Improved Parametric FITS for the Helium Dihydride AB Initio Energy Surface

A brief history of the development of ab initio calculations for the HeH_2 quasi -molecule energy surface, and the parametric fits to these ab initio calculations, is presented. The concept of "physical reasonableness" of the parametric fit, and requirements for meeting it, is then discussed. Several new improved parametric fits for the energy surface, meeting these requirements, are then proposed. One fit extends the Russek-Garcia parametric fit for the deep repulsion region to include r-dependent parameters, resulting in a more physically reasonable fit with smaller average error. This improved surface fit is applied to quasi-elastic collisions of He on H _2 in the impulse approximation. Previous classical calculations of the scaled inelastic vibrorotational excitation energy distributions by Jakacky et al are improved with this more accurate parametric fit of the energy surface and with the incorporation of quantum effects in vibrational excitation. It is shown that Sigmund's approach in developing his scaling law is incomplete in so far as the contribution of the three-body interactions to vibrational excitation of the H_2 molecule is concerned. The Sigmund theory is extended to properly take into account r-dependency of three-body interactions. A new, extended, parametric fit for the entire energy surface from essentially 0 <= R <= infty and 1.2 <= r <= 1.6 a.u., where R is the intermolecular spacing and r is the hydrogen bonding length, is also presented. This new fit is physically reasonable in all asymptotic limits, which has not been a property of past fits. This first, full surface parametric fit is based primarily upon a composite of ab initio studies by Russek and Garcia and Meyer, Hariharan and Kutzelnigg. Parametric fits for the H_2(1 ssigma_{g})^2, H_2^+(1ssigma_{g }), H_2^+(2psigma _{u}) and (LiH_2) ^+ energy surfaces are also presented. The new parametric fits for H_2, H _2^+(1ssigma_{g}) are shown to be improvements over the well-known Morse potentials for these surfaces.