The derivation of vibration-rotation kinetic energy operators, in internal coordinates

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Abstract
A straightforward method for the derivation of kinetic energy operators for molecular vibration-rotation problems is described. It is assumed that internal coordinates are used for the molecular vibrations. The operator is derived by starting with the kinetic energy operator in cartesian coordinates, followed by a succession of transformations using the chain rule. Euler angles are treated in the same way as internal coordinates. At the end derivatives with respect to Euler angles are replaced by angular momentum operators. Such operators have been derived for triatomic and tetra-atomic molecules using a computer algebra program.