The utility of AM1 calculations for estimation of the electron-transfer parameters lambda'(v) (the enthalpy part of the Marcus internal reorganization energy) and H(ab) (the electronic coupling between the charge-bearing units) is considered for some charge-localized intervalence bis(hydrazine) radical cations, for which these parameters have been experimentally determined from optical measurements. The Koopmans estimate of lambda'(v) that employs the orbital separation for the neutral compound at the radical cation geometry is far from that calculated from the enthalpies of the species involved (eq 1) and is not correct. The eq 1 lambda'(v) enthalpies estimated by AM1 are reasonably good for compounds with only alkyl substituents but are overestimated by 33-59% for aryl-substituted hydrazines. The Koopmans estimate of H(ab) as half the orbital separation for the neutral species at the transition state geometry requires adjustment for the twist angles to those of the relaxed ground state to produce useful H(ab) values. Symmetry breaking occurs for the electron-transfer transition states of the compounds with saturated bridges, and the Koopmans estimate predicts H(ab) values that are slightly less than half as large as the optical measurements.

Electron transfer in the cations of bis(hydrazines), bridged by six different π-systems (compounds 1-6) is studied using ab initio and density functional theory (DFT) methods. Due to ionization from an antibonding combination of the lone-pair orbitals of the nitrogens in one of the hydrazine units, conjugation is introduced in the N-N bond of that unit. This leads to a shortening of the N-N bond distance and an increase of the planarity around the nitrogens. Due to steric hindrance, this causes an increase of the angle, called ϕ, between the lone-pair orbital on the nitrogen attached to the bridge and the p-orbital on the adjacent bridge carbon for the ionized unit in the charge localized, relaxed state of the molecule. This angle controls the magnitude of the electronic coupling. In the fully delocalized symmetric transition state of the ion, however, this angle is low for both units, due to the fact that the conjugation introduced at the ionized hydrazine unit is now shared between both units. An extended π-system is formed including the orbitals of the hydrazine units and the bridge, which leads to a large electronic coupling. The electronic coupling derived by optical methods, corresponding to the structure of the relaxed, asymmetric cation with a large ϕ for the ionized unit, appears to be much smaller. We believe this is due to an approximate cosine dependence on ϕ of the coupling. The calculations carried out support these conclusions.

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The ground state structure of retinal has been investigated. We found that DFT and CASSCF produce different results for the bond length alternation in a model system of retinal. Quantum mechanics/molecular mechanics calculations including the closest surrounding amino acids have been performed, using DFT and CASSCF to calculate the structure of retinal in the protein cavity. The planarity of the retinal molecule is affected by the surrounding protein. DFT and CASSCF produce different twist angles. The difference between CASSCF and DFT appears to be related to the positively charged nitrogen of the Schiff base, which leads to different pi-bond orders produced by the two methods.