Nonlinear dynamics of electron localization in four-center linear and cyclic type clusters in an external electric field

Abstract

This paper presents a quantum-mechanical model to describe the electron localization dynamics in a tetrameric cluster under an external low-frequency electric field, taking into account the electron-vibrational interaction. A system of differential equations concerning the time-dependent amplitudes of the electron localization probability at each of the tetramer centers has been developed. The proposed model is used to describe the tetramers of the linear and cyclic (square-planar) configurations. For both types of tetramer configuration, the numerical calculations are performed at various values of the model parameters. At the same time, this study is focused on the tetramer in which the centers are weakly tunnel-connected and the electron-vibrational interaction with the ligand environment at each of the centers is significant. The control role of the electric field has been found, the variation of the amplitude and frequency of which allows us to implement different electron localization regimes in a cluster by adjusting the duration of the full localization of an electron on the cluster centers and switching a cluster between states with a localized and delocalized electron.