Estimation of Electron Transfer Distances from AM1 Calculations

We examine a simple approximate method for calculating the electron transfer (ET) distance suitable for extracting the off-diagonal electronic coupling element (Hab) of Marcus−Hush theory from the optical spectrum of nitrogen-centered organic intervalence radical cations. A very simple estimate of the ET distance on the adiabatic ground-state surface (d12(dm)) is employed. AM1-UHF calculation of the dipole moment component in the long axis direction (μ1) for the radical cation using the center of mass as the origin gives the estimated d12(dm) (Å) = 2μ1(Debye)/4.8023 (eq 7). Cave and Newton's Generalized Mulliken−Hush theory equation allows calculation of the diabatic counterpart (dab) in terms of d12 and the transition dipole moment (μ12), obtained from the experimental intervalence optical band. These calculations indicate that dab is significantly smaller than the distance between the nominal sites or charge localization, ratio 0.82−0.85 for the aromatic-bridged bis(hydrazines), 0.76−0.87 for the unsaturated-bridged bis(triarylamines), 0.74−0.79 for the saturated-bridged bis(diazenes), and 0.71−0.85 for the saturated-bridged bis(hydrazines) examined here. Furthermore, dab is not very different for diastereomers that differ in relative orientation of the oxidized and reduced charge-bearing units for the aromatic-bridged compounds; experimental data corresponds to a superposition of the spectra of such isomers. There appears to be a problem with the trend of calculated ET distances as methyl groups are substituted on a benzene-1,4-diyl bridge. The d12(dm) calculated is smaller for the compound with the tetramethyl-substituted bridge (DU) than that with the dimethyl-substituted bridge (XY), in contrast to the general trend in d12 as twisting increases, and to the dipolar splitting constant for the triplet form of the dication oxidation states of these compounds.