A trajectory-based approach to modeling nonlinear infrared spectra : interrogating strong hydrogen bonds and proton transfer

Abstract

This work describes a phenomenological approach for modeling linear and nonlinear infrared spectroscopy of condensed phase chemical systems, focusing on applications to strongly hydrogen bonded complexes. To overcome the limitations inherent in common analytical models, I construct full time trajectories for spectroscopic variables, here the vibrational frequencies and transition dipole moments, and use these as inputs to calculate the system response to an applied electric field. This method identifies key dynamical variables, treats these stochastically, and then constructs trajectories of spectroscopic variables from these stochastic quantities through mappings. The correspondence of such fluctuating coordinates and spectroscopic observables is demonstrated for a number of simple cases not adequately addressed using current approximations, including liquid water, strong hydrogen bonds, and proton transfer reactions using ab initio calculations, model potentials, and molecular dynamics. Dynamical information is bestowed upon these trajectories through either a Langevin-like Brownian oscillator model for the bath, full molecular dynamics calculations, or experimentally motivated empirical formulae. Utilizing the semiclassical approximation for the linear and nonlinear response functions, these constructed trajectories give us the ability to numerically calculate nonlinear spectroscopy to examine phenomena previously difficult with other methods, including non-Gaussian dynamics, correlated occurrences, highly anharmonic potentials, and complex system-bath relationships.