How far do electrons move? A semiempirical investigation of thermal electron-transfer distances in cationic bis(hydrazine) and bis(hydrazyl) mixed-valence compounds.

A computational approach for estimating thermal electron-transfer reaction distances in symmetrical mixed-valence compounds is described and applied to a series of bis(hydrazine) and bis(hydrazyl) radical cations and derivatives, some of which have been investigated experimentally by Nelsen and co-workers. Ground-state semiempirical charge distributions are obtained by using optimized reactant geometries. Advantage is then taken of the approximate C(2) symmetry, or the approximate mirror symmetry, of each of the targeted compounds, and the inherent degeneracy of the corresponding electron-transfer reactions, such that the change in dipole moment (Delta-mu) upon charge transfer can be estimated from an appropriately distance-weighted sum of charge differences between approximately symmetry-equivalent atoms found on the donor and acceptor sides of the molecule. Delta-mu can then be related directly to the effective one-electron-transfer distance. We find that calculated adiabatic electron-transfer distances can differ appreciably from the geometric donor-site/acceptor-site separation distances. Furthermore, for a fixed geometric separation distance, the effective electron-transfer distance can vary considerably, depending on chemical substituent composition and/or isomeric configuration. Further advantage is taken of the approximate donor-site/acceptor-site symmetry, in the context of a Newton-Cave type analysis, to establish the relative importance of electronic delocalization effects versus self-polarization and inductive effects in diminishing or enhancing effective one-electron-transfer distances.