Theory of molecular nonadiabatic electron dynamics in condensed phases

In light of the rapid progress of ultrafast chemical dynamics driven by the pulse lasers having width as short as several tens of attoseconds, we herein develop a theory of nonadiabatic electron wavepacket dynamics in condensed phases, with which to directly track the dynamics of electronic-state mixing such as electron transfer in liquid solvents. Toward this goal, we combine a theory of path-branching representation for nonadiabatic electron wavepacket dynamics in vacuum {a mixed quantum-classical representation, Yonehara and Takatsuka [J. Chem. Phys. 129, 134109 (2008)]} and a theory of entropy functional to treat chemical dynamics in condensed phases {a mixed dynamical-statistical representation, Takatsuka and Matsumoto [Phys. Chem. Chem. Phys. 18, 1771 (2016)]}. Difficulty and complexity in the present theoretical procedure arise in embedding the Schrödinger equation into classically treated statistical environment. Nevertheless, the resultant equations of motion for electronic-state mixing due to the intrinsic nonadiabatic interactions and solute-solvent interactions, along with the force matrix that drives nuclear branching paths, both turn out to be clear enough to make it possible to comprehend the physical meanings behind. We also discuss briefly the nonvalidness of naive application of the notion of nonadiabatic transition dynamics among free energy surfaces.