Anharmonic Potential Functions of Simple Molecules. I. Direct Numerical Diagonalization of Vibrational Hamiltonian Matrix and Its Application to CO and HCl

Abstract

Abstract The vibrational energy levels of diatomic molecules are related with the harmonic and anharmonic force constants by solving the vibrational Hamiltonian matrix numerically. The associated rotational levels are computed by two different methods; (1) perturbation treatment which utilizes the wave functions obtained, and (2) direct numerical diagonalization of the vibration-rotation submatrices. This approach, combined with the least-squares procedure, is applied to the determination of anharmonic force constants for CO and HCl molecules. Special attention is paid to the truncation effect of potential functions upon the calculated energy levels. Limitations in the usual perturbation method as well as the applicability of the present method to triatomic molecules are discussed.