1. OXIDATION-REDUCTION REACTFIQNS IN IONIZING SOLVENTS INTRODUCTORY PAPER ELECTRON-TRANSFER REACTIONS BY J. HALPERN* AND L. E. QRGEL Dept. of Theoretical Chemistry, University Chemical Laboratory, Lensfield Road, Cambridge Received 20th April, 1960 The papers in the first section of this Discussion are largely devoted to the consideration of reactions of the type : Cr2 + + co3 + +Cr3 + + Co2 +, (1) Co(NH3);' + Eo(NH3):+ *Co(NH3):+ + >o(NH~);+, (2) * * TI+ +TI3++Tl3' +T1+, (3) 2Fe2+ +TI3+-+2Fe3 i- +T1", (4) in which the overall change, apart from sometimes subtle rearrangements in the co-ordination shells of the reacting metal ions, corresponds simply to the transfer of one or more electrons between the ions. These are, at least superficially, among the simplest oxidation-reduction reactions and the ones in which the widely recog- nized, but sometimes artificial, connection between electron transfer and oxidation- reduction emerges most clearly.In view of this, it is a curious fact that tho study of such reactions, apart from considerations of stoichiometry and thermodynamics, was almost completely neglected until a few years ago; once started it has been pursued intensively by many workers. Thus a recent and fairly exhaustive com- pilation 1 lists more than a hundred simple redox reactions bctween metal ions or complexes, the kinetics of which have now been examined. With one or two exceptions these refer to work published within the last ten years and in well over half the cases within the last five. The study of electron transfer processes has thus increased very greatly in scope and taken on an entirely new emphasis since the Faraday Society last considered this subject at the Discussion on Oxidation in 1945.The elucidation of the mechanisms of electron transfer reactions between metal ions presents a problem of much greater difficulty and complexity than is sug- gested by the simplified equations by which we usually represent such reactions. The problem has been approached at various levels, both experimental and theoretical, and some of the most important studies relate to the following themes. (i) The nature and sequence, if more than onc, of the elementary steps which (ii) The composition and configuration of the activated complex in the electron * on leave from the Department of Chemistry, University of British Columbia, Van- comprise the overall reaction mechanism. transfer step.couver 8, B.C., Canada. 7ELECTRON-TRANSFER REACTIONS The atomic rearrangements accompanying the electron transfer process. Whether multi-electron redox reactions such as (3) and (4) occur in a single step or through successive one-electron steps. The significance of the large variations in rate which are observed in series of related electron transfer reactions in which the metal ions or the ligands are varied. Examples are the Cr2+-Cr3+, V2+-V3+, Fe2+-Fe3 I-, Fe(CN)% - -Fe(CN)i - and Fe( o-phen) $+-Fe( o-phen); -I- isotopic exchangc reactions whose bimolecular rate constants at 0" are of the order, < 10- ', Other examples of such variations are listed in table 1. 1, lo2 and >lo5 1.mole-' sec-', respectively.' TABLE 1 .-LIGAND EFFECTS IN VARIOUS ELECTRON-TRANSFER REACTIONS (bimolecular rate constants, 1. mole-1 sec-1) (HgN)gCo3 +X-I- Cr2 + (20") (H20)&r3+X+ Cr2+ (OO) (bridged) (bridged) H20 0.9 2 x 10-5 (250)~ F- 2.6 x 10-3d N5 > 1 -2d OH- 1-7 x 106a 0.7 (25" )c c1- > 103b 9d Br- > 6Od NCS- 1.8 x 10-4 (27")d ref. (16). b Anderson and Bonner, J. Amer. Chem. d SOC., 1954, 76, 3826. e Silverman and Dodson, J. Physic. Chem., g 1952, 56, 846. ref. (7). i Laurence, Trans. Faraday SOC., 1957, 53, 1326. Our understanding of these problems is still EXPERIMENTAL 2 x 103e 0.87f 1 x 103e 1 x 103~ 9*7g 1XlW 9.7s > 1.6 x 104e 4.9h 12-2i 2~ 103i ref. (15). ref. (24). ref. (28). Hudis and Wahl, J. Amer.Ciiem. SOC., 1953,75,4153. Bunn and Dainton, Truiu. Furuduy Soc., 1959, 55, 1267. far from complete, ASPECTS Conventional kinetic measurements have been widely used in the study of electron transfer reactions and account for much of our knowledge about their mechanisms. In most cases this approach yields information about the nature of the rate-determining step and the gross composition of the activated complex but not about its detailed configuration or about the participation of the solvent, which is normally present in large and constant excess. Sometimes the values of AH+ and, particularly, of AS* provide indirect information about these, but such information is subject to considerable uncertainty. The paper of Higginson et al.2 is of interest in this connection, Determination of the volume of activation from the pressure-dependence of the rate constitutes another potentially useful extension of the kinetic method; this has yielded information about the role of solvent and the configuration of the activated complex in a ligand exchange reaction 3 but has not so far been applied to oxidation-reduction reactions.The extension of kinetic measurements to non-aqueous solvents offers another poten- tially useful field of investigation. A number of studies of this type have recently been reported including the CeIII-PbIv and Corr-PbIV reactions in acetic acid 49 5 and the FelI-FeTI1 exchange in nitromethane and in alcohol^.^ The Fell-FelllJ . HALPERN AND L. E. ORGEL 9 reaction is much slower in these solvents than in aqueous solution, and is markedly accelerated by the addition of small amounts of water, suggesting that the latter plays a critical role in the reaction.However, these measurements also emphasize the limitations of our general knowledge about ionic reactions in non-aqueous solvents ; considerably more experience with systems of this type will be required before they can be interpreted with confidence. In many cases, kinetic measurements are limited by the high rates of electron- transfer reactions but this limitation is gradually becoming less important as various new methods for the measurement of fast reaction rates are being developed and applied. Flow methods, capable of measuring the rates of reactions with half- lives down to about 10-3 sec have been used to study the kinetics of the Mn0;- MnOi-, and Ag+-Ag2+ reactions ' 9 whose rate constants are of the order of lo3 1.mole-1 sec-1. The rate of Cu+-Cu2+ exchange (kz50 = 5 x 107 1. mole-1 sec-1 in 12 M HCI) has been estimated 10 from the broadening of the n.m.r. signal of Cu+ which occurs when Cu2-t is added and the rate of electron exchange between naphthalene and its mononegative ion (k-107-109 1. mole-1 sec-1) by a corres- ponding e.s.r. measurement ; 11 these techniques will undoubtedly find many other applications. Relaxation methods 12 which have been used to measure the rates of very rapid proton transfer and ionic association reactions (k up to 1011 1. mole-1 sec-I-) also offer possibilities which have not so far been exploited for the study of oxidation-reduction reactions.The introduction of isotopes into common laboratory use has often been cited as one of the most important factors responsible for the recent awakening of interest in the study of electron transfer reactions. One widespread use has been in the study of isotopic exchange reactions between different oxidation states of the same element. Such reactions often have the advantages of being slower than those involving a net chemical change and of providing more convenient models on which to base theoretical treatments, since there is no overall energy change. Isotopic labelling of ligands can also provide valuable information about the detailed mechanism of electron transfer and the configuration of the activated complex. An example of this is the recent demonstration by Kruse and Taube 13 that the oxidation of Cr2+ by (H~N)~CO(OH~)~+ is accompanied by transfer of oxygen from the cobalt complex to chromium.Since both the CO~+ complex and the Cr3+ produced are substitution-inert, this implies that electron transfer proceeds through the bridged intermediate 1 5 + . H (H~N)~CO-O-C~(OH~)~ II H Another important example, involving isotopic labelling of the ligands in the study of the PtT*-PtrV exchange, is described in the paper by Morris, Basolo and Pearson.14 Finally, reference should be made to the measurement of kinetic isotope effects in the study of electron-transfer reactions.15-18 Such measurements may provide information about the extent to which bonds involving the isotopically substituted atoms (0, N and H in the cases examined) are weakened in the activated complex, but unfortunately their interpretation is not always free from ambiguities. This is particularly the case for kinetic isotope effects arising from the substitution of ordinary water by D20 as solvent.MECHANISMS The resolution of complex reaction mechanisms into a sequence of elementary steps can frequently be accomplished by kinetic measurements. The paper of Higginson el aZ.2 deals particularly with this theme and only a few examples will be noted here. Most commonly this problem arises in connection with reactions in which the stoichiometric ratio of oxidant and reductant differs from unity, e.g. the10 ELECTRON-TRANSFER REACTIONS oxidation of Fe2+ by TP+ (eqn. (4)). can be written as The rate-law for this reaction 19 which kl k2 [Fe2 '1 [T13 +I/( k - [Fe3 '1 + k2 [Fe2 '1) implies the mechanism, Fe2 + + TI + k* Fe + T1 ' .( 6 ) The kinetics of simple bimolecular reactions such as (l), (2) and (3) are usually of first order in each of the reactants implying that electron transfer occurs by direct reaction between the oxidant and reductant through an activated complex involving both. However, indirect paths are sometimes found even in such cases. Thus the rate-law 20 for the reaction points to the mechanism, k i Hgi +Hg2 + Hg"(aq), k- i Hg"(aq) +TI3 + 3Hg2+ + T1+, (9) k2 (106 1. mole-1 sec-1 at 25") being at least 106 times greater than the rate con- stant for direct reaction between the Hgif and T13+. The Ag+-Ag2+ isotopic exchange 9 is another example of a simple reaction, in this case a 1-electron transfer, for which an indirect path is preferred.The rate law, Ic[Ag2+]2 suggests that the main exchange path is k 2Ag2'+Ag+ +Ag3+ with k(1 x lo3 1. mole-1 sec-1 at 0") being at least 100 times larger than the rate constant for direct electron transfer between As+ and Ag2+. While the elucidation of the steps involved in complex redox reactions continues to be an important area of investigation, it is on the detailed mechanisms of the elementary electron transfer steps themselves that much of the current interest in this field is focused. An important advance in our understanding of these has been the recognition of at least two types of electron-transfer mechanisms-" outer- sphere " and " inner-sphere " (or & & bridged ").In the first of these electron transfer between the metal ions occurs without disruption of their first co-ordination shells and in the second through an intermediate in which the two metal ions are linked by a bridging group which forms part of the co-ordination shells of both. The distinction between the two is not always sharp and many reactions cannot at this stage be assigned with certainty to either class.21 OUTER-SPHERE ACTIVATED COMPLEX In these reactions there is no change in the first co-ordination shells of the exchanging ions. Examples are the MnOZ-MnOi-, Fe(CN): --Fe(CN)z', Fe(o-phen) ;+-Fe(o-phen) $+ and Co(en) 3 +-Co(en) :+ is0 topic exchanges and theJ . HALPERN AND L. P,. ORGEL 11 oxidation of Cr(dipy)i 1- by Co(NH&+.The evidence for this typc of mechanism is based in most cases on (i) a rate-law which corresponds to an activated complex containing all the ligands in the co-ordination shells of both ions, and (ii) the demonstration that electron-transfer is fastcr than substitution into the co-ordination shells of either of the metal ions. Neither of these criteria is readily applicable to reactions between aquo-ions which can thus rarely be demonstrated to be of this type. In many instances therc is a marked dependence of the rates of such reactions on the nature and concentrations of ions of opposite sign (e.g. the Mn04 -MnOi- exchange is accelerated by cations in the order Cs-'->K+>Na+I Li+).8 One possible interpretation is in terms of an outer-sphere bridged complex such as INNER-SPHERE BRIDGED ACTIVATED COMPLEX Typical of the reactions in this class is the oxidation of Cr2f by complexes of the type (H3N)gCo3+X where X may be one of a largc number of ligands, e.g.H20, OH-, C1-, Br-, acetate, fumarate, etc.22s 23~16. In each case it is found that X appears in the co-ordination shell of the Cr3+ formed. Since both the Co3+ complex and Cr3-t- product are substitution-inert this must mean that electron- transfer occurs through a bridged intermediate of the type in which X is simultaneously co-ordinated to both metal ions. Other examples include electron exchange between Cr2f and Cr3+ complexes of the type (H20)5Cr3+X24 and (E&N)~Cr3fX25, as well as the Pt(en);+-Pt(en)2Cl;+ and related exchange reactions discussed by Morris, Basolo and Pearson.14 For reactions of most metal ions, mechanisms of this type, even if applicable, cannot be demonstrated unequivocally because of the substitution lability of the reactants and/or products.Several points connected with this type of mechanism are worthy of special mention. (i) Although the bridging ligand is generally transferred from the oxidant to the reductant it is not clear that this transfer is an essential feature of the mechanism since in the cases noted it follows simply from a consideration of the relative affinities for the ligand of the two product ions. It has been suggested 26 that the oxidation of Cr2+ by IrClg- also occurs through a C1' bridged mechanism but in this case the products are IrC1;- + Cr(OH2)i-'-. The description of such mechanisms as atom-transfer (as distinct from electron-transfer) processes may thus be somewhat mislcading ; this point is emphasized by the C1--bridged PtII-PtIv exchange re- actions 14 which involve the transfer of two electrons and are thus not equivalent simply to the transfer of a C1 atom from PtrV to Ptn.(ii) Neither catalysis by anions nor incorporation of anions into the co-ordin- ation shell of the oxidized metal ion necessarily reflect the participation of the anion as a bridging ligand. Thus SO:- and P20;- accelerate the oxidation of Cr2+ by (NH3)5Co(OH2)3+ and both are incorporated into the product Cr3+ complex.25 Similarly, during the oxidation of Cr3+ by (H3N)5CoC12+ in the presence of P20$-, both C1- and PzO$' are incorporated into the Cr3+ product.The effect of these anions as non-bridging ligands is, however, much smaller than as bridging ligands. On the other hand, C1- exerts a large catalytic effect on the oxidation of Cr2+ by C O ( N H ~ ) ~ ~ ; the product of the Cl--catalyzed reaction which pre- sumably proceeds by an outer-sphere mechanism, is CrC12-1-.27 The observation (H3N) ~CO~+-X-CO~+(OH~)~12 ELECTRON-TRANSFER REACTIONS by Zwickel and Taube 28 of a large dependence of the rate on the naturc of X in the outer-sphere oxidation of Cr(dipy): + by (H3N)SCo3+X should also be men- tioned in this connection. (iii) Fumarate and p-phthalate are of special interest as bridging ligands in the oxidation of Cr2'- by (H3N)&03+X since the rates for these are much higher than for other carboxylic acids.23 This has been interpreted in terms of a bridged intermediate in which the two metal ions are co-ordinated to different carboxylate grou PS , O-Cr(OH& 4f r (H3N)sCO-O // \ // \ C-CH=CH-C OH I 0 the electron being transferred between them by " conduction " through the con- jugated z-electron system.Strong support for this is provided by the observation that in the corresponding oxidation of Cr2+ by (H3N)5 C03+-0 \ 0 // 'c--cH=cH--c' // \ 0-Me 0 electron transfer is accompanied by hydrolysis of the ester and incorporation of both the methyl group and the acid into the co-ordination shell of the Cr3+ pr~duct.~' Hydrolysis is not observed when Cr(dipy)$+ or V(dipy);'+ is used as the reducing agent, the reaction in these cases being of the outer-sphere type.27 With maleate or monomethyl maleate ester (but not the corresponding fumarates) as the bridging group cis-trans isomerization and hydrogen exchange with the solvent (D20) also occurs as a consequence of electron transfer from V2+ or Cr2+ and this has been construed as evidence that an electron passes into the maleate group during the reaction.30 The possibilities afforded by the use of such con- jugated bridging groups for distinguishing between the two types of mechanisms and for the systematic variation of structural parameters makes these systems extremely valuable and their study will undoubtedly play an important role in the future development of the subject.HYDROGEN TRANSFER AND BRIDGING MECHANISMS The suggestion, first made by Dodson and Davidson,31 that redox reactions between metal aquo ions may occur through transfer of a hydrogen atom between their hydration shells, has continued to receive serious attention, particularly with reference to the F&+-Fe3+ exchange.A simplified representation is * * 11 11 H * l Fe2+-OH+HOFe3f-> r Fe2+-0 . . . H . . . O--Fe3+ 5+-tFeOH2-'-+H30Fe3+ * Fe3++ OH- Fez++ H30+ 1 3 H A I L H or, for the hydrolyzed ion (1 1) 8 * Fe2+0H+HO-Fe3+-+ (12) I H H the intermediate, in the latter case, being symmetrical.J . HALPERN AND L. E. ORGEL 13 Several lines of evidence have been advanced in support of this suggestion. (i) A surprisingly large number of diverse redox reactions between metal aquo ions have activation energies close to 10 kcal/mole and entropies close to -25 cal/mole deg., suggesting that they proceed by a common mechanism which probably involves water.329 1 (ii) In a number of redox reactions of metal complexes there seems to be a requirement that at least one of the inner shell ligands be a water molecule,32 e.g.one of the CN- ions must be replaced by a water molecule before Fe(CN);' is oxidized by hydroperoxide. Similarly, the electrolytic reduction of Cd(CN): - proceeds through the aquotricyano complex. The slowness of Fe2+-Fe3+ exchange ion non-aqueous solvents such as nitromethane 6 and alcohols 7 has also been attributed to this factor. (ii) The rates of the F&+-Fe3+ and Fe2+-FeOH2+ exchange reactions are re- duced by a factor of two on changing from H20 to D20 as solvent.33 This is consistent with the isotope effect expected for breaking of an 0-H bond but is not conclusive evidence for this since even larger H2O-D20 isotope effects have been observed in the oxidations of Cr2 + by (H3N)sCoOH?- and (H3N),CoOH2 I- which are known to proceed through oxygen-bridged mechanisms.16 Even Cl- bridged reactions exhibit appreciable, though somewhat smaller isotope effects in the same direction.25 Until differences in the solvent characteristics of H20 and D20 are better understood the interpretation of such effects must be approached with great caution.On energetic grounds the suggestion of a net H atom transfer between water molecules in a reaction such as (1 1) does not appear too attractive since the endo- thermicity of this process is expected to approach that of the self-ionization of water (-13 kcal).This is difficult to reconcile with an overall AH+ of 10 kcal and with the relatively small difference (2-5 kcal) in AH+ between the reactions of Fez+ with Fe(OH&+ and with Fe(OH2)50H2f. H atom transfer thus seems unlikely in reaction (1 l), although it may occur in (12), in reactions between aquo ions involving a large free-energy decrease or in the oxidation of aquo ions by free radicals, i.e. ' MOH;j+ +*R*MOH"+ +HR. (13) A related view 1 on the role of water in these reactions, which probably has more validity, emphasizes the formation of hydrogen-bridged intermediates, e.g. H 1 I Fe2+-0 . . . H-O-Fe3+ I H H or Fe2+-0 . . . H-O-Fe3+ I H I H in which coupling of the hydration shells by hydrogen bonding lowers the energy of the activated complex and improves orbital overlap thus providing a more effective conducting path for electron transfer.In this context hydrogen transfer is incidental to the bridging role of the proton and might accompany electron exchange of Fez+ with FeOH2+ but not with Fe3+. The analogy between the role of the bridging proton in such a mechanism and that of bridging groups in the inner- and outer-sphere bridged mechanisms already considered is readily ap- prec i a t ed.14 ELE C T R 0 N - TK A N S FER RE A C T 10 N S REACTIONS OF UNCERTAIN MECHANISM The uncertainties concerning the detailed mechanism of the Fe2+-Fe3+ exchange extend also to the redox reactions of most other aquo ions and labile complexes. In some cases the mechanism of a reaction which cannot be directly elucidated may be inferred with some confidence from a comparison between it and reactions of known mechanism.For example, similarities between the oxidation of Cr2+ and V2+ by (H3N)Co3+X complexes strongly suggest that the latter reaction also proceeds by an inner-sphere bridged mechanism.30 Similarly, the fact that C1- is incorporated into the co-ordination shell of the Cr3+ product during oxidation of Cr2+ by Fe3+ in the presence of C1-, while not conclusive evidence for a C1-- bridged mechanism (in view of known instances of incorporation of non-bridging ligands) makes this seem rather likely.26 The special role of the bridging ligand in the inner-sphere mechanism might be expected to give rise to a different pattern of dependence of the rate on the nature of the ligand from that observed for outer-sphere reactions, thus providing a diagnostic tool for distinguishing between the two types of mechanism. Un- fortunately the patterns observed so far, for the few reactions of known mechanism (table 1) are not sufficiently distinctive to permit a confident assignment for, say, the Fe2+-Fe3+ reaction, to be made.The value of this approach will undoubtedly be enhanced by the accumulation of data of this type for more systems of known niechanism; the papers by Stranks 30a and by Zwickel and Taube 28 represent important contributions to this field. TWO-EQUIVALENT REDOX REACTIONS The transition metals generally exhibit stable oxidation states differing by one clectron and react with each other by 1-equivalent steps.On the other hand, the stable oxidation states of the post-transition elements generally differ by two electrons, e.g. TI '-TI3' ; Sn2+-Sn4' ; Hgi'-2Hg2+, etc. The question thus arises as to whether oxidation or reduction of these ions occurs in a single step or by successive 1-equivalent steps. Two classical principles dominate much of the earlier thinking on this theme. (i) Michaelis' principle of " compulsory univalent oxidation steps ".34 This hypothesis invokes the second alternative for all reactions. It evolved from a Consideration of a restricted field of redox reactions, of which oxidation of hydro- quinones to quinones through semiquinone intermediates is typical, and is now gcnerally recognized as being without universal validity.Apart from reactions involving metal ions, many two-equivalent redox reactions are now known which proceed in one step through the transfer of a hydride ion or an oxygen atom ( e g NOT + OCl--+NOT + C1-).35* 36 (ii) Shaffer's principle of " equivalence change ".379 38 This refers to the observation that non-conplementary reactions (i.e. those between 1-equivalent oxidants and 2-equivalent reductants, or vice versa) are often slow compared with complementary ones (those between 1-equivalent oxidants and 1 -equivalent reductants, or between 2-equivalent oxidants and 2-equivalent reductants). Examples are the slow reduction of Tl3+ by Fe2+ or of Ce4-k by T1+ compared with the rapid reduction of Tl3f by Sn2+ and of Ce4f by Fez+. This is interpreted in terms of the following types of mechanism for a typical non-complementary reaction in which A is oxidized to A+ and B2+ reduced to B.2A + B2 +-+2A -I- + B, (1 Sa) ( I 51,)J. HALPEKN A N D L. E. OKGEL 15 The first of these mechanisms is expected to be slow because it involves a ter- molecular step and the last two because they involve the formation of unstable intermediates (B+ or A2+). Onc of the implications of the comparison on which the principle of equi- valence change is based is that reactions between 2-equivalent oxidants and 2- equivalent reductants occur by a concerted 2-equivalent step. This may well be the case for reactions such as the Tl+-TP+ exchange and the oxidation of Hg" and U44- by Tl3f whose rates secm too high to be reconciled with an initial 1-electron step in which two unstable intermediates (Hg+, TP+, etc.) are formed.20.389 39 It should be noted that the entropy correlations discussed by Higginson2 are also more dificult to reconcile with an initial 1-electron transfer for the Tl+-Tl3+ exchange than with a 2-electron transfer. Some reactions between 2-equivalent oxidants and 2-equivalent reductants, however, do proceed by 1-electron steps.The oxidation of V3+ by TI,+ is apparently such a case2 as is the oxidation of U4+ by 0 2 for which the following chain mechanism has been demonstrated,40 U'V+02+Uv+H0,, (174 Uv+ 02+UV'+H02, (176) t17d U IV + HQ2-+UV + H202. For non-complementary reactions the three types of mechanisms considered above have all been observed. The " termolecular " mechanism (type 1) is readily distinguished kinetically from the other two.Probable instances are the oxidation of Fe2+ and Pu3-f- by 0 2 and thc reduction of Ag+ by H2, for which the rate-laws k[Fe2+]2[02], k[Pu3+]2[02] and k[Ag+]2[H2] have been observed.41-43 One of the paths in the oxidation of CoI1 by Fblv in acetic acid, corresponding to the rate-law k[PbIV][Co1*]2, apparently is also of this type.5 In aqueous solution, however, there is no known instance of a reaction involving three metal ions which proceeds by this mechanism. A kinetic distinction between the two bimolccular inechanisms (types I1 and IlI), is normally possible only in those favourable cases where reversal of the first step is fast enough to compete with the second step, for inhibition by one of the products is then observed.Initial 1-electron steps have been demonstrated in this way for several reactions, 2Fe2++T13+ (eqn. (5) and (6)),19 Tl++2Co3+,44 and 2V4++ T13+2, and are considered likely for many others, e.g. U4++ 2Fe3f745 Hg2++2Co3+.46 On the other hand, inhibition by PbK suggests that one of the paths in the oxidation of Col' by Pblv in acetic acid involves an initial 2-equivalent step with the formation of Colv as an intermediate.5 The observation47 that Cr2+ is oxidized to Cr3f by 1-electron oxidants such as CU~+ and Fe3-1- by 1-electron oxidants such as Cu2f and Fe3-i- but to a binuclcar species (probably Cr-O-Cr4f) by 2-electron oxidants such as Tl3-f- suggests that the latter reaction also proceeds through an initial 2-electron transfer, is., Cr2 + + Ti3 + -+ Cr4 + +TI c r 4 + + Cr2 + -+(cr3 +I2.(18) (19) The factors which influence the choice of mechanism in these systems are still not well understood. THEORETICAL CONSIDERATIONS The theoretical problems associated with the mcchanisnis of clectron-transl'r reactions are of great complexity. To simplify 0111' discussion we divide i h e16 ELECTRON-TRANSFER REACTIONS process into three successive stages ; the initial approach of the, reactants, the surmounting of the Franck-Condon barrier, and the electron-transfer process itself. The paper by Marcus48 deals particularly with the first two of these themes, and that by Halpern and Orgel49 with the last. This division of the problem is somewhat artificial ; it is convenient since it permits a simple treatment or many of the most important features of the reaction mechanisms but it does not necessarily form the best starting-point for quantitative calculations, THE INITIAL APPROACH The approach to an intermolecular distance which permits electron transfer, of a pair of reactants one or both of which is uncharged, is presumably governed by the normal diffusion Iaws and can be calculated from collision theory.More often we are concerned with transfer between pairs of ions carrying the same charge, and then we have to consider the electrostatic repulsion which tends to keep them apart. The only treatments which have been attempted so far are based on classical electrostatic theory.50-52 It is supposed that the solvent can be treated as a continuous dielectric medium and the interionic potential energy estimated in terms of an effective dielectric constant. This treatment should be adequate for large intermolecular distances but must clearly break down when the inter- molecular distance becomes small, in particular when ions approach to the point of contact of their hydration shells. It is difficult to assess its validity for typical reactions between metal ions. In a general way we expect the rates of reaction to decrease as the charges (of the same sign) on the reactants increase.No doubt this repulsion between charges is important, but its significance should not be overestimated. The re- action between Fe(WG3- and Fe(CN)64-, for example, is very rapid.53 It is not unlikely that the incorporation of ions of opposite sign into the activated complex contributes to the reduction of the electrostatic barrier in this and similar reactions.The marked cation dependence of the MnO;; -MnOt- exchange, for example, is probably related to this.8 In the particular case of reactions involving bridged activated complexes there is a further stage in the initial approach, namely, the step leading to the formation of the binuclear species, e.g., C O ( N H ~ ) ~ C ~ ~ + +Cr(H,0)~+-+[(H3N)5C~-CI-Cr(H20)5J4'+ +H,O. (20) The rate of this step is presumably governed by the same factors as control simpler substitution reactions of inorganic complexes. .It has been noted, however, that the AS+ values of reactions of this type are considerably more negative than those of non-redox reactions which proceed through analogous bridged intermediates and this has been attributed to the more stringent requirements in the way of simultaneous bond readjustment in the activated complex in the case of the electron-transfer reaction.25 THE FRANCK-CONDON BARRIER The Franck-Condon principle was first proposed in connection with the analysis of molecular spectra.It states that it is extremely improbable that a large change of the nuclear configuration of a molecule will occur during an electronic transition. The physical basis of this generalization is simple ; electrons move so much faster than nuclei that an electronic transition is completed before much nuclear motion can occur. As pointed out by Libby,W the same general considerations apply also to electron-transfer reactions and they have important consequcnces. We first consider the transfer of an electron between two molecular or ionic species which differ only in the number of electrons which they contain, for example, bctweeiiJ .HALPERN AND L. E. ORGEL 17 benzene and the benzene negative ion or between Fe(H20), and Fe(H20)62+. At first sight it might seem that there can be no barrier to electron transfer since the products of the reaction are the same as the reactants. The Franck-Condon principle shows that this is not the case. The structure of each of the reactants depends on its state of ionization, for example the metal-oxygen bonds are longer in Fe(H20)62 than in Fe(H20)G3i-. If an electron is transferred between the reactants without any change in the inter- nuclear distance, as is required by the Franck-Condon principle, then the products are formed in inappropriate configurations. Thus in the ferrous-ferric exchange, one would obtain a compressed ferrous ion and an extended ferric ion.Thus direct electron exchange between partners in their equilibrium configurations leads to products which are vibrationally excited and therefore requires electronic activation energy. The same electron-transfer process can be brought about without electronic excitation energy, by following a different route. The two partners in the reaction are first symmetrized, that is they are deformed to a common configuration inter- mediate between their equilibrium configurations. This involves the expenditure of Vibrational energy, but now an electron can be transferred without further electronic activation energy.It is readily seen that the vibrational activation energy involved in this indirect route is always less than the electronic activation energy needed for direct transfer, since in the former case deformation to an intermcdiate configuration is sufficient while in the latter both products are pro- duced in extreme mismatching configurations. (We may expect the factor involved to be close to 4 in many cases.55) We shall refer to the vibrational excitation energy as the Franck-Condon rearrangement energy. Clearly the Franck-Condon barrier is most likely to be important where the oxidized and reduced forms of the reagents differ greatly in molecular geometry. For example, the Cr(H20)~~' ion has a regular octahedral structure while the Cr(H20)62' ion is extensively distorted and has a greater mean bond-length.This may be a cause of the slow electron exchange-rate observed in an aqueous system containing Cr2+ and Cr3+ ions. In general, a smaller Franck-Condon barrier is anticipated for electron-transfer between tzg orbitals than between eg orbitals.55 The Franck-Condon barrier is less likely to be important in oxidation-reduction reactions associated with large decreases in free energy, for then an electron can be transferred without extensive vibrational activation although the products are obtained in excited vibrational states. The excess vibrational energy of the products is lost as part of the process of dissipating the excess free energy. The Franck-Condon principle also applies to electron transfer between molecular species in the gas phase (e.g.H2-H$, N2-N$) although it appears that the effect in these cases is not large.56 ELECTRON CONDUCTION MECHANISMS In the gas phase there is little probability of electron-transfer between species except in collisions sufficiently close to allow the occupied orbitals of the donor molecule to overlap appreciably with the unfilled orbitals of the acceptor. Solu- tion reactions may proceed in another way, namely, by transferring electrons through intervening molecules which are not themselves permanently oxidized or reduced. The transfer between a hydrocarbon and its negative ion may be by direct contact, but many of the reactions between pairs of metal ions are known to proceed via bridging mechanisms.In very many metal ion reactions then, we are faced with the problem of electron conduction through ligands; stated in another way we must find out how the " outside " of a complex ion such as Fe(phenanthroIine)33+ receives information about the valency of the metal ion at its centre. The detailed quantitative answer to this question is not at present available, but a number of qualitative observations may be useful.18 ELECTRON-TRANSFER REACTIONS Extensive work of the paramagnetic resonance spcctra of transition-metal complexes has shown unambiguously that electrons which we are accustomed to think of as isolated on a metal ion are in fact more or less delocalized on to the ligands.57 Thus, even in fluorides such as MnF2, the unpaired d electrons are partly concentrated (perhaps 5-10 %) on the fluoride ions.It is natural to suppose that the same is true in all complex ions. This enables one to understand the transfer of electrons through small ligands such as the halide ions or the water molecule ; the electrons and unoccupied valence orbitals are partially located on the periphery of the complex ion and hence can interact with those of contiguous molecules. The ability of a ligand to facilitate electron transfer would be expected to fall off very rapidly with the number of saturated single bonds which must be traversed by the electron. On the other hand conjugated systems might be expected to con- duct electrons over longer distances on account of their extensive delocalized systems of n-orbitals.@ There is some evidence for the validity of these suggestions for reactions proceeding both by inner- and outer-sphere activated complexes. The higher rates of electron transfer gcnerally observed for complexes contaiiiing unsaturated ligands, such as cyanide and o-phenanthroline, than for those con- taining saturated ligands such as water and ammonia, are in line with these pre- dictions.However, it also appears that the geometrical configurations of the two oxidation states often differ less in the former case than in the latter so that there is also a contribution to the difference in rate from differences in the Franck- Condon barriers. The relative importance of these factors is difficult to assess. The theoretical treatment of Marcus,51 which is particularly appropriate for reactions of the outer-sphere type, assumes that the probability of electron transfer in the transition state is sufficiently high for the rate to be wholly determined by the electrostatic repulsion and Franck-Condon barrier ; this is probably valid for many reactions.TWO-ELECTRON TRANSFERS Two-electron transfers such as A+Az++A2++A are known to occur in the gas phase although their cross-sections, in accord with theoretical predictions, are somewhat lower than (+ to 3) those of corresponding resonant one-electron transfers.56 It is thus reasonable to expect similar reactions to occur in solution. They will, however, be subject to considerably larger Franck-Condon barriers 51 and this is likely to bereflected in more drastic atomic rearrangcments accompanying electron transfer.It is possible that such reactions will show a greater preference for bridged mechanisms both because a higher " electron conductivity " is more impor- tant in their case than for one-electron transfer and because of the reduction of the Franck-Condon barrier resulting from strong coupling between the metal ions and from displacement of the bridging anion from the oxidant to reductant. Unfortunately, there is still considerable uncertainty about the detailed mechanism of the Tl2+-Tl3+ and related 2-electron transfer reactions.58~ 59 SPIN-SELECTION RULES One special feature of certain reactions of metal ions and of the oxygen molecule is that they do not conserve the total spin. Thus the decomposition of anthracene peroxide involves a conversion of a singlet state to a triplet state 4 0 2 + singlet t r i p l e t s i n g l e tJ .HALPERN AND L. E. QRGEL 19 while the reaction between a cobaltic complex and a reducing agent often involves a similar departure from spin-conservation. While the significance of this selection rule is not yet understood in detail, there can be little doubt that it influences profoundly the rates of many reactions of molecules which contain more than one unpaired electron. The widespread tendency for reactions involving the reduction of 0 2 or oxidation of H202 to proceed by free-radical mechanisms rather than in a single step may be related to this. 1 Stranks, Modern Co-ordination Chemistry (Interscience Publishers Inc., New York, 2 Higginson, Rosseinsky, Stead and Sykcs, this Discussion.3 Hunt and Taubc, J. Amer. Chem. Soc., 1958, 80, 2642. 4 Benson and Sutcliffe, Trans. Faraduy Soc., 1960, 56, 246. 5 Benson, Proll, Sutcliffe and Walldey, this Discussion. 6 Maddock, Trans. Faraday Soc., 1959, 55, 1268. 7 Horne, Microfilm Diss. Abstr., 1957, 17, 1673. 8 Shcppard and Wahl, J. Anzer. Chem. Soc., 1957, 79, 1020. 9 Gordon and Wahl, J. Amer. Chem. Soc., 1958, 80, 273. 10 McConncll and Weavcr, J . Chem. Physics, 1956, 25, 307. 1 1 Ward and Weisman, J . Amer. Chem. Soc., 1957, 79, 2086. 12 Eigcn, Faraday Soc. Discussions, 1954, 17, 194; 1957, 24, 25. 13 Kruse and Taube, J . Amer. Chem. SOC., 1960, 82, 526. 14 Morris, Basolo and Pearson, this Discussion. 15 Murmann, Taube and Posey, J. Amer. Chem. Soc., 1957, 79, 262.16 Zwickcl and Taube, J. Amer. Chenz. SOC., 1959, 81, 2915, 1288. 17 Mudis and Dodson, J. Amer. Chern. Soc., 1956, 48, 91 1. l8 Newton and Rabideau, J. Physic. Clzem., 1959, 63, 365. 19 Ashurst and Higginson, J. Chem. Sac., 1953, 3044. 20 Armstrong, Halpern and Higginson, J. Physic. Chem., 1956, 60, 1661. Armstrong 21 Taube, Advances in Inorganic Chemistry and Radiochemistry (Academic Press, New 22 Taube, Myers and Rich, J . Amer. Chenz. Soc., 1953, 75, 4118. 23 Taubc, J . Amer. Chem. Soc., 1955, 77, 4481 ; Can. J . Chem., 1959, 37, 129. 24Taube and King, J . Amer. Chem. Soc., 1954, 76, 4053. 25 Ogard and Taubc, J. Amer. Cheni. Soc., 1958, 80, 1084. 26 Taube and Myers, J. Amer. Chenz. Soc., 1954, 76, 2103. 27 Taube, Chem. Soc. Spec. Publ., 1959, 13, 57. 28 Zwickel and Taube, this Discussion. 29 Fraser, Sebera and Taubc, J . Amer. Chem. SOC., 1959, 81, 2906. 30 Fraser and Taube, J. Amer. Chem. Soc., 1959, 81, 5514. 31 Dodson and Davidson, J . Physic. Chem., 1952, 56, 866. 32 Reynolds and Luniry, J. Physic. Chem., 1955, 23, 2460. 33 Hudis and Dodson, J. Amer. Chem. Soc., 1956, 78, 91 1 . 34 Michaelis, Trans. Electrochcm. Soc., 1937,71, 107; Cold Spring Harbor Symp. Quant. 35 Anbar and Taube, J. Arner. Chem. Soc., 1958, 80, 1073. 36 Stewart, Experientia, 1959, 15, 401. 37 Shaffer, J . Amer. Chem. SOC., 1933, 55, 2169; J. Physic. Chem., 1936, 40, 1021 ; 38 Halpern, Can. J . Chem., 1959, 37, 148. 4o Halpern and Smith, Can. J . Cltem., 1956, 34, 1419. 41 George, J . Clieni. SOC., 1954, 4349. 42 Baker and Newton, J . Physic. Cheni., 1957, 61, 381. 43 Webster and Halpern, J. Physic. Cheni., 1957, 61, 1239. 44 Ashurst and Higginson, J . Cheni. Soc., 1956, 343. 45 Dctts, Can. J . Cheni., 1955, 33, 1780. 1960), p. 78. Gjertsen and Wahl, J . Amer. Chem. Soc., 1959, 81, 1572. and Halpern, Cun. J . Chem., 1957, 35, 1020. York, 1959), 1, 1, and rcferences thcrein. Ball and King, J . Amer. Chem. Soc., 1958, 80, 1091. Chia and King, this Discussion. 300 Stranks, this Discussion. Biol., 1939, 7, 33. Cold Spring. Harbor Symp. Quant. Biol., 1939, 1, 50. Harkness and HaIpern, J . Anrer. Chem. Soc., 1959, 81, 3526.20 ELECTRON-TRANSFER REACTIONS 46 Rosseinsky and Higginson, J. Chem. SOC., 1960. 47 Arden and Plane, J. Amer. Chem. Soc., 1959, 81, 3197. 48 Marcus, this Discussion. 49 Halpern and Orgel, this Discussion. 50 Marcus, Zwolinski and Eyring, J. Physic. Chem., 1954, 58, 432. 51 Marcus, J. Chem. Physics, 1956, %I, 966 ; 1957, 26, 867, 872. 52 Laidler, Can. J. Clzem., 1959, 37, 138. 53 Wahl and Deck, J. Amer. Chem. SOC., 1954, 76,4054. 54 Libby, J. Physic. Chem., 1952, 56, 863. 55 Orgel, Report X Conseil Chimie Solvay, Brussels, 1956, 289. 56 Gurnee and Magee, J . Chem. Physics, 1957,26, 1237. 57 Owen, Faraday SOC. Discussions, 1958, 26, 53. 58 Jilks and Waind, this Discussion. 59 Carpenter, Ford-Smith, Bell and Dodson, this Discussion.