General formulation of the vibrational kinetic energy operator in internalbond-angle coordinates

A general formulation of the vibrational kinetic energy operator expressed in internal bond-angle coordinates is presented. This formulation is based on Podolsky's expression for the covariant form of the Laplace-Beltrami ope rator. When a valid set of internal bond-angle coordinates is employed, it is possible to adapt a systematic approach to solve for the Jacobian determ inant governing the coordinate transformation from Cartesian coordinates. I n the general case of an arbitrary N-atom system, this Jacobian always fact orizes to a simple form. This allows one to evaluate all the terms that con tribute to (V) over cap', the effective potential that arises from transfor ming the kinetic energy operator to internal coordinates. We discuss restri ctions on the choice of internal vibrational coordinates that may be includ ed in a valid set. We then provide tabular information from which the vibra tional kinetic energy operator for any molecular system can be constructed directly with no matrix inversion or chain rule manipulation required. (C) 1999 American Institute of Physics. [S0021-9606(99)01840-1].