RECURSIVE COMPUTATION OF HAMILTONIAN MATRIX-ELEMENTS USING HARMONIC-OSCILLATOR EIGENFUNCTIONS - APPLICATION TO THE INVERSION OF AMMONIA ANDTO THE METHYL TORSION PLUS ALDEHYDIC HYDROGEN WAGGING OF ACETALDEHYDE

A program able to use hybrid free rotor plus harmonic oscillator basis functions for the variational study of large and small amplitude vibr ations is developed. The Hamiltonian matrix elements between harmonic oscillator eigenfunctions and polynomial terms are calculated using a recursive algorithm. This technique permits use of only one basic algo rithm to compute the kinetic and potential parts of the Hamiltonian. I n addition, the program can handle potential functions perturbed with Gaussian barriers and obtain the quantum mechanical average of a magni tude. The program is used to test the efficiency of Taylor series vs p olynomial + Gaussian potential functions for the description of the am monia inversion mode. The data for the construction of the potential f unctions are obtained by ab initio methodology at the QCISD/6-311G + (3 df, 3 dp) level. The quantum mechanical average values for the str uctural parameters of ammonia are computed and compared to the fully o ptimized ab initio results. The simultaneous methyl torsion + aldehydi c hydrogen wagging motions in the S-0 state of acetaldehyde are used t o illustrate the efficiency of mixed free rotor + harmonic oscillator basis functions.