DENSITY-MATRIX THEORY OF CHARGE-TRANSFER

A dynamic theory is presented for the description of dissipative charge transfer in molecular systems. The quantum dynamics of the coupled electron-vibration motion are described in the framework of the density-matrix theory. The equations of motion of the density matrix are given in a representation that uses the Born-Oppenheimer states of the different localization centers of the electron together with the vibrational modes coupling to the electron. A dissipative environment is introduced by separating all molecular vibrations which do not couple to the transferred electron and providing thermal equilibrium for them. The description allows (a) the introduction of any type of potential surfaces, (b) the description of any microscopic model for the coupling between the vibrational modes and the dissipative environment, and (c) the consideration of any strength of electronic intercenter coupling. Therefore the approach allows one to study the transition from the wavelike to the hoppinglike electron motion between the centers as well as nonadiabatic transfer, adiabatic transfer, and any intermediate type. Besides the derivation of the basic density-matrix theory, the numerical solution of the density-matrix equations is presented for the model of a two-center single-vibrational-mode system. The exact results of the density-matrix equations are compared with those of approximate rate equations.