Large amplitude quantum mechanics in polyatomic hydrides. I. A particles-on-a-sphere model for XH(n)

A framework is presented for converged quantum mechanical calculations on large amplitude dynamics in polyatomic hydrides (XH(n)) based on a relatively simple, but computationally tractable, "particles-on-a-sphere" (POS) model for the intramolecular motion of the light atoms. The model assumes independent two-dimensional (2D) angular motion of H atoms imbedded on the surface of a sphere with an arbitrary interatomic angular potential. This assumption permits systematic evolution from "free rotor" to "tunneling" to "quasi-rigid" polyatomic molecule behavior for small, but finite, values of total angular momentum J. This work focuses on simple triatom (n=2) and tetratom (n=3) systems as a function of interatomic potential stiffness, with explicit consideration of H2O, NH3, and H3O+ as limiting test cases. The POS model also establishes the necessary mathematical groundwork for calculations on dynamically much more challenging XH(n) species with n>3 (e.g., models of CH5+) where such a reduced dimensionality approach offers prospects for being quantum mechanically tractable at low J values (i.e., J=0, 1, 2) characteristic of supersonic jet expansion conditions.