Effect of kinetic energy terms on the vibrational frequencies (ν1,ν3) in the1B2(1A′) excited state of SO2

The effect of various kinetic energy terms on the solution of the two-dimensional Schrödinger equation; involving the two large-amplitude stretching modesv1 andv3 of SO2 in its1B2 excited state, is discussed. Employing two large amplitude HamiltonianHs0(ρ1,ρ3) obtained earlier, three sets of force constants were obtained. In obtaining set 1, all the 6 coefficients of the kinetic energyA, H, B, G, F, andC were taken into account and varied with (ρ1,ρ3). For set 2, only the three coefficientsA, H, andB, evaluated at the absolute minima (ρ1e+δ, ±ρ3e) were considered. In obtaining the set 3 constants, only the two coefficientsA andB evaluated at the saddle point (ρ1e, 0) were retained. The nine force constants of the potentialV0(ρ1,ρ3) which includes a double minimum function inρ3, were obtained in each case by a least squares fit to the 12 vibrational frequencies corresponding to the levels (v1, v3)=(0, 2), (1, 0), (1, 2), (2, 0), (0, 6) and (3, 0) of S16O2 and S18O2. It is found that set 2 is superior to set 3, and sets 1 and 2 fit the frequencies essentially to the same degree of accuracy.