| New methods are presented for carrying out calculations by variational transition state theory with multidimensional tunneling (VTST/MT). These methods are used to calculate reaction rate constants for several cases. This thesis consists of three parts. First, improved algorithms for using dual-level dynamics are presented. The dual-level direct dynamics method has been shown to be an efficient algorithm to carry out VTST/MT calculations for polyatomic systems. Detailed comparisons of the original dual-level method to the new schemes are presented. Second, use of curvilinear coordinates to estimate the harmonic vibrational frequencies along the reaction path is demonstrated, and the curvilinear treatment is extended to allow use of redundant internal coordinates. The curvilinear coordinate representation has been shown to generate physically meaningful vibrational frequencies. Vibrational frequencies obtained in curvilinear and rectilinear coordinates are compared. Finally, methods are developed to combine VTST/MT and a free energy of solvation model to calculate reaction rate constants in liquid solution. With these methods, it is possible to calculate reaction rate constants in solution and obtain good agreement with the experimental values. The solvent friction effect has been included in a general nonequilibrium solvation treatment. |
