CHAPTER 10: Quantum-Classical Liouville Dynamics of Condensed Phase Quantum Processes

The simulation of quantum processes occurring in condensed phase environments is difficult due to the large number of degrees of freedom that such systems possess. Since a full quantum–mechanical treatment is difficult to carry out and is often not feasible, mixed quantum–classical approaches have been developed to describe the dynamics. In such methods the system is partitioned into a subsystem comprising a few degrees of freedom to be treated quantum mechanically and a bath which is treated classically. In this chapter, the focus is on a description of the dynamics in rate processes and optical response in terms of the quantum–classical Liouville equation. The manner in which this equation and transport/spectroscopic properties follow from a full quantum description is considered. Calculations of a rate constant and linear and nonlinear vibrational spectra are presented within the context of an application to proton transfer in a condensed phase polar solvent.