Anharmonic Potential Functions of Simple Molecules. II. Direct Numerical Diagonalization of Vibratinal Hamiltonian Matrix and Its Application to CO2 and CS2

Abstract

Abstract A general formalism is presented for the calculation of the vibration-rotation energy levels of linear symmetrical XY2 type molecules through direct numerical diagonalization of the vibrational hamiltonian matrix. This method is applied to the CO2 and CS2 molecules, of which the general quartic force fields have been known accurately. The results are compared with those obtained by an ordinary perturbation treatment, and the truncation effects of the matrix sizes as well as of the expansions of the potential functions are discussed. Special attention is paid to the peculiarities in the potential function of CO2 for which very strong mixings of the basis harmonic oscillator wave functions are observed. The general formula for evaluating the matrix elements of the transition moment are also discussed and its applicability to the problems of vibrational intensities and the dipole moment functions is discussed.