Electron tunneling in molecular solids. An orbital overlap model

Abstract

The long-range transfer processes (range, R ~20-50 Á) of excess electrons produced by radiolysis of molecular solids are analyzed in terms of an orbital overlap model. A united atom approximation makes possible the separation of angular and radial factors. The angular dependence is used to treat the effect of the relative orientation of donor and acceptor molecules on the transfer rate; variations of up to a factor of ~1000 are predicted. A distinction is drawn between reactions of electrons with scavengers (or transfer between additives), where the significant overlap is localized around donor and acceptor sites, and recombination with a cation produced by the radiolysis, where the overlap is largely spread out over the intervening volume. In the former case, interference due to nodes in the wave functions is significant, while in the latter, various powers of R appear in the preexponential factor. The role of the Franck-Condon principle in determining the effective barrier height is discussed. Though Franck-Condon factors play a major role, electronic interaction is also important in determining transfer rates for different donors and acceptors.

Electron transfer reactions dynamically coupled to a dielectric medium: Orientational effects and bridge assistance

“…From (28) (34) we are able to calculate the time-dependent ET probability for a given encounter complex with energy e and relative orientation W, once the equation set (3 1~) is solved for P ( t ) .…”

“…Some of the first theoretical studies of distance and orientation effects of the encounter were more or less based on arguments concerning changes in the overlapelement and did not involve explicit calculations (Ratner and Madhukar [16], Brockelhurst [34], and Rice and Pilling [35]). …”

Long Range Electron Tunneling in Biological and Model Systems

“…Theoretically the dependence of electron tunneling efficiency on mutual reagents' orientation in vitreous matrices is not strange. The anisotropy of electron tunneling can be explained by the anisotropic pattern of wave functions or by the non-sphericity of the reagents (Doctorov er al., 1982;Brocklehurst, 1979: Siders et al, 1984. The suggestion that the electron tunneling rate depends on mutual reagents n It,) orientation is quite reasonable for metalloporphyrins since the a-orbitals of pigments take part in the process.…”

A model for orientation effects in electron-transfer reactions

“…In an earlier theoretical study of orientation effects 19 it was assumed that the matrix element HsA is approximately proportional to the overlap integral SsA. For (m,l) = (0,0) states (i.e., states for which I= m = 0 with spherical wells of radius b ) the overlap is given by Since H sA is the overlap of the two functions in well B multiplied by V~ the quantity plotted would be approximately constant if S 8 A were proportional to HsA.…”