On the non-adiabatic dynamics of solvation: A molecular hydrodynamic formulation

An extended hydrodynamic formulation is developed to describe non-adiabatic solvation dynamics for coupled electronic states. Starting from a hybrid quantum-classical kinetic equation, coupled equations for the solvent local density and momentum density are derived which feature the characteristic population/coherence coupling of the non-adiabatic quantum evolution. These equations have the same formal structure as the non-adiabatic quantum hydrodynamic equations described in [I. Burghardt, L.S. Cederbaum, J. Chem. Phys. 115 (2001) 10312]. In accordance with the molecular hydrodynamics approach, a generalized free energy functional is introduced, adapted to the hybrid quantum-classical setting. A microscopic Marcus-type functional for polar solvation is considered as a special case. The present formulation is particularly appropriate to describe ultrafast solvation dynamics coupled with charge transfer, for example in photochemical charge transfer processes. By the explicit consideration of quantum coherence, the details of the population transfer and its susceptibility to decoherence effects, become amenable to direct investigation.