On the derivation of the vibrational kinetic operator for polyatomic molecules in internal coordinates

Abstract

The use of the vector formalism to derive analytic expressions for the (internal coordinates) vibrational kinetic operator of a polyatomic molecule with a large (arbitrary) number of atoms have been analysed. The present study has been restricted to the case in which the molecule has one central atom, and spherical coordinates have been chosen as internal ones. The study has been performed in three steps. First, a short revision of the vector formalism is performed. Next, the formaldehyde tetra-atomic (vibrational) Hamiltonian (previously obtained by N. C. Handy) is reproduced. Finally, an analytic representation of the general vibrational Hamiltonian is obtained.