 3.0 x 100 (1.0 x 100) 9.0 x 100 1.8 x 103 1.8 x 101 8.6 x 101 6.0 x 101 1.4 x 103 2.8 x 103 4.4 x 103 4.5 x 104

9.0 x 10-2 6-3x 10-1 1.1 x 100 (1.0 x 100) 2.6 x 101 6.9 x 101 6-3x 10' 4.0 x 102 1.4 x 102 1.3 x 104 143x 104 2.9 x 104 9.7 x 104

6.0x 10-4 1.6 x 10-1 2.1 x 100 (1.0 x 100) 2.0 x 102 4.0 x 102 3.4 x 102 2.0 x 103 8.0 x 104 2.4 x 105

Mackor et al. (1968b). MacCaulay and Lien (1951). C Kilpatrick and Luborsky (1953), cf. Table 11. d Relative values of reactivity in halogenation: de la Mare and Robertson (1943); Condon (1948),cf. Table 10. b

eleven powers of ten. If condensed aromatic substances are included, then the basicity constant increases by roughly sixteen powers of ten on going from benzene to benzo[a]pyrene. Comparable with this effect is the strongly increasing reactivity in the series of condensed aromatic substances (cf. Clar, 1952). As may be seen from the pKBvalues in Table 19, specific substitution effectsmay be noted for the methyl derivatives, and these may be directly related to the electron density of the ring C-atoms which is modified by substitution. The position to which the proton is preferentially added depends on the position of the methyl groups. The ortho- and parapositions relative to a methyl group are always preferred for addition,

274

H.-H. PERKAMPUS

whereas the meta-position is less favoured. The values of basicity constants are therefore determined not only by the number of methyl groups but also by their positions. Thus mesitylene is considerably more basic than 1,2,3,4- and 1,2,4,5-tetramethylbenzene.I n mesitylene, for example, three points available for proton addition are strongly activated in the same manner, since in each case two methyl groups in the orthopositions and one methyl in the para-position cooperate. For reasons of symmetry these three positions cannot be distinguished. However, they can be distinguished where one is dealing with substitution of low symmetry, when the occurrence of isomeric proton addition complexes must be considered. Using I.R. spectroscopy, i t proved possible to demonstrate isomeric proton addition complexes of toluene, o-xylene and pseudocumene in the solid state (Fig. 10) (Perkampus and Baumgarten, 1964b). This means that the basicity constant measured in solution represents the total basicity of the dissolved aromatic substance. I n order therefore to obtain the true basicity constant the measured figure K B evidently has to be divided by the number of active C-atoms in the molecule. This number, z, which is related to the symmetry of the molecule, is six for benzene, four for p-xylene, one for pentamethylbenzene, six for hexamethylbenzene, four for naphthalene, two for anthracene, etc. (see Tables 19 and 22). Thermodynamically, this correction can be justified as an entropy contribution (Mackor et al., 1958a). Since practically the same protolytic reaction takes place for all aromatic substances, it may be assumed that the reaction entropy is largely independent of the structure of the aromatic substance itself. If, however, several points of identical proton afinity are present, then AG will contain an entropy contribution which depends on z. This contribution is given by RT.lnz, so that one obtains the relation pK$ = pKB+log 2

(41)

The pK8 values corrected in this way are also included in Tables 19 and 22. If the assumption that the entropy of the reaction according to equation (5) is independent of the aromatic substance applies, the entropy contribution T A S * must assume a constant value. Mackor et al. (1958b)were able to demonstrate the correctness of this assumption by determining the thermodynamic data for some methylbenzenes and condensed aromatic hydrocarbons. Whereas A H and AG* change considerably, the entropy term TAS* remains largely unaltered (Table 21).

In the case of condensed aromatic substances their low solubility

THE BASICITY OF UNSATURATED COMPOUNDS

275

renders a direct determination of the heat of solution difficult, so that the measured heat evolution represents the sum of the heat of reaction AH and the heat of solution AHL, and the heat of solution is to be understood as the heat evolution which occurs on transition of the aromatic hydrocarbon from the hydrocarbon phase to the HF phase. Here again the corresponding values for the entropy change show good constancy, whereas the values for AH + A H Lvary greatly. This probably proves that the entropy of reaction for (‘one active position” in the molecule is practically independent of the structure of the aromatic substance. The tabulated basicity constants were based on activities, as detailed in Section 111, A, B, so that the use of the Gibbs-Helmholtz equation is thermodynamically justified. I n view of the change in electron density distribution arising from the position of the methyl TABLE 21

+

+

Thermodynamic data for the reaction A HF p AH+ F- in HI?; kcd mole-1 (Mackor et al., 1968b) Aromatic substance

AH

AG*

-T x AS*

Toluene p-Xylene m-Xylene Mesitylene

5.1 3.8 1.5 2.9

8.5

3.3 4.1 3.1 4.0

-

7.9 4.6 1.1

groups, the o- andp-positions relative to a methyl group are particularly favoured for the introduction of a proton (Table 19). If there are several CH, groups in the o- and/or p-position relative to such an active site, then the pKB value is particularly greatly reduced, whereas methyl groups in the m-position exert less effect. The most active position in a molecule is therefore that which has the largest number of methyl groups in o- and/or p-positions relative to it ( 2 , J. The number of such methyl groups is zero in benzene, one in toluene, two in m-xylene, and three in mesitylene. I n the same sequence, the pKB values decrease by approximately 2-9 units in each case, from + 9.2 (benzene) via + 6 - 3 (toluene), and +3.2 (m-xylene) down to +0.4 (mesitylene). If, however, one methyl group each is present in the o- and m-positions relative to the active position, as in the case of p-xylene (pKB= + 5.7) then the pK,-value of benzene of pKB= + 9.2 decreases by 2.9 units as a result of the o-substituent but only by a further 0.6 unit

276

H.-H. PERKAMPUS

for the m-group. This rule is confirmed for hexamethylbenzene (pKB= - lea), which is derived from mesitylene by adding three (2,) methyl groups in the m-position and/or directly to the activated position itself. The change of the pKB-value compared to mesitylene (pKB= + 0.4) is here 1-8units, i.e. three times 0-6 for each m-substituent. One thus obtains a simple empirical relation for the calculation of the pKB-value of methylbenzenes, by which, for example, the figure given for pentamethylbenzene in Table 19 was calculated (Perkampus and Baumgarten, 1964c) :

2. Condensed aromatic substances The pKB-values of condensed aromatic substances collected in Table 22 show a basicity which increases with anellation. The basicity increases more strongly in the acene series than in the phene series, in agreement with spectroscopic behaviour and with the reactivity of the aromatic substances. This connection can be clearly recognized if the logKB-valuesare plotted as a function of the excitation energy of the 'La bands. There is a regular relationship which becomes a linear one with decreasing excitation energies (Fig. 24). Since it has been repeatedly pointed out that the basicity can also be interpreted as donor strength, a connection with the ionization potential must also be expected. I n Fig. 25, pKB is plotted as a function of the ionization potential for the substances quoted in Table 22. The scatter is somewhat greater than in Fig. 24 but nevertheless a straight line can approximately be drawn through the points. The greatest deviations are noted for triphenylene and phenanthrene. If, however, one compares this with the dependence of the pKB values on the excitation energy of the 'La bands in Fig. 24, then this deviation is incomprehensible since the pKB-values correlate well with the excitation energies. If Scheibe's rule is valid (Scheibe and Briick, 1950; Scheibe, 1961) one would therefore expect an analogous correlation with the ionization potentials. However, the range of variation of these ionization potentials is very great (Hedges and Matsen, 1958). I n general, the ionization potentials determined from the excitation energies of the CT-bands agree very well with the best values in the literature (Briegleb, 1961). I n the case of triphenylene and phenanthrene, one, however, again finds variations for various acceptors, these amounting to about 0.3 e.v. (Briegleb and Czekalla, 1959). If one takes this into account, then the ionization energies of phenanthrene, naphthalene and triphenylene are close to one another and also closer to the straight line. I n the light of this discussion, the

THE BASIUITY O F UNSATURATED C O M P O U N D S

277

ionization potential of triphenylene is probably somewhat greater than that of naphthalene and is about 8.2-8.3 e.v. The low basicity of triphenylene is explained by the fact that according to investigations by Clar (1959) there is a pronounced tendency for localization of the T electron sextets in the outer rings in this aromatic hydrocarbon. Thus this condensed aromatic substance resembles a benzene derivative in its properties.

-101 40

I

35

I

30

I

25

I

20

J

15

FIG.24. IogK; aa E function of the frequency of lLa bands of condensed aromatic substances.

The data in Fig. 25 corrected in this way then show that the basicity correlates with the ionization potential of the donors, and thus the angular and linear aromatic substances as well as the peri-condensed aromatic substances can be understood from a consistent viewpoint. However, it should here be pointed out that an analogous dependence of the long-wavelength excitation energies of the proton addition complexes on ionization potentials could not be demonstrated (Perkampus and Baumgarten, 1964b). This is probably also intelligible, since as a result of the newly formed o-bond in the proton addition complex, one is dealing with additional interaction energies which are not taken into account in the theoretical treatment of the EDA-complexes. Similarly to the methylbenzenes, the condensed aromatics also show a clear increase in bmicity with methyl substitution, as may be seen for

278

H.-H. PERKAMPUS

the naphthalene and anthracene derivatives which are included in Table 22. The effect entirely corresponds to the effect of methyl substituents on the electron distribution as has already been discussed in connection with the EDA-complexes. The effect can, however, not be explained by the reduction in ionization potential alone, since this only contributes about 0.15 e.v. in the case of the two methylnaphthalenes. Against this, pK,-value changes by 2.9 and 3.2 units. Therefore, effects which must be described as inductive effects must also play a part.

FIG.25. p K i as a function of the ionization potential of condensed aromatic hydrocarbons.

The pKB-values of the methyl derivatives of benz[a]anthracene, summarized in Table 23, are particularly interesting. I n the case of the unsubstituted compound, two positions of approximately equal proton afinity have to be taken into account. Thus two isomeric proton addition complexes A and B are present in solution (cf. IID, page 229). The basicity constant determined thus gives the total basicity. Because of methyl substitution, it is however possible to vary the ratio of ions A and B present in solution. The two ions A and B differ characteristically in their electron excitation spectra so that one has an analytical method for determining the concentration ratio of the two ions (Mackor et al., 1956). The analysis of these measurements assumes that the extinction

T H E BASICITY O F UNSATURATED COMPOUNDS

279

coefficients of ions A and B are identical for all isomeric methylbenz[u]anthracenes. With this assumption, the concentration ratio of ions A and B could be determined from the measured extinction coefficients. It is thus possible, in conjunction with the total basicity constants determined by partition measurements, to calculate the pKB-values for ions TABLE 22 pK, and pK,* values for some condensed aromatic substances and methyl derivatives of naphthalene and anthracene. (Mackor et al., 1968a, b ; Brouwer et al., 1965a) Aromatic substance

PKB

Benzene Diphenyl Naphthalene Anthrmene Tetrmene Pentmenen

9.2 6.5 4.0 3.8 -6.8 - 7.6

Phenanthrene Triphen ylene Chrysene Benz[u]mthracene Dibenz[a,h]anthracene Pyrene Perylene Benzo[a]p yrene

3.6 4-6 1.7 2.3 - 2.2 -2.1 - 4.4 - 6.6

1-Methylnaphthalene 2-Methylnaphthalene 2-Methylanthrecene 9-Methylanthraoene 9-Ethylanthrmene 9,lO-Dimethylanthracene

1-7 1-4 - 4.7 6.7 - 6.4 - 6.4

z

10.0 6.3 4.6 - 3.6 - 6.2 - 7.3

-

-

-

PK,*

4 6 2 2 2 4 4 1

4.1 6.4 2.0 2.0 1.9 1.6 - 3.8 - 6.6

-

1.7 1-4 4.7 6.7 - 5.4 -6.1

-

a The value for pentacene was extrapolated from the correlation between pK,* and the ionization energy.

A and B. This calculation is, of course, not very precise but it does correctly reflect the effect of methyl substitution on the basicity. Table 23 summarizes the values obtained in this way for all monomethyl derivatives and for the 7,12-dimethyl derivative of benz[u]anthracene (Mackor et ul., 1956; Dallinga et ul., 1958b). pKBgives the figure of the total basicity, pK(A) the vdue for ion A, pK(B) the value forion B, and the columns p- K(A) K(B) give the change in basicity as a K,(A) and p-KdB)

280

H.-H. PERKAMPUS

result of methyl substitution, with pK,(A) and pK,(B) respectively representing the values for the unsubstituted ions A and B. The values in Table 23 show that in unsubstituted benz[a]anthracene the ion A has the greater basicity. On substitution of the angular ring, the basicity increase is approximately equal. Ion A is favoured for substituents in the vicinity of the 7-position (positions 5, 6, 8, 9), and ion B is favoured by substituents in the vicinity of the C-atom 12 (10 TABLE23 Basicity constants of methyl derivatives of l,2-benzanthracene according to Mackor et al. (1956). For explanation, see text

PKW PKW

pKo(A) plio(B)

PKB Benz[a Janthracene 1-methyl %methyl 3-methyl4 -methyl6 -methyl 6-methyl7-methyl8-methyl9-methyl10-methyl11-methyl12-methyl7,12-dimethyl-

@

- 2.6 -3.2

- 3.3 - 3.0 - 4.0 - 3.1 - 4.6 - 3.2 -3.9 - 3.8 -3.1 -5.9 - 6.2

- 2.22 - 3.03 - 2.86 - 3.05 -3.11 - 2.68 -2.81 -2.37

-3.93 -2.96 -3.8 - 3.08 -3.82 - 3.36 - 2.72 -5-4

- 3.4

- 2.73 - 4.6 - 2-87 - 3.35 - 3.68 - 2.95 - 6.8

-

0

0.66 0.74 0.44 1.66 0.68 1.4 0.71 1.45 0.99 0.35 3.0

-

0

-

0.63 0.83 0.46 1.2 0-51

2.2 0-45 1-1 1.46 0.73 3.6

-

C7

Cia

-2.1 -2.9 -2.8 -2.8 -2.8 -3.6 -2.7 -33.5 -2.7 -3.6 -3.1 -2.4 -5.1

-1.9 -2.3 -2.7 -2.7 -2.7 -3.1 -2.4 -4.3 -2.4 -3.1 -3.4 -2.7

-

-5.5

-

Corrected values (Dallinga et al., 1958b).

and 11). A methyl group in the 12-position very greatly increases the basicity of both ions, whereas substitution in the 7-position greatly favours ion B. These effects can in part be interpreted with the aid of HMO-theory, taking into account an inductive parameter for the methyl groups (Mackor et al., 1956). As with the methylbenzenes the methyl derivatives of condensed aromatic substances show an increase in basicity compared to the unsubstituted compound. Thus, the methyl groups exert a very profound influence on the electron distribution. The extension of these considerations by theoretical methods will be discussed in Section V.

T H E BASICITY O F UNSATURATED COMPOUNDS

281

D. Basicity of the Azulenes Of unsaturated bond systems other than aromatic hydrocarbons, the proton addition complexes of azulene have been particularly investigated. A reason for this is probably the fact that their solubility in concentrated aqueous acids was utilized in the f i s t isolation of azulenes (Sherndal, 1915). Aqueous sulphuric acid (50-60 yo)and phosphoric acid (85%) were dainly used. Attention was also drawn a t a relatively early stage to differences in the acid solubility of azulenes with different substituents (Ruzicka and Rudolph, 1926; Ruzicka and Haagen-Smit, 1931). Plattner et al. (1949) carried out systematic investigations of the partition of azulenes between aqueous acid solutions and organic solvents, and set up a scale, depending on the acid strength, for the distribution of substituted azulenes between the two phases. Plattner (1950) later showed that this was an acid/base equilibrium, in which the formation of a proton addition complex of the azulene in the acid solution has to be assumed. The conditions for investigating the partition equilibria of the azulenes correspond to the statements made in Section 111, A, and the results should therefore be evaluated by equation (12c) :

According to this, there is a linear relationship between the logarithm of the partition coefficients, log ( c A H + / c ~ ) ,and the Hammett acid function H,. Plattner et al. (1949)were able to confirm this relationship for a substantial number of methyl-substituted azulenes. However, the further analysis of these measurements with a view to obtaining pKB proved difficult since the partition coefficient PAof the free azulene between the two phases, which enters into equation (12c), is unknown. For this reason, the authors took the H,-value for which c A H + = c ias a characteristic measure of the stability of the proton addition complex. From equation (12c), this Ho-value is identical to pKB +logPA. The partition experiments were carried out for the systems H,S04-light petroleum, HzSO4-toluene, H,P04-light petroleum, H,P04-toluene (Plattner et al., 1949). Heilbronner (1959) subsequently showed that the results for the different systems could be uniformly represented. The change in the acid or organic solvent can be allowed for as an additive parameter since for practical purposes there is no interaction determined by the type of acid and the type of solvent. Using these additive quantities, 10

282

H.-H. PERKAMPUS

the H,-value for which the partition coefficient has the value unity can be converted into a value M , which is independent of the system. The figures for seven azulenes are summarized in Table 24. Again, the basicity of the unsaturated system increases with the substitution of methyl groups. The differences are such that M , (the Ho- value for P = 1) represents a characteristic quantity which is useful for the identification of azulene derivatives, and for testing their purity. The interpretation of these effects as the formation of a proton addition complex was further supported by Plattner et al. (1952) by means of spectroscopic and conductimetric investigations. I n these interactions the change of the absorption spectrum is characteristic, since the blue colour of the azulene in organic solvents is changed to a yellow colour in TABLE24 Mo-values for some azulene derivatives (Heilbronner, 1959) Mo=pK,

Azulene l-methyl2-methyl4-methyl5-methyl6-methyl3-methyl5-isopropyl-

+ logp,

- 2.78 f 0.06

- 2.66 0.08 - 2.38 f 0.04 - 2.48 f 0.02 - 2.08 f 0.08 -2.50f0.14 - 2.22 f 0.07 - 2.22 f 0.07

50% sulphuric acid. Thus, one has a hypsochromic displacement of light absorption, in contrast to the observations made with aromatic hydrocarbons. As shown by theoretical investigations by Heilbronner and Simonetta (1952),using the HMO-method, the change in light absorption agrees with the postulation of the following proton addition complex :

The theoretical calculations further permitted the high basicity to be explained and the effect of methyl groups on the basicity to be estimated, with some limitations. The question of how many protons are added to azulene in acid

T H E BASICITY O F UNSATURATED COMPOUNDS

283

solution could be answered by the conductimetric investigations (Plattner et al., 1952). According to these, one is dealing with a 1 :1complex. Wbssermann (1955) carried out spectroscopic and conductimetric measurements of the interaction of azulene with trichloracetic and dichloracetic acids in benzene as the solvent. The basicity constant determined in these systems cannot, for the reasons explained in Section IVA, be compared with the M o (P= 1) values and with the basicities of the aromatics in HF. However, the measurements carried out by Wassermann in the range of 10-50°C permit the determination of thermodynamic quantities. TABLE 25 Approximate pK, values for some azulene derivatives in Ha04/HzO (Long and Schulze, 1964)

Azulene l-methyll-formyll-chloro1 -nitro-4,6,8-trimethylI-carboxy l-cyano1 -nitro-

0.92 0.36 1.12 1.80 2.26 3.5 4.59 4.68

Comparison with the entropy change for the analogous proton addition to carotene (Wassermann, 1954) is interesting. I n both cases, AS is negative and of about equal magnitude ( - 10 & 7 e.u.). This figure is comparable with the figures given by Mackor et al. (1958b) for aromatic hydrocarbons in the system HF + BF,, from which one obtains a mean value of AS of - 13 e.u. Carotene is more basic than azulene (Wassermann, 1954, 1955). Long and Schulze (1961) determined spectroscopically, in perchloric acid, the Ho-value for which the concentration ratio CAH+/CA = 1. This value can be regarded as an approximate uncorrected pK,-value. These investigations were extended to other azulene derivatives, permitting a study of the effect of polar substituents on the basicity (Long and Schulze, 1964). The results of these investigations are summarized in Table 25. I n the case of 1-formyl-azuleneand 1-nitro-azulene the addition of the

284

H.-H. PERKAMPUS

proton takes place a t the oxygen atom of the substituent, as is found from the N.M.R. and U.V. spectra of the protonated compounds (Long and Schulze, 1964). If one ignores these two compounds, then it is clearly seen that chlorine and the nitrile group greatly reduce the basicity of the azulene. One thus has the same effect as in the case of the aromatic hydrocarbons.

V. THEORETICAL TREATMENT OF PROTON ADDITION COMPLEXES When a proton addition complex is formed, the particular evennumbered hydrocarbon is converted to an odd hydrocarbon ion. The r-electron number remains even, but is reduced by two as a result of the formation of the a-bond. Thus we are dealing with a diamagnetic positive hydrocarbon ion. The theoretical treatment of this n-electron system has to reflect the following: (i) the change of the r-electron energy from that of the nonprotonated hydrocarbon, (ii) the influence of partly saturated substituents and, in connection therewith, (iii) the effect of substitution in the benzene nucleus. A. Localization Energies and Basicity Questions concerned with the energy can in the first instance be treated to a good approximation by means of the HMO theory if the effect of substituents is neglected. If HMO theory is used it must be specified to which C-atom the proton is added. In the case of anthracene, for example, three positions of the molecule must be considered. A decision as to which of these three positions is energetically the most favoured can easily be reached by means of the HMO theory. From the known starting points of HMO theory, the r-electron energy of the neutral r-electron system (Ex)*and the corresponding energy of may be calculated. The difference of the the protonated system (E,,)AH+ two energies AE = (E,)AH+ - (En)4 (43) represents the amount of energy which is necessary for the localization of an electron pair of the basic n-electron system (cf. Streitwieser, 1961). The localization energy AE, is therefore a measure of the change of the r-electron energy on converting the aromatic hydrocarbon into a a-complex. I n determining this energy one has to remember that the influence of the positive charge is not dealt with by the HMO theory, so

THE BASICITY O F UNSATURATED COMPOUNDS

285

that the results are uncertain to the extent of this factor (Coulson and Dewar, 1947 ;Coulson and Longuet-Higgins, 1947). With the assumption that the effect of the positive charge will be of constant magnitude for the proton addition complexes of aromatic substances, Gold and Tye (1952~)calculated these energies for a series of r-electron systems. Consideration of isomeric proton addition complexes together with tho corresponding localization energies affords the possibility of selecting the most stable proton addition complex. Table 26 summarizes some of the examples given by Gold and Tye. Since /3 is negative, the localization energies are positive. This means that a proton addition complex will be formed the more easily the lower this energy. It is recognized that in those cases where isomeric proton addition complexes may be expected, the differences between the localization energies are in part considerable, so that the differentiation as to which proton addition complex is the most stable may be made in the light of these energy data. If the localization energies of different unsaturated systems are compared, one notes that a change in basicity is also noticeable in these values. This gradation becomes very obvious if the analogous data of Heilbronner and Simonetta (1952) for azulene are compared with those for naphthalene. One then notes that azulene is more basic than naphthalene (cf. Streitwieser, 1961). The low localization energies of the polyenes, which would cause one to expect a high basicity of these hydrocarbons, are interesting. The requisite relation between the basicity constants and the localization energy can easily be obtained. The followingrelation exists between the thermodynamic quantities :

Aa*

=

-RTlnK;t; = A H - T A S *

(44)

Since T A S * is practically independent of the structure of the aromatic substances (cf. IV, C), one obtains the simple relation

-RT In K$

=

A H + const.

(45)

The value of AH of the proton addition is given as :

AH

=

C vi Hi

=

AHA,+

- AHA-

AH,+

(46)

The enthalpies of formation AHi of the components AH+ and A are however made up of the bonding enthalpies, so that they can be separated into a- and n-bonding components. One then finds : = [ ( E ~ ) A H + - (Eu)AI

+[(En)AH+-

(En)AI

-

Since the a-bonding energies of all complexes and of the corresponding compounds differ by the constant contribution of a C-H-bond, the

H.-H. PERKAMPUS

286

TABLE26 Localization energies of some isomeric proton addition complexes (Gold and Tye, 1952c)a (C, =location of proton addition)

dE, Compound 1

2

9

CH2=CH-CH=CH-CH=CHz

Cf

B

1 3 2

1.5 2.13 2-49

1

1.7 2.37 2-42

4

2

2.54

1 2

2.3 2-5

5 4

2.3 2.31

1 2 3

2.4

2.5 2.6

9 1 2

2.01 2-2 2.6

7

1.8

_Cf. also the values for the transition states on substitution of aromatic substances, Wheland (1942) and Dewar (1949). Further values for the localization energies are given by Dallinga et al. (1957); Mackor et al. (1958a); Streitwieser (1961). a

T H E BASICITY O F UNSATURATED COMPOUNDS

287

change in A H may thus be solely attributed to the n-bonding components : -RT In KB = AE, const. (474 or 4.57311. pK$ = AE, + const. (47b) This means that a simple linear relationship exists between the localization energy AE, and the logarithm of the reduced basicity constant KB.

+

I

2.0

I

I

2.1

2.2

I

23

I

I

24

2.5

FIU.26. p K , aa a function of the HMO localization energies of some aromatic hydrocarbons. (Dallinga et al., 1967, Mackor el al., 1968a.)

The pKg-values of Table 22 are plotted against the localization energies in Fig. 26. The straight line which can to a good approximation be drawn through these points confirms this relationship. Greater deviations occur particularly in the case of the peri-condensed aromatic substances pyrene and perylene. The pK$ values are lower than one would have expected on the basis of localization energies. As has already been mentioned above, the localization energies calculated by the HMO theory can only be used for these considerations

288

H.-H. PERKAMPUS

with reservations, since the influence of the positive charge cannot be included in the starting calculation. Nevertheless the expected linear relationship is obeyed to a good approximation. Verrijn Stuart and Kruizinga (1958) were able to compensate for the deviations which occur with the peri-condensed aromatic substances, using an HMO-SCF calculation as introduced by Roothaan (1951) and

I0.C

8

O

*/

5-c

t

*

- 0

'C

P

- 5.0

- 10.0 L -0.2

0

0.2

0.4

0.6

0.8

1.0

FIG.27. pK, as a function of the HMO-SCF localization energies of some aromatic hydrocarbons. (Dallinge et al., 1957; Mackor et al., 1958a.)

Pople (1953, 1955). I n these calculations the HMO method forms the first part of the procedure (cf. Daudel et al., 1959; Streitwieser, 1961). I n contrast to the HMO method, the repulsion forces of the electrons are taken into account when carrying out the SCF method, so that it may be expected that the results of these calculations will give better results for the positive aromatic ions than do the HMO calculations. If the pKg-values are plotted against the localization energies obtained by this method, one obtains excellent conformity with the requisite linearity, as shown in Fig. 27. The figures for peri-condensed aromatic

THE BASICITY O F UNSATURATED COMPOUNDS

289

substances no longer show any deviations. The calculations indicate that the influence of the positive charge is not constant for the various types of ring systems of aromatic hydrocarbons. I n continuation of these calculations, the electron excitation spectra of positive aromatic ions have been calculated (Verrijn Stuart and Kruizinga, 1958; Mackor et at., 1957). I n order to make these and the calculations referred to above self-consistent, the calculated spectrum of neutral naphthalene was made to agree with experiment (Dallinga et al., 1957). The calculations were in some cases elaborated by including configuration interaction (Verrijn Stuart and Mackor, 1957, 1958). The detailed discussion shows that the calculated spectra agree very well with experiment (Dallinga et al.,1958a) (cf. Table 7). I n agreement with the localization energies, the spectra calculated for various isomeric proton addition complexes permit the most stable proton addition complex present in solution to be identified. I n the case of the pericondensed aromatic substances pyrene, benzo[a]pyrene and perylene, several energetically equally favoured proton addition complexes are present, according to these calculated spectra, so that the observed spectrum represents a mixture of the different ions. This is also the case for benz[a]anthracene, as shown by spectroscopicinvestigations (Mackor and collaborators, 1956), and theoretical calculations (Verrijn Stuart and Mackor, 1957).

B . Consideration of the Influence of Substituents I n calculations on proton addition complexes of azulene and methylazulenes by means of the HMO method, Heilbronner and Simonetta (1952) took the effect of methyl groups into account by adjustment of the tl and values, as had already been done by Pullmann and collaborators (1950) in calculating the spectra of the methylazulenes. These calculations correctly reproduce the effect of a methyl group on the basicity of azulene. I n contrast to the case of naphthalene, the position of addition of the proton remains independent of the position of the methyl group :

Methyl groups in five- and seven-membered rings always exert a stabilizing effect, though the effectiveness of the methyl group is greater in the seven-membered ring than in the five-membered ring. This difference is correctly reproduced by the HMO calculations. The cause of this special behaviour of azulene lies in the fact that in the structure given above a 10'

290

H.-H. PERKAMPUS

tropylium ion is conjugated with a double bond (Heilbronner, 1959). I n azulene there is thus a certain tendency for electron transfer from the seven-membered ring to the five-membered ring. This tendency also manifests itself on consideration of the charge densities. Whereas in the neutral molecule a charge excess in the seven-membered ring can be deduced from the q,-values, the situation is reversed in the azulenium ion. This is also the reason why the methyl groups are more effective in the seven-memberedring than in the five-memberedring. The effectiveness of the methyl groups in this is caused by inductive and electromeric effects as well as by hyperconjugation (Heilbronner and Simonetta, 1952). The question of the effect of the -CH,-group which is present after proton addition is connected with the question as to the extent to which hyperconjugation in methyl-substituted proton addition complexes has to be taken into account. This question was treated in detail in an investigation of the proton addition complex of benzene by Muller et al. (1954). I n an MO calculation, the effect of this CH2-group was treated as a hyperconjugation effect. I n contrast to a simple HMO calculation without overlap, the overlap between adjacent C-atoms was taken into account. The calculations were based on the model:

and were followed by SCF calculations. The detailed discussion of these calculations shows that the effect of hyperconjugation on the stability of the C6Hg ion is admittedly considerable, but that it is also accompanied by an inductive effect which is better interpreted as a chargetransfer effect. Both effects operate additively as regards stabilization. The electron excitation energy calculated by means of this model causes one to expect, in agreement with experiment, transitions at approximately 25,000 and 31,000 cm-l, the first one polarized in the direction of the axis of symmetry and the second vertical thereto. The calculated oscillator strengths off = 0.2 and 0.5 satisfactorily agree with the observed values. The results of these calculations show that taking the hyperconjugation effect into account gives good agreement between theory and practice. A t the same time, however, i t also becomes obvious that it is not a matter of a pure hyperconjugation effect but that inductive components are also involved. In order to study the effect of methyl groups on the basicity of benzene more exactly, Ehrenson (1961, 1962) carried out calculations for the

THE BASICITY O F UNSATURATED COMPOUNDS

291

methylbenzenes and set up a basicity scale. Ehrenson used an SCF-MO method and allowed for the hyperconjugation between methyl groups and ring C-atoms (Ehrenson, 1961),following the calculations of Muller et aZ. (1954). I n order to be able to deduce a basicity scale from such calculations, the r-electron energy has to be related to the basicity constant. According to equation (47a) one then obtains, for K$

KB

= exp(-AE,/RT)

(49)

If the equation is related to a standard equilibrium, it is possible to write : -RTIn- KjCr = AG-AG0 = AAE,

KO*

In this formula AE, denotes the difference of the resonance energies (localization energies) between the hydrocarbon and the proton addition complex. The difference AAE, shows the difference relative to a standard difference (LIE,),. Equation (50) uses the fact that the o-bond energies and the entropy components may be assumed constant. However, this formula does not allow for the fact that several isomeric proton addition complexes may be present in the solution. I n that case one obtains the more general relation :

K,

zi.exp ( -pAAE,/RT)

Here zi denotes the number of isomeric equilibria, which have to be summed from i = 1 to i =n. p denotes a proportionality constant relating the rr-electron energy and free energy differences. The results of these calculations are summarized in Table 27. I n contrast to the tables given by Ehrenson (1961),no account is taken of proton addition complexes in which the addition of the proton takes place a t a C-atom which carries a methyl group. Table 27 thus includes only proton addition complexes which could actually be demonstrated in solution or in the solid state. Neither N.M.R. spectra (MacLean et al., 1961a, b, c, 1962) nor I.R. spectra (Perkampus and Baumgarten, 1963a, 1964%)could demonstrate the addition of a proton to a ring C-atom carrying a methyl group. Thus

292

H.-H. P E R K A M P U S

TABLE27 Basicity calculations for methylbenzenes (Ehrenson, 1961)

0

1.07837

1

6

2.02594

0.94757

- 4 . 9 2 6 ~ 10-2

+2.40

1.09878

2 4

2 1

2.09286 2.09286

0.99408 0.99441

- 0 . 2 7 5 ~10-2 - 0 . 2 4 2 ~ 10-2

+0*13 +O.ll

1.11926

3 4

2 2

2.11731 2.11627

0.99805 0.99701

0 . 1 2 2 ~10-2 0 . 0 1 8 ~10-2

-0.05 -0.01

2

1 2

2.15652 2.15518

1.03740 1.03606

4.057~10-2 3 . 9 2 3 ~10-2

-1.95 -1.89

1.11912

4

1.14035

b

1.14059

3

1

5

1

2.17844 2.17830

1.03809 1.03795

4 . 1 2 6 ~10-2 4.122 x 10-2

-1.98 -1.97

4

2

2.18047

1.03988

4 . 3 0 5 ~10-2

-2.08

293

T H E BASICITY O F UNSATURATED COMPOUNDS

TABLE27--continued

1.16081

2.20314

1.04233

4.55 x 10-2

-2.18

1.13936

2.21229

1.07293

7.660 x 10W

-3.65

1.16112

2.23653

1.07541

7.558 x 10-2

-3.78

1.18279

2.26158

1.07879

8.196 x 10-2

-3.93

1.20302

2.28575

1.08273

8.590 x 10-2

-4.11

even if a proton is first added to such a position, it evidently immediately migrates to the most favoured position of the ring (Perkampus and Baumgarten 1964d). The calculation of the relative values according to equation (50) was carried out with a Bo-value of 60 kcal mole-l. With this, one obtains from (50),for 2 7 3 ° K : AAE x 60 x lo3 -log- K: = (52) K,* 4.573~273 If the statistical factor zi is taken into account for each ion, then one obtains :

294

H.-H. PERKAMPUS

The values from (53) give the overall basicity constants reIative to a standard substance. The last column of Table 27 gives the differences pK;I;-pK$ calculated according to (52), since the pKS-values are known from the investigations of Mackor and collaborators (1958a, b). The resonance energies listed in Table 27 show the expected pattern. The stability increases with increasing number of methyl groups, both for the aromatic substance and for the proton addition complex. The pK,-values given in the last column and related to p-xylene decrease with the number of methyl groups, i.e. the basicity constant K B increases. However whereas the experimental values extend over 11 powers of ten from benzene to hexamethylbenzene (cf. Table 20), the theoretically calculated values only reflect a range of 6.5 powers of ten. For this reason Ehrenson in a later paper (1962) also discussed the influence of an inductive effect, and the combination of both effects. The inductive effect alone already produces a considerable improvement on the results. The combination of both effects causes the values to approach the experimental results even more closely, with the thermodynamically reliable values of Mackor and collaborators (1958a, b) serving as a reference point. Flurry and Lykos (1963)also carried out calculations on the basicity of methylbenzenes. The effect of the methyl groups was attributed by these authors to a hyperconjugation effect, in which no rr-electron character of the C-H,-group was assumed. The effectiveness of the methyl groups was described in terms of an inductive effect only. The authors used orbitals of the Slater type for the central atoms, and carried out an SCF-MO calculation which corresponds to a modification of the Roothaan SCF-MO method (Roothaan, 1960). The results of these calculations showed very good agreement between the calculated and experimental basicity gradations. Table 28 gives these values in comparison to those of Ehrenson (1961, 1962). The results of these calculations show that hyperconjugation by itself does not correctly reproduce the basicity gradation, but that the inductive effect of the methyl groups predominates. Dewar (1963)came to the same conclusion, by comparing the models critically with one another and taking only an inductive effect into account for the determination of the basicity gradation. In his considerations, Dewar started from the basis that the rr-electron distribution in the benzene nucleus and in the proton addition complex was only slightly perturbed by the substituents. In that case the ionization energy of the methylbenzenes should depend only on the number of substituted methyl groups but not on their position. This agrees well with experiment. If one uses this assumption then the weak inductive effect of the methyl

T H E BASICITY O F UNSATURATED COMPOUNDS

295

groups can be dealt with by a perturbation calculation according to Coulson and Longuet-Higgins (1947). It is further assumed that only a first-order perturbation has to be taken into account and that higher orders, which, e.g., relate to the polarization of n-electrons, may be TABLE28 Comparison of theoretical pKB values with experiment (C,= position of proton addition) pKB relative to p-Xylene

Benzene Toluene p-Xylene o-Xylene m-Xylene Pseudocumene Durene Mesitylene Isodurene Pentamethylbenzene Hexamethylbenzene Difference : Benzene - Hexamethylbenzene

@

1 2 192 4 2 3 3 2 4 6 1

2.40 3.00 1.10 0.50 (0.00) (0.00) 0.29 - 1.53 -1.00 - 1.62 - 1.70 - 1.99 -2.50 - 3.28 -2.80 - 3.34 - 3.70 - 3.48 4.40 -4.04 - 5.20

-

6.4

8.2

3.85 0.95 (0.00)

3.75 0.64 (0.00)

2-10 0.22 (0.00)

- 1.95 - 2.60 - 1.67 - 2.05 - 3.06 - 1.69 - 2.80 -3.92 - 1.98 - 4.45 - 5.21 - 3.52 -4.90 - 5.56 - 3.52 - 5.20 -5.65 - 3.53 - 6.00 - 6.67 - 3.82

9.9

10.5

5.9

3.7 0.60 (0.00) 0-50 - 2.60 - 3.00 - 3.8 - 5.4 - 6.1 - 7.1 - 6.9

10-6

Hyperconjugation, Ehrenson (1961).

b Inductive effect, Ehrenson (1962). c Hyperconjugation+ inductive effect, Ehrenson

(1962).

Inductive effect, Flurry and Lykos (1963). Inductive effect, Dewar (1963). f Experimental values, Mackor (1958b). d

neglected. If a methyl group is substituted at a C-atom i, then the change of ionization energy of an alternant hydrocarbon is given as :

SI

=

C6q,.Su e

(54)

where Sq, denotes the change of n-electron density a t atom i on transition from the hydrocarbon to the positive ion. 6a is the change, caused by an inductive effect (-I), of the Coulomb integral of the C-atom a t which the methyl group is substituted.

296

H.-H. PERKAMPUS

x

According to (54), there is a linear relationship between 6 1 and 6qi. The slope of this straight line equals 6a. The required linearity is obeyed for a considerable number of compounds, as Dewar (1963) was able to show. The value of 6a is found to be 1.08 e.v. If the assumption that the substituents do not cause any great change of electron distribution is valid, and if one assumes that as a first approximation it is only the inductive effect of the methyl groups which causes the change of the Coulomb integral, then the additional stabilization energy can be specified as

AE

= +ni.6a

(55)

where ni is the number of methyl groups in the o- and p-positions relative to the methylene group in the ion. One thus finds that the basicity constant is given by:

AE RT

logKB-logK,,

= --

In calculating these relative basicity constants, the value of 0.34 e.v. was used for 6a. The results so obtained are listed in Table 28 in comparison with the values of Ehrenson (1961, 1962), Flurry and Lykos (1 963) and the experimental values of Mackor and collaborators (1958a, b). I n compiling this table, only values which could directly be compared with the experimental values were used. The table shows that the gradation is relatively successfully reproduced by all methods. The best agreement is given by the calculations of Flurry and Lykos (1963). This at the same time very clearly indicates that the greatest effect is to be ascribed to the inductive effect, and this is also reflected in the results of Ehrenson. Mackor et al. (1958b) had also interpreted the effect of the methyl groups as an inductive effect, in that they followed their HMO calculation by a perturbation calculation following the suggestion of LonguetHiggins (1951). The change of localization energy as a result of substitution is, according to Longuet-Higgins, given by

AE,

=

-CC;.~E

(57)

T

where ci denotes the coeficient of the non-bonding HMO’s in the proton addition complex, and the influence of alkyl substitution is taken to be additive. The sum should comprise all atoms r which are substituted. 6a has the same significance as in (54). As for (56), one finds that the

THE BASICITY O F UNSATURATED COMPOUNDS

297

change of the basicity constant K Oof the unsubstituted compound on substitution is given by : logK* -logK,* = - 26.4 cf Sa

2 r

Within the series of methylbenzenes, the effect of the methyl groups is very well reproduced by this relationship. Using the values for the squares of the coefficients and the experimental K-values, -Sa/,9 is found to have a value of 0.4. On taking hyperconjugation into account in the case of m-xylene, Sa/P is found to have a value of 0.08, which does not explain the difference log K - logKO= 6.5 (Mackor et al., 1958b). Similar results were obtained by Mackor et al. (1956) in the theoretical treatment of the effect of the methyl group position in isomeric methyl benz[a]anthracenes. The theoretical calculations therefore suggest that the greater importance is to be attributed to the inductive effect. I n this context, we would further draw attention to a general theoretical consideration by Longuet-Higgins (1955) as to proton affinity. Using perturbation calculations, an expression was deduced which represents the change in energy i f a proton is brought from an infinite distance up to an atom. The relationship so obtained applies universally and states that each non-positive atom has a certain proton affinity. I n order to be able to distinguish between the basicity of aromatic hydrocarbons, the change in electron density as a result of the field of the introduced proton has to be considered. This quantity is, according to Coulson and LonguetHiggins (1947), given by the “self-polarizability ” of the atoms, and permits a decision as to the position of greatest proton affinity, i.e. of greatest reactivity in a n-electron system. Simonetta and Heilbronner (1964) recently carried out calculations by the valence bond (VB) method for some simple cations, and compared the results obtained by this method, inter alia, with the results of Colpa and collaborators (1963) and of Koutecky and Paldus (1963). I n the case of the proton addition complexes of mesitylene and cycloheptatriene, the electron excitation energies calculated by the VB method agree very well with experiments, and also agree to a good approximation with the results of C I calculations. The calculations also successfully reproduce the electron density of the cycloheptatriene cation. I n this, a perturbation calculation allowed for the AO’s adjoining the -CH 2-CH 2-linkage. VI. SUPPLEMENTARY REMARKS The experimental and theoretical results summarized in the preceding sections were limited to a discussion of n-complexes, EDA complexes

298

H.-H. PERKAMPUS

and proton addition complexes in relation to the basicities of the unsaturated n-electron systems which may be deduced therefrom. Questions of reactivity of these systems could only be briefly touched upon, though the relationship between reactivity and basicity is of exceptional importance for the course and mechanism of numerous reactions. I n ternary systems, which, e.g., are present in Friedel-Crafts alkylation, the proton addition complex affects the course of the reaction as an intermediate (Gould, 1959;Perkampus and Baumgarten 1964d). since FriedelCrafts reactions have recently been thoroughly reviewed (Olah, 1963) a presentation in this context becomes unnecessary. Particular significance here attaches to H-D exchange processes, the speeds of which depend on the basicity of the aromatic substances. There is a linear relationship between the logarithm of the basicity constants and the logarithm of the velocity constants (Mackor et al., 1957; Dallinga et al., 1957; Lauer et al., 1958a, b ; Lauer and Stedman, 1958). As a result of this linear dependence, it is possible to determine the basicity of weakly basic compounds, such as benzene, from exchange experiments (Mackor et al., 1957). Thus the methods for the determination of the base constants are augmented by this kinetic method. Gold and Long (1953) investigated the H-D exchange in anthracene in sulphuric acid solution, this exchange again taking place via the proton addition complex. Gold and Satchel1 (1955a, b, c) suggested in addition the formation of an “outer complex” between the proton and the aromatic substance for the H-D exchange of benzene in aqueous sulphuric acid. According to Dallinga et al. (1957) the exchange speed should, however, be determined by the basicity of the aromatic substance in this case also. I n addition to these kinetic investigations, which were in part carried out with a view to the basicity of the aromatic substances, numerous investigations have also been carried out on the subject of electrophilic substitution of aromatic systems, and all of these ultimately show, directly or indirectly, a dependence on the basicity of the aromatic substance (cf. Mason, 1958, 1959; Gould, 1962; Brown and Stock, 1962). No attention has been paid to numerous spectroscopic investigations which are concerned with the interaction between substituted aromatic substances and proton acids or Lewis acids, and from which no basicity gradations have been deduced. Reference should, however, be made to N.M.R. spectra of methoxy-benzenes in acid solutions, where a proton addition complex is formed (MacLean and Mackor, 1962; Brouwer et al., 1965a, b, c, d, e). I n a summarizing treatment, Brouwer et al. (1965a) also quote pK,, values for various protonated hydroxy-

THE BASICITY O F UNSATURATED COMPOUNDS

299

derivatives of benzene. Whereas a proton addition complex is still formed with these substituents, the proton and the Lewis acid attack the NO2-group in nitrobenzenes (Hoffmann, 1964). The proton is also added to the substituent group in the case of I-formyl- and I-nitroazulene (Long and Schulze, 1964; Schulze and Long, 1964). I n the case of arylmethanols an OH-ion is eliminated, and a phenylcarbonium ion is formed. Olah (1964)and Farnum (1964)have published and discussed N.M.R. spectra of these ions. Finally, it should be pointed out that the question of connecting the pK,-values measured in the system anhydrous hydrofluoric acid + NaF and/or BFs, to the Hammett Ho-scale still remains. I n order to answer this question, Hyman and collaborators (1957) determined the H o function for the systems HF+H20 and HT+NaF. For the latter system, these authors obtained the following values :

and

H o = - 10.13 for pure HF, H o = - 9.62 for HF + 0.1 M NaF, H , = - 8.4 for HF + 1 . 0 Nap. ~

Since the Ho-values were determined spectrophotometrically on the basis of the same indicators as are usual for the H o scale in H2S04 (Hammett, 1940),these Ho-values may be qualitatively compared with data for the system H2S04-H20. Unfortunately, the measurements were not extended to lower H,-values, so that extrapolation to higher NaF or KF concentrations is extremely dubious. Transferring H,-values in H2S04-H20,in which one is dealing with a half-protonated aromatic substance, to the system HF + NaF is therefore beset with a large error. According to Den0 and collaborators (1959),hexamethylbenzene is halfprotonated at Ho= - 8.45. The corresponding pKB-value is - 1.4. According to Brouwer et ul. (19654 benzo[u]pyrene is half-protonated at an Ho-value of - 6-9 with the corresponding pKB-value being - 6.6. Here again, a comparison with the H,-values in H2S04-H20is difficult, since this Ho-value relates to the system H1F-ethanol. If one includes the data of Gold and Tye (1952b)for 1,l-diphenylethylene and those of Long and Schulze (1964) for the azulene derivatives, then the following order of basicity with reducing Ho-values may be quoted: t

Ho -

Halobenzenes < Benzene derivatives < Condensed aromatics Diphenylpolyenes < Azulene derivatives

-K

B

+

300

H . - H . PERKAMPUS

ACKNOWLEDGEMENT The author expresses his sincere thanks to Dr. C. MacLean and Dr. E. L. Mackor and to Professor H. C. Brown for making manuscripts available and for communicating unpublished results. REFERENCES Aalbersberg, W. Ij., Hoijtink, G. J., Mackor, E. L., and Weijland, W. P. (1959). J . Chem. SOC.(a)3049, (b) 3054. Anderson, H. D., and Hammick, D. L1. (1950). J . Chem. SOC.1089. Andrews, L. J.,and Keefer, R. M. (1949). J . Am. Chem. SOC.71, 3644. Andrews, L. J., and Keefer, R. M. (1951). J . Am. Chem. SOC.73,4169. Andrews, L. J., and Keefer, R. M. (1952). J . Am. Chem. SOC.74, 4500. Andrews, L. J., and Keefer, R. M. (1964). “Molecular Complexes in Organic Chemistry ”, Holden-Day Inc., San Francisco, London, Amsterdam. Baumgarten, E. (1962). Dissertation, Technische Hochschule Hannover. Baumgarten, E. (1964). Unpublished measurements. Bellamy, L. J. (1960). “The Infrared Spectra of Complex Molecules”, 2nd Ed., Methuen & Co., London. Benesi, A. H., and Hildebrand, J. H. (1949). J . Am. Chem. SOC.71, 2703. Bier, A. (1956). “Proceedings of the International Conference on Coordination Compounds”, 1955, Amsterdam, Rec. Trav. chim. 75, 866. Booth, D., Dainton, F. S., and Ivin, K. J. (1959). Trans. Faraday SOC.1293. Briegleb, G . (1961). “Elektronen-Donator-Acceptor-Komplexe”, SpringerVerlag, Berlin. Briegleb, G., and Czekalla, J. (1955). 2. Elektrochem. 59, 184. Briegleb, G., and Czekalla, J. (1959). 2. Elektrochem. 63, 6. Briegleb, G., Czekalla, J., and Hauser, A. (1959a). 2. physik. Chem. N.F. 21, 99. Briegleb, G., Czekalla, J., and Hauser, A. (195913). 2. physik. Chem. 21, 114. Briegleb, G., Czekalla, J., and Reuss, G. (1961). 2. physik. Chem. N.F. 30, 333. Bronsted, J. N. (1932). Rec. traw. chim. 42, 718. Brouwer, D. M., Mackor, E. L., and MacLean, C. (1965a). I n “Arenonium Ions”; Report from the Koninklijke/Shell Laboratorium, Amsterdam. Brouwer, D. M., MacLean, C., and Mackor, E. L. (196513). Disc. Faruduy SOC. Brouwer, D. M., Mackor, E. L., and MacLean, C. (19654. Rec. truw. chim. I n press. Brouwer, D. M., Mackor, E. L., and MacLean, C. (1965d). Rec. trav. chim. I n press. Brouwer, D. M., Mackor, E. L., and MacLean, E. (196%). Rec. traw. chim. I n press. Brown, H. C., and Brady, J. D. (1949). J . A m . Chem. SOC.71,3573. Brown, H. C., and Brady, J. D. (1952). J . A m . Chem. SOC.74, 3570. Brown, H. C., and Melchiore, F. F. (1966). J . Am. Chem. SOC. I n press. Brown, H. C., and Pearsall, H. W. (1952). J . Am. Chem. SOC.74, 191. Brown, H. C., and Stock, L. M. (1962). J . Am. Chem. SOC.84, 3298. Brown, H. C., and Wallace, J. W. (1953a). J . Am. Chem. SOC.75, 6265. Brown, H. C., and Wallace, J. W. (195313). J . A m . Chem. SOC.75,6268. Clar, E. (1952). I n “Aromatische Kohlenwasserstoffe ” 2. A d a g e , SpringerVerlag, Berlin. Clar, E. (1959). Tetrahedron 5, 98; 6, 355. Colpa, J.-P., MacLean, C., and Mackor, E. L. (1963). Tetrahedron 19, Suppl. 2, 65. Condon, F. E. (1948). J . A m . Chem. SOC.70, 1963. Cook, D. (1956). J . Chem. Phys. 25, 788.

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SPECTROSCOPIC OBSERVATION OF ALKYLCARBONIUM IONS IN STRONG ACID SOLUTIONS GEORGE A. OLAH and CHARLES U. PITTMAN, JR.

Department of Chemistry, Western Reserve University Cleveland, Ohio, U.S. A . I. Introduction . . 11. Remarks on Nomenclature . . 111. Alkyl HalideLewis Acid Halide Systems . A. General Observations . . B. The Alkyl Fluoride (Chloride)-Antimony Pentafluoride System . . IV. Alcohols and Olefins in Strong Bronsted Acids A. Electronic Spectra in Sulphuric Acid B. The Fate of Precursors in Sulphuric Acid Systems . C. The Fluorosulphonic Acid-Antimony Pentafluoride and the Hydrogen Fluoride-Antimony Pentafluoride Solvent Systems V. CyclopropylcarboniumIons . . . VI. AlkylarylcarboniumIons References .

.

. .

.

. . . . .

305 307 307 307 309 324 324 328 331 333 338 346

I. INTRODUCTION SIMPLE alkylcarbonium ions that have been discussed in the chemical literature were considered until very recently only as transient entities. Their existence had been inferred from the study of the course of certain reactions. No reliable physical measurements other than electron impact measurements were reported until recently for any of the simple alkylcarbonium ions. The formation of gaseous organic cations under electron bombardment of alkanes, haloalkanes and other precursors has been widely investigated in mass spectral studies (Field and Franklin, 1957 ; McLafferty, 1963). Measurements by electron impact methods have led to experimental stabilization energies of a number of alkylcarbonium ions. Muller and Mulliken (1958) compared these with calculated values obtained by a procedure based on the LCAO-MO approximation, the large stabilization energies found for carbonium ions being attributed to the combined effects of hyperconjugation and charge redistribution (Table 1). The heat of formation, A H f , of a series of alkylcarbonium ions from

306

G . A . O L A H A N D C . U . P I T T M A N , JR.

electron impact data calculated by Field and Franklin (1957) from their tabulated data is shown in Table 2. From the AHfvalues in Table 2, it can be seen that the isopropyl cation is more stable than the n-propyl cation by some 26 kcal mole-I. Similarly the t-butyl cation is substantially more stable than any of the other butyl cations, as is the t-pentyl cation compared with any of the other pentyl cations. These considerations are based upon the energetics of ions in the TABLE1 Stabilization Energies of Alkylcarbonium Ions in kcal mole-]

CH: CH3. CH: CH3. CH+.CH3 (CH3)3C+ CH2==H=CH,f

0bserved

Calculated

0

0 41 66 83 64

36 66 84 58

TABLE2 Heat of Formation of Alkylcarbonium Ions, AHt

AH1 kcal mole-1

AHt kcal mole-'

CH: CH3. CH; CH3. CHz .CH; CH3.CH+.CH3 CH3. CH2.CHz .CHZ CH3. CHz .CH+.CH3

262 224 216 190 207 181

(CH3)&+ (CH1)zCH.CH: (CHa)3C.CH; (CH3)2C+.CH2CH3 (CH3)zCH.CH.CH3 CHz==H==CHt

166 21 1 194 152 170 220

gas phase and as such can give only qualitative interpretations for their behaviour in solutions. It would, of course, be very useful if the energies of the ions in solution were available. Unfortunately, the heats and entropies of solvation of gaseous ions have never been measured directly. However, several methods of estimating the energies of solvation have been proposed. These methods are of course approximations, but they have provided some insight into the behaviour of ions in solution (McLafferty, 1963). Evans (1946) calculated the solvation energy of a number of alkyl-

ALKYLCARBONIUM IONS: SPECTROSCOPIC OBSERVATION

307

carbonium ions. He assumed that the carbon atom would be in an sp2 state of hydridization and would thus be planar. The ion would be solvated by one molecule of the solvating agent (water) each above and below of the plane of the charged carbon and by two molecules in the plane of the ion. With the aid of bond lengths and van der Waals radii, the in-plane and out-of-plane energies were estimated separately and the total solvation energy could thus be determined. Franklin (1952) estimated the solvation energies of several carbonium ions using graphically determined average ionic radii. The solvation energies were somewhat different from those estimated by Evans, but the conclusions concerning stabilization of the ions by solvation were similar.

11. REMARKS ON NOMENCLATURE There exists no general agreement on the nomenclature of carbonium ions. Both the “carbonium ion” and “cation” nomenclatures are used intermittently. Although the use of both of these naming systems is admissible, certain basic rules must be obeyed. Using the carbonium ion nomenclature the electron-deficient carbon atom is named as the “carbonium ion ” and the attached ligands by their usual names. Accordingly the ion 1 is the trimethylcarbonium ion. The same ion, . using the cccation”nomenclature, which is based on the naming of the parent hydrocarbon, is the t-butyl cation. From the foregoing it is, however, obvious that the ion 1 cannot be named the t-butyl carbonium ion, which is the alternative name for the neopentyl cation 2. CH3

I CHs-C+ I

CH3

I I

CH3-C-CHZ

CH3

CHs

1

2

111. ALKYLHALIDE-LEWISACIDHALIDESYSTEMS A. General Observations The transitory existence of alkylcarbonium ions in alkyl halide-Lewis acid halide systems has been inferred from a variety of observations, such as vapour-pressure depressions of CH,CI and C2H5C1in the presence of gallium chloride (Brown et al., 1950), the electric conductivities of aluminium chloride in ethyl chloride (Wertyporoch and Firla, 1933) and of alkyl fluorides in boron trifluoride (Olah et al., 1957), as well as the

a. A .

308

O L A H A N D C . U. P I T T M A N , J R .

effect of ethyl bromide on the dipole moment of aluminium bromide (Fairbrother, 1945). However, in no case have well-defined stable ionic salts or complexes been established, even at low temperatures. Byrne (1958) reported that methyl chloride forms 1 : 1 compounds with stannic chloride (CH3C1:SnCl,, dissociation pressure 40.3 mm at - 64", calculated m.p. -5O", heat of formation -4.69 kcal mole-l) and antimony pentachloride (CH3C1:SbCl,, dissociation pressure 6-5 mm at -5O", calculated m.p. go", heat of formation -8.92 kcal mole-l). Nelson subsequently (1962) investigated the infra-red spectrum of methyl chloride in stannic chloride solution (at 30" and -40") and antimony pentachloride solution (at 28" and -12'). No evidence of compound formation was found in the CH,Cl-SnCl, solutions. A temperature-dependent band at 688 cm-l in the CH3C1-SbCl, solutions was assigned to the C-Cl stretching motion in the CH3C1:SbC1, addition compound. The spectra of the CH3C1-SbC15 solutions are consistent with a linear C-C14b bond in CH3C1-SbCl, but the evidence is insufficient to rule out an angular bond which seems more probable from other considerations. The results suggest that the CH3Cl:SnCI, and CH3Cl:SbC15 addition compounds are more accurately described as slightly polarized donor: acceptor complexes than as ion pairs. Alkyl fluoride :boron trifluoride systems were first investigated by Olah et al. (1957). 1 : 1 Addition complexes were observed a t low temperatures, and their specific conductivity was measured. The specific conductivity of the propyl and butyl fluoride :boron trifluoride systems was found three orders of magnitude larger than those of the methyl- and ethyl-fluoride systems. The latter systems on heating dissociated into their starting materials, whereas the former gave polymer mixtures (Olah, unpublished). Nakane et al. (1964) established equilibrium constants of boron isotope exchange between boron trifluoride gas on one side and boron trifluoride : methyl fluoride, methyl chloride, isopropyl chloride and t-butyl chloride. The value of the equilibrium constants, which represents the thermodynamic isotope effect,was related to the polarity, stability and catalytic activity of the complexes. The results indicated that all the investigated complexes are only polarized covalent complexes and the polarity of these Complexes decreases in the order 8-

8+

8-

84-

8-

8+

8-

8+

BF, +CIC(CH3)3 > BF3cFCH3 > BFs+-CICH(CH3)2, BF3cClCHa

In more recent work (1965) Nakane et al. extended their investigation also to boron trifluoride :ethyl fluoride and boron trifluoride :isopropyl

ALKYLCARBONIUM IONS: SPECTROSCOPIC

OBSERVATION

309

fluoride systems. They found these systems also to be donor acceptor complexes in order of polarity a+

8-

8+

8-

BF3-+PCH(CH& > BF3cFCHzCHs

The boron trifluoride :alkyl fluoride (chloride) complexes gave no evidence of alkylcarbonium ion formation. It must, however, be emphasized that ( a )the physical investigation of the binary system was carried out at such low temperatures (generally below -100') that ionization of the halides could hardly be expected (with exception of highly reactive tertiary halides); (b) the methods used could not be relied on to detect a small ionization equilibrium even if it existed. The fact that the boron trifluoride :t-butyl fluoride (and chloride) system and the boron trifluoride :isopropyl fluoride systems on thermal decomposition yielded polymer mixtures may indicate the equilibrium in equation (1). On measuring absorption spectra of boron trifluoridea+

8-

BF3 + FC(CH&

$

BFCC+(CH&

+ HBF4+CH2 = C(CH3)z

(1)

methyl, ethyl, isopropyl fluoride and isopropyl and t-butyl chloridecomplexes no absorption bands were reported above 220 mp. Finally, these workers found that the polarity of alkyl halide boron trifluoride complexes (hence the electron deficiency of polar cations in the complex) decreases in the order : 8+

8+

8-

8-

8+

8-

8+

8-

(CH3)2CHF---BFa > CH3. CHzF---BFa > (CH3)3CCl---BF3> CHsF---BFs 8+

8-

8+

8-

(CH3)2CHCI---BFs> CHaCI---BFs

B . The Alkyl Fluoride (Chloride)-AntimonyPentaJlwwideSystem Attempts to obtain alkylcarbonium complexes by dissolving alkyl chlorides (bromides) in liquid Lewis acid halides (stannic chloride, titanium (IV) chloride, antimony pentachloride, etc.) as solvent were unsuccessful. Although stable solutions could be obtained at low temperature with, for example, t-butyl chloride, the observed N.M.R. chemical shifts were generally not larger than 0.5 p.p.m. and thus could be attributed only to weak donor-acceptor complexes, but not to the carbonium ions. The negative result of these investigations seems to indicate that either the Lewis acids used were too weak to cause sufficient ionization of the C-C1 bond, or that the solvating effect of the halides

310

G. A . O L A H A N D

U. PITTMAN, J R .

was not sufficient to stabilize the carbonium ion salts formed (an equilibrium containing a certain concentration of the carbonium ion cannot be excludedin any of these systems, but in order to obtain suitable N.M.R. spectra a concentration of 3-4% of the carbonium ion would bo needed). It is possible that the donor (base) strength of the alkyl halide also plays an important role. This could explain why alkyl fluorides were found to ionize more readily than chloridesor bromides. The bond energy of the C--F bond to be cleaved is compensated for by the bond energy of the metal-halogen bond to be formed in the case of ionization with the Lewis acid halide catalysts. It is rather unfortunate that owing to halogen exchange alkyl fluorides generally cannot be used in investigations involving other halogen-containing Lewis acid halides. Olah and co-workers in 1963 fist observed the formation of stable alkylcarbonium ion complexes when t-butyl fluoride was dissolved in excess antimony pentafluoride (serving as both the Lewis acid and the solvent). They had also found that t-butyloxocarbonium (pivalyl) hexafluoroantimonate easily loses carbon monoxide in sulphur dioxide solution even at low temperature, and a new, electron-deficient species, the trimethylcarbonium ion, is formed (CH3)3CCO+SbFc 3 CO

+ (CH3)&+Sbl?c

In order to establish the identity of the trimethylcarbonium ion, the t-butyl fluoride-antimony pentafluoride system was investigated. It was found that when the vapour of t-butyl fluoride was passed over the surface of purified liquid antimony pentafluoride (with exclusion of moisture and oxygen) a stable complex layer is formed on the top of the antimony pentafluoride. When this layer was separated and its proton magnetic resonance investigated (see subsequent discussion) the spectrum was found to be identical with that of the least-shielded species formed by decarbonylation of the t-butyloxocarbonium salt (CH3)3CF+SbFs Z? (CH3)3C+SbFc

The possibility of obtaining stable alkylcarbonium hexafluoroantimonate salts by interaction of alkyl fluorides with antimony pentafluoride (neat or in sulphur dioxide and later in sulphuryl fluoride or sulphuryl chloride fluoride solution) was then evaluated in detail, extending the investigations to all isomeric C3-, C4-, Cg- alkyl fluorides. Propyl, butyl and pentyl fluorides gave with excess antimony pentafluoride substantially stable ionic complexes (see subsequent discussion of spectroscopicinvestigations). The complexes always contained excess antimony pentafluoride over that needed for the 1 : 1 complex formation,

ALKYLCARBONIUM IONS: SPECTROSCOPIC

+

OBSERVATION

311

.

C3H7F SbFs Z CHa CH+.CH3 SbFF

+

C4HgF SbF5 Z? CH3-C+-CH3

SbFc

I

CH3 C ~ H I+ ~ SbFs F Z CH3-C+-CH2-CH3

SbF,

I

CHI

It was indeed found necessary to have excess antimony pentafluoride present in order to obtain stable alkylcarbonium hexafluoroantimonate complexes. Antimony pentafluoride is a liquid Lewis acid fluoride (b.p. 148-150”) of low dielectric constant ( E N 3), which has been shown by fluorine N.M.R. studies in the pure liquid state and in solution to exist in both cyclic and acyclic polymeric forms involving fluorine bridges. The antimony is in approximately octahedral co-ordination with predominant bridging by coordinating fluorines (Gillespie and Rothenbury, 1963). As fluorine generally does not show bridging properties, the structure of antimony pentafluoride itself indicates the very

high acidity and co-ordinating ability of the compound. The conjugate acid HSbF, at a concentration of 3~ has a Hammett acidity function H o value of -15.2 (in HF) indicating again the very high acid strength (Olah, 1963). The high Lewis acidity of antimony pentafluoride obviously causes the easy cleavage of the C-F bonds of alkyl fluorides, together with the energy of Sb-F bond formation compensating that of the cleavage of the C-F bond. The role of excess antimony pentafluoride can best be explained by assuming that it is capable of solvating the alkylcarbonium ion salt through interaction of the unshared electron pairs of fluorine with the vacant p-orbital of the sp2-hybridizedplanar central carbon atom of the carbonium ion. I n the system of low dielectric constant the alkylcarbonium ion is present not in the “free” form, but as a tightly bound ion-pair ; solvation affects this species rather than the free ion. 1. Nuclear magnetic resonance spectra

(

a. Proton resonance. Methylfluoride when absorbed into a cold solution - 60’) of antimony pentafluoride in sulphur dioxide show no evidence

N

312

0 . A . O L A H AND C . U . PITTMAN, J R .

of ionization to CHg. The proton magnetic resonance spectrum however indicates a slightly deshielded species, in all probability the polarized covalent complex, 8-

8+

SbFsc FCH3

When methyl fluoride was absorbed into neat antimony pentafluoride at room temperature a low field band a t - 12.5 p.p.m. appears. The relative intensity of this species compared with the covalently polarized methyl fluoride complex is, however, small and it could originate from impurities in the system. CI3H3CI in SbF6 shows no evidence of ionization, based on C13resonance investigations, but only a moderate deshielding effect due to polarized complex formation 8-

8+

SbFsc ClCH3

No similar investigation with C13H3Fhas so far been carried out. Ethyl Jluoride shows more tendency to ionize in antimony pentafluoride, than does methyl fluoride. The solutions in neat antimony pentafluoride are, however, not stable and a rapid formation of t-butyl and t-hexyl cations is observed. This observation indicates self alkylation of ethylene formed in equilibrium of equation (2).

+

CHs. CHzF SbFs Z CH3. CH: SbFT

Z?

CHz=CHz +HSbFe

1

CHsCHn+

CeH&

CHa=CHa

(2)

(CH3)3C+ c [CH~-CHZ-CHZ-CH.$]

IsopropylJluoridegives a substantially stable ionic complex with excess antimony pentafluoride (see Table 3). n-Propyl fluoride in antimony pentafluoride gave the identical secondary carbonium ion complex.

+

.

CsH7F SbF5 Z? CH3. CH+ CH3SbFT

(3)

i.e. dimethylcarbonium ion). The proton spectrum of the antimony pentafluoride complex of isopropyl fluoride in excess antimony pentafluoride is displayed in Fig. 1. It represents a spectrum obtained on a Varian A60 instrument without temperature control, at an average probe tempera-

A L P Y L C A R B O N I U M I O N S : SPECTROSCOPIC O B S E R V A T I O N

313

ture of about 37'. It illustrates the high stability of the carbonium ion complexes in the antimony pentafluoride solvent system even at this TABLE3 Proton Magnetic Resonance of Isopropyl Fluoride and its Antimony Pentafluoride Complex (in SbF5)

JHF

~R-F

R

CH3-CH-CH3

I

F

8bFr

(p.p.m. from TMS)

c.p.8.

(p.p.m. from TMS)

- 1.23

23.5

- 5.06

- 4.64

48

Peak area ratio

- 13.5

5.95: 1

TABLE 4 Proton Magnetic Resonance Shifts of t-Butyl Fluoride and its Antimony Pentafluoride Complex (in SbFS)

R

8R-F

JIIF

8R+8bFs-

(p.p.m. fromTMS)

(c.P.s.)

(p.p.m. fromTMS)

- 1.30

20

- 4.35

CH3

I

CH3--CF

I

CH3

temperature. The resolution of the isopropyl cation under these conditions is not very good (due to obvious exchange) but still the methyl group is a fairly well resolved doublet at - 5.06 p.p.m. with the CH group being an only partially resolved septuplet at - 13.5 p.p.m. The resolution improves when the temperature is lowered, but exchange is still appreciable at + 2", the lowest temperature obtainable owing to the relatively high freezing point of SbF,. For the study of the trimethylcarbonium ion, the system t-butyl fluoride :antimony pentuflwwide was investigated (Olah et al., 1964b) (see Table 4). 11

0. A . O L A H A N D C . U . P I T T M A N , J R .

314

t-Butyl, s-butyl, isobutyl and n-butyl$uorides all gave the same tertiary carbonium ion complex (i.e. trimethylcarbonium ion). Figure 2 shows the spectra for t-butyl fluoride with the corresponding ionic complex. t-PentylJEuoride in antimony pentafluoride at room or slightly elevated temperature gives only one hybrid band around - 4.6 p.p.m. Taking the

A

(CH,),

), (CH,),

CF in SbF, at 60 M c

CF neat

c

C-CH3

C-CH, J n ~ 2 0CPS

jj

'I $ h

'I

II

I1 II

FIG.2.

spectrum a t 0"-2" gave only partial resolution, as shown in Fig. 3A. Substantial exchange in the CH2.CH, group is not sufficiently slowed down a t this temperature. Use of the sulphur dioxide dilution technique allows the temperature to be lowered further: it avoids freezing of antimony pentafluoride (antimony pentafluoride solutions freeze around 0") and leads to non-viscous solutions. Figure 3B shows the proton spectrum of t-pentyl fluoride: SbF,: SO2 system at -3O", with good resolution of the dimethylethylcarbonium ion (t-pentyl cation). This

ALKYLCARBONIUM IONS: SPECTROSCOPIC OBSERVATION

315

spectrum was obtained on a Varian A-60 spectrometer using a lowtemperature probe. It is interesting to find strong coupling of approximately 7 c.P.s., of the (CH,),C+ protons through the sp2-hybridized positive carbon, to the methylene protons, resulting in a well-resolved triplet.

I

I

7

+

CH3-C-CH2CH3

I

CH3

I

5

6

I

4

-

I 3

2

SbFs in

1

SO2-SbF?!f,

1

I

I

I

I

I

I

6

5

4

3

2

1

0

ppm (6)

FIG.3.

Seven isomeric pentyl fluorides, including neopentyl Jluoride, gave the same tertiary carbonium ion (i.e. dimethylethylcarbonium ion, Table 5). Thus, in the strongly acidic antimony pentafluoride, complete

G . A . O L A R A N D C . U. P I T T M A N , J R .

316

isomerization to the thermodynamically most stable carbonium ion takes place, and this is the only ion observed. (CHs)zCP.CH2. CHa (CH3)zCH.CHF .CH:,

&?+

(CH3)2C‘H.CH2.CHzF

.

CH3. CH2. CHz .CHz CHzF -(CHa)aC

. a s. a s

(3)

.

CH3.CHs .CHB CH2. CH3’

A systematic investigation of the CBto CIScarbonium ions is currently being carried out in our laboratories. Extension of the carbonium ion formation method to the use of FS03H-SbFb and HF-SbF5 allows the formation of stable carbonium ions from precursors such as alcohols, olefins (Olah et al., 1964, 1965) and tertiary hydrogen-containing alkanes and cycloalkanes (Brouwer and Mackor, 1964). The experimental observations point to the fact that, in the strongly acidic solvent system used, the isomeric precursors all isomerize to give tertiary carbonium ions in which two methyl groups are directly attached to the electron-deficient carbon atoms, the remaining carbon chain showing branching. TABLE 5 Proton Magnetic Resonance of t-Pentyl Fluoride and its Antimony Pentafluorirle Complex (in SbFs-SOZ) horide

(p.p.m. from TMS)

CH3-GCH-CH3

I

CHI

- 1.25 - 1.55 - 1.85

&carbonlum Ion

JHF

(p.p.m. from TMS)

0.5

- 2.27 - 4.50 - 4.93

20 24

Relative peak areas

2.96:5.97 :2

Some of the stable carbonium ions we were able to obtain and the structure of which was established (N.M.R. spectra) are shown in Table 6.

ALKYLCARBONIUM

IONS: SPECTROSCOPIC

OBSERVATION

317

TABLE 6 Stable Tertiary Alkyl Carbonium Ions

CH3

CH3

CS

CH3 CH3 C8

c7

CH3 CHs CH3 + I I \C--C--C-CHa CHI’ I 1 CH3 CH3

CH3 CH3 CH3 -C-C--C--CH3 CH3 CH3 CH3

c13

ClO

b. Deuterium r a m n c e . I n order to obtain further evidence for the validity of assignment of the proton shifts to the investigated alkylcarbonium ions, the corresponding completely deuteriated carbonium ions were prepared and their H2 resonance spectra were obtained (Olah et al., 1964b). Perdeuteriated isopropyl, t-butyl, and t-pentyl fluorides were prepared from the corresponding deuteriated alkyl chlorides (bromides) by halogen exchange. The perdeuteriated alkyl fluorides were then used in the formation of the deuteriated carbonium ions under similar conditions as those for the protium complexes. The H2 resonance spectra were obtained at 9.2 Mc/s and the data are summarized in Table 7 The data indicate good agreement with those of the H1resonance data. TABLE7 H2 Resonance of Deuteriated Alkylcarbonium Ions [at 9.2 Mc/s; 6 in p.p.m. from (CD&Si]

4 D 3

(CDs)sC+SbF; (CDs)&D+SbFT (CD3)&+.CDz.CDaSbF;

-4.35 4.90 -2.25

-

-CDz

-4.47

- 4.89

4

D

- 13.48

318

G . A . OLAH A N D C . U . P I T T M A N , J R .

Thus it was possible to reproduce the chemical shifts of the alkylcarbonium ions in an independent system ; when corrected for the ratio of magnetogyric ratios the chemical shifts are well in the limit of experimental error. c. Fluorine-19 rmonance. The main feature of the observed proton spectra of alkyl fluorides in antimony pentafluoride is the very substantial deshielding of the protons in the carbonium ions as compared with the starting alkyl fluorides. No H-F coupling was observed in any of the spectra of the carbonium ion complexes, which would, of course, not be expected in the ionic forms (where the covalent C-F bond of the starting alkyl fluorides must be cleaved). However, this observation can be used only as supporting, but not as conclusive evidence for the ionic dissociation. Fast exchange in a highly polar donor: acceptor complex, in the strongly acidic solvent, could equally well result in the absence of observable H-F coupling. The Fl9 spectra of the carbonium hexafluoroantimonate complexes indicated the absence of covalent C-F bonds in accordance with the uniformity of fluorine atoms in the ionic SbF; forms. However, there is no evidence to exclude the possibility of an exchanging, highly polarized -F+SbF5 system. The possibility of fluorine exchange in a highly polarized complex of the type R-F+SbF5, where the C-F bond must be considerably weakened (and in the limiting case ionized), must be considered. There is also a possibility of exchange involving solvent SbF,. Fluorine resonance probably cannot differentiate between a line due to S b K and one corresponding to an exchanging F-tSbF, system. Attempts were made to see if, owing to decreased exchange, differences are observable a t lower temperature, but this was not the case. d. Carbon-13 resonance. To confirm that stable, solvated alkylcarbonium hexafluoroantimonate complexes were obtained, C13resonance investigations were carried out of complexes in which the potentially electropositive sp2 carbon atom was C13-1abelled. Data obtained are shown in Table 8 (as it was found that tertiary alkyl chlorides generally ionize well in antimony pentafluoride, i t was possible to carry out the investigation with (CH3)3C13C1without preparing the fluoride). (Olah et al., 1964b.) The observed very substantial shift of the C13 resonance line in the trimethylcarbonium complex, as compared with the position of the C13 line in the starting covalent sp3-hybridized halide, amounting to 373 p.p.m., is difficult to interpret in any other way than as a direct proof (a) that the state of hybridization of the carbon atom involved is changed in the complex to sp2 and, at the same time, ( b ) that the carbon atom carries a substantial positive charge.

ALKYLCARBONIUM IONS: SPECTROSCOPIC OBSERVATION

319

TABLE 8 C13-H Indor Resonance of the (CH3)3C13+ Ion

. . . . . . . . BcLa (from (CH3)3CWl) . . . from (CH3)3CWl) . . . (CH3)3CW1 at

(CH3)&13+SbF,at .

. . . .

15.090440 Mc/s (CH3 at 60.0097848 Mc/s) 15.094530 Mc/s (CH3 at 60.0099475 Mc/s) 4090 c.p.s.-273 p.p.m. 162.6 c.p.s.-2.7 p.p.m.

The investigations were also extended to the triphenyl-C13-carbonium ion (Olah et al., 1964a), where charge delocalization through conjugative interaction with the three benzene rings was expected to decrease the C13-chemicalshift of the carbonium ion, as compared with that of the trimethylcarbonium ion. Labelling the aliphatic carbon atom with C13 (53%) allowed comparison of the nuclear magnetic C13-shifts of the covalent sp3-hybridized triphenyl-C13-methanol (in tetrahydrofuran solution) with that of the labelled triphenylcarbonium ions, (C,H,) 3C13+HSOy (triphenyl-CI3methanol in sulphuric acid solution). A shift of 129.6 p.p.m. to lower shielding was observed in the triphenylcarbonium ion, as compared with the covalent triphenylmethanol. To assess, at least qualitatively, how much of the observed shift in the triphenylcarbonium ion is due to the change of hybridization from sp3to sp2and how much to the effect of the positive charge, a comparison of the chemical shifts of the triphenyl-C13-carbonium and trimethyl-C13carbonium ions with their parent sp3-hybridizedcovalent precursors and with some C'3-compounds having sp2-hybridization is useful. Data of Table 9, indicate that the C13-shifts of sp2-hybridized compounds (olefins and aromatic hydrocarbons), at least in the molecules studied (Lauterbur, 1957,1962), are very similar and fairly independent of the nature of the molecules. Assuming that the C13-shiftof an uncharged sp2-hybridizedcompound corresponding to a planar carbonium ion should be around + 65 p.p.m. (from CS2 as reference), the observed C13-shift at - 18.1 p.p.m. in the triphenylcarbonium ion shows the additional deshielding effect (about 80 p.p.m.) of the positive charge. As the positive charge is much more delocalized in the triphenylcarbonium ion than it is in the trimethylcarbonium ion, the larger deshielding effect observed in the case of the latter is to be expected. The comparison of charged sp2-hybridized carbonium ions with uncharged sp2-hybridizedhydrocarbons (or their derivatives) does not take

320

0. A . O L A H A N D C . U. P I T T M A N , JR.

into account the possible effect of the anisotropy of the magnetic susceptibility of the sp2-carbon atoms. Only the "chemical " substituent and electronegativity effects are taken into consideration, resulting in the expected low fieId shifts. However, with p-orbitals, there is a TABLE 9 C13 Chemical Shifts of Some Representative apz-Hybridized Compounds (In p.p.m. from CSz &B reference) Compound

Solvent

(CH3)3C13+SbF, (C~HS)~C'~+HSO, Cyclohexene(-CHi3= =CHz--) C H z 4 ' 3 H . CO .OH C13Hz===CH.CO .OH CHCI==CHCl(c i a ) Benzene Naphthalene Mesitylene (2,4,6-) Mesitylene (1,3,5-)

SbFs/SOz

,a,

- 146.9 - 18.1

+ 67 + 64 + 60 + 71 + 65 + 65 + 66 + 55

neat neat neat neat neat

csz neat neat

TABLE 10 Proton-C'3 Spin-Spin Coupling Constants of Secondary Carbonium Ions and their Parent Hydrocarbons

J C L l -11

(CH3)&1aHz (CHs)zC'SH+SbFsCl(caH~i)zC~~Hz (C&,)aCl3H+SbF&l-

Calculated percentage State of c.p.8. a-character hybridization

108 168 126 164

25.6 33.6 25.2 32.8

8P3 aP3 SP2

possibility of paramagnetic contributions, and these could cloud somewhat the attractive electron withdrawal argument. The anisotropy effect is known to be significant with sp-hybridized compounds, but probably less important in the case of sp2-hybridization. The C13-resonanceinvestigations also provide a further possibility in the investigation of the carbonium ion complexes through evaluation of

A L K Y L c A R B O N I U M ION

s:

S P E c T R o sc o P I C

o B sE RVATI oN

321

the C13-Hcoupling values. The coupling data are shown in Table 10 for the isopropyl and benzhydryl systems. Numerous investigations have been directed toward elucidation of the factors affecting proton - ClS coupling. The general linearity between JCl,-=and fractional s-character of the C13 hybrid atomic orbital has led to the conclusion that the Fermi contact term is essentially the sole contributor to the coupling, as suggested from the valence bond theory. The linearity between JCL,-H and fractional s-character of the C13 hybrid atomic orbital is also valid in the case of positively charged carbon atoms. The s-character observed is in excellent agreement with the suggested sp2-hybridization of the involved carbonium ions (Olah et al., 1966). 2. Infra-redspectra

The infra-red spectra of the trimethyl, dimethyl- and dimethylethylcarbonium salts in excess antimony pentafluoride are shown in Figs. 4a, b, and c. The IRTRAN cells used are not transparent below 770 cm-l, thus obscuring the 650 cm-l SbF;;- absorption which would, however, be overlapped by the solvent SbF, absorption. The broad, intense absorption band which appears in all the spectra near 1550 cm-l is present in the solvent spectrum. It was found to be dependent on the purity of the SbF5,but the nature of the impurity was not established. It should also be mentioned that Den0 found an intense absorption at 1533 cm-l in cyclohexenyl cations : thus, secondary carbonium ions formed from the reaction with olefins (which arise from deprotonation) could add to this broad absorption. Using assumed molecular models and force constants based on the force constants derived from the paraffin series, normal co-ordinate calculations for the simple alkylcarbonium ions were carried out. These calculations were made in order to predict the vibrational spectra. Comparison with the experimentally obtained infra-red spectra show that the main observed features can indeed be reasonably explained in terms of the modes calculated for the planar models of the ions and allowed an assignment of the fundamentals (Table 11). The following conclusions can be established from the infra-red spectra : (a) the G-H stretching fundamentals are exceptionally low in frequency ; (b) the asymmetrical stretching mode of the carbon skeleton is exceptionally high in frequency.

G . A . O L A H A N D C. U. P I T T M A N , J R .

322

The exceptional features can be reasonably interpreted in terms of the planar structure of the alkylcarbonium ions, H

VHS

CH3

I

/(’iCH3 CHs

I

/Y CH3 CH3

CH3

(’H3

Wovelength ( p )

2.5

3

4

5

7

6

8

9 10

12

15 l

20 25 I J

U al

6 40-

c c

.-

5

P

200-

4000

I

I

3000

2000

1600

1200

400

800

Frequency (crn-’1 Wavelength ( p )

2.5

7

-5

c .-

E

P

I-

looL

3

4

5

6

I

I

I

I

I

40-

7

8 I (CD3)&D

-___ I

9 10

12

I I I SbFz in SbF5

15 20 25 I

1

-

-

I

20O r 4000

I

3000

2000

400

800

1200

1600

Frequency (crn-’) Wavelength ( p )

2.5

4

3

5

6

7

8

I (CD3),E

9 10 I

1

12 I

15

I CD2CD3 S b F i in SbF5

20 25 1:

-

c .-

4000

3000

2000

1600

Frequency (crn-’)

FIQ.4.

1200

800

-l

400

ALKYLCARBONIUM IONS: SPECTROSCOPIC OBSERVATION

TABLE11 Infra-red Fundamental Frequencies of Alkylcarbonium Hexafluoroantimonate Complexes and their Assignment Trimethylcarbonium Ion (t-butyl cation)

(CH&C+ 2830 s 2500 w 1455 w 1290 VB 1070 m 962 mw ( N 1300) obscured

v7, v12

Assignment"

(CD3)3C+

CHI stretch

2062 s

us, +v9 CH3 deformation CCC asym. stretch US, CH3 rocking V 1 7 , CH3 rocking v15, CH3 deformation YE, Y14

N

Y16,

1050 vw 1330 s 955 s

Dimethylcarbonium Ion (isopropyl cation)

CH3 stretch in-plane bend V I E , CCC asym. stretch Yg, mixed mode v?, mixed mode

2730 s 1499 s 1260 s 1175 w 930 vw

2013 8 930 s 1378 s

v g , v2

Y16, CH

Dimethylethylcarbonium Ion (t-pentylcation)

(CH3)2C+CHz.CHa

2815 s 2505 w 1463 s 1295 s 1065 w 935 w ( 1300) obscured N

Assignment"

CH3 stretch 1463+1065 CH3 deformation CCC asym. stretch CH3 rocking CHI rocking mixed mode

(CD3)2C+CDz.CD3

2071 8 N

1060 vw 1377 s 964 s

Descriptions are based on the calculated potential energy distributions for the trimethyl and dimethyl carbonium ions.

323

324

0 . A . OLAH A N D C.

U. P I T T M A N , J R .

since we may assume a number of resonance structures such as

contributing. The effect of these structures is to : (a) lower the C-H bond strength and hence lower the C-H force constant which, in turn, results in a lower-than-normal frequency ; (b) raise the C-C bond strength which similarly results in ahigherthan-normal stretching frequency. However, part of the frequency increase is due to the planar geometry of the skeleton in the ions. 3 . Electronic spectra

The observation of the stability of alkylcarbonium ions in antimony pentafluoride solutions led to the measurement of N.M.R. and I.R. spectra. It also opened the possibility to investigate the electronic spectra of these solutions. Olah and co-workersreported in their original investigation (1963) that solutions of alkyl fluorides in excess antimony pentafluoride at room temperature gave a single weak absorption maximum around 290 mp with a low extinction coefficient (generally less than 500). It was, however, not possible to decide whether the observed absorptions were indeed due to the simple alkylcarbonium ions (as suggested for sulphuric acid systems by Rosenbaum and Symons, 1959, 1960 ; see subsequent discussion) or whether secondary products formed (mainly cyclopentenyl cation type compounds or oxidized allylic ions) or impurities present in very low concentrations are responsible for the absorption maxima. Subsequently a detailed reinvestigation of solutions of alkyl carbonium ions in FS03H-SbF5 solution at - 60" showed no absorption maxima above 210 mp. I n view of this observation it is now highly probable that absorption maxima shown by alkyl fluorides in antimony pentafluoride at room temperature are due entirely to impurity ions and that no absorption of the simple alkyl cations is observed (Olah et al., 1966).

IV. ALCOHOLS AND OLEFINSIN STRONG BRONSTED ACIDS A. Electronic Spectra in Sulphuric Acid Electronic absorption spectra of alcohols in strong proton acids (H2S04)were obtained by Rosenbaum and Symons (1969, 1960). They observed for a number of simple aliphatic alcohols absorption maxima

A L E Y L C A R B O N I U M I O N s : SP E C T R o s c o PIC

oB s ERVAT ION

325

in the 290 mp region and ascribed this absorption to the corresponding simple alkylcarbonium ions. An alternative explanation, i.e. that the absorption maxima are due to oxidized allylic ions was considered by these authors, but was rejected. There was considerable disagreement over the question whether simple carbonium ions should have an absorption maximum in the 290 mp region. Matsen and co-workers (1955) noted that an absorption band (at 295-310 mp) was rapidly produced on addition of olefins to sulphuric acid, and attributed this band to the corresponding alkyl cations. They also noticed SO2 in these systems (SO2absorbs in this range). However, after a re-examination of the systems Matsen et al. (1956) retracted this view and attributed this absorption band to products arising from oxidation processes. Lavrushin and Verkhouod (1957) reported that a series of tertiary alcohols formed an absorption band in sulphuric acid in the 300 mp region, and assigned this band to the corresponding alkyl cations. As stated above, Rosenbaum and Symons (1959,1960) reported that a series of alcohols and olefins in concentrated H2S04gave U.V. absorption maximum at 292 2 mp. According to their data the bands were formed by first-order kinetics ; but recent reinvestigation of the formation of this band showed, that i t was formed with second-order kinetics (Denoetal., 1964). Thus, the explanation that the corresponding alkyl cations gave the 292 mp band by simple ionization of the alcohols was shown to be invalid since the kinetics are second order. The extinction coefficients reported by Rosenbaum and Symons were large (log,,e = 3.5 to 4) which directly conflicts with the observations of Olah et al. (1964b) which put a limit of 500 on the extinction coefficient of alkyl fluorides in antimony pentafluoride, a system which was shown by N.M.R. spectroscopy to contain high concentrations of stable alkylcarbonium ions. A survey of the literature of the chemistry of the carbonium ion precursors in strong acids strongly suggests that the absorption at 292 mp must come from alkylation products. I n 1884 alkanes were recognized by Friedel and Crafts as products from t-pentyl chloride and AlCl,. The oxidation-reduction nature of the reaction of olefins and their alcohols in concentrated acids was first expressed by Ipatieff (Ipatieff and Linn, 1947; Ipatieff et al., 1953). He showed that mono-olefinic hydrocarbons are polymerized to higherweight hydrocarbons in the presence of BF,, H2S04and FSOsH at temperatures ranging from 50" to 250". This procedure is useful in producing saturated hydrocarbons of six to twelve carbons from C2H50H,CsHs, and C4H8. Saturated hydrocarbons are formed when olefins such as ethylene are N

N

326

G . A . OLAH A N D C . U . P I T T M A N , J R .

run into CaFe and 50-60% oleum (Ipatieff et al., 1953). The acid layer was proposed to contain a high proportion of conjugated diolefins. No study of the reaction of olefins in oleum was reported until 1964 (Pittman, 1964).

The complex mixtures of products in the acid layers long defied complete characterization. The U.V. spectra of H2S04used in alkylation reactions of olefins showed an intense absorption at 295-310 mp, and this was attributed to polyene polymers in the acid by Hughes et al. (1951). Block (1946-52) postulated that the absorption was due to fivemembered rings, highly substituted with small alkyl and alkenyl groups, containing an average of two double bonds per molecule. Unsaturated six-carbon rings were ruled out because no aromatic products were found on dehydrogenation. More recently Miron and Lee (1962) analysed the hydrocarbons removed from strong acid catalysts in some detail, and suggested unsaturated cyclic structures. These structures contain from one to five five-membered rings with various methyl and alkenyl substituents and a minimum of two double bonds per molecule. However, during their drowning procedures, as the acid is diluted, considerable polymerization occurs. This conclusion is based on work by Hodge (1963),who showed that cyclopentenyl cations are rapidly destroyed by alkylation at 1 0 - 5 ~ concentrations in 35% H2S04. The insight into how saturated hydrocarbons could be produced from olefins in strong acids was provided by Bartlett’s studies of a different alkylation system. I n alkylation reactions between mono-olefins and alkanes in strong acids, saturated alkane products are formed. Bartlett et al. (1944) were the first to propose a hydride transfer step to account for this behaviour. It has now been generally accepted (see Kennedy, 1958; Schmerling, 1955; Den0 et al., 1960b) that in protonic acids, such as sulphuric acid, the olefin is protonated to yield a carbonium ion (equation 4 ) which undergoes a hydride transfer reaction with a molecule of alkane to generate a tertiary alkyl cation (equation 5 ) . This cation reacts with more olefin to form the alkylatedion (equation 6 ) which may then undergo a second hydride transfer regenerating the tertiary alkyl cation and the saturated alkylated molecule (equation 7 ). From this survey of the chemical literature it can be seen that one would not expect tertiary alkyl cations to exist as stable species in sulphuric acid. Den0 and his coworkers (Denoand Pittman, 1964 ;Den0 et al., 1964 ; Pittman, 1964; and Turner, 1965) carried out an extensive study of the fate of alkyl cations in H,S04 based on the products formed on dissolving alcohols and olefins in concentrated HeS04 and oleum. t-Butyl (or isobutyl) alcohol produces equal amounts of a saturated hydrocarbon

ALKYLCARBONIUM IONS: SPECTROSCOPIC OBSERVATION

I 1

H-C-C+

I I

+ i-C4H10

t-C4HJ +'C=C'

/

I I + i-CdH10

t-C4H9-C-C+

I 1

--f

I I I I

+ t-CdH,+

H-C-C-H

1 1

\ --t

--f

t-C4Hs-C-C+

I I I I I I

t-C4Hg-C-C-H

+i-C4H,+

mixture insoluble in H2S04(C, to CIS) and a mixture of cyclopentenyl H2S04layer (C, to -C2,,). These cations exhibit strong U.V. absorption in the 300 mp region and are formed by second-order kinetics. The low-intensity band previously observed in SbF5solutions of alkyl fluorides at room temperature could arise from a n impurity (Olah et al., 1964b),but the question whether alkyl cations can absorb weakly in the 300-mp region was still open. Simple MO theory does not predict an absorption maximum above 220 mp for simple alkyl cations. The U.V. absorption spectra of protonated aliphatic ketones which might be used as models for carbonium ions have been examined and show no absorption above 210 mp (Campbell and Edward, 1960; Den0 and Liu, unpublished). Thus, if protonated ketones would serve as crude models for carbonium ions, alkyl cations might not be expected to absorb above 200 mp. Other possible alkylcarbonium ion models such as isoelectronic trialkylboranes (Davies et al., 1959) and (CH,O),C+ (Taft et al., unpublished) also do not absorb above 220 mp. Olah et al. (1966) have recently carried out a detailed U.V. investigasolution of alkyl cations in FS03H-SbF5 solution tion of lo-' to 1 0 - 2 ~ at -60" and were able to confirm that they have no U.V. absorption above 210 mp. Solutions of t-butyl, t-pentyl and t-heptyl cations in FS03H-SbF5 are stable for hours at -6O", and N.M.R. studies have demonstrated that the ions are quantitatively formed from their corresponding alcohols in these systems (Olah et al., 1965). As mentioned above, previous U.V. studies by Olah et al. (1964) of alkyl fluorides in antimony pentafluoride at room temperature had shown a weak absorption around 290 mp, ~ g 5 0 0 .It must now be cations in the

328

G . A . OLAH A N D C . U . P I T T M A N , J R .

suggested that solvent impurities or the presence of a trace of alkenyl cations must be the absorbing species in this system, since in FS03HSbF, at low temperatures ( - 60") alkyl cations do not absorb above 210 mp. B. The Fate of Precursors in Sulphuric Acid Systems The fate of alkyl cations in proton acid systems has been well investigated, especially in sulphuric acid. The ability to vary continuously the acidity of this solvent and study the fate of alkyl cations as a function of acidity has provided insight into the problem. Alcohols, their corresponding olefins and alkyl cations are in equilibrium, with the alcohol generally predominating over the olefin (Purlee et al., 1955; Taft and Riesz, 1955; Boyd et al., 1960). The alkyl cation concentration is extremely low and this species never exists as more than a transient intermediate whose relation to the solvent is little known. In 5% HzS04the ratio of alcohol to olefin is about 1200 to 1 at 50" for the isobutylene-tertiary butyl alcohol system (Taft and Riesz, 1955). As the temperature increases the ratio of alcohol to olefin at equilibrium decreases (Boyd et al., 1960). This can be illustrated by examining the position of equilibrium in equation (8). Values of K p , [alcohol (1)]/ [olefin (g)], were shown to vary from 5-54 at 50" to 1.34 at 70". The equilibrium constant Ke, [alcohol (l)]/[olefin(l)] can be calculated from 2-methyl-2-butene (g)+ HzO (1)

+ t-pentyl alcohol (1)

(8)

equation (9) but lack of knowledge of the Henry's law constant h prevents accurate calculation at this time.

The rate of hydration of an olefin increases with acidity. It has recently been demonstrated that the hydration of isobutylene follows the H o acidity function, i.e. (dlog k/- dH,)= 1, where H , is the acidity function defined by equation (10). The behaviour of secondary and tertiary alcohols in 0-55y0 HzS04is very similar (Beishlin, 1963).

I n 55 to 80?4 aqueous HzS04 the simple alcohol olefin equilibrium (found in 0-557'0 H2S04)is complicated by a polymerization process which produces predominantly dimer, trimer, and some traces of higher boiling olefins. This behaviour was first noticed by Butlerow (1879). Two fundamental papers by Whitmore (1932, 1934) first presented the now generally accepted mechanistic pathway with carbonium ion

A L K Y L C A R B O N I U M I O N S : SP E C T R o sc O P I C

oB sERVATI O N

329

intermediates to account for this behaviour. Initial protonation of a monomer olefin leads to the intermediate carbonium ion whose lifetime in this strongly acidic medium is now sufficient for it to alkylate a second molecule of olefin in competition with its deprotonation. The alkylation product is a dimeric cation which now loses a proton and becomes a dimer olefin with such a low solubility in the acid that it tends to separate. However, further alkylation can lead to trimer cations, which on deprotonation to the trimer olefins are insoluble and separate from the acid. The products are mainly dimer and trimer olefins. I n this range of acidity the intermediate carbonium ions do not fragment to smaller species. Isobutylene (C,) produces C8 and C12 olefins but no Cg,Co, C7,C9 Clo or Cll products. This lack of fragmentation has been demonstrated for the co-polymerization of secondary and tertiary butyl alcohols and for mixed butyl and amyl alcohols (Whitmore and Mixon, 1941 ; Whitmore et al., 1941). I n 80 to 100% aqueous H2S04,aliphatic alcohols and their corresponding olefins disproportionate to produce cycloalkenyl cations in the acid layer and saturated hydrocarbons which separate. The oxidationreduction nature of this reaction (Ipatieff and Linn, 1947; Ipatieff et al., 1953) has only recently been extensively elucidated by Den0 and coworkers. Accompanying and competing with the disproportionation are alkylation, rearrangement, and fragmentation. The degree to which these processes complicate the disproportionation varies greatly with the structure of the alcohol (Deno, 1964; Den0 et al., 1964; Pittman, 1964; Turner, 1965). Cyclic alcohols exhibit the simplest behaviour. Cyclic aliphatic alcohols and olefins immediately form alkyl cations which can abstract hydride from their equilibrium olefins giving the corresponding hydrocarbon and the corresponding cycloalkenyl cation (equations 11 and 12).

330

0. A . O L A H A N D C . U. P I T T M A N , J P .

However, it is possible for the alkyl cation intermediate to rearrange before hydride transfer. I n this case monomeric saturated hydrocarbons and rearranged monomeric cations are produced (equation 13 ).

The next step in complexity are systems in which alkylation competes with hydride transfer to give dimeric alkyl cations which, when hydride abstraction occurs, yield dimeric saturated hydrocarbons (equation 14 ). This reaction path for cyclic aliphatic alcohols and olefins is often accompanied by some rearrangement (Deno et al., 1964; Pittman, 1964).

The most complex behaviour is exhibited by acyclic alcohols and olefins which alkylate, rearrange, cyclize and fragment (Deno et al., 1964 ; Pittman 1964; Turner, 1965) before final hydride transfer. t-Butyl alcohol produces equal amounts of saturated hydrocarbons and cyclopentenyl cations. The hydrocarbons are acyclic, highly branched and range from isobutane (C,) to cl6 with only about 20% of the hydrocarbons being larger than cl6. The cyclopentenyl cations range largely from Clo to cl6 with only about 20% of the hydrocarbons being larger than Cl6. Ion 4 is representative. This behaviour of acylic alcohols contrasts sharply with cyclic alcohols which do not fragment but give

A L K Y L C A R B O N I U M IONS: S P E C T R O S C O P I C O B S E R V A T I O N

331

4

only monomer, dimer, trimer, etc., hydrocarbons and cations. Since cycloalkanes have not been found in the hydrocarbon products from acyclic alcohols, the intermediate cycloalkyl cations formed in the reaction must deprotonate and then lose a hydride ion to acyclic alkyl cations at a rate far greater than they can abstract hydride ion. I n this range of acidity the residence time of the intermediate alkyl monomer, dimer and trimer cation is greatly increased owing to the greater acidity level. This allows time for the other processes to take place. I n H2S04-S03systems acyclic alcohols and olefins no longer disproportionate (Pittman, 1964 ; Den0 et ul., unpublished). No hydrocarbon products are found. The products at 15OC consist entirely of a cyclopentenyl cation mixture similar to that produced in 96% H2S04. The fundamental difference in H2S04-S03 is that SO3 functions as an oxidizing agent and SO2is abundantly produced as the reductionproduct. The alkyl cations initially formed are in equilibrium with the corresponding olefins and alkylation, fragmentation and cyclization proceed as in concentrated H2S04. However, alkyl cations in this medium do not abstract hydride ions, and this absence of hydride abstraction is simply due to the faster rate of oxidation of the equilibrating olefins by SO3. The activity ratio, uSOa/ualkyl+, increases by at least 103-104in going from 96% H2S04to 20% SO3 in H2S04. The activity of olefins decreases on going into oleum systems but this suppression of the olefin activity affects the competition between SO3 and alkyl cations for hydride ion equally. An example of this oxidation is shown in equation (15) where the 1,3-dimethylcyclohexenyl cation 5 is generated in 30% oleum by removal of an allylic hydride ion from 1,3-dimethylcyclohexene.

> MY/, 5

C . The F l w o s u l p h i c Acid-Antimony P e n t a j m J e and Hydrogen Fluoride-Antimony Pentajuoride Solvent Systems Attempts to generate simple alkyl-, arylalkyl-, and cycloalkylcarbonium ions in sulphuric acid or oleum solution generally result in

332

0. A . O L A H A N D C . U. P I T T M A N , J R .

the formation of complex mixtures in which the stable carbonium ions present are of the methylated cyclopentenyl cation type (stabilized allylic cations). Sulphuric acid and oleum as solvents have the serious disadvantage that they are quite viscous and possess relatively high freezing points. This generally results in the need to carry out the investigations a t or above + 10". At these temperatures the rate of secondary reactions leading to the cyclized allylic type ions is so high that no simple alkyl(cycloalkyl-) carbonium ions corresponding to the alcoholic precursors are observable. Alkyl cations are thus not directly observed in sulphuric acid systems, because they are transient intermediates present in low concentrations and react with the olefins present in equilibrium. From observations of solvolysis rates for allylic halides (Vernon, 1954), the direct observation of allylic cation equilibria, and the equilibrium constant for the t-butyl alcohol/2-methylpropene system (Taft and Riesz, 1955), the ratio of t-butyl cation to 2-methylpropene in 96% HzS04has been calculated to be 10-3'5. Thus, it is evident that sulphuric acid is not a suitable system for the observation of stable alkyl cations. I n other acid systems, such as BF3-CH3COOH in ethylene dichloride, olefins, such as butene, alkylate and undergo hydride transfer producing hydrocarbons and alkylated alkenyl cations as the end products (Roberts, 1965). This behaviour is expected to be quite general in conventional "strong" acids. Olah and co-workers recently (1965) found it possible to stabilize carbonium ions by increasing the acidity of the system by adding a coacid and by lowering the temperature of observation. Fluorosulphonic acid is one of the strongest pure acids that has yet been studied (Gillespie, 1963). H , for the neat acid is about -12.6 (compared with - 11 for 100% sulphuric acid and - 10 for anhydrous hydrogen fluoride). At the same time fluorosulphonic acid has a low freezing point ( - 87.3") and can be readily purified. As is to be expected, very few co-acids are capable of enhancing the acidity of fluorosulphonic acid. Gillespie and his co-workers, however, observed that antimony pentafluoride acts as an acid in fluorosulphonic acid solution by enhancing ionization according to SbF, + 2FS03H + H2SO3F+SbF5(SO3F)-. Solutions of SbF, in fluorosulphonic acid are considered the most acidic media that have yet been studied. When alcohols such as t-butyl alcohol, t-amyl alcohol, t-hexyl alcohol, were dissolved in fluorosulphonicacid-antimony pentafluoride solutions diluted with sulphur dioxide (in order to achieve better mixing of the less viscous solutions and to avoid the possibility of local overheating) at temperatures ranging around - 60°, stable, slightly coloured solutions

ALKYLCARBONIUM IONS: SPECTROSCOPIC OBSERVATION

333

are formed. The proton magnetic resonance spectra of these solutions are those of the corresponding carbonium ions with generally good resolution. It was also found that solutions of the alcohols in SbF5-S0, show formation of the corresponding carbonium ions, indicating ionization in the strong Lewis acid itself ROH

SbFs

R+SbFSOH-

The resolution of the spectra, however, is generally poorer, and frequently substantial peak broadening occurs. When solutions of alcohols in fluorosulphonic acid or fluorosulphonic acid-sulphur dioxide were prepared, tertiary carbonium ions could be generally observed, but peak broadening (due to exchange) and side products are observed. Secondary and primary alcohols form generally only the monosulphates. Brouwer and Mackor (1964) found that concentrated and stable solutions ofa series of tertiary alkyl cations can be prepared in HF-SbF5 and their proton magnetic resonance spectra were recorded. The t-butyl, t-pentyl and t-hexyl cations were observed in this solvent system. The spectra were identical with those obtained previously in SbF5 and FS03H-SbF5 solvent systems.

V. CYCLOPROPYLCARBONIUM IONS Cyclopropylcarbonium ions are alkyl cations. The cyclopropyl ring is saturated and formally an alkyl substituent. However, cyclopropyl groups have a very great stabilizing effect on carbonium ions and effectively delocalize charge. The direct observation of cyclopropylcarbonium ions by N.M.R. spectroscopy provides a good example of delocalization of charge into the cyclopropane ring. The only cyclopropylcarbonium ions discussed here will be those with a cyclopropane ring attached directly to a single carbon atom bearing the formal positive charge, such as 6. Ions such as 7, where the cyclopropane ring is attached to an allylic carbonium ion, although well studied (Deno, 1964; Roberts, 1965) will not be considered.

6

7

a.

334

A . OLAH AND C . U . P I T T M A N , J R .

A 8

The first cyclopropylcarbonium ion to be directly observed was the tricyclopropylcarbonium ion 8 (Liu, 1964). Den0 et al. (1962) showed that the N.M.R. spectrum in H2S04consists of a single sharp band at -2.26 p.p.m. It was shown that this single band did not result from rapid equilibration of the hydrogens with solvent, from both its location

9

10

11

H 12

13

14

a,&r I

t'H3

ir

H

15

16

17

18

A L K Y L C A R B O N I U M IONS: S P E C T R O S C O P I C O B S E R V A T I O N

335

and from the lack of hydrogen deuterium exchange in 96% D2S04. Exchange between a- and /3-positions within a cyclopropyl ring was eliminated with deuterium labelling experiments. Tricyclopropylcarbinol was labelled with deuterium at the a-position and then the carbonium ion was formed in sulphuric acid. On drowning the H2S04 solution of the labelled ion in base by rapid dispersal methods, the alcohol was recovered unchanged. Further N.M.R. studies of 8 by Pittman and Olah (1965a, b) in SO2-SbF,-FSO,H solutions at - 70" also gave only a single sharp band a t - 2.52 p.p.m. Finally, tricyclopropylmethyl tetrafluoroborate was prepared and dissolved in the aprotic solvent SO2and only a single sharp band was observed, a t - 1.90 p.p.m. (Pittman and Olah, 1965b). The tricyclopropylmethyl cation is half-formed (COH= CR+)in 22% H,S04, which shows it to be far more stable than the triphenylcarbonium ion which is half-formed a t 50yo H2S04(Deno et al., 1962). Its U.V. spectrum contains an intense absorption maximum at 270 nip, E = 22,000. Several mono- and di-cyclopropylcarbonium ions (9 to 18) have been

SO2-SO2CI F-SbF5

-75°C

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

4.0

I I I I I

3.0

PPm

FIQ.5.

1

1

1

1

1

1

2.0

1

1

1

1

1

1

~

336

G. A . OLAH A N D C. U . PITTMAN, JR.

observed by Pittman and Olah (1965a) b) in FS03H-S02-SbF5 at low temperatures. The resonances a- and /I-hydrogen atoms on the cyclopropyl ring are resolved in the N.M.R. spectrum of each of these ions. Most interesting of these is the dimethylcyclopropylcarbonium ion 9 (Fig. 5). The methyl groups are not equivalent and are separated by 0.54 p.p.m. It has been shown in non-charged systems that hydrogens lying in the face of the cyclopropane ring experience an upfield shift of from 0.3 to 0.5 p.p.m. (Forshn and Norin, 1964; Pate1 et al., 1963). This leads to the conclusion that the cyclopropane ring lies in a plane perpendicular to the plane of the +/CHI C

\CH3

system. The plane of the cyclopropane ring is parallel to the axis of the vacant p orbital of the positive central carbon. This is shown in Fig. 6.

Sitli. View

FIG.6.

I n this configuration one methyl group is “cis’) to the cyclopropane ring and the other is “trans”. This “cis’) methyl group now experiences the diamagnetic anisotropy of the cyclopropane ring which accounts for its observed position 0.54 p.p.m. upfield from the trans methyl group. The methyl bands do not coalesce a t -30” where the ion is rapidly destroyed. This shows that the cyclopropane ring does not rotate at this temperature. I n the N.M.R. spectrum of the dicyclopropylcarbonium ion a sharp triplet is found at - 8.14 p.p.m., 3 J = 13.5 C.P.S. for the hydrogen atom attached to the central charged carbon (Pittman and Olah, 1956a) b). This sharp triplet demonstrates that the a-hydrogen atoms on the two cyclopropane rings are equivalent and this, coupled with the known preference of the cyclopropane ring to lie perpendicular to the plane of the

A L K Y L C A R B O N I U M I O N S : S P E C T R 0 S C O P I C 0B S E R VA T I O N

337

system, leaves two probable conformations (Fig. 7) for the ion. Model (b) is favoured because of the large value of the coupling constant J and the steric interactions of the j?-hydrogenatoms in model (a). These studies have provided the basis to account for the single sharp band formed in the N.M.R. spectrum of the tricyclopropylcarbonium ion. The face of the cyclopropane rings lying in a plane parallel to axis of the vacant p orbital would see one a-hydrogen atom and the diamagnetic anisotropy of the rings will cause the u-hydrogen atoms to be shifted upfield in the spectra. This upfield shift causes the a- and j?-hydrogen reconances to be found together.

(only 2 j hydrogrris on rarh ring shown)

FIG.7. Top views of the Dicyclopropyl Carbonium Ion.

H

A

FIG.8. Top view of the TricyclopropylcarboniumIon.

The most striking feature of cyclopropylcarbonium ions is the large charge delocalization into the cyclopropane rings. The large and approximately equal downfield shifts of the a- and p-hydrogens in the N.M.R. spectra indicate to a crude first approximation that the positive charge densities a t these positions are approximately equal. Thus, previous evidence for delocalized orbitals in the cyclopropane ring (in uncharged systems) from U.V. (Eastman, 1954, 1955; Kosower and Ito, 1962), I.R. (Wiberg and Nist, 1961; Cross, 1962; Williams and Bhacca, 1963), N.M.R. (Pate1 eta,?.,1963), and theoretical (Walsh, 1949; Coulson and Moffitt, 1949) studies has been strongly supported in charged systems. The U.V. spectrum of the dimethylcyclopropylcarbonium ion in FS0,H-SbF6 at - 60' exhibits a single absorption maximum at 298 mp, e = 10,800 (Olah et al., 1966). The close resemblance to the U.V. spectra 12*

338

a.

A . OLAH AND C. U . PITTMAN, J R .

of allylic carbonium ions (Deno, 1964)demonstrates the frequently cited double-bond character of the cyclopropyl ring. This character appears to be strongly enhanced when the cyclopropyl ring is located adjacent to a vacant p-orbital. The reported U.V. absorption of the tricyclopropylcarbonium ion in sulphuric acid solution is at 270 mp, E = 22,000 (Deno et al., 1962). Thus, an increase of the number of cyclopropyl groups located adjacent to the vacant p-orbital does not shift the wavelength of the absorption maximum (in marked contrast to the successive addition of double bonds to allylic cations which causes a marked shift of the absorption maximum to longer wavelengths) (Pittman, 1964; Den0 and Pittman, 1964;Kosower and Ito, 1962;Sorensen, 1965),but only enhances the intensity. The U.V. spectrum of the dicyclopropylcarbonium ion exhibits a single intense band at 273 mp, E = 12,200(Olah et al., 1966).

VI.

ALKYLARYLCARBONIUM

IONS

Mono- and di-arylalkylcarbonium ions will be considered here as alkylcarbonium ions with aryl substituents. The diphenylethylcarbonium ion 19 and the phenylmethylethylcarbonium ion 20 are representative examples. The N.M.R. spectra of 19 and 20 have been obtained in SbF,-FS03H-SO2 systems (Olah et al., 1965),and are shown

19

20

in Figs. 9 and 10. The phenyl hydrogen resonances are shifted downfield in the N.M.R. spectrum, as are the methylene quartets and the methyl triplets in these ions. The resonances of aliphatic hydrogen atoms adjacent to the charge are shifted much further downfield than are aliphatic hydrogen atoms one carbon removed. Diarylalkylcarbonium ions are stable in HzSO4, FS03H, and CHzClz-AIC1,. However, mono-phenyldialkylcarbonium ions are much less stable and have only recently been unequivocally observed. In 1951 Newman and Den0 reported i-factor measurements consistent cation 21 and with the formation of the 2,4,6,u,~-pentamethylbenzyl the heptamethylbenzyl cation 22 in 100% H2S04. Three U.V. studies

ALKYLCARBONIUM IONS: SPECTROSCOPIC OBSERVATION

339

(Grace and Symons, 1959; Den0 et al., 1960; Williams, 1962) of monoarylcarbonium ions appeared later. It was claimed in these studies that monomeric monoarylcarbonium ions were formed by dissolving mono-

-60"

SOz-FS03H-SbFs

I

I

1

1

I

I

I

I

8.0

7.0

6.0

5.0

4.0

3.0

20

I .o

FIG.9.

PPm

FIQ.10.

arylcarbinols or their corresponding olefins in concentrated HzS04. However, since that time N.M.R. studies have shown that even the tertiary 2-phenyl-2-propyl cation 23 is not stable in 100% HzS04 or even HZSO4--lO%SO3 (Pittman, 1964; Wisotsky, 1964). Instead one must use H,SO4--25% SOs(Pittman, 1964; Wisotsky, 1964)or S02-SbP5

340

0 . A.

O L A H A N D C . U. P I T T M A N , J R .

at - 30" (Olah, 1964)or chlorosulphonic acid (Farnum, 1964)to observe 23. Thus, one must suspect and carefully analyse the U.V. data in these earlier papers. Some of the assignments previously made have now been retracted (Deno, 1964)-andit appears that the spectra of ions 21 and 22

23

reported in these studies are the only reliable ones. I n general, U.V. observations of carbonium ions should preferably be checked by N.M.R. in the same solvents and at the same temperature as that at which the U.V. observations were made. This has been done for the indanyl ions 24 and 25 (Deno el al., 1965). A 100% yield of the 1,3,3-trimethylindanylcation 24 was obtained by dissolving 2-phenyl-4-methyl-2,4-pentadiene in 85% or 96% H2S04 (Pittman, 1964; Den0 et al., 1965). The 1-methylindanyl cation is prepared on dissolving I-methylindane in 85% or 96% H2S04. These observations were extended to six-membered rings by generating the 1 -methyltetrahydronaphthyl cation 26 from l-methyltetrahydro-lnaphthol. The U.V. spectra of ion 24 gave absorption maxima at 315 mp

24

26

ALKYLCARBONIUM

IONS:

SPECTROSCOPIC

OBSERVATION

341

and 400 mp with extinction coefficients of 15,700 and 6600 respectively. Similarly ion 25 showed absorption maxima at 310 mp and 401 mp with extinction coefficients of 14,100 and 2200. The chemical and thermodynamic stabilities of ions 24 and 25 were surprising in view of the scarcity of direct observations of monoarylalkylcarbonium ions. These indanyl ions were kept unchanged for months in 15% (by weight) HzS04solutions. Each ion would develop the maximum rr-overlap of the p-orbital of the carbonium carbon with the ring orbitals at planarity. The stability of indanyl cations can be partially attributed to the inherent planarity locked in the system. However, the 1-methyltetrahydronaphthyl cation must be strained in order to approach 120" bond angles and planarity. Thus, i t would be more likely to equilibrate with its olefin, and this is reflected in the higher acidity necessary to generate it (Pittman, 1964). The stabilizing effect of a methyl group at C-1 in these systems was demonstrated by lack of observation of monomeric carbonium ions even in H2SO4-6O% SO9 (Olah et al., 1963) or SOZ-SbFS-FSO3H at -60" (Pittman and Olah, unpublished). These systems have a great propensity toward polymerization.

Stronr. acids

Equations (19)-(24) summarize the formation of a number of arylalkylcarbonium ions from alcohols in S02-SbFS--FS03H at low temperatures (Olah and Pittman, 1965). The diphenylisopropylcarbonium ion 27 can be formed by direct ionization of the corresponding alcohol or by ionization of its corresponding 6-alcohol,followed most probably by a 1-2 hydride shift. The phenylisopropylcarbonium ion 28 is formed from its 6-alcohol by a similar 1-2 hydride shift. The formation of a secondary ion from a tertiary ion here is possible, because stabilization by the phenyl group is gained. The diphenylbenzylcarbonium ion 29 can be formed by direct ionization, a

342

0. A . O L A H A N D C . U . P I T T M A N , J R .

27

t-

(22)

ALKYLCARBONIUM IONS: SPECTROSCOPIC OBSERVATION

343

1-2 phenyl shift or a 1-2 hydride shift. Equation (22) demonstrates that, when 30 is formed from 1,2,2-triphenyl-l-deuterio-l-ethanol, the deuterium is not exchanged with the protons in the acid solvent. A simple 1-2 hydride shift mechanism is indicated. However, this does not establish whether or not phenyl groups migrate before the 1-2 hydride transfer occurs to stabilize the system. Equation (24)illustrates this possibility. Experiments completed in our laboratory using CHs labels have elucidated this point. The phenyl migration does not occur. Using FSOsH-SbF5 at low temperatures Olah et al. (1966) recently obtained U.V. spectra of several alkylaryl- and cycloalkylaryl-carbonium ions. The data are summarized in Table 12. These data were obtained in concentrated solutions (1O-I to 1 0 - 2 ~ at ) low temperature ( - 50 to -60") under the exact conditions for which the N.M.R. spectra had demonstrated the existence of the ions. Earlier results of Williams (1962) and Grace and Symons (1959) reported absorption maxima above 400mp for a number of alkylmonoarylcarbonium ions. It must be suggested that in this earlier work, done in H2S04,dimeric and polymeric ions must have actually been the absorbing species, since it has now been shown by N.M.R. spectroscopy that such ions are not stable in sulphuric acid. The last years have seen a rapid development of the direct spectroscopic observation of stable carbonium ion intermediates in strongly acidic solutions. Thus many alkylcarbonium ions, previously suggested TABLE12 Ultraviolet Absorption of Aryldkyl- and Arylcycloelkyl-Carbonium IOIM in FSOsH-SbF5 at - 60 to - 60" Ion 390 326

11,200

397 321

1320 10,200

394 347

900 22,300

1600

344

G . A . OLAH A N D C . U. P I T T M A N , J R .

TABLE12-continued Ion

E

382 334

6000 22,000

440 292

38,000 2900

422 312

37,000 11,050

427 316

27,600 11,800

185 331

21,500 4300

427 338

36,100 17,100

422 322

29,500 18,800

434 334 291

24,000 25,400 13,000

@)-?a CH3

ma c1

only as transient entities, can now be directly observed. There is every reason to believe that the spectroscopic observation of reactive carbonium ion intermediates will continue at a fast pace. It is hoped, therefore, that this article will serve a useful purpose in reviewing the early development of a new field.

A L K Y L C A R B 0 N IU M I 0 N S : S P E C T R 0 S C 0 P I C 0 B S E R V A T I 0 N

345

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Deno, N. C. (1964). “Carbonium Ions”, I n “Progress in Physical Organic Chemistry”, Vol. I1 (Ed. by S. G. Cohen, A. Streitwieser, Jr., R. W. Taft, Jr.) Interscience Publishers. Deno, N. C., and Liu, J. S. Unpublished results. Deno, N. C., and Pittman, C. U., Jr. (1964). J. Am. Chem. SOC. 86,1744. Deno, N. C., Groves, P. T., Jaruzelski, J. J., and Lugasch, M. N. (1960a). J. Am. Chem. SOC. 82,4719. Deno, N. C., Peterson, H. J., and Saines, G. S. (1960b). Chem. Revs. 60, 7. Deno, N. C., Richey, H. G., Jr., Liu, J. S., Hodge, J. D., Houser, J. J., and Wisotsky, M. J. (1962). J. Am. Chem. SOC.84,2016. Deno, N. C., Boyd, D. B., Hodge, J. D., Pittman, C. U., Jr., and Turner, J. 0. 86, 1745. (1964). J . Am. Chem. SOC. Deno, N. C., Pittman, C. U., Jr., and Turner, J. 0. (1965). J . Am. Chem. SOC.87, 2153.

Deno, N. C., Pittman, C. U., Jr., and Booker, E. Unpublished. Eastman, R. H. (1955). J. Am. Chem.Soc. 76,4115,4118; (1955) 77,6643. Evans, A. G. (1946). Trans. Faraday SOC. 42,719. Fairbrother, F. (1945). J. Chem. SOC. 503. Farnum, D. G. (1964). J. Am. Chem.Soc. 86,934. Field, F. H., and Franklin, J. L. (1957). “Electron Impact Phenomena and the Properties of Gaseous Ions”, Academic Press, New York. ForsBn, S., and Norin, T. (1964). Tetrahedron Letters, No. 39, 2845. Franklin, J. L. (1952). Trans. Faraday SOC.48,443. Friedel, M. C., and Crafts, J. M. (1884). Ann. Chim. (6) 1, 451. Gillespie, R. J. (1963). In “Friedel-Crafts and Related Reactions”, Vol. 1 (G. A. Olah, Ed.), Interscience Publishers, New York. Gillespie, R. J., and Rothenbury, R. A. (1963). Chem. Can. 15, No. 8, 46. Grace, J. A., and Symons, M. C. R. (1959). J. Chem. SOC. 958. Hodge, J. D. (1963). Ph.D. Thesis, Pennsylvania State University. Hughes, E. C., Stevens, D. C., and Veatch, F. (1951). Ind. Eng. Chem. 43, 1447. Ipatieff, V. N., and Linn, C. B. (1947). U.S. Patent 2,421,946 ;Chem.Abst. 41,5296. Ipatieff, V. N., Schaad, R. E., and Shanley, W. B. (1953). “The Science of Petroleum”, Oxford University Press, Vol. V, part 11, pp. 14 and 15.

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Kennedy, It. M. (1958). “Catalysts”, Vol. 6, Rcinhold Publ. Corp., New Yorli, pp. 1-41. Kosower, E. M., and Ito, M. (1962). Proc. Chem. SOC.25. Lauterbur, P. C. (1957). J . Chem. Phys. 26,217; Lauterbur, P. C., In “Determination of Organic Structure by Physical Methods”, Vol. I1 (F. C. Nachod and W. D. Phillips, eds.), Academic Press, New York (1962). Lavrushin, V. F., Verkhouod, N. N., and Monchan, P. K. (1956). Dokludy Akad. Nauk,SSSR, 105,723; (1956). C . A . 50,11256h. Lavrushin, V. F., and Verkhouod, N. N. (1957). Dokludy Akad. Nauk, SSSR 115, 312; (1958) C . A . 52,6251e. Liu, J. S. (1964). Ph.D. Thesis, Pennsylvania State University. McLafferty, F. W. (ed.) (1963). ‘‘Mass Spectrometry of Organic Ions”, Academic Press, New York. Matsen, F. A., Gonzales-Vidal,J.,Harwood, W. H., andKohn, E. (1955). Abstracts of General Papers, A m . Chem. SOC., Div. of Petroleum Chem. 33, 21. Matsen, F. A., Gonzales-Vidal, J., and Kohn, E. (1956). J . Chem. Phys. 25, 181. Miron, S., and Lee, R. (1962). Ind. Eng. Chem. 1, 287. Muller, N., and Mulliken, R. 5. (1958). J . A m . Chem. SOC. 80, 3489. Nakane, R., Kurihara, O., and Natsubori, A. (1964). J . Phys. Chem. 68, 2876. Nakane, R., Natsubori, A., and Kurihara, 0. (1965). J . A m . Chem. SOC.87,3597. Nelson, H. M. (1962). J . Phys. Chem. 66, 1380. Newman, M. S., and Deno, N. C. (1951). J . A m . Chem. SOC.73,3644. Olah, G. A. (1963). In “Friedel-Crafts and Related Reactions” (G. A. Olah, ed.), Vol. I, Interscience Publishers, New York, pp. 212, 880. Olah, G. A. (1964). J . A m . Chem. SOC.86,934. Olah, G. A. Unpublished observations. Olah, G. A., and Pittman, C. U., Jr. (1965). J . A m . Chem. SOC.87, 3597. Olah, G. A., Kuhn, S. J., and Olah, J. (1957.) J . Chem. SOC.2174. Olah, G. A., Tolgyesi, W. S., Kuhn, S. J., Moffatt, M. E., Bastien, I. J., and Baker, E. B. (1963). J . A m . Chem. SOC.85, 1328. Olah, G. A., Baker, E. B., and Comisarow, M. B. (1964a). J . A m . Chem. SOC.86, 1265.

Olah, G. A., Baker, E. B., Evans, T. C., Tolgyesi, W. S., McIntyre, J. S., and Bastien, I. J. (1964b). J . A m . C h m . SOC.86, 1360. Olah, G. A., Cupas, C. A., Comisarow, M. B., and Pittman, C. U., Jr. (1965). J . A m . C h m . SOC.87, 2997. Olah, G. A., Pittman, C. U., Jr., Waack, R., and Doran, M. A. (1966). J . A m . Chem. SOC.I n press. Patel, D. J., Howden, M. E., and Roberts, J. D. (1963). J . A m . Chem. SOC.85,3218. Pittman, C. U., Jr. (1964). Ph.D. Thesis, Pennsylvania State University. Pittman, C. U., Jr., and Olah, G. A. (1965a). J . A m . Chem. SOC.87, 2998. Pittman, C. U., Jr., and Olah, G. A. (1965b). J . A m . Chem. SOC.87, 5123. Pittman, C. U., Jr., and Olah, G. A. Unpublished. Purlee, E. L.,Taft, R. W., Jr., andDeFazio, C. A. (1955). J . A m . Chem.Soc. 77,837. Roberts, J. M. (1965). J . Chem. SOC.314. Rosenbaum, J., and Symons, M. C. R. (1959). Proc. Chem. SOC. 92; (1960). Mol. Phys. 3, 205. Schmerling, L. (1955). “The Chemistry of Petroleum Hydrocarbons”, Vol. 3, Reinhold Publ. Corp., New York, pp. 363-408. Sorensen, T. S. (1965). Can. J . Chem. 43, 2744. Taft, R. W., Jr., and Riesz, P. (1955). J . A m . Chem. SOC.77, 902.

THE BASICITY OF UNSATURATED COMPOUNDS

347

Taft, 12. W., Jr., Ceska, G., and Lampe, F. W. Unpublished. Turner, J. 0. (1965). Ph.D. Thesis, Pennsylvania State University. Vernon, C. A. (1954). J . Chem. SOC.425,4462. Welsh, A. D. (1949). Trans. Furaday Soc. 45, 179 (1949). Wertyporoch, E., and Firla, T. (1933). Ann. Chem. (Liebigs) 500, 287. Whitmore, F. C. (1932). J . A m . Chem. SOC. 54,3274. Whitmore, F. C. (1934). Ind. Eng. Chem. 26, 94. Whitmore, F. C., and Mixon, L. W. (1941). J . A m . Chem. SOC. 63, 1460. Whitmore, F. C., Laughlin, K. C., Matuszeski, F., and Surmatis, J. D. (1941). J . A m . Chem. SOC. 63,736. Wiberg, K. B., and Nist, B. J. (1961). J . A m . Chem. SOC. 83, 1226. Williams, J. F. (1962). Tetrahedron 18, 1487. Williams, D. H., and Bhacca, N. S. (1963). J . A m . Chem. SOC.85,2861. Wisotsky, M.J. (1964). Ph.D. Thesis, Pennsylvania State University.

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AUTHOR INDEX &-umbers i n italics refer to the poges on wliich references are listed at the e n d of each article.

A Aalbersberg, W. Ij., 227, 232, 300 Adkins, H., 11, 27 Ahrens, M. L., 4, 9, 10, 20, 21, 27 Albery, W. J., 25, 27 Al-Joboury, M. I., 43, 44, 45, 49, 50, 51, 66, 69, 70 Alquier, R., 17, 27 Anderson, H. D., 258, 300 Andrews, L. J., 256, 256, 257, 258, 263, 264,265,266, 267, 300, 302, 303 Askani, R., 189,191 Avram, M., 183, 189, 191

B Baba, H., 57 70, 100,143 Baird, M. D., 161, 193 Baker, E. B., 310, 313, 317, 318, 324, 325, 327, 346 Baldock, G. R., 127,143 Ballinger, P., 13, 14, 15, 27 Bartlett, P. D., 326, 345 Bartley, W. J., 193 Basila, M. R., 61, 69 Bastien, I. J., 310, 313, 317, 318, 324, 325, 327,341, 346 Baughan, E. C., 16,27 Baumgarten, E., 197, 215, 216, 217, 218, 219, 220, 221, 222, 232, 272, 274, 27G, 277, 291, 293, 298, 300, 303 Beishlin, R. R., 328, 345 Bell, R:P., 3, 4, 5 , 9, 10, 11, 12, 13, 15, l G , 17, 19, 20, 21, 22, 23, 25, 27 Bellamy, L. J., 219, 300 Bender, M. L., 6, 12, 27, 28 Benesi, A. H., 254, 255,265, 300 Benson, S. W., 150, 172, 180, 184, 191 Berlin, A. J., 158, 191 Berliner, E., 119, 120, 143 Berthier, G., 289, 303 Bezzi, S., 7, 20, 27 Bhacca, N. S., 337, 347 Bieber, R., 7, 9, 16, 21, 27 Bier, A,, 270, 300

Binks, J. H., 143, 145 Bishop, E. O., 1, 27 Blades, A. T., 160, 191 Bloch, C., 3, 9, 29 Block, H. S., 326, 345 Booker, E., 331, 345 Booth, D., 267,268, 300 Booth, V. H., 16,26,27, 27 Borchert, A. E., 155,192 Borretzen, B., 187, 191 Boyd, D. B.. 326, 326, 329, 330, 345 Boyd, R. W., 328, 345 Brady, J. D., 119, 143, 198, 238, 239, 240, 266, 300 Brmdaur, R. L., 179,191 Branton, G. R., 161, 188,191 Brdicka, R., 16, 21, 23, 27, 29 Briegleb, G., 197, 264, 268, 263, 265, 266, 270,276, 300 Brion, C. E., 41, 69 Bronsted, J. N., 16, 24, 27, 196, 300 Brouwer, D. M., 208, 209, 211, 214, 224, 231, 272, 279, 299, 300, 316, 333, 345 Brown, H. C., 68, 69, 119, 120, 143, 145, 119, 238, 239, 242, 265, 298, 300, 307, 345 Brown, H. T., 16, 27 Brown,R. D., 79,86,95,107,115,143 Briick, D., 269,276, 303 Brune, H. A., 187,191 Bunnett, J. F., 14, 28 Butler, J. N., 171, 191 Butlerow, A., 328, 345 Buttgereit, D., 261, 301 Byrne, J. B., 266, 303 Byrne, J. J., 308, 345 Bystrow, D., 197, 304

C Cadenbach, G., 233,235,244,251, 301 Campbell, H. J., 327, 345 Ceska, G., 327, 347 Chalvet, O., 83, 145 Chambers, T. S., 148, 191 Chang Shih, 88,143

350

AUTHOR INDEX

Chesick, J. P., 163, 164, 164, 166, 179, 191,192 Choi, E. I., 9, 12, 28 Chollar, B., 161,193 Chowdhury, M., 60,62, 70 Christman, D. R., 328, 345 Cizek, J., 144 Clancy, D. J., 61, 69 Clar, E., 198,269,273, 277, 300 Clementi, E., 32, 69 Cloutier, G. G., 41, 69 Clunie, J. C., 3, 9, 10, 20, 27 Cohen, S. G., 167, 180,192 Cohn, M., 6,16,21,28 Collin, J. E., 49,61, 70 Colpa, J. P., 230, 231, 297, 300, 301 Comisarow, M. B., 327, 332,338,340 Compton, K. T., 36, 70 Condon, F. E., 240,273,300,326,345 Cook, D., 66, 70,260,300 Cook, E. H., 13,29 Cooper, W., 183,191 Cope, A. C., 183,191 Corner, E. S., 149,191 Coulson, C. A., 78, 79, 81, 87, 89, 90, 97, 98, 99, 106, 131, 143, 144, 270, 286, 296,297, 301, 337, 345 Crable, G. F., 68, 70 Crafts, J. M., 345 Criegee, R., 187, 189, 190, 191 Cross, A. D., 337, 345 Cupas, C. A., 326, 332,338, 346 Czekalla, J., 268, 270, 276, 300

D Dahmlos, J., 244, 248, 301 Dainton, F. 5.. 267,268, 300 Dallaporta, N., 7,20,27 Dallinga, G., 224, 226, 227, 228, 229, 278, 279, 280, 286, 287, 288, 289, 298,301,302 Danckwerts, P. V., 26,27,29 Darwent, B. deB., 16, 20, 23, 27, 28 Das, M. N., 172,191 Daudel, R., 83, 99, 144, 145, 288, 301 Davies, A. G., 327, 345 Davies, M. M., 269, 301 DeBoer, C. D., 176, 177, 178, 192 De Boer, E., 230, 231, 301 De Fazio, C. A., 328, 346 de la Mare, P. B. D., 240,273, 301 Deno, N. C., 299, 301, 326, 326, 327, 330, 331, 333, 334, 336, 338, 339, 345,346

238, 297,

329, 340,

Derbyshire, D. H., 83, 144 Dertooz, M., 2, 10, 28 Dewar, M. J. S., 82, 83, 90, 103, 116, 117, 119, 121, 144, 198, 264, 286, 286, 294, 296, 296, 301 Dibeler, V. H., 43, 70 D i e c b n n , W., 16,28 Diercksen, C., 134, 136, 136, 138, 144 Dinulescu, I. G., 183, 189, 191 Doering, W. vonE., 160,166,169,191,193 Doran, M. A., 321,324,327, 337,338,343, 346 Dorr, F., 261, 301 Dresdner, R. D., 248, 304 Dzcubas, W., 267, 268, 302

E Eaatman, R. H., 337, 345 Echte, A., 262, 304 Eddy, L. P., 307, 345 Edsall, J. T., 6, 26, 28 Edward, J. T., 327, 345 Edwards, J. O., 9, 12, 28 Egger, K. W., 167,191 Ehrenson, S., 16, 29, 34, 70, 290, 291, 292, 294, 296,296,301 Eigen, M., 18, 24, 26, 28 Eley, E. D., 224,226,231, 301 Elliott, C. S., 161, 169, 167, 191 Ellis, R. J., 161, 162, 176, 191, 192 Elofson, R. M., 27, 27 El-Seyed, M. F. A., 66,61, 70 Ettlinger, M. G., 164, 191 Evans, A. G., 223,301,306, 345 Evans, J. C., 145 Evans, P. G., 4, 6, 9, 20, 21, 22, 23, 27, 28 Evans, T. C., 313, 317, 318, 326, 327, 346

F Fahey, R. C., 86, 145 Fahrenhorst, E., 87, 88, 144 Fairbrother, F., 308, 345 Fanshawe, W. J., 164,193 Farnum, D. G., 299, 301,340,345 Federlin, P., 3, 9, 10, 28 Field, F. H., 306, 306, 345 Filimonow, W., 197, 304 Firla, T., 307, 347 Fischer, E. 0..267, 301 Fisher, L. P., 168,191 Flood, S. H., 145 Flowers, M. C., 163, 166, 166, 168, 191, 192

351

AUTHOR INDEX

Fluendy, M. A. D., 26,27 Flurry, R. L., Jr., 294, 295,296, 301 F o r d n , S., 336, 345 Foster, R., 268, 301 Fox, R. E., 40, 70 Franck, J., 36, 70 Franklin, J. L., 305, 306, 307, 345 Fredenhagen, K., 233, 235, 244, 248, 261, 301 French, D. M., 6,9, 29 Frey, H. M., 161, 163, 165, 169, 161, 162, 166, 166, 167, 168, 176, 185, 188, 191, 192 Friedel, M. C., 345 Friedhelm, G., 264, 302 Frost, D. C., 41, 70 Fujiwara, S., 4, 9, 28 Fujiwara, Y., 4, 9, 28 Fukui, K., 86, 90, 101, 103, 107, 108, 109, 111, 112,114,144 Furrer, H., 189, 191

G Gabriel, S., 198, 222, 301 Gajek, K., 163, 193 Gauditz, I. L., 7, 28 Genaux, G. T., 170,191 Gerberich, H. R., 173,192 Giacometti, G., 7, 20, 27 Gibbons, B. H., 26, 28 Gibert, R., 19,28 Gillespie, R. J., 311, 332, 345 Glick, R. E., 16, 29 Goebel, P., 166, 193 Gold, V., 126, 144, 198, 200, 222, 223, 227, 234, 236, 286, 286, 298, 299, 301 Golden, A. S., 191 Golike, R. G., 160,192 Gonzales-Vidal, J., 326, 346 Goodman, L., 34, 70 Goodwin, E. T., 127,144 Goudsmith, A., 267, 268, 302 Could, E. S., 298, 301 Grace, J. A., 339,343, 345 Greenwood, H. H., 83, 86, 88, 90, 93, 94, 100, 106, 134, 140, 144, 145 Grimley, T. B., 127,144 Grimme, W., 162,192 Grove, D. J., 40, 70 Groves, P. T., 299, 301, 345 Gruen, L. C., 3, 7, 9, 10, 12, 19, 20, 22, 28 Grunwald, E., 11, 28 Gubareva, M. A., 11, 28 Guggenheim, E. A., 16, 27

Gurney, R. N., 196,301 Gustafsson, C., 14, 28 Gustavson, G. G., 198,222, 301 Gutowsky, H. S., 302

H Haagen-Smit, A. J., 281, 303 Halberstadt, M. L., 163, 154, 16G, 192 Hall, E. L., 6, 29 Hall, G. G., 33, 70, 124,144 Haller, I., 165, 192 Hambling, J. K., 88, 144 Hammett, L. P., 23, 29, 299, 302 Hammick, D. Ll., 268,300,301 Hammond, G. S., 120, 144, 176, 177, 178, 192 Harwood, W. H., 326,346 Haae, D. G., 327,345 Hasting, A. B., 26,27, 28 Hauser, A., 268,300 Hauser, W. P., 184,192 Haven, A. C., Jr., 191, 191 Hawes, B. W. V., 198, 301 Hayward, T. H. J., 134, 140,144 Hedges, R. M., 276,302 Heilbronner, E., 227, 234, 236, 281, 282, 283, 286, 289, 290, 297, 302, 303, 304 Henaff, P. L., 6,21, 23, 28 Henry, J. P., 178, 193 Herbert, J. B. M., 6, 16, 21, 28 HBrold, W., 2, 7, 28 Hertz, G., 36, 70 Hey, D. H., 88,143,144 Hibben, J. H., 1, 28 Hickam, W. M., 40, 70 Higasi, K., 67, 70 Higginson, W. C. E., 16, 1'1, 20, 22, 23, 27 Hildebrand, J. H., 264,266,266,300 Hine, J., 4, 9, 14, 16, 21, 28 Hirst, J. P. H., 16 Ho, C., 26, 28 Hodge, J. D., 325, 326, 329, 330, 334, 336, 338,345 Hoffmann, H., 197,299,302,303 Hoffmann, R., 186,193 Hofstra, A., 206, 227, 228, 234, 236, 237, 238, 242, 243, 244, 246, 263, 272, 273, 274, 276, 278, 279, 280, 283, 286, 287, 288,289, 294,296, 297, 302 Hoijtink, G. J., 227, 230, 232, 300, 301 Homfray, I. F., 2, 28 Houser, J. J., 334, 336, 338, 345 Houston, J. G., 4, 9, 14, 16, 21, 28

AUTHOR INDEX

352 Howden, M. E., 336, 337, 346 Hoyland, J. R., 34, 70 Hughes, E. C., 326, 345 Hurwitz, P., 167, 180, 192 Hurzeler, H., 42, 70 Hyman, H., 299, 302

I Ibne-Rasa, K. M., 9, 12, 28 Iliceto, A., 5, 7, 9, 10, 20, 27, 28 Inghram, M. G., 42, 70 Ingraham, J. N., 222, 303 Inn, C. Y., 71 Inoue, Y., 25,28 Ipatieff, V. N., 325, 326, 329, 345 Isaacs, L. D., 48, 70 Ito, M., 337, 338, 346 Ivin, K. J., 267, 268, 300

Kohn, E., 325, 346 Kooyman, E. C., 87, 88, 144 Kortum, G., 249, 254, 255, 256, 257, 262, 263,265,270, 302 Kortiim, K., 197, 303 Kortum-Seiler, M., 255, 302 Koski, W. S., 48, 70 Kosower, E. M., 337, 338, 346 Koutecky, J., 144, 297, 302 Kranz, Th., 231, 303 Kreevoy, M. M., 4, 9, 21, 28 Krishna, V. G., 60, 62, 70 Kruger, U., 261,265,303 Kruizinga, J. H., 227, 228, 238, 278, 279, 280,288,289, 297, 302, 304 Kuhn, S. J., 145, 307, 308, 309, 310, 324, 341, 346 Kuppermann, A., 36,37, 70 Kurbatov, B. L., 43, 70 Kurihara, O., 308, 346 Kustin, K., 25, 28

J Jackman, L. M., 302 Jacobs, J., 98, 144 Jaruzelski, J. J., 345 Jensen, J. H., 4, 9, 14, 15, 28 Jensen, M. B., 20, 22, 27 Johanson, M., 14, 28 Jones, J. G., 302 Jones, J. M., 12, 28

K Kallmann, H., 45, 70 Kasha, M., 56, 61, 70 Kaufman, J. J., 48, 70 Katz, J. J., 299, 302 Kearns, G. L., 58, 70 Keefer, R. M., 265, 256, 257, 258, 263, 265,266, 267, 300, 302, 303 Kellner, S. M. E., 171, 172, 179, 191, 192 Kennedy, R. M., 326, 346 Kenny, C. L., 266, 303 Kern, F., 170,192 Kenvin, L., 41, 70 Ketelaar, J. A. A., 267, 268, 302 Ketley, A. D., 158, 160, 161, 191, 192 Kiese, M., 26, 27, 28 Kilpatrick, M., 246, 247, 249, 250, 251, 253, 272,273, 299, 302 Kilpatrick, M. L., 302 King, P. J., 224, 225, 231, 301 Kistiakowsky, G. B., 148, 191 Kjeldaas, J., 40, 70 Koch, H. von, 51, 70

L Lampe, F. W., 327, 347 Lampman, G. M., 165, 193 Landquist, N., 5, 9, 28 Langrish, J., 171, 192 Larkworthy, L. F., 327, 345 Lauder, I., 5, 6, 16, 20, 21, 28 Lauer, W. M., 298, 302 Laughlin, K. C., 329, 347 Lauterbur, P. C., 319, 346 Lavrushin, V. F., 325, 346 Lee, R., 326, 346 Lefebvre, R., 288, 301 Leffler, J. E., 11, 28 Lennard-Jones, J. E., 124, 144 Leupold, E., 198, 222, 301 Levi, A. A., 165, 181, 183,192 Levy, M., 144 Lewis, G. N., 196, 302 Lewis, I. C., 15, 29 Lien, A. P., 242, 273, 302 Lieser, K. H., 238, 302 Lindholm, E., 45,51, 70 Linn, C. B., 325, 329, 345 Linquist, R. H., 150, 192 Liu, J. S., 327, 334, 335, 338, 345, 346 Lombardi, E., 4, 9, 28 Long, F. A., 13, 14, 15, 27, 205, 227, 283, 284, 298, 299, 301, 302, 304 Longuet-Higgins, H. C., 78, 79, 81, 89, 90, 97, 98, 99, 105, 106, 131, 144, 285, 295, 296, 297, 301, 302

353

AUTHOR INDEX

Lowry, T. M., 16, 28 Luborsky, F. E., 246, 247, 249, 250, 251, 253, 272, 273, 302 Lugesch, M. N., 345 Luther, H., 197, 227, 231, 302 Luttke, W., 259, 302 Lykos, P. G., 294,295,296, 301

M MacCaulay, D. A., 242,273, 302 McClanahan, J. L., 160, 161, 192 McDougall, A. O., 3, 9, 11, 12, 27 McDowell, C. A., 41, 70 McIntyre, J. S., 313, 317, 318, 325, 327, 346 McKenzie, A., 17, 28 Mackor, E. L., 126,145,201, 203, 203,206, 207, 208, 209, 210, 211, 214, 221, 224, 225, 227, 228, 229, 230, 231, 232, 234, 236, 237, 238, 242, 243, 244, 245, 253, 272, 273, 274, 275, 278, 279, 280, 283, 286, 287, 288, 289, 291, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 316,333, 345 MacLachlan, A. D., 90, 145 McLafferty, F. N., 305,306,346 MacLean, C., 126, 145, 201, 202, 203, 206, 207, 208, 209, 210, 211, 214, 224, 230, 231, 272, 279, 291, 297, 298, 299, 300, 303 MacLean, E., 299, 300 McTigue, P. T., 3, 7, 9, 10, 12, 13, 19, 20, 22, 27, 28 McWeeny, R., 83, 86, 129, 130, 131, 132, 133, 134, 135, 136, 138, 139, 142, 144, 145 Maitlis, P. M., 83, 144 Mann, D. E., 66, 71 Marcia, E., 183, 189, 191 Marmet, P., 41, 70 Marmo, F., 71 Marshall, D. C., 151, 153, 185, 192 Mason, S. F., 61, 70, 298, 303 Mateescu, G., 183, 189,191 Matsen, F. A., 68, 70, 276, 302, 325, 346 Matson, G. W., 298, 302 Matsushima, M., 4, 28 Matuszeski, F., 329, 341 May, D. P., 44, 46, 69 Mayot, M., 289,303 Meadows, G. W., 16, 28 Meany, J. E., 23, 29 Mecke, R., 259, 302,303 Melander, L., 119,145 Melchiore, J. J., 240, 300

Merrifield, R. E., 258, 265, 303 Miles, J. H., 14, 28 Miller, G. R., 4, 9, 21, 28 Miron, S., 326, 346 Mitchell, A. G., 17, 28 Mixon, L. W., 328, 347 Moffatt, M. E., 310, 324, 341, 346 Moffitt, W., 337, 345 Mole, T., 82, 103, 144 Monchan, P. K., 346 Montague, D. C., 187, 191 Mootz, D., 197, 302 Morokuma, K., 144 Morrison, J. D., 42, 70 Moser, C., 288, 301 Mottl, J., 47, 49, 50, 71 Moulden, H. N., 88,144 Muller, N., 95, 103, 123, 145, 290, 291, 303, 305, 346 Mulliken, R. S., 35,46, 49, 70, 95, 103, 117, 123, 139, 145, 290, 291, 303, 305, 346

N Nagata, C., 90, 101, 103, 107, 108, 109, 111, 112, 114,144 Nahabedian, K. V., 14, 28 Nakajima, T., GO, 70 Nakane, R., 308, 346 Nakayama, T., 47,49, 50, 71 Nangia, P. S., 150, 172, 191 Nasielski, J., 2, 10, 28 Natsubori, A., 308, 346 Natterer, M., 20, 28 Nelson, H. M., 308, 346 Nelson, K. L., 119, 143 Nenitzescu, C. D., 183, 189, 191 Nesbet, R. K., 129, 145 Newman, M. S., 17, 29, 338, 346 Nicholson, A. J., 70 Nist, B. J., 337, 347 Norin, T., 336, 345 Norris, J. F., 198, 222, 303

0 O’Brien, S. J., 266, 303 Ogawa, R. B., 171,191 Ogimachi, N., 255,258,263,264, 265,266, 267,303 58, 69 Okamoto, Y., Olah, G. A., 119, 145, 238, 298, 299, 303, 307, 308, 310, 311, 313, 317, 318, 321, 324, 325, 327, 332, 334, 336, 337, 338, 340, 341, 343, 346 Olah, J., 307, 308, 346

354

AUTHOR I N D E X

Olechowski, J. R., 267, 268, 304 Omura, I., 57, 70 Onwood, D. P., 13, 15, 23, 27 Ott, K. H., 163, 193 Overberger, C. O., 155, 192

P l’aldus, J., 297, 302 Pappas, 8.P., 189, 193 Pariser, R., 131, 139, 145 Parr, R., 131, 139, 145 Parsons, B. N., 258, 301 Pataracohia, A. F., 172,192 Patel, D. J., 336, 337, 346 Patterson, A., 6, 9, 29 Pauling, L., 78, 102,145 Pavelich, W. A., 11, 29 Peacock, T. E., 139, 145 Pearsall, H. W., 238, 300,307, 345 Pease, R. N., 149,191 Pedersen, K. J., 24, 27 Perkampus,H. H., 197,215,216,218,219, 220, 221. 222, 231, 232, 261, 265, 272, 274,276, 277,291,293,298, 303 Perkin, W. H., 2, 16, 29 Perrin, D. D., 25, 28 Peterson, H. J., 326, 345 Pettersson, E., 51, 70 Pfluger, C. E., 238, 302 Phillips, W. D., 268,265, 303 Pickering, P. S. U., 16, 27 Pickett, L. W., 95, 103, 123, 145, 290, 291, 303 Piret, M. W., 5, 29 Pittman, C. U., Jr., 321, 324, 325, 326, 327, 329, 330, 331, 332, 335, 336, 337, 338, 339, 340, 341, 343, 345, 346 l’lattner, PI. A., 227, 234, 236, 281, 282, 283, 303 Pockels, G., 227, 231, 302 Pocker, Y., 12, 23, 26, 29 Pope, M., 66, 70 Pople, J. A., 129, 131, 140, 145, 288, 303 Powell, A. L., 25, 27 Price, W. C., 48, 70 Pritchard, H. O., 149, 171, 192 Pullmann, A., 270, 303 Pullman, B., 60, 70, 270, 289, 303 Purlee, E. L., 328, 346

R Rabinovitch, B. S., 150, 192 Radwitz, F., 197, 302 Ramp, F. L., 183, 191 Ramsay, W., 2, 29

Rand, M. H., 19, 20, 22, 27 R e d i n g , R., 4, 9, 28 Reese, R. M., 43, 70 Reid, C., 125, 145, 225, 227, 231, 503 Reuss, G., 258, 270, 300 Rice, C. L., 9, 12, 28 Richards, R. E., 1, 27 Richey, H. G., Jr., 334, 335, 338, 345 Ridd, J. H., 83, 145 Ridley, R. G., 48, 70 Riesz, P., 328, 332, 346 Ritchie, P. D., 17, 28 Roberts, J. D., 332,336, 337, 346 Roberts, J. M., 346 Robertson, P. W., 240, 273, 301 Robinson, C. C., 11, 27 Rollefson, G. K., 150,192 Roothaan, C. C. J., 129, 145, 288, 294, 306 Roquitte, B. C., 176, 192 Rosen, B., 45, 70 Rosenbaum, J., 324,325,346 Rossow, A. G., 27, 27 Roth, W. R., 160, 169,191 Rothenbury, R. A., 311, 345 Roughton, F. J. W., 16, 26, 27, 27 Rubinstein, D., 198, 222, 303 Rudolph, E. A., 281, 303 Ruff, L. M., 36,37, 70 Rnmpf, P., 3, 9. 29 Rushbrooke, a. S., 89, 106,144 Ruzicka, L., 281, 303

S Sadler, P. W., 11, 29 Saika, A., 302 Saines, G., 299, 301 Saines, G. S., 326, 348 Sampson, R. J., 82, 144 Sandorfy, C., 83, 145 Satchell, D. P. N., 298, 301 Schsad, R. E., 325, 326, 329, 345 Schaefgen, J. R., 17, 29 Scheibe, G., 269, 276, 303 Schiff, H. I., 41 Sohlag, E. W., 150,192 Schmerling, L., 326, 346 Schmid, E. W., 217, 304 Schneider, A., 326, 345 Schneider, F. W., 150, 192 Schou, S. A,, 2, 29 Schulze, J., 205, 227, 283, 284, 299, 302, 304 Searless, S., 265, 303 Seebach, D., 187,191 Setser, D. W., 150, 192

355

AUTHOR I N D E X

Shanley, W. B., 325, 326, 329, 345 Sharma, A., 26,27,29 Sherndal, A. E., 281, 304 Shingu, H., 112,144 Short, B., 179, 191 Shull, H., 33, 70 Simonetta, M., 282, 285, 289, 290, 297, 302,304 Simons, L. H., 248, 304 Skinner, R. F., 185, 192 Slater, N. B., 149, 192 Sliam, E., 183, 189, 191 Smit, P. J., 279, 280, 286, 287, 288, 289, 298,301 Smith, F. T., 55, 70, 151, 192 Smith, G. F., 16, 28 Smith, P. J., 221, 289, 298, 302 Smith, R. C., 168,192 Sogo, P. B.. 4, 9, 28 Sorensen, T. S., 338, 346 Sowden, R. G., 149,171,192 Srinivasan,R., 165, 171, 181, 183, 132 Staats, G., 232, 242, 304 Stechl, H.-H., 170,192 Stedman, G., 298,302 Steel, C., 167, 180, 192 Stefani, A. P., 58, 71 Stegemeyer, H., 227, 304 Stevens, D. C., 326, 345 Stevens, I. D. R., 166, 166,192 Stewart, R., 13, 14, 15,29 Stock, L. M., 119, 120, 145, 298, 300 Strehlow, H., 4, 9, 10, 20, 21,25,27, 28, 29 Streitwieser, A., Jr., 31, 66, 68, 70, 78, 85, 87, 96, 100, 107, 145, 284, 285, 286, 288, 304 Strohmeier, W., 262, 304 Sturtevant, J. M., 26, 28 Sullivan, D. G. O., 11, 29 Sunderman, R., 163,193 Surmatis, J. D., 329, 347 Swinehart, D. F., 171,193 Symons, M..C. R., 324, 325, 339, 343, 345, 346 Szwarc, M., 58,71, 87,143,144,145

Traynham, J. G., 267, 268, 304 Trecker, D. J., 178, 193 Trotman-Dickenson, A. F., 149, 171, 182, 192,193 Trumbull, E. R., 183,191 Triimpler, G., 7, 9, 16, 21, 27 Turner, D. W., 43, 44, 45, 48, 50, 61, 56, 69, 70 Turner, J. O., 325, 326, 329, 330, 340, 345, 347 Turner, R. B., 166,193 Tye, F. L., 125, 144, 198, 200, 222, 223, 227, 234, 236, 285, 286,299, 301

T

Waack, R., 321, 324, 327, 337, 338, 343, 346 Wachsmann, E., 217,304 Walker, J. F., 10, 29 Wallace, J. W., 238,240, 242, 300 Walling, C., 177, 193 Walsh, A. D., 337,347 Walters, W. D., 170, 172, 173, 176, 182, 184,191,192,193 Walz, H., 257, 302

Taft, R. W., Jr., 10, 11, 13, 15, 29, 327, 328,332, 345, 346, 347 Tamres, M., 259,266,266,303, 304 Terenin, A. N., 43, 70, 197, 304 Thaler, W., 177, 193 Tolgyesi, W. S., 310, 313, 317, 318, 324, 326,327,341, 346 Trautz, M.,148,193

U Ullmann, E. F., 164, 193 Urey, H. C., 6, 16, 21, 28

V Valenta, P., 5 , 7, 9, 29 Van de Stolpe, C., 267, 268, 302 Van der Linden, R., 13, 14, 15,29 van der Wads, J. H., 126, 145, 201, 202, 203, 206, 207, 221, 234, 236, 237, 238, 242, 243, 244, 245, 253, 272, 273, 274, 276, 279, 283, 286, 287, 288, 289, 294, 296, 297,298, 302,303 Van Dyke, R. E., 238,301 Van Tamelen, E. E., 189,193 Vanus, D. W.. 182,193 Veatch, F., 326, 345 Verhoek, F. H., 17,29 Verkhouod, N. N., 325, 346 Vernon, C. A., 332, 347 Verrijn Stuart, A. A., 224, 225, 227, 228, 229,286, 287, 288, 289, 298, 301, 304 Vesely, A., 16,21, 29 Vilesov, F. I., 43, 52, 70 Vogel, E., 163, 176, 193 Vogel, W. M., 255, 256, 257, 262, 263, 270, 302 Vreeland, R. W., 171, 193

W

356

AUTHOR INDEX

Warford, E. W. T., 82, 103, 144 Wassermann, A., 283, 304 Watanabe, K., 40, 47, 49, 50, 52, 71 Waters, W. A., 83, 144 Weber, S., 227, 234, 236, 281, 282, 283, 303 Weijland, W. P., 227, 232, 300 Wellington, C. A., 155,193 Wellman, R. E., 172, 193 Werner, H., 267, 301 Wertyporoch, E., 307, 347 Weston, R. E., 150, 193 Wheland, G. W., 66, 71, 78, 88, 102, 103, 107,145,286, 304 Whiffen, D. H., 216, 304 Whitmore, F. C., 328, 329, 347 Whittemore, I . M., 58, 71 Wiberg, K. B., 150, 192, 193, 337, 347 Wiberg, K. W., 165, 193 Wilke, G., 267, 304 Williams, D. H., 337, 347 Williams, G. H., 88, 143, 144 Williams, J. F., 339, 347, 347 Winkler, K., 148, 193 Winter, R. E., 186, 187, 191, 103

Wisotsky, M. J., 334,335,338,339,345,347 Wissbrunn, K . F., 6 , 9, 29 Woburn, J. F., 166, 193 Wolf, A. P., 328, 345 Wolf, I<. L., 2, 28 Wolinsky, J., 161, 193 Woodward, R. B., 186,183 Wooten, L. A., 23, 29 Wright, G. A., 4, 27 Wyman, J., 6, 26, 28 Wynne-Jones, K . M . A., 19,20, 22, 27

Y Yonezawa, T., 90, 101, 103, 107, 108, 109, 111, 112, 114, 144 Young, R. P., 258,302 Young' "' 2' 29 Yvan, P., 83, 146

Z Zahradnik, It., 144 Zand, It., 167, 180,192 Zuercher, R. A., 266, 303 Zupan, M., 172,193

CUMULATIVE INDEX OF AUTHORS Bell, R. P., 4, 1 Brand, J. C. D., 1, 365 Brown, H. C., 1, 35 Collins, C. J., 2, 1 Ferguson, G., 1, 203 Frey, H. M., 4, 147 Greenwood, H. H., 4, 73 Le FBvre, R. J. W., 3, 1 Long, F. A,, 1, 1 Maccoll, A., 3,91 McWeeny, R., 4, 73 Olah, G. A., 4, 305 Perkampus, H. -H., 4, 195 Pittman, C. U., Jr., 4, 305 Reeves, L. W., 3, 187 Robertson, J. M., 1, 203 Samuel, D., 3, 123 Schaleger, L. L., 1, 1 Shatenshtein, A. I., 1, 156 Silver, B. L., 3, 123 Stock, L. M., 1, 35 Symons, M. C. R., 1, 284 Turner, D. W., 4, 31 Whalley, E., 2, 93 Williamson, D. G., 1, 305 Wolf, A. P., 2, 201 Zollinger, H., 2, 163

CUMULATIVE INDEX OF TITLES Acid solutions, strong, spectroscopic observation of alkylcarbonium ions in, 4, 306 Activation, entropies of, and mechanisms of reactions in solution, 1, 1 Activation, volumes of, use for determining reaction mechanisms, 2, 93 Alkylcarbonium ions, spectroscopic observation in strong acid solutions, 4, 305 Ammonia, liquid, isotope exchange reactions of organic compounds in, 1, 156 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 Basicity of unsaturated compounds, 4, 195 Carbon atoms, energetic, reactions with organic compounds, 2, 201 Carbonium ions (alkyl), spectroscopic observation in strong acid solutions, 4, 306 Carbonyl compounds, reversible hydration of, 4, 1 Conjugated molecules, reactivity indices in, 4, 73

358

CUMULATIVE I N D E X O F TITLES

Directive effects in aromatic substitution, a quantitative treatment of, 1, 35 Electronically excited molecules, structure of, 1, 365 Electron spin resonance, identification of organic free radicals by, 1, 284 Energetic tritium and carbon atoms, reactions of, with organic compounds, 2, 201 Entropies of activation and mechanisms of reactions in solution, 1, 1 Equilibrium constants, N.M.R. measurements of, as a function of temperature, 3, 187 Exchange reactions, hydrogen isotope, of organic compounds in liquid ammonia, 1, 156 Exchange reactions, oxygen isotope, of organic compounds, 3, 123 Excited molecules, structure of electronically, 1, 365 Free radicals, organic, identification by electron spin resonance, 1, 284 Gas-phaseheterolysis, 3, 91 Gas-phase pyrolysis of small-ring hydrocarbons, 4, 147 Heterolysis, gas-phase, 3 , 9 1 Hydration, reversible, of carbonyl compounds, 4, 1 Hydrocarbons, small-ring, gas-phase pyrolysis of, 4, 147 Hydrogen isotope effects in aromatic substitution reactions, 2, 1G3 Hydrogen isotope exchange reactions of organic compounds in liquid ammonia, 1, 156 Ionization potentials, 4, 31 Isotope effects, hydrogen, in aromatic substitution reactions, 2, 163 Isotope exchange reactions, hydrogen, of organic compounds in liquid nmnionin, 1, 150 Isotope exchange reactions, oxygen, of organic compounds, 3, 123 Isotopes and organic reaction mechanisms, 2, 1 Mechanisms, organic reaction, isotopes and, 2, 1 Mechanisms, reaction, use of volumes of activation for determining, 2, 93 Mechanisms of reactions in solution, entropies of activation and, 1, 1 N.M.R. measurements of reaction velocities and equilibrium constants as a funrtion of temperature, 3, 187 Non-planar and planar aromatic systems, 1, 203 Nuclear magnetic resonance, Bee N.M.R. Oxygen isotope exchange reactions of organic componnrls, 3, 1 2 3 Planar and non-planar aromatic systems, 1, 203 Polarizability, molecular refractivity and, 3, 1 Pyrolysis, gas-phase, of small-ring hydrocarbons, 4, 147 Radicals, organic free, identification by electron spin resonance, 1, 284 Reaction mechanisms, use of volumes of activation for determining, 2, 93 Reaction mechanisms in solution, entropies of activation and, 1, 1 Reaction velocities and equilibrium constants, N.M.R. measurements of, as a function of temperature, 3, 187 Reactivity indices in conjugated molecules, 4, 73 Refractivity, molecular, and polarizability, 3, 1 Resonance, electron spin, identification of organic free radicals by, 1, 284 Small-ringhydrocarbons, gas-phase pyrolysis of, 4, 147 Solution, reactions in, entropies of activation and mechanisms, 1, 1 Spectroscopic observation of alkylcarbonium ions in strong acid solutions, 4, 306 Structure of electronically excited molecules, 1, 365 Substitution, aromatic, a quantitative treatment of directive effects in, 1, 35 Substitution reactions, aromatic, hydrogen isotope effects in, 2, 163 Temperature, N.M.R. measurements of reaction velocities and equilibrium constants as a function of, 3, 187 Tritium atoms, energetic, reactions with organic compounds, 2, 201 Unsaturated compounds, basicity of, 4, 196 Volumes of activation, use of, for determining reaction mechanisms, 2, 93