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On the Theory of Oxidation‐Reduction Reactions Involving Electron Transfer. I
1.See review articles: Zwolinski, Marcus (Rudolph J.), and Eyring, Chem. Revs. 55, 157 (1955);
1.C. B. Amphlett, Quart. Revs. 8, 219 (1954);
1.O. E. Myers and R. J. Prestwood, Radioactivity Applied to Chemistry, edited by Wahl and Bonner (John Wiley and Sons, Inc., New York, 1951), Chap. 1;
1.Betts, Collinson, Dainton, and Ivin, Ann. Repts. on Progr. Chem. (Chem. Soc. London) 49, 42 (1952);
1.R. R. Edwards, Ann. Revs. Nuclear Sci. 1, 301 (1952);
1.M. Haissinsky, J. Chim. Phys. 47, 957 (1950);
1.and recent reviews in Ann. Rev. Phys. Chem.
2.W. F. Libby, J. Phys. Chem. 56, 863 (1952).
3.Marcus (Rudolph J.), Zwolinski, and Eyring, J. Phys. Chem. 58, 432 (1954). These authors summarize some of these data in their Table I. In Table II, reactions are given having apparent positive entropies of activation. However, in at least all but one of the reactions in Table II the mechanism is complex and the concentrations of the actual reactants are unknown. Accordingly, the so‐called entropies of activation of such reactions have no immediate theoretical significance. The lone possible exception, incidentally, does not involve reacting ions of like sign.
4.J. Weiss, Proc. Roy. Soc. (London) A222, 128 (1954), has also discussed the electronic jump process. Unlike reference 3 the necessity for the reorganization of the solvent occurring prior to the electronic transition was not considered there.
5.The mechanism used there was incomplete in that only one fate of the intermediate state in the reaction was considered. It was tacitly assumed that this state involving the reorganized solvent could only produce products, but not reform the reactants. (The former would occur by an electron jump process, the latter by a disorganizing motion of the solvent.) It is shown later that this omission can significantly affect the role played by the electronic jump process. The number of times per second that the electron in one of the reactants struck the barrier was not included in the over‐all calculation. Effectively, this made electron tunnelling appear about one thousand‐fold less frequent than would otherwise have been estimated.
6.The Schrödinger equation can be written as is the energy of an atomic configuration. The Hamiltonian operator H includes terms expressing the interaction of the electrons and nuclei of the reacting particles with each other and with the solvent molecules. In the case of no overlap, and were shown to be solutions to this wave equation. Let their corresponding energies be and respectively, so that we have: and If c is any constant, a linear combination of and is When introduced into the wave equation this yields: Only when equals is the right‐hand side equal to That is, only under these conditions does satisfy the equation It is also seen that for such a linear combination, the total energy E equals and therefore
6.(a) L. Pauling and E. B. Wilson, Introduction to Quantum Mechanics (McGraw‐Hill Book Company, Inc., New York, 1935).
7.Glasstone, Laidler, and Eyring, The Theory of Rate Processes (McGraw‐Hill Book Company, Inc., New York, 1941).
8.R. A. Marcus, J. Chem. Phys. 24, 979 (1956).
9.Numerous theoretical treatments of the free energy of solvation which have assumed this model include: (a) J. D. Bernal and R. H. Fowler, J. Chem. Phys. 1, 515 (1933);
9.(b) D. D. Eley and M. G. Evans, Trans. Faraday Soc. 34, 1093 (1938);
9.(c) E. J. W. Verwey, Rec. Trav. Chim. 61, 127 (1942);
9.(d) R. W. Attree, Dissertation Abstr. 13, 481 (1953).
10.This is especially true when the valence of the ion before and after the reaction differs by only one unit. This will be shown to be the case of greatest interest, in later applications of this paper.
11.See R. Platzman and J. Franck, Z. Physik 138, 411 (1954).
12.E.g., if during some point of the charging process the ion has a charge q, then the potential at any point in the dielectric medium distant r from the center of the ion is The potential at the surface of the sphere is . The work required to add an infinitesimal charge dq to the ion is therefore Upon integrating this from to the total work required to charge up the ion is seen to be In passing it is observed that when one subtracts from this the work, required to charge up the sphere in a vacuum one obtains the usual expression for the contribution to free energy of solvation of an ion, arising from the dielectric outside of the sphere. See reference 9.
13.E.g., A. A. Frost and R. G. Pearson, Kinetics and Mechanism (John Wiley and Sons, Inc., New York, 1953), Chap. 7.
14.C. E. Moore, Atomic Energy Levels (National Bureau of Standards, 1952), circular 467, Vol. II.
15.Hasted, Ritson, and Collie, J. Chem. Phys. 16, 1 (1948).
16.See D. H. Everett and C. A. Coulson, Trans. Faraday Soc. 36, 633 (1940).
17.Equation (48) of the present paper may be obtained from Eq. (53) of reference 8 by observing that in that equation, (a) (b) (c) is the value of E when (vacuum).
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