Theoretical study of single-molecule spectroscopy and vibrational spectroscopy in condensed phases

In this thesis, theoretical models and computer simulations are employed to study several problems of single-molecule spectroscopy and vibrational spectroscopy in condensed phases. The first part of the thesis concentrates on studying dynamic disorders probed by single molecule fluorescence spectroscopy. Event statistics and correlations of single-molecule fluorescence sequences of modulated reactions are evaluated for multi-channel model, diffusion-controlled reaction model, and stochastic rate model. Several event-related measurements, such as the on-time correlation and the two-event number density, are proposed to map out the memory function, which characterizes the correlation in the conformational fluctuations. A semiflexible Gaussian chain model is used to determine the statistics and correlations of single-molecule fluorescence resonant energy transfer (FRET) experiments on biological polymers. The distribution functions of the fluorescence lifetime and the FRET efficiency provide direct measures of the chain stiffness and their correlation functions probe the intra-chain dynamics at the single-molecule level. The fluorescence lifetime distribution is decomposed into high order memory functions that can be measured in single- molecule experiments. The scaling of the average fluorescence lifetime on the contour length is predicted with the semi-flexible Gaussian chain model and agrees favorably with recent experiments and computer simulations. To interpret the fluorescence measurements of the mechanical properties of double-stranded DNA, a worm-like chain model is used as a first-principle model to study double-stranded DNA under hydrodynamic flows. The second part of the thesis concentrates on nonperturbative vibrational energy relaxation (VER) effects of vibrational line shapes. In general, nonperturbative and non-Markovian VER effects are demonstrated more strongly on nonlinear vibrational line shapes than on linear absorption.