Born-Oppenheimers Approach in Electron Tunneling Transfer

Violation of Born-Oppenheimer s Approach in Electron Tunneling Transfer 

The consideration of the reactions of the electron tunneling transfer was until now based on Born-Oppenheimer s adiabatic approach (see Section 2 of Chapter 2) that was used for the description of the wave functions of the initial and final states. The electron tunneling interaction V results in the non-adiabatic transition between these states, if the matrix element Vtf 

Let us use the method of calculating the asymptotics of the wave function from Section 2, but for the united electron-vibration system. For simplicity, the donor and the acceptor are presented below as the one-electron centers with the vibration degrees of freedom. Hamiltonian of the donor system in 

He(j) is Hamiltonian of a free electron, V,-(r) is Coulomb s interaction of the electron with the donor ion residue, Hlv( q ) is Hamiltonian of the vibration subsystem depending on the set of the vibration coordinates qj that corresponds to the movement of nuclei without taking into account the interaction of the electron with the vibrations. The short-range (on r) potential Ui(r, q ) describes the electron interaction with the donor ion residue and with the nuclear oscillations. The wave function of the system donor + electron may be represented in MREL in the adiabatic approach (see Section 2 of Chapter 2)  

The asymptotics of the wave function (48) at r e AR (AR is the asymptotic region, out of MREL) may be expressed similarly to formula (8)  

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