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Several new techniques were developed and appUed to investigate various nontrivial aspects of vibrational motion. In particular, a novel strategy for accurate determination of vibrational energy levels in the presence of intramolecular hy­ drogen 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 (/-matrix elements which appear in the kinetic energy operator. Individual ^-matrix elements were modeled by series of shifted Gaussian fimctions, a newly proposed functional form that assured phys­ ically correct behavior for the entire domain of internal c;oordinates. The success in reproducing experimentally observed frequencies should be partly attributed to a new basis set of modified Herraite-type fimctions wliich 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 tliis work. The new representation, consisting of products of shifted Gaiissians and sliifted Morse fimctions, reproduces all local features near the bottom of the well and also posesses correct asympototic behavior. Determination of the functional parameters for the PES fits involved a simultaneous optimization of many linear and non-linear parameters, and required a development of an efficient minimization roxitine. The new routine consisted of an iterative procedure, which treated sets of linear and non-linear parameters separately and in successive order in each iteration.