Photodynamics of extended molecular systems. I. A theoretical approach for strongly coupled primary and secondary regions

A general time-dependent quantum mechanical approach to the interaction of visible and UV light with extended polyatomic systems is presented. It is treated as a two-step process: a photon absorption excites electronic transitions in the target system, and this is followed by a dynamical evolution of the system on the excited potential energy surface. The time evolution in a large polyatomic system is treated within a molecular time-correlation function (TCF) approach. For a general two-surface electronic excitation problem, an extension of these molecular TCFs from real to complex times is introduced to facilitate their computation. Time-dependent self-consistent field (TDSCF) equations for transition amplitudes are derived from a variational approach and are used for large polyatomic systems to factor the molecular TCFs into primary and secondary region TCFs. The primary and secondary regions are modeled by considering a general primary motion coupled to many harmonic degrees of freedom in the secondary region. In the strong coupling case, the Hamiltonian has a general dependence on the variables of the primary region, whereas it has linear and bilinear terms in the variables of the secondary region. A weak coupling limit is obtained by dropping the bilinear terms in the coupling. The complex time propagators for the secondary region dynamics are constructed analytically for both cases. The present treatment provides a quantal version of the generalized Langevin equations of molecular dynamics. It allows for the derivation of a fluctuation–dissipation theorem similar to the classical one, by introducing a displaced Boltzmann distribution and identifying dissipation and fluctuation forces within the TDSCF approximation.