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 (H ab ) 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 (d 12(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 d 12(dm) (Å) = 2μ1(Debye)/4.8023 (eq 7). Cave and Newton's Generalized Mulliken−Hush theory equation allows calculation of the diabatic counterpart (d ab ) in terms of d 12 and the transition dipole moment (μ12), obtained from the experimental intervalence optical band. These calculations indicate that d ab 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, d ab 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 d 12(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 d 12 as twisting increases, and to the dipolar splitting constant for the triplet form of the dication oxidation states of these compounds.