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 C₂ 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 (Δμ) 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. Δμ 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.