Vibrational model for electron transfer in the limit of small activation barriers

Abstract

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.

Chemical model for superconductivity

“…The polarization forces when the electron pairs move around should be of the same type as in the well‐known electron (pair) transfer models that have been developed in physics and chemistry over many years 7–20. Here, we in particular emphasize the all‐ accepted theory for mixed valence systems.…”

“…The reorganization energy has to be balanced by a strong electronic coupling between the sites 21, 22. The electron pairing of relevance to superconductivity further requires that the corrections of the Born–Oppenheimer approximation be introduced to obtain a vibronic ground‐state wave function 20.…”

“…Electronic wave functions may radically change character depending on the positions of the nuclei. In other words, there is a coupling between electronic and nuclear motion, familiar from and well described in electron transfer, polaron, or mixed valence theory 7–20. It is not too far fetched that if corrections to the Born–Oppenheimer approximation are introduced in the zero‐point vibrational motion for mixed valence systems an energy gap appears 20 that can be associated with the superconducting gap 21, 22.…”

Applications of CASSCF

“…If Δ in Figure 2 is very small, surface hopping occurs and there is no ET. A quantum mechanical theory has been advanced by Klimkans and Larsson 24.…”

Mixed valence and superconductivity

“…There is no general way to treat anharmonicities and non-adiabaticities of the type of a double-well potential, although the problem has been discussed (Zacher 1987;Hardy & Flocken 1988) not least in connection with MV-3 theory (Prassides et al 1986). Non-adiabaticity has been included in the MV-2 case (Klimkāns & Larsson 2000). Softening is determined experimentally with reference to some standard system, for example an un-doped system such as La 2 NiO 4 or La 2 CuO 4 , where the doped system is La 2Kx Sr x NiO 4 or La 2Kx Sr x CuO 4 , with xO0.…”