Non-adiabatic coupling as a frictional force in (He, H, H)⁺dynamics and the formation of HeH₂⁺

Abstract

It is shown that the Born–Oppenheimer–Huang non-adiabatic coupling terms (NACTs) in a molecular Hamiltonian can be considered as equivalent to a friction force in classical mechanics and consequently responsible for the formation of triatomic species like HeH₂⁺. The classical equation of motion is solved accordingly for a test case of a helium atom approaching an H₂⁺ molecule at its potential minimum along the collinear axis and lines parallel to it and also for the C_2v geometry. It is shown that the singular NACTs between the first two excited states slow down the motion of the three quasi-ions (He, H, H)⁺ while approaching each other and result in substantial loss of kinetic energy in the collision process. These results have profound implications for the formation of di- and triatomic species in the early universe, during the chemical synthesis epoch following the nucleosynthesis that followed the Big Bang.