Model of electron tunneling through molecular junction: Numerically exact solution and performance of approximation methods

Abstract

We propose a model of the electron tunneling through a molecular junction, with torsional vibrational motion of the molecule coupled to the electron. The quantum dynamics for this two dimensional model is solved numerically by expansion of the wave-function in the Fourier series in the vibrational coordinate and the inversion of the system of equations resulting from the integral Lippmann-Schwinger equation. The fast convergence of this spectral method is observed and essentially exact solution is obtained. The resulting transmission functions are discussed in different regimes and the performance of some common approximation techniques (frozen vibrations, Chase (adiabatic) approximation, method of the local complex potential) is tested.