# Discretized real-time path integral simulations of solvent-induced vibrational transition probability of small molecules

## Description

In this dissertation two theoretical models for calculation of solvent-induced vibrational transition probability are introduced. These models are based on Feynman's real-time discretized path integral techniques. In the first model, discretized real-time path integral is applied to a system consisting of a diatomic in a small cluster of two solvent atom. The system considered consists of Br$\sb2$ in Ar. An adiabatic separation of variables is assumed. The solvent as well as the Br$\sb2$ center of mass are gathered into a vector called bath or solvent coordinates. The forced harmonic oscillator approximation is used to analytically obtain the vibrational contribution to the transition amplitude. The discretized real time propagators (bath dependent only, since the vibrational part is carried out analytically) are highly oscillatory and, therefore, not suitable for Monte Carlo calculations. The local averaging technique introduced by Filinov and developed by Freeman and Doll, and Miller and Makri is employed to make the integrands more suitable for a Monte Carlo evaluation (the oscillations are pre averaged before the Monte Carlo procedure is applied). The computations are carried out for five different times. For each time, we study the convergence of the technique for a range of Gaussian widths used as local averaging functions. We also study convergence as a function of the number of time divisions in the discretized description of the solvent path In the second model, a new approximate technique for real-time discretized path integral simulations are introduced. The technique transforms the oscillatory integrands into non-oscillatory functions for accurate Metropolis Monte Carlo evaluation. The method is applied to the same prototype system of a Br$\sb2$ diatomic in a cluster of solvent atoms. The solvent-induced vibrational transition probability of finding the diatomic in its ground vibrational state is calculated at time t. The diatomic is initially in its first vibrational state. Computations are carried out for two different times and the results are compared to the results of full discretized path integral calculations of the first model. The convergence of the technique is tested as a function of the number of time divisions in the discretized description of each solvent path