The new theory of electron transfer. Thermodynamic potential profiles in the inverted and superverted regions

Abstract

In a previous paper (S Fletcher, J Solid State Electrochem 11:965, 2007) a non-Marcus theory of electron transfer was developed, with results applicable to the normal region of thermodynamic driving forces. In the present paper, the theory is extended to highly exergonic reactions (the inverted region) and to highly endergonic reactions (the superverted region). The results are presented mathematically and in the form of Gibbs energy profiles plotted against a charge fluctuation reaction coordinate. The new theory utilizes the concept of donor and acceptor “supermolecules,” which consist of conventional donor and acceptor species plus their associated ionic atmospheres. The key findings are as follows. (1) In the inverted region, donor supermolecules are positively charged both before and after the electron transfer event. (2) In the normal region, donor supermolecules change polarity from negative to positive during the electron transfer event. (3) In the superverted region, the donor supermolecule is negatively charged both before and after the electron transfer event. This overall pattern of events makes it possible for polar solvents to catalyse electron transfer in the inverted and superverted regions. Because this new effect is predicted only by the present theory and not by the Marcus theory, it provides a clear means of distinguishing between them.

Appendix: List of symbols

a _A :

the radius of the acceptor supermolecule in the transition state

a _D :

the radius of the donor supermolecule in the transition state

d :

the centre-to-centre distance between D and A

−e :

Charge on the electron

ɛ ₀ :

the permittivity of free space

ɛ ₍₀₎ :

the relative permittivity (dielectric constant) of the solution in the low frequency limit

ɛ _(∞) :

the relative permittivity (dielectric constant) of the solution in the high frequency limit

f ₁, f ₂ :

constants that quantify the extent of polar screening

ΔG ⁰ :

the total Gibbs energy change of the reaction

H _DA :

electronic coupling matrix element

k _et :

the rate constant for electron transfer

λ :

the reorganization energy of the reaction

Q ₁ :

charge fluctuation on a donor supermolecule

y :

charge number on a donor supermolecule