Electron transfer (ET) is treated as a vibrational quantum mechanicalproblem in a symmetric Born-Oppenheimer (BO) biparabolic potential of Marcus type, where the distance between the energy minima is given by the reorganization energy λ and force constant k. The interaction is characterized by a gap at the avoided crossing. Nonadiabaticity is accounted for by including the correction terms of the Born-Oppenheimer approximation. The energy splitting E 12 = E 2 − E 1 between the two lowest energy eigenvalues is related to the rate of ET in a wave packet model. For large and λ, E 12 becomes the frequency of the promoting vibrational mode, independent of . The theory is illustrated by internal ET in symmetric positive molecular ions with two double bonds, separated by single bonds. Completely delocalized ionization is obtained in the conjugated case when only one single bond separates the double bonds. More than one separating bond leads to mode softening and partial localization, whereas a completely localized, ionized double bond is obtained if many single bonds separate the double bonds.

The gauge‐invariant method of London is used to solve the molecular orbital (MO) equations in a square planar slab, with one electron per site, in a perpendicular magnetic field. Pair currents appear because of the degeneracy and incomplete filling of highest occupied molecular orbital (HOMO). This type of electronic structure may alternatively result in an antiferromagnetic (AF) state or a charge density wave (CDW) state. The CDW state has alternating oxidation states which are different in two units, for example, in BaBiO3, where the valence state of Bi is alternating between +3 and +5, depending on whether the Bi6s2 electron pair is present at the site. The AF state, on the other hand, appears if only the middle valence state is stable. It is shown here that appearance of electron pair currents requires that all three oxidation states are at about the same total energy. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75: 543–548, 1999