Variational calculation of vibration-rotation energy levels for triatomic molecules

A variational method has been used to calculate the low-lying vibration-rotation energy levels of various triatomic molecules. The wavefunctions were expanded as a linear combination of products of polynomials of the normal coordinates multipled by suitable spherical harmonics of the Euler angles. The molecular vibration-rotation Hamiltonians given by Watson for nonlinear (1) and linear (2) molecules were employed. Using numerical integration, the method can be applied to any molecule for any form of the potential surface. Calculations have been carried out on the nonlinear triatomics H2O and SO2 and the linear system OCS. Potential-energy surfaces expressed in terms of variables Δr12, Δr13, and Δθ, where Δr represents a change in bond length and Δθ a change in bond angle, have been derived by many workers using perturbation theory and potential functions of this form were used in the calculations. The results for H2O indicate that none of the surfaces employed are satisfactory. For the best surface, although the band origin for the (000)-(010) transition is within 4 cm−1 of the experimental value, the band origins for the (000)-(100) and (000)-(001) transitions are in error by at least 60 cm−1. The results for SO2 are much closer to experiment, which indicates that perturbation theory is more accurate for the potential surface determination in this case. The results for OCS are similarly much closer to the experimental values. This variational method is recommended as a means of investigating the quality of potential surfaces.