Calculation of Time Correlation Functions and Rate Constants in Liquid Solutions.

Abstract

In this thesis, we have used the time correlation formalism (TCF) to calculate the rates of dynamic processes in liquid solutions. This formalism allows us to cal- culate of dynamic properties with time scales that are usually inaccessible to normal molecular dynamics simulations. Within this framework we have studied vibrational energy relaxation (VER), di¤usion, and isomerization reaction kinetics. We have de- veloped an extension to the previously derived linearized semiclassical local harmonic approximation (LSC-LHA) that eliminates the need to calculate di¢ cult derivatives of the forces. This method was applied to VER in nonpolar solvents and found to agree well with experiment. We then applied the new method to the problem of VER in polar solvents. We found that the classical electrostriction explanation of the enhanced VER rate in polar solvents does not hold if quantum mechanical e¤ects play an signi cant role. We also derived another extension to the LSC-LHA that eliminates a major computational bottleneck involving a normal mode analysis that must be preformed for every trajectory. This new method was applied to the calcu- lation of di¤usion coe¢ cients in quantum liquids and was found to agree well with experimental results, but also overestimated the imaginary part of the TCF (which is purely quantum mechanical) greatly. Lastly we used a linear response approach to model the isomerization of hexatriene in methanol and cyclohexane. We found that we were able to qualitatively predict experimental trends and were able to create a microscopic model from our simulations to explain the experimental results.