MECHANISMS OF SOME ELECTRON EXCHANGE REACTIONS BY D. R. STRANKS" School of Chemistry, The University, k d s 2 Received 3rd February, 1960 Electron exchange between ferrocene and the ferricinium cation proceeds with half- times of a few milliseconds between -65" and -75°C. The second-order rate constants are best reproduced by calculations based on the Marcus tunnelling theory. Electron exchange between a series of aqua-ammines of CoII and Con' proceeds through bridged transition states. The energy of activation remains constant in this series but the entropy of activation becomes less negative as ammine ligands are replaced by hydroxo-ligands. Bridging mechanisms may operatc in other systems in which substantial reorganization of the primary co-ordination sphere is involved. 1.INTRODUCTION The rate at which the mutual oxidation and reduction of two valence states of an element proceeds : is largely determined by the two electronic configurations of M, the sizes of the two species MX,, and the character of both the ligands X and the solvent. Since the standard free energy of these reactions is zero, the importance of such factors can be asscssed directly in systematic studies of these so-called " electron exchange reactions 77. This paper aims to summarize the results of recent kinetic investiga- tions of some selected electron-exchange reactions (the details of which are being submitted for publication independently) and to compare the observed rates with those predicted by the electron-tunnelling models proposed by Marcus 1 and by Laidler.;! Conclusions are then drawn as to the detailed mechanism of the actual electron-transfer steps.2. THE FERROCENE+ FERRICINIUM SYSTEM Little accurate information is available on the rates of electron exchange be- tween a neutral and a charged species. In the absence of Coulombic interactions, the theory of Marcus ascribes the free energy of activation solely to the need for reorganization of solvent molecules to form a non-equilibrium transition state. Since the Laidler model includes solvent rearrangement in Coulombic terms, the rate of such an electron-exchange reaction would be attributed to the rate of a diffusion-controlled reaction with no charge barrier. Both models ignore any possible polarization of the reactants by each other. The bis-cyclopentadienyl complexes of iron (11) and iron (111)-usually desig- nated as " ferrocene " and " ferricinium " (cation) respectively-are relatively inert to substitution and do not interact markedly with hydroxylic solvents such as methanol.This exchange system therefore seemed to be a suitable one for the comparison of measured rates with those calculated from the alternative theoretical * present address : Chemistry Department, University of Melbourne, Melbourne, Australia. 7374 ELECTRON EXCHANGE REACTIONS models. The '' sandwich '' structure of ferrocene is shown in fig. 1, which has been constructed on the basis of the following molecular dimensions : FeTr-C= 2.045 A, C-H = 1-09 A, half-thickness of the cyclopentadkne ring = 1.70 A, van der Waals' radius of the hydrogen atom = 1-2& and covalent radius of Fen = 1.23 A.Excepting the central void of the ferrocene molecule, the maximum distance from the centre to the periphery is 4.10A and the minimum distance is 3.54 A. It is anticipated that the dimensions of the ferricinium cation will closely resemble those of ferrocene and for the subsequent calculations the average mini- mum and maximum " radii " (a) of the ferrocene and ferricinium species will be taken to be 334A and 4-10A respectively. TheZencounter diameter 0 required for calculations based on Laidler's theory will be&taken as either 7-08 or 8.2081. FIG. 1 .-Scale diagram of the ferrocene molecule (side view). In an earlier publication 3 we reported that 10-4 M methanolic solutions of ferrocene and ferricinium nitrate or perchlorate underwent complete isotopic exchange in 50 msec at 0°C.The flow apparatus has now been modified to achieve contact times as low as 3 msec. The exchanging solution is led into a second jet- mixing chamber into which flows a much larger volume of petroleum ether (in which ferricinium salts are insoluble) and from a third jet, a carrier ferricinium solution enters. The separations are then conducted at - 80°C. In this manner, I have been able to obtain definite estimates of the rates of this electron exchange in 10-4-10-5 M methanolic solutions between - 75" and - 65°C. Exchange half- times are some milliseconds even at these temperatures and cannot be measured at higher temperatures. Mean half-times values are quoted in table 1.These rates appear to be the fastest yet reported for an electron-exchange reaction studied by means of isotopic tracers. At -75", a second-order rate law has been estab- lished within the limits of experimental error. Ferricinium nitrate or perchlorate exhibit the same rate behaviour but with the chloride salt, the rate becomes im- measurably fast at -75". The addition of " inert " electrolytes at concentrations exceeding 10-3 M also causes the rate to be immeasurably fast at -75". (These observations demonstrate that anion catalysis is possible even for redox reactions involving two substitution-inert species.) Worthwhile estimates of the activation energy cannot be made ; values ranging from 4-4 to 15.6 kcal mole-1 are covered by the upper and lower limits of the rate constants.Table 1 compares the experi- mentally-determined values with those calculated from the theories of Marcus and of Laidler.D . R . STRANKS 75 TABLE 1 .-RATES OF ELECTRON EXCHANGE BETWEEN FERROCENE AND FERRICINIUM calc. rates expt. rates Laidler theory a Marcus Theory k k k k k b teyz. G = 7.08 A G = 8-20 A a = 4-10 A a = 3-54 A 'g- M-1 sec-1 M-1 sec-1 M-1 sec-1 M-1 sec-1 msec M-1 sec-1 25 9.1 x 108 l * O X 109 1.6X 109 3.1 x 108 <0*5 >7 x 106 0 4.9 x 108 5.6 X 108 4.5 X 10s 9.2 X 107 <0.5 >7x 106 -65 5.1 X 107 5.9X 107 1-4X 107 1 . 6 ~ 106 1*0fO*S 3.5f1.8x 106 -70 4.0X 107 47X 107 9*4X 106 1.2X 106 2-0f0.5 1*7&0*4X 106 -75 3 . o ~ 107 3 . 5 ~ 107 6 . 5 ~ 106 7 . 5 ~ 105 4 . o ~ . o s.7f2-2~ 105 a Assuming D (ferrocene) = 3 x 10-5 cm2 sec-1, B (ferricinium) = 1.2 x 10-5 cm2 sec-1 b both reactant concentrations = 1.0 x 10-4 M.at 25"C, and Eact (diffusion) = 4 0 kcal mole-1. The apparent agreement between the experimentally-determined rate constants and those calculated from Marcus' theory, assuming a = 3.54 fn, is extraordinarily close considering the probable shortcomings of both theory and experiment. The experimental rates are significantly less than those calculated on the basis of simple diffusive encounters ; the latter are considered to be the minimum values permitted by the Laidler theory. Whilst a preference can therefore be expressed in favour of the Marcus theory, the differences in rates are not sufficiently large to justify the rejection of the diffusion model entirely nor could one infer that the exchanging reactants approach end-on (a = 354& rather than side-on (a = 4.10fn).It is considered that the isotopic studies need verification by means of n.m.r. and e.s.r. techniques before any completely reliable deduction can be made. Most of the " covalent " cyclopentadienyl complexes have dimensions which do not differ by more than 0.3 fn (e.g. Fe, Coy Ni, Rh, Ru) and one would anticipate that similar exchange rates, within a factor of five, would exist in all such cases. Resonance studies should be performed below 0" since at higher temperatures, the exchange process is probably diffusion-controlled (see table 1). Around - 70", the Marcus theory suggests an activation energy of either 6-83 kcal mole-1 (a = 3.54&, or 5.96 kcal mole-1 (a = 4.10 fn), whereas that for diffusion probably does not exceed 4.0 kcal mole-1.On the Marcus model, the entropy of activation is only - 1 cal (mole deg.)-1 in both cases since the entropy changes on solvent reorganization around the two reactants almost cancel. Should it be possible to perform more extensive measurements of the exchange rates in analogous systems, a distinction between the two models might be drawn with more certainty. 3. ELECTRON EXCHANGE BETWEEN COBALTAMMINES OF Con AND Corn The Marcus theory has had reasonable success in calculating rates of electron exchange between pairs of complex ions which are inert to substitution and whose molecular dimensions are essentially the same in the two valence states. How- ever, with pairs of aquated cations, such as F e ~ ~ + F e ~ ~ , the calculated rates are lo5 times greater than the observed rates.This discrepancy has been attributed 1 to the need for reorganization of the primary hydration spheres in addition to the normal solvent reorganization process, Laidler's model yields a calculated rate which only exceeds by a factor of about ten the rate observed for the Fei;+ Fe: exchange. Nevertheless, this calculated rate includes a major contribution from electron-tunnelling at distances of separation (3.5 to 6.0fn) which are less than the minimum separation of the two aquated cations (-6-88A). The latter value is the tunnelling distance assumed in the Marcus model. At such close distances of approach, significant interactions between the reactants might well occur.Ac- cordingly alternative redox mechanisms, involving the bridging or transfer of76 ELECTRON EXCHANGE REACTIONS groups, have been proposed especially for labile species.4 The " hydrogen-atom transfer " mechanism proposed as a general mechanism for aquated cations is an unfortunate description.5 The need to transfer a hydrogen atom does not really arise in these systems and indeed the observation of a DzO-solvent isotope effect (often presented as substantiating evidence) merely indicates considerable stretching of 0-H bonds in the hydration spheres of the two reacting ions. Thus when bridging anions such as the halides are absent, it is suggested that the transfer of an electron occurs between two aquated cations via a hydrogen bridge temporarily formed between the waters of hydration of the two ions.This hydration bridge would serve to couple the two reactants in the activated state and so reduce any energy differences between the two orbitals principally involved in the electron transfer step.6 (This case of " significant orbital overlap " is not treated by the Marcus theory.) It is further postulated that, even if substantial energy differences do remain after the formation of this bridge, electron transfer will proceed by a quantum-mechanical-tunnelling mechanism whose probability is temperature-inde- pendent and little influenced by the energy barrier. The distinction between this mechanism and the models already proposed for electron tunnelling is that the former involves a more specific participation of the solvent with weak orbital overlap of the two reactants.The measurement of the rates of electron exchange between pairs of cobalt- ammines was undertaken for these two main reasons. (i) Exchange between Co(NH&+ and Co(NH&+ has been often cited as a system in which reorganization of primary co-ordination spheres is necessary as a prelude to electron transfer. The Corn-N distance in CO(NH~):+ is 2-05A whereas the CoXr--N distance is reported as about 2.5 &7 although we have suggested that 2.39 A might be a more realistic value.8 If preliminary rearrangement is necessary to equalize the Co-N bond distances before electron transfer can occur, then it may be shown 8 that this would require an expenditure of some 30 kcal mole-1. A detailed kinetic investigation of the Co(NH&++ Co(NH3);f exchange system therefore seemed appropriate to assess the mechanistic importance of this large energy barrier.(ii) In electron exchanges involving aquated cations, water performs the duaI function of solvent and ligand and due to the rapid exchange between primary and outer hydration spheres, it is difficult to devise unambiguous tests of these functions. Consequently we have studied the variation in the rates of electron exchange in aqueous solution between a series of redox pairs of the formula, Co(NH&_,(H20): ,+, where n varies from 0 to 6. At least for the higher members (n>3), the aqua-ligand is reasonably inert to exchange with solvent water. It has transpired that the eventual displacement of six ammine ligands by six aqua ligands in this series accelerates the rate of electron exchange by a factor of lo5.TABLE 2.-RATES OF ELECTRON EXCHANGE BETWEEN AQUA-AMMINES OF COX' AND cOIT' reactants k EX& AS* (64.5'C. p = 1.0) 1. mole-1 min-1 kcal/mole cal/mole deg. Co(NH,)Z ++CO(NH~)~+ < 10-8 - - Co(NH,)$.+CI-+ Co(NH,)g + (44-tO.7) X 10-2 - - cis-Co(NH3),(OH)2+Co(NH),2+ (15f2.4) x 10-1 t t Co(NH,)$. +OH-+ Co(NH,)z + (3.3 f0.2) X 10-1 12.9 & 1.6 - (35 15) Co(NH,), OH2 ++ Co(NH,)$' (5.4f0.3) X 10-2 13.4rt0.4 -(33.1 fl.4) trans-Co(NH,),(OH)~+Co(NH,), + (2-5ikO.2) x 10-1 13*8&0.9 -(29.0k2.0) t This system is currently under study. Table 2 summarizes the kinetic data obtained so far. We have found that great care is required to avoid catalysis of these exchanges by dissolved oxygen and by an insoluble hydroxo-species of Co" which tends to precipitate under certainD.R. STRANKS 77 conditions. The rate constant for direct electron exchange between Co(NH,);+ and Co(NH3)g+ is less than M-' min-' at 64.5". Calculations based on the Marcus model show that if reorganization of the arnmine co-ordination spheres is unnecessary, then the rate constant for the direct exchange should be 2x lo8 M-1 min-1 at 64.5". The Laidler model would yield a value of approximately lo5 M-1 min-1. If the reorganization energy barrier is included, then the rate constant on the Marcus model would be 10-12 M-1 min-1 with an extraordinarily high activ- ation energy of 38 kcal mole-1. Instead of this direct exchange reaction, an alter- native pH-dependent mechanism operates : Co(NH&+ + H20+Co(NH&.+OH- + H+, K1 Co(NH,);.+OH- + 6oCo(NH3)~+-+Co(NH3)~+ + 60Co(NH3),"+ + OH-.(3.2) (Our analytical scheme detects only the net conversion of 6OCo to the CoIX1 state rather than the formation of 60Co(NH3);+ alone.) We exclude the alternative amide entity Co(NH,),NH$+ since the value of K1 derived from the kinetic analysis (Kl = 4x 10-12 at 64.5") is in satisfactory agreement with an extrapolated value derived by independent workers. Nevertheless, the value of K1 is uncertain by a factor of at least three so that the energy and entropy of activation for (3.2) are subject to a larger error than the normal experimental error. The most striking result is that the energy of activation for reaction (3.2) is quite low considering the magnitude of the energy barrier to direct exchange.The entropy of activation on the other hand has a rather large negative value. More- over the exchange is also catalyzed by chloride ion but after due allowance is made for the degree of ion association, the rate constant is eight times less than that for the hydroxide-catalyzed path. Finally, we find that Co(NH3)2+ exchanges at equal rates with the cobaltous ammines from n = 3 to n = 6. As required by reaction (3.2), isotope dilution analysis has established that the 6OCo isotope is distributed among the various ColIr ammines and a net conversion of cobaltic hexammine to lower hydroxo-ammines is observed spectrophotometrically. (This conclusion is quite general for all members of the aqua-ammines studied so far.This inter- pretation is contrary to that of Taube and co-workers9 for the exchange of CO(NH,)~OH~+ with cobaltous-ammines although our measured rates do agree within the experimental error.) Two possible transition states might be proposed for reaction (3.2). The first involves a hydroxo-bridge formed by prior expulsion of one ligand from the COT' species : e 4 f I* 4- - 0- - CO"(NH,),(OH),-~ I H + One might expect that as a consequence of the eIectron-transfer process, the hydroxide ion would be completely transferred to the newly-created Con1 species. After exchange has proceeded to equilibrium, the Co(NH&+ ion should be entirely converted to lower hydroxo-ammines. The second transition state would involve a hydrogen bridge without net substitution on the newly created Co"1 centre, although motion of OH- during electron transfer may well occur : H H H H Our tracer studies reveal that hydroxide-ion transfer and substitution occur in 50 % of all transfers.Either the first mechanism operates alone (with only 50 % (NH3)SCo ''I-N-H - - 0 - - H-N-CO Ir(NH3),- I ( OH), -n.78 ELECTRON EXCHANGE REACTIONS OW- substitution) or equal contributions are made by the two mechanisms (the first involving 100 % OH- substitution). The first mechanism might be preferred since it involves greater overlap of the two reactants. Since clilorammines of ColI1 are rapidly hydrolyzed in basic solution, net transfer of C1- cannot be demonstrated although one would anticipate transition states analogous to those suggested for the OH--catalyzed path.The superior hydrogen-bonding tendency of OH- as compared to C1- seems related to the higher electron transfer rate for the OH--catalyzed path. Electron transfer between spin-paired CoI'I and spin-free Corr complexes may be represented in the general equation : Orgel 6 predicted that the spin-multiplicity restriction and the d,-d, energy separ- ation should lead to a high activation energy whereas the observed value is quite low. The discrepancy seems to be due to the nature of the bridged transition state. It is postulated that the vital part of the mechanism is the formation of a bridge of sufficient strength to facilitate electron transfer by tunnelling. The activation energy required for electron transfer is largely devoted to the formation of a bridge between the two exchanging species. Once this bridge is established, then an electron will tunncl across the bridge despite the energy differences between the two critical dr orbitals.The probability of tunnelling will be small, tem- perature-independent and soniewhat influenced by the height of the energy barrier, i.e. the separation between the dE and d, orbitals. Since all the CoII complexes are highly labiIe, the initial expulsion of one ligand to form a penta-co-ordinatcd intermediate requircd for the main mechanism is not difficult and all complexes can exchange with equal ease despite differences in the ligand field strengths of -OH and -NH3. The other results summarized in table 2 suggest that this mcchanism is also operative for the two lower hydroxo-ammines of ColIr.The activation energy for electron transfer remains constant within experimental error at a value of 1 3 3 kcal mole-1, whilst the entropy of activation becomes steadily more positive. As -NH3 ligands are replaced by -OH ligands of weaker field strength, the d,-d, orbital separation in the ColIr species will be reduced. In addition, the lability of ligands-and presumably the ease of stretching to form a bridge with Coll-will be increased and thus lead to a more positivc AS* value. It is especially note- worthy that cis-Co(NEI,),(OH)~ exchanges six times faster than does trans- Co(NH,),(OH)$. If thc d,-d, orbital separation were the critical Factor deter- mining the electron transfer rate between ColI and ColI1, then the reverse would be expccted.6 On the other hand, it is well cstablished that cis-Colll complexes are more labile than the trans-isomers.It is also noteworthy that the Co(en),"++ Co(en)i+ electron cxchange exhibits in chloride ion media an activation energy of 13.7 kcal mole-1 whilst AS* = - 39 cal (mole deg.)-l.lO Here a chloride bridge may be operating although bridged paths have been hitherto ignored for substitu- tion-inert species like Co(en)g-+. Finally, ii is tempting to suggest from our limited results, that each successive introduction of an -OH group in the aqua-ammine series would increase AS* by 3-4 cal (mole deg.)-l. For the Co,?,'+Co:i- ex- change one might then expect Eact = 13.5 kcal mole-1, AS* ;= - 13 cal (mole deg.)-1 yielding AF* = 17-4 kcal mole-1. The experimental value 11 is AF* = 16.4 kcal mole-1 although the energy and entropy of activation are as yet undeter- mined.The apparent agreement may well be fortuitous and there is a necd for an experimental detcrmination of this rate over wider conditions. Elcctron exchange bctwecii CrIJ and CrrJ1 species also involves transfer of a dy elcctron but without thc additional rearrangement of othcr d electrons as with Co[I and Co"' spccics. Exchange bctwecri CrF2 1 and Cr2-I- procccds via a bridgcd path and exhibits thc rate piirametcr's : Ei,ct - 13.7 and ASQ -= -20 cal (molcD . R. STRANKS 7 deg.)-1 12 whilst our recent studies of the exchange of urea-14V with Cr(urea)ii reveal that the catalysis by added Cr2+ may be attributed to electron exchange be- tween Cr(urea)z+ and Cr(urea);+ for which Eact = 13.0 kcal mole-1 and AS* = - 4( cal (mole deg.)-1.Once again when there is a significant reorganization energj barrier, a bridged mechanism as already described may operate. With Feu+ Fe1] exchanges, it is difficult to decide on the constancy or otherwise of the activatior energy for electron transfer. As always, further experimental work is needed. I am indebted to Miss Emma Movsessian, Dr. N. S. Biradar, Dr. D. J. Simysor (on sabbatical leave from the University of the Witwatersrand) and Dr. M. S Vaidya for their enthusiastic co-operation in undertaking aspects of the problem5 described here. I am also indebted to Prof. F. S. Dainton, F.R.S., for his constani encouragement and interest. The studies described in this paper were supported by grants from the Royal Society and the Chemical Society to whom gratefu: acknowledgement is made. 1 Marcus, J. Chem. Physics, 1956, 24, 966 ; 1957,26, 867. 2 Laidler, Can. J. Chem., 1959, 37, 138. 3 Dainton, Laurence, Sclineider, Stranks and Vaidya, Radioisotopes in Scient$c 4 Taube, J. Chem. SOC. Special Publ. no. 13, 1959, 57. 5 See, for example, Stranks in Modern Co-ordination Chemistry, ed. Lewis and Wilkins 6 Orgel, Report 10th Solvay ConJ, 1956, p. 289. 7 Biltz, 2. anorg. Chem., 1927, 164, 246. 8 Biradar, Stranks and Vaidya, submitted for publication. 9 Appelman, Anbar and Taube, J. Physic. Chem., 1959,63, 126. 10 Lewis, Coryell and Irvine, J. Chem. SOC., 1949, S386. 11 Bonner and Hunt, J. Amer. Clzem. Soc., 1952, 74, 1886. 12 Ball and King, J. Anzer. Chem. SOC., 1958, 80, 1091. Research (Proc. 1st UNESCO Int. Conf.), vol. 11, p. 305. (Interscience Hnc., New York, 1st ed., 1960), chap. 2.