Quantum-Classical and Semiclassical Path Integral Methods for Condensed Phase Dynamics.

다국어 초록 (Multilingual Abstract)

Chemical dynamics are essentially quantum mechanical processes. A great variety of chemical processes such as electron transfer and energy relaxation occur in condensed phase, reactants and products embedding in a non-reactive solution/environment. Therefore, quantum dynamics in condensed phase is the study of the behavior of the quantum system coupled to an interacting bath. The development of robust methodologies and efficient computational tools for condensed phase dynamics remains central to theoretical chemistry. Since the full quantum treatment only limits to a system with a few degrees of freedom, the partition of the entire system into a subsystem for which quantum mechanical description is necessary and the bath which can be modeled by the less expensive classical dynamics, is a common strategy. Due to the decoherence nature of the bath on the system, the quantum dynamics of the system is often described by the density matrix. Path integral formulation of the density matrix provides a versatile tool for studying quantum dynamics in condensed phase. Unlike the Schro ̈dinger equation in which the wavefunction is central, Feynman’s path integral formulation is trajectory based, and therefore offers a natural connection between quantum mechanics and classical mechanics. This work will investigate path integral formulation in treating a quantum system coupled to anharmonic environment and the semiclassical formulation of path integral. A big achievement in using Feynman’s path integral to study condensed phase dynamics is the development of quantum-classical path integral (QCPI) methodology. Taking advantage that the non-reactive environment can be modeled accurately by classical mechanics, a great reduction of computational cost is achieved. Previous studies have been largely focusing on a quantum system interacting with harmonic environment, mainly because the analytical expressions of harmonic oscillator can be obtained. In this work, we extend the QCPI method to anharmonic environment by making numerically accurate approximations. Semiclassical approach reduces all the possible quantum paths into one or several classical trajectories, therefore automatically eliminates the exponential growth of paths with time evolution. The distinct forward and backward trajectories in the density matrix allows quantum interference. This work explores the semiclassical-system classical-bath formulation of path integral. The stationary phase condition makes the phase smooth and makes Monte Carlo sampling very efficient with respect to the bath initial phase space distribution. The continuous coordinate formulation offers a potential utility of the method to treating multi-level systems.