Exploring molecular motions in collinear HeH₂⁺ and its isotopic variants using periodic orbits

Abstract

Principal families of periodic orbits (POs) are identified and their (in)stabilities examined for collinear HeH₂⁺ and its isotopic variants, HeHD⁺ and HeDH⁺, on an abinitio potential energy surface. Continuation/bifurcation diagrams of these periodic orbits over a range of energies reveal a number of bifurcations and the period doubling route to classical chaos. The existence of a number of POs at any given energy suggests that there could be constructive and destructive interference between their contributions to the eigenfunction at that energy resulting in quantum mechanical resonances for these systems.