Linearized nonadiabatic dynamics in the adiabatic representation

In this chapter we generalize a recently developed approximate method for computing quantum time correlation functions based on linearizing the phase of path integral expressions for these quantities in terms of the difference between paths representing the forward and backward propagators. The approach is designed with condensed phase applications in mind and involves partitioning the system into two subsystems: One best described by a few discrete quantum states, the other represented as a set of particle positions and momenta. In the original formulation, adiabatic basis was used to describe the quantum subsystem states. Here we extend the technique to allow for a description of the quantum subsystem in terms of adiabatic states. These can be more appropriate in certain dynamical regimes and have the formal advantage that they can be defined uniquely from the electronic Hamitonian. The linearized algorithm in the adiabatic basis is derived first, and its properties are. then compared to those of alternative dynamical schemes.