ELECTRON TRANSFER TO AROMATIC MOLECULES BY A. C. ATEN, J. DIELEMAN AND G. J. HOIJTINK Chemical Laboratory of the Free University, Amsterdam Received 8th February, 1960 A qualitative discussion is given of the mechanism of the electron transfer to aromatic molecules in solution and at electrode surfaces. The rate of electron transfer depends on whether the aromatic negative ions are free or associated with the positive ions to ion-pairs. In the latter case, the electron transfer is coupled with the " transfer " of the positive ion so that the overall process may be regarded as an atom transfer. The experi- mental data indicate that a re-orientation of the solvent molecules takes place after the electron transfer. During the last few years, electron-transfer processes have been studied by various investigators, particularly the isotopic exchange reactions and electron- transfer processes at electrode surfaces at the standard potential of the ox-red couple.Among these processes, the more simple ones are those in which the co-ordination of the participating ions remains unchanged. These reactions have in common that the activation entropy is markedly negative, e.g. for the isotopic exchange reaction : 1 one finds AS+ = -25 cal/mole deg. Although the various theories lead to a reasonable estimate of the rate constant and predict a large negative activation entropy, the authors differ about what is the rate-determining factor in these processes. According to Weiss,2 the electron transfer in ionizing solvents takes place by quantum-mechanical tunnelling of the electron through the compact solvent layers which separate the two ions in the collision complex.Re-orientation of the solvent molecules is assumed to occur after tunnelling, which seems to be a reason- able supposition, since the average velocity of the electron will be high compared with the frequency of tumbling of the solvent molecules. Eyring 3 and Marcus,4 on the other hand, assume that a reorientation of the solvent molecules should take place before the electron tunnels. Among the various possible conformations of the collision complex only those would be favourable for electron transfer in which the orientation of the solvent molecules around the two ions is such that the potential energy of the electron is the same at either side of the barrier.In an elegant treatment, Marcus derived general equations for the free enthalpy of such a non-equilibrium state with minimum energy. From these equations it follows that the electrostatic repulsion between the two ions gives the greatest contribution to the negative activation entropy. The electron tunnelling enters the expression for the rate constant as a trans- mission coefficient, which Marcus believes to be equal to about unity. Both Weiss and Marcus started from the simplified model in which the dielectric constant changes abruptly at the boundary between the compact solvent layer and the solution, taking the optical value for the dielectric saturated solvent layer and the static value for the surrounding solution. Recently, Laidler 5 has shown that this simplification may lead to serious errors for that part of the activation entropy due to the repulsion between the ions.Following Weiss, this author assumed that re-orientation of the solvent Fe2+ + Fe* + %Fe3 + + Fe* 2 + , (1) 182A . C. ATEN, J . DIELEMAN A N D G . J. NOIJTINK 183 molecules takes place after electron tunnelling. Contrary to the authors mentioned above, he took into account the continuous decrease of the dielectric constant with increasing field strength of the ion. In addition, the encounter rate was corrected for the electrostatic repulsion between the ions. The final results of his calculations revealed that the greatest contribution to the negative activation entropy was due to a low probability of electron tunnelling, whereas the repulsion between the ions gave rise to a small positive entropy value.In the light of this treatment, the mechanism proposed by Marcus becomes somewhat doubtful, since the negative activation entropy should be largely due to repulsion. Laidler’s results, however, do not contest the idea that re-orientation of the solvent molecules should precede electron transfer, the contribution of this orientation to the activation entropy being small in comparison with other con- t ri bu tions. Similar considerations as for the isotopic exchange reactions may be given for the electron transfer at electrodcs at the standard potential of the ox-red couple. As a consequence one is here again confronted with the alternative viewpoints, re-orientation of the solvent molecules before or after electron transfer.A completely different standpoint has been taken by Hush 6 who assumed the orientation of the solvent molecules to be in equilibrium at any stage during the electron transfer with the probability density of the electron at the ion. In order to check the above theories, it is worthwhile considering electron-transfer processes in which one of the collision partners is neutral, since then the relatively strong contribution of the electrostatic interaction between the reaction partners to the activation free enthalpy is absent. A simple type of such a process is the electron transfer between an aromatic molecule and its mono-negative ion in solution and the corresponding electrode reaction, which will be discussed in this paper.Special stress will be laid on the behaviour of aromatic hydrocarbons, since their negative ions have been studied in some detail in the past few years. Before considering the electron-transfer processes, a brief review is given of the properties of negative ions of aromatic hydrocarbons and related compounds which are of significance for the study of the electron transfer. PROPERTIES OF AROMATIC NEGATIVE! IONS Aromatic hydrocarbon mono- and di-negative ions are formed by the reaction with alkali or alkali-earth metal in ethers, amines and similar solvents. Measure- ments of the electrical conductance of these solutions indicate that under favourable conditions (high dielectric constant, small radius of the metal ion and low tem- perature) the ions are free.Thc association of hydrocarbon negative ions with alkali ions has recently been investigated by one of us (J.D.).7 The results un- equivocally show that the association leads to the formation of ion pairs in which the ions are separated by at least one layer of solvent molecules. Since the results are of particular interest for the present discussion they are briefly summarized below. (i) The solvation free enthalpy increases with increasing dielectric constant and with decreasing radii of the ions. In accordance with the negative temperature coefficient of the dielectric constant, the solvation becomes stronger when the temperature is lowered. (ii) Ionic association increases with increasing radius of the metal ion, with decreasing dielectric constant and with increasing temperature.The di-negative ions, which are not further considered in this paper, are associated with at least one, and usually with two, gegen-ions. From the above results it becomes very likely that the physical behaviour of these hydrocarbon negative ions in ionizing solvents is closely similar to that of uncomplexed inorganic ions. Accordingly, a reasonable estimate of the solvation184 ELECTRON TRANSFER T O AROMATIC MOLECULES free enthalpies of these negative ions may be obtained with the aid of Born’s equation : Ags(M-) = --?( 1 -;), in which N is Avogadro’s number, D is the static dielectric constant and Y the radius of the negative ion with one compact solvent layer. The following solvation free enthalpies have been calculated by Lyons 8 for aqueous solutions; the radii were obtained from the molar volumes of the hydrocarbons.benzene - Ag,(M-) = 46 kcal mole-1, naphthalene = 43 kcal mole-1, anthracene = 40 kcal mole-1. The solvation entropies follow from --(--.-) Ne2 8 1 . 2r d7’D (3) From eqn. (2) and (3), one finds for the solvation enthalpy : For solvents like tetrahydrofuran this equation becomes ( 0 ~ 7 9 5 , (dD/aT),w -0.03, T = 300K”)’ Ahs(M-)z 1*2Ags(M-). In comparison with the solvation energies of the mono-negative ions those of the hydrocarbon molecules may be neglected. In ion-dipoles of hydrocarbon negative ions with a relatively low polarizability, such as the ions of the peri- and cata-condensed hydrocarbons, the solvated metal ion will be located at the centre of the plane of the ion.In the ion dipoles of the strongly polarizable polyphenyl ions, on the contrary, the position of the ions may be quite different.7 ELECTRON TRANSFER IN SOLUTION Ward and Weissman 10 have investigated the rate of electron transfer for the reaction using as solvents dimethoxyethane and tetrahydrofuran. Various hydrocarbon mono-negative ions display an e.s.r. spectrum with a well-resolved hyperfine pattern. At a given concentration of the molecule, the hyperfine structure bands broaden owing to a rapid electron transfer between the mono-negative ion and the corresponding molecules. From the widths of the fine structure bands and the concentrations of the molecule and the ion at which broadening is observed, the rate constant of electron transfer could be calculated.Unfortunately, owing to the high concentration of the hydrocarbon molecule required, these experiments remained restricted to naphthalene. The results found by Ward and Weissman for sodium naphthalene are : [naphthalene]-+ naphthalene+naphthalene+ [naphthalene]-, (6) dimethoxyethane : tetrahydrofuran : k = lo9 1. mole-1 sec-1, k = lo7 1. mole-1 sec-1. These rate constants differ only very slightly with temperature, the activation enthalpy being lower than 2-6 kcal mole-1. Since the free enthalpy of diffusion will amount to a few kcal mole-1, the residual factors can contribute only to the activation entropy.A . C . ATEN, J . DIELEMAN AND G . J . HOIJTINK 185 On the basis of eqn. (5) and the solvation free enthalpies listed in table 1, the equations derived by Marcus predict an activation enthalpy for re-orientation of the solvent of about 5 kcal mole-1.This implies that re-orientation of the solvent molecules does not take place before electron transfer, so that the mechanism proposed by Marcus 4 may be disregarded. The absence of an activation enthalpy also means that the reaction partners remain solvated in the collision complex. From our investigations, it appeared that in dimethoxyethane sodium naph- thalene is completely dissociated into ions whereas in tetrahydrofuran it dissolvcs as an ion-pair. In all probability, the two different rates of electron transfer thus refer to different structures of the reacting species. The absence of an activation enthalpy for the electron transfer as such suggests the following formula for the rate constant : k = k, exp (APIR), (7) where k, stands for the encounter rate constant.Taking lc, = 1010 1. mole-1 sec-1 one obtains for the electron transfer between the molecule and its free mono- negative ion AS* = - 4.5 cal/mole deg., which is appreciably less negative than the value found for similar electron-transfer processes of inorganic ions.1 Most authors ascribe this negative activation entropy to a low probability of electron tunnelling. In our opinion, however, these authors localize the orbital of the electron at the donating ion too strongly within the crystallographic sphere of the ion. With Mulliken,ll one may say that the electron acceptance volume of the molecule or ion is much larger than the van der Waal's or crystallographic volume.This means that the electron may pass into the accepting orbital of the collision partner without an appreciable change of energy even when the two partners are separated by two compact solvent layers. The probability of such a transfer will depend on the overlap between the accepting and donating orbitals and the electrostatic interaction between the electron and the accepting molecule or ion. As for the present case, one may say that the orbitals possess more anti-bonding character and consequently will give stronger overlap according as the interaction between the electron and the neutral molecule is weaker. Hence, the two effects may compensate each other for a great deal, so that the probability of electron transfer very likely does not differ too much for different hydrocarbons.In tetrahydrofuran the mechanism is quite different. For this case one obtains in the same way AS!' x - 13.5 cal/moIe deg. The absence of an activation enthalpy for the electron transfer as such again suggests that the reacting systems remain solvated and no re-orientation of the solvent molecules takes place before electron transfer. Since the mono-negative ion of naphthalene is strongly associated with the sodium ion the collision complex will possess a sort of sandwich structure, the solvated sodium ion lying between the two hydrocarbon systems. Owing to the opposite charges the alkali ion and the molecule and molecule-ion will very likely be separated by one layer of solvent molecules. In comparison with the foregoing case, the electron transfer requires a much higher order of the collision complex so that the more negative activation entropy is not surprising.Owing to the presence of the alkali ion in the collision complex the rate of electron transfer will depend on the nature of the positive ion. as has indeed been observed by Ward and Weissman.10 An important result of this type of electron transfer is, that after the molecule has accepted the electron the sodium ion changes partner. Every successful collision thus involves the transfer of an electron and a sodium ion. As a con- sequence, electron transfer is here identical with atom transfer.I86 ELECTRON 1’KANSI;EK ‘I0 AKOMATlC MOLECULES Recent iiivestigations by Adam and Weissman 12 strongly support this mechan- ism.They investigated the e.s.r. of a solution of sodium benzophenone in di- methoxyethane. From measurements of the electrical conductivity of this solution in our laboratory, it appeared that the benzophenone ion must be strongly associated with the sodium ion. In this connection Adam and Weissman speak about a “ ketyl molecule ”, a name which unjustly might be associated with the classical description of benzophenone with the oxygen linked to a sodium atom. It should be emphasized, however, that such a “ molecule ”, or rather radical, has a much higher electron affinity than the benzophenone molecule so that it disproportionates into the corresponding radical ion and benzophenone, according to the reaction 2MNa+MNa- +M+Na+. Hence, we must conclude that the benzophenone ion forms an ion-dipole with the sodium ion.Nevertheless, Adam and Weissman observed that a finite electron density exists at the sodium ion, which in the light of the foregoing discussion means that a fairly strong overlap exists between the orbital of the benzophenone ion and that of the solvated sodium ion. In the electron-transfer complex where the sodium ion on either side is neighboured by a benzophenone system, this electron density at the sodium atom may even be higher. Adam and Weissman indeed found that at high concentrations of benzophenone the spectrum of the ion-dipole collapses, after which a fine structure remains corresponding to the interaction of the magnetic moment of the electron with that of the sodium nucleus. From this result the authors rightly concluded that an “ atom transfer ” takes place.ELECTRON TRANSFER AT ELECTRODE SURFACES The rate constants of electron transfer to various aromatic molecules in dimethyl-formamide at the dropping mercury electrode have recently been measured by one of us (A. C. A.). Following an experimental technique closely similar to that used by Randles,l3 the faradaic impedances were measured at the d.c. half-wave potentials, using tetrabutyl ammonium iodide as supporting electro- lyte. These investigations have been described in more detail elsewhere.14 Unfortunately, the rate constants of electron transfer to the aromatic molecules appeared to be too high to be measured. The only conclusion that may be drawn is that these rate constants are higher than 5 cm s e c l .If one assumes that the molecule is separated from the electrode surface by two solvent layers this corre- sponds to a lower limit for the frequency of electron transfer of about 5 x 107 sec-1. Since the diffusion of the molecules and ions has been taken into account explicitly the rate constant is given by k = (kT/h) exp (- AG*/RT). (9) Owing to the large excess of supporting electrolyte, the potential at a distance from the electrode of two solvent layers will differ only slightly from that in the bulk of the solution, so that repulsion of the negative ion by the electrode will not contribute very much to the activation enthalpy. By analogy with the electron transfer in solution, one may therefore suppose that the activation enthalpy is very small and the rate constant is practically determined by the activation entropy.This leads to a lower limit for the activation entropy of about -20 cal/mole deg. The high dielectric constant of dimethyl formamide ( D rn 37) suggests that the mono-negative ions are practically free. In that case one may expect a rate constant comparable with the homogeneous rate constant for sodium naphthalene in dimethoxyethane, which implies that the activation entropy should be roughly -4.5 caljmole deg., and consequently the rate constant should be about three orders higher than the lower experimental limit, provided the extent of overlap between the molecular orbital and electrode orbital is about the same as between two molecular orbitals.A . C . ATEN, J . DIELEMAN AND G . J . NOIJTINK 187 An important conclusion may be drawn from the measurements of the rate of electron transfer to the aromatic mononegative ions.14 The rate constants of these processes which are appreciably lower than those for the transfer of the first electron are practically independent of the structure of the aromatic compound. On the basis of these results it seems reasonable to assume that the rate constant for the first reduction step will also be of the same order of magnitude for all aromatic compounds. 1 Silverman and Dodson, J. Physic. Chem., 1952, 56, 846. 2 Weiss, Proc. Roy. SOC. A, 1954, 222, 128. 3 Zwolinski, Marcus and Eyrhg, Chem. Rev., 1955, 55, 157. 4 Marcus, Can. J . Chem., 1959, 37, 155 and related papers. 5 Laidlcr, Can. J. Chem., 1959, 37, 138. 6 Hush, J. Chem. Physics, 1956,24, 965. 7 Dieleman and Hoijtink, to be published. 8 Lyons, Nature, 1950, 166, 93. 9 Critchfield, Gibson and Hall, J. Amer. Chem. SOC., 1953, 75, 6044. 10 Ward and Weissman, J . Ainer. Cheni. SOC., 1957, 79, 2086. 11 Mulliken, Rec. trclv. chirn., 1956, 75, 845. 12 Adam and Weissman, J. Amer. Chem. SOC., 1958, 80, 1518. 13 Randles and Somerton, Tram. Furuday SOC., 1952, 48, 937, 14 Aten, Thesis (Free Univcrsity, Amsterdam, 1959). Aten and Hoijtink, Int. Congr. Poiurogruphy (Cambridge, 1959).