Quantum Dissipative Dynamics of Electron Transfer Reaction System: Nonperturbative Hierarchy Equations Approach

A multistate displaced oscillator system strongly coupled to a heat bath is considered a model of an electron transfer (ET) reaction system. By performing canonical transformation, the model can be reduced to the multistate system coupled to the Brownian heat bath defined by a non-ohmic spectral distribution. For this system, we have derived the hierarchy equations of motion for a reduced density operator that can deal with any strength of the system bath coupling at any temperature. The present formalism is an extension of the hierarchy formalism for a two-state ET system introduced by Tanimura and Mukamel into a low temperature and multistate system. Its ability to handle a multistate system allows us to study a variety of problems in ET and nonlinear optical spectroscopy. To demonstrate the formalism, the time-dependent ET reaction rates for a three-state system are calculated for different energy gaps.