RESOLUTION OF A CONVERGENCE PROBLEM IN DIRECT-POTENTIAL-FIT DATA ANALYSES US-ING THE HERMAN-ASGHARIAN HAMILTONIAN

\underline{ROBERT J. LE ROY}, Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada; JOHN A. COXON, Department of Chemistry, Dalhousie University, Halifax, Nova Scotia, B3H 4J3 Canada; MICHAEL REY and VLADIMIR G. TYUTEREV, Group de Spectrométrie Moléculaires et Atmosphérique, CNRS UMR 6089, BP 1039, F-51687, Reims Cedex 2, France.

The effective radial Schrödinger equation based on the Herman-Asgharian^{a} Hamiltonian for a diatomic molecule in a ^{1}Σ state has the form

− \frac{h̄^{2}}{2μ} [1 + β(r)] \frac{d^{2}ψ_{v,j}(r)}{dr^{2}} + \{[V_{CN}(r) + ΔV_{ad}(r)] + \frac{h̄^{2}}{2μ r^{2}} [1 + α(r)] [J(J + 1)] \} ψ_{v,j}(r) = E_{v,J} ψ_{v,j}(r)  (1)

in which β(r) and α(r) represent the effects of non-adiabatic corrections to the radial and angular kinetic energy operators, respectively, and ΔV_{ad}(r) is the adiabatic correction to the “clamped nuclei” potential energy function function V_{CN}(r) . An internal convergence problem encountered when utilizing wavefunction propagator methods for directpotential-fit diatomic data analyses using this Hamiltonian is described and corrected. Improved Hamiltonian parameters for the ground states of GaH and ArH^{+} will be reported.

a R. M. Herman and A. Asgharian, J. Mol. Spectrosc. 19, 305 (1966).