Kinetics of Proton Transfer ProcessesGeneral IntroductionBY M. EIGENMax-Planck-Institut fur physikalische Chemie, GottingenReceived 4th May, 1965Proton transfer processes-although they have never appeared in the titles-have repeatedly been the subject of Discussions of the Faraday Society. Theconference on Homogeneous Catalysis held at Cambridge University in 1928 wasalmost entirely dedicated to the catalytic action of proton donors or acceptors,i.e., acids and bases according to Bronsted's definition. One of the main concernsof the speakers at that meeting was the quantitative establishment of the fact thatthe catalytic effect of acids and bases is not an exclusive property of the hydrogenor hydroxyl ion-a view which was first adopted by Ostwald. Thus, the highlightof the meeting was Bronsted's paper on The Theory of Acid and Basic Catalysisin which he gave a quantitative account of the catalytic effects of acids and basesin relation to their dissociation constants.On reading these papers, it is inter-esting to note how close our modern views come to the original concepts. In themeantime these were partly obscured because most data were specifically selectedas a consequence of practical limitations. Experimental limitations may alsoexplain the fact that the chemists at that time turned their interest more towardsan investigation of complex reaction mechanisms rather than towards the study ofthe more simple elementary steps involved in acid-base catalysis.The success in establishing and categorizing such more complex mechanismswas reflected in another famous meeting, the discussion of Mechanisms andChemical Kinetics of Organic Reactions in Liquid Systems held at London in 1941.The illuminating papers given by Ingold, Hughes and others certainly represent alandmark in establishing the discipline of " physical organic chemistry ".The efforts of physical chemists to penetrate the mechanism of catalysis by study-ing the elementary steps were thwarted until suitable methods for the study of rapidreactions were found.Again it was the Faraday Society who opened the discussionof such possibilities at their Birmingham meeting on The Study of Fast Reactionsin 1954. Almost no experimental data were available at that time, but the expecta-tions expressed by Bell in his introductory remarks that chemists as a whole maytake advantage of the new methods are now apparently being fulfilled, especiallyin the field of protolytic reactions.Almost all simple proton transfer processesare rapid. Thus, many of the experimental results which will be reported at thismeeting could only be obtained by use of the techniques which were introduced atthe 1954 meeting. These include :THE SAMPLING TECHNIQUES such as isotope exchange [papers by Bell, Ausloos andLias, Challis and Long, Kresge et al., Gold and Kessick] and nuclear mag-netic resonance [papers by Grunwald and Cocivera, Ahrens and Strehlow,Mackor and co-workers],8 KINETICS OF PROTON TRANSFER PROCESSESRELAXATION OR PERTURBATION TECHNIQUES such as temperature, pressure and electricfield pulse, as well as sound and dielectric absorption techniques [cf.belowand papers by Bewick, Fleischmann, Hiddleston and Wynne-Jones] andflash photolysis or radiolysis Cpapers by Ausloos and Lias, Porter and co-workers],FLUORESCENCE TRANSFORMATION AND OPTICAL LINE BROADENING Cpapers by Wellerand co-workers, Kreevoy and Mead, Wynne-Jones and co-workers], andTHE ELECTROCHEMICAL METHODS [papers by Nurnberg, Bewick et al., Salomon andOther papers in this discussion deal with the behaviour of protons under extremeconditions such as :Conway Bockris, et aZ.1.HIGH TEMPERATURE AND PRESSURE [papers by Franck and co-workers, Hillis et al.]andLOW TEMPERATURE [paper by Caldin and Kasparian].Measurements of this type, especially when carried out under such a wide rangeof external conditions as reported by Franck and co-workers, give a much broaderbasis for theoretical considerations (energy surfaces, tunnel effect, etc.) than theclassical data, which were usually restricted to the liquid state under normal tem-perature and pressure conditions.However, there is no longer any justification for categorizing these papers onlyaccording to their technical approach.The techniques are sufficiently well estab-lished that we no longer merely have to look for " applications ". Rather, we maynow start from the chemical problem itself, and use at will any technique that isdesirable. It is this approach to the problem which will be at the centre of ourdiscussion, and to which I shall here add a few general remarks.*NATURE OF PROTON TRANSFER PROCESSESThe rate of proton transfer is decisively determined by the distance betweenthe donor and acceptor group at the moment of transfer.In the classical picturethis distance will have a great influence on the activation energy since it will deter-mine how well the potential curves along the reaction co-ordinate overlap. Fora tunnelling mechanism the rate will be even more sensitive to this distance. There-fore the formation of an H-bond, providing an optimal overlap of the potentials,is a most important prerequisite for a fast proton transfer. Furthermore it minim-izes any rearrangements of the heavier atoms. Restrictions of the Franck-Condontype are therefore much less important for proton- than for electron-transfer re-actions.Experimental data 1 9 2. show that proton transfer processes can becomequite slow when interference with the H-bond formation between the donor andacceptor group occurs. One would expect that following the tendency to H-bondformation, the rate of proton transfer parallels the series :O H . . . O > O H . . . N, N H . . . O > N H . . . N > S H . . . X, X H . . . S >P H . . . X, X H . . . P > C H . . . X, X H . . . CIn aqueous solutions the rates of the reactions with H3O+ and HO- have been* For a more detailed discussion reference is made to some recent reviews.ls 2(charge and steric effects may lead to certain distortions)M. BIGEN 9studied for a great variety of compounds including almost all well-known typesof inorganic and organic acids and bases.As is shown by comprehensive tablesin ref. (1) and (2), in most cases the rate constants of recombination (H3O+ + base,or HO- + acid) approach the limiting values for diffusion-controlled reactions (1010-1011 M-1 sec-1). They show certain influences of charge, steric requirements, solvent-H-bonding, etc., which have been discussed in detail.17 2 Where larger deviationsfrom this theoretically well understood behaviour occur, they can usually be relatedto more complex reaction mechanisms involving tautomeric or isomeric changes.Since H30+ is a very strong acid and HO- a very strong base, in most cases an ap-preciable gain of free energy is connected with the proton transfer : pK~,o+<pK~xor p K ~ , o % ~ K H x .If this condition is not fulfilled, i.e., if the pK of the acid formed-3 - 2 - I 0 I 2 3-3 - 2 -1 0 I 2 3FIG. 1 .-Theoretical dependence of log k (rate constant for proton transfer) on ApK (pK-differencefor donor and acceptor) assuming maximum rates (i.e., no potential barrier in favourable direction).rate constants are normalized by the rate Constan-kD for a diffusion-controlled process.Reactions including no charge neutralization :(e.g., XH+Y-+X-+YH,or XH++Y+X+YH+).Reactions including charge neutralization :(e.g., XH++Y-+X+HY: ZD>ZD).in the reaction is not higher than that of H3O+ (example : protonation of carbonyl-groups of ketones and aldehydes), the reaction can no longer be diffusion controlled,but-at least when oxygen is the acceptor-the reverse reaction might be.Aslong as the reactions are diffusion controlled-as most reactions of H3Of and HO-are-they provide little information about the nature of the proton transfer, sincethis step is not the rate-limiting one10109654KINETICS OF PROTON TRANSFER PROCESSES- 4 - 3 - 2 - 1 0 I 2 3 4 5 65* M0 -0-5APK(b)FIG. 2.-Measured dependences of log k (rate constant for proton transfer) on ApK. (pK-differ-(a) Upper curves : phenol with different acceptors (around pK 10) ; lower curves : thyoglycole(b) Acetylaceton (ketonic) with different acceptors (PK values between -2 and 16) ; cf. alsoence for donor and acceptor.)with different acceptors (around pK 10)M.EIGEN 11More information about this step may be obtained from studies of proton transferreactions in those acid-base systems which show only small pK-differences for thedonor and acceptor. Fig. 1 represents what is to be expected if the rates are maximal.For a pK-difference of 0 the rates in both directions are equal and half of themaximum value. For a positive pK-difference (increase of pK in direction ofthe transfer : pKm > pKm for XH + Y -tX + HY) the rate approaches the maximumvalue and hence becomes independent of the pK-difference (for acids and bases otherthan H30+ and HO- k is usually 109-1010 M-1 sec-1) whereas for the reverse reactionlog k depends linearly on the pK-difference. Again, charge and steric effects (alsointernal H-bonding) might lead to certain distortions (cf.fig. 121).Some representative examples of experimentally determined dependences forthe different types of acid-base systems (studied with a great variety of differentdonors and acceptors) are shown in fig. 2. Here the rates show the above-mentionedbehaviour. For certain transfer processes of the type OH . . . 0 the rates approachthe ideal behaviour according to fig. 1 throughout the whole ApK-range. ForNH . . . N-systems deviations around ApK=O become perceptible. For SH-compounds these deviations become quite pronounced and for CH-compoundsthey extend over a very large ApK-range. However, even for these systems thegeneral character of the curves is still maintained, i.e., log k becomes independentof or linearly dependent on ApK for extreme values of ApK.According to somemeasurements of Grunwald et al. and Luz and Gill 3 one may expect the curvefor phosphine-compounds to come below that of sulf hydril-compounds. Further-more, recent studies of the properties of the solvated electron4 in water allows anestimation for the behaviour of its conjugate acid: the H-atom (which is an acidcomparable in strength to phenols). This curve would fall in between the -SHand -CH-compounds. There is no single curve describing all the different CH-compounds and the larger the deviation from the ideal curve in fig. 1 the larger therange of scatter (the curve in fig. 2 refers to the group of aliphatic ketones). Evenfor OH-compounds one can still distinguish several classes of curves.The idealbehaviour is only shown for " hard " acids and bases where the charges are con-centrated at the donor or acceptor site. The presence of resonance stabilization ofthe acid or base with respect to its conjugate compound introduces small butperceptible deviations from the ideal curve.ACID-BASE CATALYSISThe behaviour of the different classes of acids and bases as shown in fig. 2 shouldgive us a key for an understanding of the mechanisms of acid-base catalysis. TheBronsted relation, which describes the dependence of the log of the rate constantof catalysis on the pK of the catalyzing acid or base respectively, is nowadaysusually known as a linear relationship of the form log k = a (pK)i-c, with a and cbeing constants (c might include an individual statistical correction for multifunctionalgroups).It should be emphasized, however, that Bronsted originally expected abehaviour as shown in fig. 2, is., a continuous variation of a between 0 and 1.The linear relation (resulting from a McLaurin expansion) should then hold only fora limited pK-range. The limitations of the time-range of classical techniques ledto the fact that mostly only those rates were measured which are sufficiently farfrom diffusion controlled and where a remains constant over a wide pK-range.There is no reason to assume that a really changes continuously with pK. Fromsimple models of potential curves one might even expect that a remains almostconstant in a relatively wide pK-range. However, this can only be true fo12 KINETICS OF PROTON TRANSFER PROCESSESprocesses in which there are high barriers of free energy of activation in both directions.In this range the overlapping branches of the potentials can be approximated bylinear functions which is only possible if the region of overlapping is sufficientlyfar from the bottom of the potential curves.Examples of a continuous variationof a with ApK are provided by certain keto-enol changes which have been studiedby Bell and his school 5 using the bromination technique. It was found that for aseries of related compounds the observed value of a changes with the substrate pK,whereas for each substrate there was a constant a in the limited pK-range of thecatalyst which was studied. Relaxation studies in a wider pK-range show thatmost curves for different substrates and catalysts if plotted as a function of ApK,can be combined in a single curve with an a continuously varying from 0 to 1 (cf.acetylacetone in fig.2). More constant U-values in a wider pK-range have beenfound by isotope exchange studies, as reported at this Discussion by Challis andLong, and Kresge et al. However, the absolute values of the rate constants are muchlower than in the cases mentioned above, so the range of validity of the linear ap-proximation in the McLaurin expansion might here include the whole pK-rangestudied.There is a great number of thoroughly studied6 reactions which require botha catalyzing acid and a base (examples: mutarotation of glucose, hydration-dehydration reactions, certain hydrolysis reactions and other prototropic changes).Their general mechanismHS+HA +B+SH+ B+HAis often written in the form of a stepwise mechanism :HS + HAgHSH + BB + HSH+HA + SH(HA being the acid catalyst and HS the substrate).In such a formulation one has to assume that one of the protonation or de-protonation processes is the rate-limiting step.Thus the overall rate constant kmight consist of the product of an equilibrium constant and a rate constant k*.If one plots this rate constant k* as a function of pK one often encounters a constanta< 1 extending over a large range up to k*-values of 109-1010 M-1 sec-1, or even rateconstants exceeding the limiting values for diffusion-controlled reactions which is incontradiction to what has been found for other simple proton transfer processes.The only way out of these difficulties is the formulation of a concerted or co-operativemechanism where both the acidity of the catalyst HA and the basicity of its con-jugate base B come into play at the same encounter. In aqueous solution one canformulate this easily with the help of one or several H20 molecules (having thebifunctional effect of an acid and a base). Lowry in his introduction to the 1928meeting, has already emphasized the importance of H20, I quote :rapid ++“ In aqueous solution the action will generally be :base + HS + HOH +acid + SH + OH(-)OH2 + HS + acid+OH(i) + SH + base orwhere the water plays the part of an acid when the catalyst is a base, or of a basewhen the catalyst is an acid.”With our present knowledge we can now say that the mechanism must involveboth processes at the same encounter, e.g.13H - - - - ‘ H be A\o’- - - .- HA -./ - / # - - - - O - - - - HA __c s’ S‘ - - - c- -H’ ‘H. . . _ . ”possibly including several water molecules in the ring.Such a co-operative mechanism would be favoured since it avoids the solvationand desolvation of any charged intermediate. Restrictions of the Franck-Condontype impose a certain structure on the substrate-solvent-catalyst complex. Thisstructure (and therefore the whole concerted mechanism) may be disfavoured ifone (or both) of the donor-acceptor sites include a non-H-bonding group (e.g.,CH).Here the stepwise mechanism might be more effective.16 I4 12 10 8 6 4 2 0 -2- log10 (qK4d.P)FIG. 3.-Bronsted plot of the catalytic rate constants [M-1 sec-11 of various acids in the dehydrationof acetaldehyde hydrate according to Bell and Higginson.8 Solid line: measured rate constantagainst PKA of catalyst (including statistical correction factors p and q). This linear relationshipis obeyed by more than 50 substances showing a mean deviation of 0.15 log units throughout thewhole pK-range (note measured point for H20 which shows positive deviation). Broken line:rate constant k* for ratelimiting step (deprotonation) assuming a stepwise mechanismrapidHS + HA+HS+H+BHS+H+B +SH+HA.For p K ~ s @IS = hydrated acetaldehyde) a value of -2 has been chosen arbitrarily.(Note thatthe rate constant k* for HO- as a base would be above diffusion controlled and that no chang ofIX according to fig. 2 is present.14 KINETICS OF PROTON TRANSFER PROCESSESIn an H-bonded substrate-solvent-catalyst complex the potential surfaces alongthe path of proton transfer have very similar forms for a given substrate and a varietyof different catalysts, resulting in a persistently constant a over a wide pK-range.(The rate constants for the concerted transfer are still far from diffusion controlled ;in other words, o! must tend to 0 if the rate constants approach these limits.)In the concerted mechanism the catalyst merely triggers the reaction, and itselfremains essentially unchanged. This does not exclude an intermediary protontransfer from or to the catalyst. However, the lifetime for the intermediate shouldnot exceed the time necessary for orientation or disorientation of the solvent mole-cules, i.e., the time for the solvation of the intermediates.Similarly, the term“ concerted ” does not necessarily require a concerted motion of all the protonsinvolved, but means a correspondence between these motions within times of< 10-10 sec. This correspondence might be quite strong since the intermediatestates are not solvated. Further experimental and theoretical studies are requiredto resolve all the couplings and normal modes in the transition complex whichare effective for the co-operative proton transfer.In aprotic solvents the reaction requires bifunctional catalysis as Swain andBrown have clearly demonstrated. If the catalyst itself is not bifunctional bothan acid and a base in a ternary complex with the substrate are required.(Athorough discussion of these experiments is given in ref. (5).) The bifunctionalrole of water is also expressed in Grunwald’s experiments on proton transfer be-tween an acid and its conjugate base via H20 by the finding of a pK dependencecorresponding to an “ a-value ” between 0 and 1. A more detailed descriptionof such concerted proton transfer processes, which are of great importance for anunderstanding of the catalytic properties of enzymes, is given in a forthcomingpaper?CONCLUSIONSWe have seen at least the possibility of an understanding of the nature of acid-base catalysis in terms of the elementary steps of the reactions involved.A numberof such steps has already been identified and categorized and we might expect thatthis procedure is applicable to any type of reaction. It should then be possiblenot only to predict a certain catalytic mechanism but also to define its optimalconditions. This might also bring us close to a solution of the problem of enzymeswhose turnovers often include concerted internal acid-base catalysis (hydrolases,etc.). At present we can only give upper limits for a most favourable mechanismof this kind and-surprisingly enough-the measured turnover-numbers comefairly close to these figures. Other applications include a revision of certain ruleswhich have been proposed for the kinetics and mechanisms of organic reactionsincluding prototropic changes (such as keto-enol tautomerism and others29 7.On the other hand, while we now have some understanding of the relations be-tween rates and structure, many of the details are still obscure.What influencesdetermine the potential energy surface in a proton transfer reaction? What isthe nature of the activated state? Can we find any correlation of the isotope effectswith the variation of the Bronsted coefficients? Both quantities should be relatedto the form and height of the potential barrier. As Bell points out in his paper,there is no doubt that systematic experiments with isotopes will bring us moreinformation about these questions. The same may be true for the study of protontransfer processes at electrodes, where one can change the variables continuouslyin a defined manner. However, any progress in this field depends largely on abetter understanding of the metal/solution interface propertiesM. EIGEN 15I might close by expressing the hope that this conference will live up to the standardso excellently defined by Ingold in his introductory remarks to the 1941 discussions :“The Council of the Faraday Society has always shown a remarkable facility forselecting subjects for discussion in so timely a manner that the discussions them-selves do not merely record chemical history but make it. ’’la Weller, Prog. React. Kin., 1961, 1, 189.1b Eigen, Kruse, Maass, De Maeyer, Prog. React. Kin., 1964, 2,285.ZEigen, Angew. Chern., 1963, 75, 489; int. edn., 1964, 3, 1 ; (part TI on “ Mechanisms of3 For references cf. Grundwald‘s paper in this Discussion.4 Matheson and Rabani, in press ; cf. also Rad. Research, 1963, 19, 180 ; 1964, 4, 1.5 Bell, The Proton in Chemistry (Cornell University Press, New York, 1959).6 Bell, Acid-Base Catalysis (Oxford University Press, Oxford, 1941).7 Ingold, Structure and Mechanism in Organic Chemistry (Cornell University Press, New York,8 Bell and Higginson, Proc. Roy. SOC. A , 1949, 141, 197.Catalysis ” in preparation).1953)