Variational and perturbative descriptions of highly vibrationally excited molecules

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Abstract
Two theoretical approaches to the calculation of the highly excited vibrational states are reviewed. Particular emphasis is placed on the choice of coordinates, and the ramification this choice has on the quality of the ensuing calculations. The essential ingredients of variational calculations are highlighted via four illustrative calculations. The standard approach of using a product basis of harmonic oscillators based on a rectilinear normal mode framework is discussed using the work of Maessen and Wolfsberg. The improvements to this basis are presented within the context of the calculation of Romanowski et al. in which a self-consistent-field basis is employed. Bond-angle coordinates and the advantages they provide are demonstrated. This discussion focuses on the efficient algorithms which Carter and Handy developed for evaluating eigenvalues and eigenvectors of tri- and tetra-atomic molecules. For yet larger amplitude motion, associated with ‘floppy’ molecules, the combination of Jacobi coordinates and the discrete variable representation are reviewed in the context of a study of the eigenstates of HCN/HNC by Bacic and Light. Perturbative approaches are also considered. In particular, the application of canonical Van Vleck perturbation theory in a superoperator framework using curvilinear coordinates is reviewed. This section draws chiefly from the work of Sibert, McCoy, and Fried and Ezra.