Spiers Memorial Lecture The Development of Ideas about Proton Transfer Reactions BY R. P. BELL Department of Chemistry University of Stirling Scotland Received 29th September 1975 The amount of quantitative information available about proton transfer (acid-base) reactions in solution probably exceeds that for any other class of reaction and this is true both for equilibrium and for kinetic measurements. In view of the importance of such reactions in biological systems and their mechanistic simplicity (at least on paper) it is easy to see why their interpretation and further study has attracted much attention including a Faraday Society Discussion in 1965 and two recent This lecture will attempt to give some account of the early history of the subject and to call attention to some of the main points of current interest.In keeping with most of the contributions to this Symposium the emphasis will be mainly on kinetic problems. The recognition that certain reactions involved the transfer of a proton between two species was implicit in the early days of the ionic theory. Thus if it is accepted that ammonium acetate is ionised its formation from ammonia and acetic acid becomes NH3+ CH3C02H-+ NH; + CH,CO; though even here many chemists would have supposed that in solution this reaction necessarily proceeded through the dissociation of the reactants to give OH-and H+ respectively which then combined. However the generality and importance of proton transfer reactions was first realised in Bronsted's acid-base deBnition first published in 1923,4 and subsequently elaborated in his monograph " Acids and Bases ".5 This definition gave a unified presentation of the dissociation of acids and bases neutralisation hydrolysis of salts indicator equilibria buffer action etc.all of which were traditionally treated as separate topics much to the confusion of the student. In order to include the dissociation of acids in the same scheme it was necessary to acknowledge that the hydrogen ion in aqueous solution is a hydrated proton and an extension of the same ideas showed that the behaviour of acids and bases in non-aqueous media is largely determined by the acid-base properties of the solvent itself. Bronsted's definition owed much to the analogy between proton transfer and electron transfer in redox systems and table 1 compares the two types of function in aqueous solution.It may be noted that many of the differences in usage arise from essentially practical points. In particular redox systems are characterised by potentials rather than by equilibrium constants because they rarely enter into mobile equilibrium with solvent species. For the same reason the accessible range of redox power in aqueous solution is enormously greater than the range of acid-base strength since it is possible to obtain stable aqueous solutions of many species which are thermodynamically capable of reducing water to hydrogen or of oxidising it to hydrogen peroxide or oxygen. Acid-base strengths are normally characterised by the equilibrium constants of their mobile reactions with solvent species but it would 7 SPIERS MEMORIAL LECTURE be equally logical to use the potential of a hydrogen electrode in a solution containing equal concentrations of conjugate acid and base this has been proposed,6 but never generally adopted.TABLE OF ACID-BASE AND REDOX SYSTEMS IN AQUEOUS SOLUTION 1.-COMPARISON ac i d-base redox definition A + B+H+ definition R + 0+e-reaction Al +B2 + B1+A2 reaction R1+ O2+ O1+R2 standard system standard system H30+ + H20+ H+ +HZ+H20+ H,O++e-Reactions nearly always Reactions frequently slow fast hence equilibria hence equilibria difficult to directly measurable. measure. Equilibricm with solvent Equilibrium with solvent always present. usually absent.Hence measurable range of Hence range of redox potentials dissociation constants about -3 V to +3 V corresponding limited to about 10l2 to 1O1O0 in equilibrium constants. corresponding to 0.7 V. Equilibrium constants more Redox potentials more convenient convenient to use than to use then equilibrium constants. "acidity potentisls ". The pursuit of verbal definitions is not usually a profitable pastime in the physical sciences but Bronsted's acid-base definition did have immediate consequences in the field of acid-base catalysis. This had long been attributed solely to hydrogen and hydroxide ions respectively (or the analogous species in non-aqueous solvents) and for many organic molecules plausible mechanisms had been suggested by which the addition or removal of a proton could lead to the observed reaction.Once it was realised that hydrogen and hydroxide ions were representatives of whole classes of acids and bases the possibility arose that the catalytic power of a solution could depend not only on its pH but also on the concentrations of other acids or bases present especially in buffer solutions. This behaviour general acid-base catalysis had already been observed by Dawson and his collaborators in their work on the acetone-iodine reaction,"' but its full significance was not realised until the publica- tion by Bronsted and Pedersen * of their work on the base-catalysed decomposition of nitramide. This 50-page paper which appeared one year later than the acid-base definition is truly remarkable in its scope and repays careful reading to this day it will be referred to several times in the course of this lecture.Bronsted and Pedersen show that the rate of decomposition of nitramide is independent of [OH-] over a considerable range but varies linearly with the concentration of other basic species such as carboxylate anions or amines and they correctly interpret this as evidence for slow proton transfer from nitramide (or an isomer) to these bases. It is interesting to note that the original object of the nitramide work was to obtain a kinetic method for measuring [H+] or [OH-] and hence to study salt effects on the dissociation of weak electrolytes. It is not clear whether the study of general base catalysis was stimulated by the acid-base definition or vice versa but in any event the coincidence was a fortunate one.* The quantitative estimates made by Dawson for the catalytic effect of undissociated carboxylic acids need revising in the light of later views on salt effects and the interpretation of conductivity data but his qualitative conclusions remain largely unaffected. On the other hand several other claims to have detected general catalysis by acids do not survive such re-examination. R. P. BELL The experimental distinction between specific and general acid-base catalysis depends upon the relation between the velocity constants of the proton transfer step and of other processes which follow or precede it. This was first clearly formulated by Bronsted for reactions involving a single proton transfer and extended by Pedersen to processes such as prototropic isomerisations which involve two successive proton transfers.Many of the expressions thus derived have been re- discovered by later workers in connection with particular reactions. Bronsted also showed how experiments could best be planned to avoid complications due to salt effects on equilibria or velocity constants and his procedures are now generally accepted though not always adhered to. log K FIG.1.-Carboxylate ion catalysis in the decomposition of nitramide reproduced from ref. (8). Many studies of general catalysis have followed the pioneer work of Bronsted and his collaborators and no attempt will be made to describe them. In principle simpler behaviour might be anticipated in aprotic solvents where there is no possibility of catalysis by solvent species but in practice complications are often caused by association and lack of information about relevant equilibria.1° Most of the useful results for catalysed reactions therefore relate to aqueous solutions and a considerable amount of information about the rates of proton transfer reactions can be obtained by a correct analysis.However there are severe limitations to the types of system which can be studied in this way since the existence of a catalysed reaction implies that one of the partners in the proton transfer reaction must be unstable or reactive. In most reactions exhibiting general acid-base catalysis proton transfer either takes place to or from carbon (formation of carbonium ions or carbanions) or else is accompanied by drastic changes in other parts of the molecule as in the mutarotation of glucose and related addition reactions of the carbonyl group.Moreover the conventional techniques for studying catalysed reactions were limited to rather slow processes while the much faster thermodynamically favourable reactions of simple oxygen and nitrogen acids were inaccessible to direct measurement. This position has of course been transformed during the last twenty five years by the introduction of new techniques for studying fast reactions notably by Eigen and his collaborators SPIERS MEMORIAL LECTURE and published velocity constants for proton transfers now range over some twenty powers of ten and a wide variety of chemical types.In spite of this wealth of information its quantitative interpretation in molecular terms was slow to develop and is still the subject of much enquiry as shown by the papers presented to this Symposium.* Such interpretations often depend upon the discovery of some empirical quantitative relation and subsequently of deviations from it and for proton transfers discussion has centred around the Brunsted relation. This was put forward by Bronsted and Pedersen * to correlate the catalytic effect of anion bases in the decomposition of nitramide with their basic strength ; the excellence of this correlation is shown by fig. 1 reproduced from their original paper.? Similar results have been obtained for many other reactions in both water and non-aqueous solvents and also for directly measured rates of proton transfer though there are very few instances in which the correlation is as good as for the decomposition of nitramide possibly because the small size of the nitramide molecule minimizes deviations due to steric interactions.The Bronsted relation represents the earliest example of a linear free energy relation and can be expressed as dR(AG*) = P6R(AGo) (1) where AG* is the free energy of activation AGO the standard free energy change for the overall proton transfer reaction (both corrected for statistical factors) dR denotes a change caused by substitution in one or both reactants and /I is a constant originally assumed to be positive and less than unity.The Bronsted relation differs from most rate-equilibrium correlations in that AG* and AGO refer to the same reaction and this together with the low steric requirements of the proton probably accounts for the accuracy with which it is frequently obeyed. Many problems of interest can be expressed in terms of the range of validity of the Bronsted relation and in particular the following questions may be asked :$ (a) What types of structural variation are consistent with the validity of eqn (I)? (b)Has /I the same value for substitution in both reactants and can 6 include variations in the nature of the solvent ? (c) Need the value of p lie between zero and unity? (d)Does p remain constant over a large range of AGO? These queries will now be considered separately.(a) It was always envisaged that a single Bronsted relation would apply accurately only to a series of similar acids or bases for example carboxylic acids or ring- substituted anilines and individual deviations were soon recognised and to some extent explained. Thus in the decomposition of nitramide basic catalysts of differing charge were found to generate different Bronsted relations and plausible explanations were given similar charge effects have been recently reported for the acid catalysed hydrolysis of ethyl vinyl ether.12 Similarly primary secondary and tertiary amines are found to give separate Bronsted plots in the decomposition of nitramide,13 which * Many early workers especially Bronsted himself showed little curiosity about the molecular mechanism of the reactions which they studied.Their attitude might be likened to that attributed to Dr. Johnson who explained his lack of interest in horse-racing by saying " Sir it is already known to me that one horse can run faster than another! " f This plot should strictly speaking be modified slightly to allow for statistical factors which Bronsted and Pedersen applied in an incomplete form. However the correlation is equally good when the modified factors are used. $ Recent developments in the Bronsted relation are discussed in two reviews by Kresge," to which the writer is much indebted. R. P. BELL can be accounted for in terms of the solvation of the amine cations.14 Because of the small size of the proton steric hindrance is not often prominent in proton transfer reactions but there are a number of instances in which 2,6-substituted pyridines react more slowly than anticipated l5 conversely cases are known in which the presence of large polarisable groups in both reactants leads to an abnormally fast reaction presumably because of hydrophobic attraction between these groups.The above effects are all relatively small but if comparisons are made between species of widely differing structures very large deviations from eqn (1) appear. For example although phenol acetylacetone and nitromethane have approximately the same pK-values the velocity constants for their reactions with hydroxide ions are about lolo lo5and 10 dm3 mol-1 s-l respectively. The original explanation of the slow reaction of nitromethane l7 regarded it as a pseudo-acid which could only react with bases after its slow isomerisation to the "true " acid CH2 :NOOH.According to current views the aci-form could only be produced after the reaction of the normal form with base to produce the anion. The reason for the slowness of this and similar reactions is still not fully understood but it is almost certainly connected with the extensive structural and electronic reorganisation involved which may result in a two-stage process. Returning to acid-base systems of similar structures Bronsted and Pedersen pointed out a number of ways in which apparent deviations from the Bronsted relation (regarded as an empirical correlation) could be used to obtain information about equilibria or structures in solution.For example since solutions of carbon dioxide involve the equilibria C02+H,0 $ H2C03*H++HCO; with the ratio [C02]/ [HZC03]= 270 the catalytic power of the bicarbonate ion will be related to the "true " pK of H2C03 3.89 rather than to pK = 6.35 measured by conventional means. Bronsted and Pedersen were not able for technical reasons to test this idea for the decomposition of nitramide but it has been found subsequently that the bicarbonate ion does have an abnormally low catalytic effect in other reactions,20 and this offers in principle a method for determining the degree of hydration of carbon dioxide. Various types of isomerisation equilibrium can also be investigated and we have used this principle recently to investigate the lactol-ketoacid equilibrium HO 0 RCO v\ RC CO I I I I 1 lactol keto-acid carboxylate ion for 27 aliphatic and aromatic keto-acids.2 The overall dissociation constant was determined by conventional means and the "true " dissociation constant of the keto-acid form by measuring the catalytic effect of the carboxylate ion in the decom- position of nitramide.In the few cases where comparison is possible our values for the [lactol] :[keto-acid] ratio agree well with other sources. Mention may be made of two other applications proposed by Bronsted and Pedersen for nitramide kinetics which of course apply in principle to any systematic study of rates of proton transfer for a series of related acid-base pairs. The first refers to the dissociation of an unsymmetrical dibasic acid according to the scheme Hf +-XYH +HXYH +HXY-+H+ where the measurement of the rate of proton transfer to the equilibrium mixture of the ions -XYH and HXY-offers a method of determining the ratio of their concentrations.The second relates to the structures in solution of oxyacids and their anions for example phosphorous acid might exist 1- SPIERS MEMORIAL LECTURE as P(OHj3 OPH(OH), OzPH20H or OPOH. Bronsted and Pedersen show that the different statistical factors which these formulations imply lead to different kinetic consequences and hence to the possibility of distinguishing between them. It would seem worthwhile to investigate further the potentialities of these and similar applica- tions.(6) Although a simple molecular picture of proton transfers predicts that p should have the same value for substitution in both reactants there is no thermodynamic necessity for this to be the case. There are not many investigations in which syste- matic variations of both acid and base have been carried out but it is already clear that unequal values of p will be frequently encountered particularly when the two acid-base pairs are of very different structural types. The most striking example relates to the nitro-alkanes discussed in the next section but the reaction of diketones and keto-esters with carboxylate anions can also give unequal p-values as shown by the results in table 2.22 TABLE 2.-BRONSTED EXPONENTS FOR SUBSTITUTION IN BOTH REACTANTS (SIXCOMPOUNDS OF EACH CLASS WERE INVESTIGATED).acid base P C6H5CH2( MeCO)CHC02E t XC6H4CH2( MeCO)CHC02Et xco; CH,CO 0.44 0.77 xco 1.oo CH2ClCO 0.98 A related question is how far changes of AGO produced by changing the solvent can be represented by eqn (1) with the value of p derived from substitution in the reactants. Although this appeared to be the case in some instances,23 it is now clear that in general the effect of solvent upon the rate of proton transfer bears little relation to its effect on AG". This has been shown particularly clearly by Cox and Gibson,24 and certainly reflects the importance of changes in solvation as discussed in a later section. (c) The assumption that 0 < < 1 implies that the properties of the transition state are intermediate between those of the reactants and the products and in particular that substituent effects which affect only the transition state are unimportant.These conditions are satisfied for most systems but recent work by Bordwell 25 on the reactions of nitroalkanes with bases has revealed a number of exceptions. Whereas the reaction of a single nitroalkane with a series of bases (e.g. carboxylate ions) obeys a " normal " Bronsted relation with p z 0.5 the reaction of a single base with a series of nitroalkanes can give values of p which are either negative or greater than unity thus representing an extreme case of the behaviour described in the last paragraph. These " deviant " Bronsted exponents have been rationalised by different authors in different ways including the superposition of two effects which vary differently with the extent of proton transfer and the dissection of the process into two stages.Since this topic is the subject of another paper in this Symposium 25 it will not be pursued here. (n)The original formulation of the Bronsted relation represented an integrated form of eqn (1) with p assumed constant and it was realised by Bronsted and R. P. BELL Pedersen that plots of In k against In K (i.e. of AG* against AGO) for a series of similar acids or bases would remain linear only over a limited range. In practice it is difficult to detect curvature experimentally without covering several powers of ten in k and K, and such ranges are often attainable only by introducing chemical variations which may conflict with the requirement of a “ similar” series.For example it has recently been claimed 26 that one of the frequently quoted examples of a curved Bronsted plot (for the reaction of bases with compounds containing the carbonyl group) is better represented by two straight lines one for monocarbonyl and the other for P-dicarbonyl compounds. Nevertheless there is now good semi- quantitative evidence for such curvature for a number of reactions 27 and much interest attaches to its theoretical interpretation or prediction. There are three main causes of such curvature. The first arises when the reaction involves two or more consecutive stages and a change in reactivity causes a shift in the rate-limiting step.It has been considered particularly by Jencks,28 and will not be discussed further here. The second is usually referred to as Eigen curuature though it was in fact predicted in the 1924 paper of Bronsted and Pedersen. The argument is that for a highly exoergic proton transfer reaction will take place at every encounter independent of AGO SO that P = 0 similarly for a highly endoergic transfer the rate of the reverse reaction is independent of AGO giving p = 1 for the forward reaction. The complete curve will therefore resemble fig. 2 reproduced from Bronsted and Pedersen with a FIG.2.-Relation between catalytic power and acid-base strength over a wide range reproduced from ref. (8). curved transition region in which p is varying with AGO. The same argument was produced subsequently by Eigeq2’ who gave a more quantitative treatment and showed that the whole transition region would extend effectively over only a few powers of ten in k and thus could not explain the more extended linearity (with p < 1) commonly observed.The third type of effect is termed Marcus curvature and focuses attention on the chemical activation barrier. There is no general reason why the height of this barrier should be a linear function of AGO over an extended range and the simplest inter- pretation of the Bronsted relation in terms of intersecting potential energy curves 30 shows that linearity will be maintained only over the range in which the two inter- secting curves themselves remain linear. Predictions of Bronsted curvature therefore demand some assumption about how the energy profile varies with AGO and this is SPIERS MEMORIAL LECTURE what is done in Marcus' theory originally developed for electron transfers 31 and subsequently applied to proton transfers.32 By assuming that AG* is determined by the point of intersection of two identical parabolae and that the only effect of varying AGO is to displace these parabolae vertically with respect to one another he derives the following expressions AG* = -RTln(k/Z) = (1 +AGo/4AG:)2AG,f p = dAG:/dAGo = +(1 +AGo/4AGz) dp/dAGo = 1/8AG where Z is a collision number and AG: (assumed constant for a given type of reaction) is the so-called "intrinsic barrier " corresponding to AGO = 0.Eqn (2) has also been derived by procedures which superficially differ fundamentally from Marcus' procedure but they all contain the same assumption about intersecting parabolic energy curves or else the equivalent assumption that j? is a linear function of AGO.AG"/AG$ FIG. 3.-Relations between Bronsted exponent and AGO based on intersection Morse curves. (R. P. Bell to be published). There is little doubt that Marcus' theory gives a qualitatively sound basis for understanding the curvature of Bronsted plots and in particular its prediction that the curvature (d/?/dAG") will increase with the intrinsic rate is borne out by experiment. However it suffers from the limitations of the model on which it is based and care must be taken in applying it quantitatively. Thus the fact that p is often found to have different values for variation of the two reactants is evidence against the model of identical intersecting parabolae a fixed distance apart and Koeppl and Kresge have shown 34 that if the curvatures and separation of the parabolae are allowed to vary the resulting plots of p against AGO are sigmoid rather than linear as in eqn (2).Although such plots may be effectively linear over a limited range their slopes differ considerably from 1 /8AG$ and application of Marcus' equations would lead to incorrect values for AG;. If the picture of intersecting potential energy curves is adhered to Morse curves may be more realistic than parabolae and I have recently made calculations on the basis of this Fig. 3 shows the results for three R.P. BELL 15 typical Morse curves it is clear that the curvature may be either greater of less than the Marcus value and may even have the opposite sign. The picture of intersecting curves represents a particular approximation (small overlap) and the opposite extreme is represented by the BEBO treatment which has been applied extensively to hydrogen atom transfers. Marcus has shown 32 that this assumption leads to relations similar to eqn (2) but the quantitative results are again different. The real difficulty here lies in devising a model to represent the forces acting on the proton during its transfer and it is not clear at present whether these differ in any major way from those operating in hydrogen atom transfers. The above considerations apply to the process of proton transfer between two reactants which are correctly positioned and solvated.It is now generally believed that the observed free energies of activation contain a substantial contribution from the energy needed to bring the separated reactants together and to re-organise the solvent and this process is envisaged as taking place before the proton transfer.* This can be allowed for by adding to eqn (2) two further energy terms (for the forward and reverse reactions) usually denoted by wr and wp. In principle it is possible to determine both AG and wr (and sometimes also wp) from experimental curved Bronsted plots and this kind of analysis has been carried out by a number of authors. 27 However the values of AG and w thus derived must be regarded with caution partly because the curvatures are not accurately defined experimentally and partly because of the reservations about energy profiles expressed in the last paragraph.? These problems are of course appreciated by the authors concerned and some of the points are considered in the papers by Marcus and by Hassid Kreevoy and Liang in the present Symposium.The terms w' and wp in the last paragraph are one example of a general problem the role of the solvent in proton transfer reactions. The solvation of the proton and of other ions is of course of prime importance in determining the position of proto-lytic equilibria but we are concerned here more with the kinetic effect of changes of solvation which must accompany the redistribution of charge during a proton transfer.This may be thought of in terms of the solvation of the transition state though this implies an equilibrium situation and it is still an open question whether the re- orientation of the solvent may lag behind the movement of the proton so that equilibrium solvation exists only in the initial and the final states. Much interesting information has been derived from the effect of varying the solvent and more should soon be available from the study of proton transfers in the gas phase though so far the latter have yielded more information about equilibria than about kinetics. In amphiprotic solvents such as water there may be a more intimate involvement of solvent in which proton transfer takes place through one or more intervening solvent molecules.The oldest example of this is the Grotthus chain mechanism for explaining the high mobilities of hydrogen and hydroxide ions in water and a similar explanation has been given for the high rate of the reaction H,O++OH-+ 2H20 though it should be noted that more recent determinations 46 gave a considerably lower value for this rate. Direct evidence for proton transfer through a water molecule was first obtained in n.m.r. studies by Grunwald Lowenstein and Meibo~m,~~ who showed from the broadening of the water singlet that in proton exchange between amine molecules and their cations the indirect process was more important * The separation of these two processes is probably justifiable for electron transfer but less clearly so for proton transfers.iIf the intrinsic barrier heights AG$ are really as low as concluded in the analyses quoted a treatment in terms of parabolae becomes more reasonable however there is an obvious danger of a circular argument here! SPIERS MEMORIAL LECTURE than direct exchange. Many other systems were found subsequently to show similar behaviour which seems to be fairly general for oxygen and nitrogen acids. A special situation arises in the reversible addition reactions of water and similar substances to carbonyl compounds which are catalysed by acids and bases. Reason-able mechanisms involving two successive proton transfers are as follows Acid cataZysis R2C(OH) +HB +R2C(OH)OHi+B-+R2C0+H20+HB Basic catalysis R,C(OH) +B-+R,C(OH)O-+HB +R2C0+H20+B-.However it was pointed out by Eigen 37 that the observed rates in some systems would imply individual velocity constants in excess of the diffusion-controlled limit. He therefore proposed a "one-encounter " or "intimate " mechanism in which both proton transfers take place within a single encounter. Such mechanisms are sterically more plausible if the transition state contains one or more extra water molecules leading to mechanisms such as the following H H H H \ / \ / 0-H-0 0--H-0 I \ I \/ C H C H 1 L /\ /\ I 0 H-0 0-H--0 \ \ H H Support for this view comes from the high orders with respect to water and the large negative entropies of activation which are found when such reactions are studied in solutions of water in non-aqueous though there is no direct evidence for a cyclic transition state and the position may be different in aqueous solution.In these and similar cases it is also debatable whether the two or more proton transfers involved take place synchronously or step-wise. In general it is true to say that there is a growing realisation that solvent participation is important in a large proportion of proton transfer reactions but that there is still much uncertainty about the details of such participation. The final section of this survey deals with the use of liydrogen isotopes in proton transfer reactions. Soon after the discovery of deuterium in 1932 it was realised that isotopic exchange provided a means of studying rates of proton transfer and a number of mechanistic investigations by Ingold and others depended on a comparison of rates of deuterium exchange with other processes such as racemisation or bromina- tion.Subsequently tritium has proved a more useful tool in this respect especially for studying very slow proton transfers. However more interest attaches to kinetic isotope eflects and I shall consider only primary effects though it should be mentioned that in principle measurements in H20+D20mixtures can give information about the number of water molecules involved in the transition state. The current theory of kinetic isotope effects conveniently described as semi-classical derives through transition state theory from the corresponding theory for equilibria first formulated by Urey and by Mayer and Bigeleisen.It has been fully described many times and will not be discussed here.39 In the harmonic approxima- tion the expression for the isotope effect involves only the normal vibration frequencies of the initial and transition states and since computer programs are available for calculating normal frequencies in terms of force constants even for relatively compli- cated systems isotope effects can be calculated for a wide range of models. Since R. P. BELL the transition state frequencies are inaccessible to experiment comparisons of theory and experiment can serve as a method of probing transition state structures and have been widely used for this purpose. A particular problem which has attracted much attention is the variation of kH/kD(or kH/kT)with AGO in a series of similar reactions or with the symmetry of the transition state.It was first suggested by Westheimer 40 that kH/kDwould have a maximum value for a symmetrical transition state for which AG' should be close to zero. This has been confirmed experimentally for a number of proton transfer reactions and fig. 4 gives a further example recently studied in this laboratory.*22 AGO FIG.4.-Hydrogen isotope effects in proton transfer from 3-nitrocamphor to anion bases. (Unpub-lished results by Dr. S. Grainger). Even when no maximum is observed the dirzction in which kH/kDis changed by changes of reactivity can be used to judge whether the transition state is reactant-like or product-like and the result compared with evidence from other sources for example the deviation of the Bronsted exponent from the value one half.Such comparisons make good qualitative sense but it is doubtful whether any quantitative agreement can be expected between different approaches. The concepts of " transi-tion state symmetry " or " extent of proton transfer " are not well defined since they could refer to various properties of the transition state-geometrical position of the proton bond orders ratio of force constants charge distribution etc.-and there is no reason to expect that these properties will all vary in parallel. The semi-classical theory of isotope effects is consistent with a large proportion of the experimental data for proton transfer reactions but there is growing evidence that it does not tell the whole story.A recent survey 41 listed 27 examples of proton transfer reactions for which the isotopic dependence of either the reaction velocity or the Arrhenius parameters (or both) could not be explained by semi-classical theory as well as 25 further reactions involving transfer of hydrogen atoms or hydride ions. I have argued elsewhere 41 that these discrepancies are due to a neglect of the twinel L>flect i.e. the quantum correction which applies to the passage of light particles across energy barriers several authors 42 suggested around 1930 that this *It has also been suggested that the same type of relation would hold between variations of kH/kD and AGO caused by changes in solvent composition and such behaviour has been observed in a few instances.However the work reported by Cox and Gibson at this Symposium *' shows clearly that in general neither the rates nor the isotope effects of proton transfer reactions can be correlated with solvent effects on AGO. SPIERS MEMORIAL LECTURE effect might be important for the movement of protons in chemical reactions but it is only recently that experimental confirmation has been forthcoming. It should be stressed that the tunnel correction has just the same logical status in quantum theory as zero point energy since both are a direct consequence of the uncertainty principle and it is interesting to note that in the harmonic approximation the tunnel correction can be incorporated in the semi-classical expression for the isotope effect merely by including one imaginary frequency to represent motion along the reaction co-ordinate.Moreover model calculations 43 suggest that the tunnel correlation is at least as important as the real vibrations of the transition state and in particular that the variation of kH/kDwith AGO is attributable almost entirely to a variation in tunnel effect the contribution of the real vibrations being negligible. If this result applies generally it means that we can still accept the correlation between isotope effect and transition state symmetry though the reason is no longer that given originally by We~theimer.~~ A number of authors have invoked tunnelling to account for experimental results on proton transfer reactions and in particular Caldin 44 has used it to explain some very large isotope effects and deviations from the Arrhenius equation at low tem- teratures.His latest work reveals a remarkably large solvent dependence of some isotope effects probably attributable to the influence of solvent interaction on the effective mass of the proton and hence on the tunnel c~rrection.~~ This promises a new approach to the investigation of coupling between proton transfer and solvent motion. It should however be mentioned that there are difficulties in the theory of the tunnel correction which do not arise for real vibrations of the transition state. In a complete quantum-theoretical treatment tunnelling would not arise as a separate issue and the usual procedure of multiplying the transition state expression by a tunnel correction is strictly valid only when this correction is small and the same limitation applies to the assumption that tunnelling takes place along a single separable coordinate.Moreover the shape of the barrier for specific reactions is even more difficult to guess than the transition state frequencies though it can be derived from a complete treatment of any model. Thus our conclusion must be that we can have some confidence in the fundamental ideas behind the tunnel correction but that there is still much to be done in relating our models to the reactions which we investigate. The same conclusion applies to several other aspects of proton transfer studies and it is interesting to see how many of the questions raised at the 1965 Faraday Society Discussion on proton transfers are still matters of current concern.Disc. Faraday SOC. 1965 39. R. P. Bell The Proton in Chemistry (Chapman and Hall London 2nd. edn. 1973). E. F. Caldin and V. Gold (ed.) Proton-Transfer Reactions (Chapman and Hall London 1975). J. N. Bronsted Rec. Trav. Chim. 1923 42 718. J. N. Bronsted Om Syre- og Basekatlyse (University of Copenhagen 1926) English translation Chem. Rev. 1928 5,231. E. Wiberg 2.phys. Chem. A 1934 171 1. 'H. M. Dawson and F. Powis J. Chem. SOC. 1913 2135 ; H. M. Dawson and C. K. Reiman J. Chem. SOC.,1915,1426. J. N. Bronsted and K. J. Pedersen,2.phys. Chem. 1924 108 185. K. J. Pedersen Den almindelige Syre- og Busekatalyse (Copenhagen 1932) ; J. Phys. Chem.1934 38 581 ; Trans. Faraday SOC. 1938 34 237. lo For references see ref (2) p. 148. l1 A. J. Kresge Chem. SOC. Reu. 1973 2 475 ; also Chapter 7 of ref. (3). l2 A. J. Kresge and Y. Chiang,J. Amer. Chem. SOC. 1973 95 803. l3 R. P. Bell and A. F. Trotman-Dickenson J. Chem. SOC.,1949 1288; R. P. Bell and G. L. Wilson Trans. Farnday SOC. 1950 46,407. R. P. BELL l4 A. F. Trotman-Dickenson J. Chem. SOC. 1949 1293 ; A. G. Evans and S. D. Hamann Trans. Furuduy SOC. 1951 47 34. l5 R. P. Bell M. H. Rand and K. M. A. Wynne-Jones Trans. Faruday SOC., 1963 85 1773 ; J. A. Feather and V. Gold J. Chem. SOC.,1965 1752. l6 R. P. Bell E. Gelles and E. Moller Proc. Roy. SOC. A 1949 198 308. l7 A. Hantzsch Ber. 1899 32 575. R. P. Bell and W. C. E.Higginson Proc. Roy. SOC. A 1949,197,141 ; R. P. Bell J. Phys. Chem. 1951 55 885. l9 F. G. Bordwell and W. J. Boyle J. Amer. Chem. SOC.,1975.97 3447. 2o F. J. W. Roughton and V. H. Booth Biochem. J. 1938 32 2049; A. R. Olson and P. V Youle J. Amer. Chem. SOC., 1940 62 1027. 21 R. P. Bell B. G. Cox and B. A. Timimi J. Chem. SOC.B 1971 2241 ; R. P. Bell B. G. Cox and J. B. Henshall J.C.S. Perkin 11 1972 1232 ; R. P. Bell and J. B. Henshall J.C.S. Perkin II 1975 39; R. P. Bell and A. D. Covington J.C.S. Perkin II 1975 1343. 22 Unpublished measurements in this laboratory by Dr. S. Grainger. 23 R. P. Bell and B. G. Cox J. Chem. SOC B 1970 194; 1971 783. 24 B. G. Cox and A. Gibson Furaduy Symp. Chem. SOC., 1975 10 107. 25 For references see F. G. Bordwell Faraday Symp.Chem. SOC.,1975 10 100. 26 D. S. Kemp and M. L. Casey J. Amer. Chem. SOC. 1973,95 6670. 27 For references see ref. (11). 28 W. P. Jencks and J. M. Sayer Faraday Symp. Chem. SOC.,1975 10,41. 29 M. Eigen Z. phys. Chem. (Frankfurt) 1954 1 176 ; Angew. Chem. (Int. Edn.) 1964 3 1. 30 R. P. Bell and 0. M. Lidwell Proc. Roy. SOC. A 1940 176 114. 31 R. A. Marcus J. Chem. Phys. 1956 24,966; Disc. Faruday SOC. 1960 29 21 ; J. Phys. Chem. 1963 67 853 2889; Ann. Rev. Phys. Chem. 1964 15 155; J. Chem. Phys. 1965 43 679. 32 R. A. Marcus J. Phys. Chem. 1968 72 891; J. Amer. Chem. SOC.,1969 91 7224; A. 0. Cohen and R. A. Marcus J. Phys. Chem. 1968 72 4249. 33 V. G. Levich R. R. Dogonadze and R. M. Kuznetsov Electrochim. Acta. 1968 13 1025; Elektrokhimiyu 1967 3 739 and later papers ; J.R. Murdoch J. Amer. Chem. SOC.,1972 94 4410. 34 G. W. Koeppl and A. J. Kresge J.C.S. Chem. Comm. 1973 371. 35 R. P. Bell to be published. 36 E. Grunwald A. Loewenstein and S. Meiboom J. Chem. Phys. 1957 27 630. For later summaries see A. Loewenstein and T. M. Conner Ber. Bunsenges. 1963 67,280 ; also chapter 4 of ref. (3). 37 M. Eigen Disc. Faruday SOC. 1965 33 7. 38 R. P. Bell J. F. Millington and J. M. Pink Proc. Roy. Soc. A 1968,303 1 ; R. P. Bell and P. E. Sorensen J.C.S. Perkin 11 1972 1740. 39 See e.g. C. J. Collins and N. S. Bowman (ed.) Isotope Eflects in Chemical Reactions (Van Nostrand New York 1970). 40 F. H. Westheimer Chem. Rev. 1961 61 265. 41 R. P. Bell Chem. SOC. Rev. 1974 3 513. 42 F.Hund Z. Phys. 1927 43 805 ; D. G. Bourgin Proc. Nat. Acud. Sci. 1929 15 357 ; R. M. Langer Phys. Rev. 1929 34 92 ; S. Roginsky and L. Rosenkewitsch Z. phys. Chem. B 1930 10 47; E. Wigner Z. ghys. Chem. B 1932 19 203; R. P. Bell Proc. Roy. SOC.A 1933 139,466; C. E. H. Bawn and G. Ogden Truns. Furudzy SOC. 1934 30,434. 43 R. P. Bell W. H. Sachs and R. L. Tranter Truns. Faruduy SOC. 1971 67 1995. 44 E. F. Caldin Chem. Rev. 1969 69 135 and later papers. 45E. F. Caldinand C. J. Wilson FarudqSyrnp. Chern. SOC., 1975 10 121. 46 G. Brikre and F. Gaspard J. Chem. Phys. 1967 64 463 ; G. C. Barker and D. C. Sammon Nature 1967 213 65.