ANHARMONICITY OF THE VIBRATIONAL KINETIC ENERGY FOR SPHERICAL TOP MOLECULES WITH CURVILINEAR INTERNAL $COORDINATES^{\ast}$
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Date
1982
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Ohio State University
Abstract
As part of the development of the interaction of vibrations with rotations in spherical top molecules using curvilinear internal coordinates for the vibrational degrees of freedom, the anharmonic contributions to the vibrational kinetic energy have been derived. In the series expansion to the order $S_{t""}$ and $S_{t""t"" '}$ the coefficients $G^{(1)}_{tt'}, t""$ and ${G^(2)}_{tt', t""t"" '}$ have been obtained where $T = 1/2 \sum G_{tt'}P_{t}P_{t'}$ and $G_{tt'} = G^{0}_{tt'} + \sum {G^(1)}_{tt', tt""} S_{tt""} + \sum {G^(2)}_{tt', t""t"" '} S_{t""}S_{t"" '}.$ Of special interest is the development of the general method for handling redundant internal coordinates in a symmetry coordinate basis for values of the internal coordinates away from the equilibrium position of the atoms in the molecule. This technique preserves the concept of the conjugate momenta.
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$^{\ast}$Supported by the Robert A. Welch Foundation and the National Science Foundation.