Vibration–rotation calculations for using a Morse-based discrete variable representation

Abstract

The Hamiltonian operator for the X3 symmetric triatomic molecule, using Eckart axes with the three internuclear distances as internal coordinates, is derived and applied to numerical calculations of the vibration–rotation spectrum of [Formula: see text]. A C2ν-symmetrized discrete variable representation based on Morse functions is employed for the J = 0 vibrational problem. The unphysical points with ri < 0 or ri + rj < rk are avoided by giving them a large potential energy (106 cm−1). This procedure is not exact, but is adequate for vibrational levels well below the barrier to linearity. The matrices of the complete Hamiltonian in a D3h-symmetrized basis of products of the lowest 50 vibrational eigenvectors with the complete set of rotational functions for each J are set up and diagonalized, and the eigenvectors are used to calculate line strengths. Initially, the well-known potential surface of Meyer et al. (1986) was employed. Subsequently, 7 of the 30 coefficients in this potential were adjusted to give a least-squares fit to the published observed lines of [Formula: see text].