Recursive computation of Hamiltonian matrix elements using harmonic oscillator eigenfunctions: Application to the inversion of ammonia and to the methyl torsion + aldehydic hydrogen wagging of acetaldehyde

Abstract

A program able to use hybrid free rotor plus harmonic oscillator basis functions for the variational study of large and small amplitude vibrations 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 algorithm to compute the kinetic and potential parts of the Hamiltonian. In addition, the program can handle potential functions perturbed with Gaussian barriers and obtain the quantum mechanical average of a magnitude. The program is used to test the efficiency of Taylor series vs polynomial + Gaussian potential functions for the description of the ammonia inversion mode. The data for the construction of the potential functions are obtained by ab initio methodology at the QCISD/6-311G+ +(3 df, 3 dp) level. The quantum mechanical average values for the structural parameters of ammonia are computed and compared to the fully optimized ab initio results. The simultaneous methyl torsion + aldehydic hydrogen wagging motions in the S 0 state of acetaldehyde are used to illustrate the efficiency of mixed free rotor + harmonic oscillator basis functions.