Centrifugal distortion constants for diatomic molecules: an improved computational method

[1] J.M Hutson, J. Phys. n. (At. Mol. Phys.) 14, 851 (1981). [2] D.L. Albritton, W.J. Harrop, A.L. Schmeltekopf and R.N. Zare, J. mol. Spectrose. 46, 25 (1973).Centrifugal distortion constants are important when fitting molecular parameters to spectroscopic data, but it is often difficult to separate the effects of centrifugal distortion from those of other parameters on experimental grounds alone. However, if an accurate potential energy curve is available, centrifugal distortion constants may be calculated theoretically. Several methods have been proposed for this, and work well for low vibrational levels, but all are either inaccurate or computationally difficult for highly excited vibrational states. We have developed an alternative approach which eliminates this problem. In the present method [1], the perturbation theory approach of Albritton et al. [2] is reformulated to eliminate sunmations over excited vibrational levels. In the usual formulation of Rayleigh-Schrodinger perturbation theory, these summations arise when the solution of an inhomogeneous differential equation is expressed as a sum over the eigenfunctions of the unperturbed Hamiltonian. In the present method, this differential equation is solved numerically, eliminating the summations and giving an exact solution using much less computer time than in the original perturbation theory approach. The effects of continuum levels are included exactly, so that the results remain valid for virational levels near dissociation. Calculations of centrifugal distortion constants have been performed for the $\mu$ state of $T_{2}$ for vibrational levels up to $\upsilon = 79$; the $\upsilon = 79$ level is bound by less than 0.05% of the well depth. The calculated centrifugal distortion constants give excellent agreement with experiment up to at least $\upsilon = 72$