Refinement of the HeH₂ potential surface through inversion of nuclear spin relaxation data

Proton spin relaxation times, T₁/p (the slope of the longitudinal relaxation time, T₁, vs density, p) in the infinite dilution limit as measured by Lemaire and Armstrong [J. Chem. Phys. 81, 5275 (1984)] at temperatures between 86 and 298 K are used to refine the anisotropic term of the Rodwell-Scoles HeH₂ potential [J. Phys. Chem. 86, 1053 (1982)]. Prior to the refinement, a sensitivity study is performed which indicates that the data are primarily sensitive to the relative anisotropy of the repulsive wall. The inversion problem is posed as a first-order Fredholm integral equation with a kernel composed of functional sensitivities that relate potential perturbations to spin relaxation rate perturbations. The inversion scheme consists of a least-squares regularization procedure with singular system analysis and stabilization as used previously to refine atom-atom potentials [T.-S. Ho and H. Rabitz, J. Chem. Phys. 89, 5614 (1988); 90, 1519 (1989); 91, 7590 (1989)] with modifications which incorporate a priori information about the quality of the experimental data and the starting potential. The inversion yields a refined anisotropic term which in the repulsive region increases the anisotropic radial function V₂(R) by approximately 10% and eliminates more than 80% of the discrepancy between the values of T₁/p predicted by the potential and the values determined by experiment. The relative anisotropy, V₂/V₀, of the refined repulsive wall closely matches that of two potentials recently derived from ab initio calculation.