Several new techniques were developed and applied to investigate various non-trivial aspects of vibrational motion. In particular, a novel strategy for accurate determination of vibrational energy levels in the presence of intramolecular hydrogen bonds was proposed. A small subset of convenient internal coordinates was chosen to represent a vibrational mode of interest, while the interdependence among all other coordinates was encoded in the g-matrix elements which appear in the kinetic energy operator. Individual g-matrix elements were modeled by series of shifted Gaussian functions, a newly proposed functional form that assured physically correct behavior for the entire domain of internal coordinates. The success in reproducing experimentally observed frequencies should be partly attributed to a new basis set of modified Hermite-type functions which has been introduced in this work and employed in all presented vibrational energy calculations. A novel functional representation for potential energy surfaces (PES) was also proposed in this work. The new representation, consisting of products of shifted Gaussians and shifted Morse functions, reproduces all local features near the bottom of the well and also possesses correct asympototic behavior. Determination of the functional parameters for the PES fits involved a simultaneous optimization of many linear and nonlinear parameters, and required a development of an efficient minimization routine. The new routine consisted of an iterative procedure, which treated sets of linear and nonlinear parameters separately and in successive order in each iteration. The above-mentioned set of developed tools was applied to study the intramolecular vibrational energy redistribution (IVR) in HDO molecule. The time-evolution of the O-H stretching local mode was studied by a time-propagation method based on matrix representation of the evolution operator. The energy transfer among the local modes was modeled by non-diagonal g-tensor terms in the kinetic energy operator and by three-dimensional potential energy operator. The results indicate that the O-H stretching local modes must be substantially long-lived within the chosen model. A new recursive programming technique combined with a very effective passing by reference methodology was developed and used in this study to implement the time-propagation routine. The introduced concept of a shared compound pointer in Fortran 90 automatically accounts for the changing sizes of all data structures, while working with only a single parameter, a pointer to a parent object
