The ground state of the ${\rm H}_3^+$ molecular ion: physics behind
Abstract
Five physics mechanisms of interaction leading to the binding of the molecular ion are identified. They are realized in a form of variational trial functions and their respective total energies are calculated. Each of them provides subsequently the most accurate approximation for the Born-Oppenheimer (BO) ground state energy among (two-three-seven)-parametric trial functions being correspondingly, H-molecule plus proton (two variational parameters), H-ion plus H-atom (three variational parameters) and generalized Guillemin-Zener (seven variational parameters). These trial functions are chosen following a criterion of physical adequacy. They include the electronic correlation in the exponential form , where is a variational parameter. Superpositions of two different mechanisms of binding are investigated and a particular one, which is a generalized Guillemin-Zener plus H-molecule plus proton (ten variational parameters), provides the total energy at the equilibrium of \ a.u. The superposition of three mechanisms: generalized Guillemin-Zener plus (H -molecule plus proton) plus (H -ion plus H) (fourteen parameters) leads to the total energy which deviates from the best known BO energy to \ a.u., {\it it reproduces two-three significant digits in exact, non-BO total energy}. In general, our variational energy agrees in two-three-four significant digits with the most accurate results available at present as well as major expectation values.
Keywords
Cite
@article{arxiv.1212.4552,
title = {The ground state of the ${\rm H}_3^+$ molecular ion: physics behind},
author = {A. V. Turbiner and J. C. Lopez Vieyra},
journal= {arXiv preprint arXiv:1212.4552},
year = {2015}
}
Comments
26 pages, 2 figures, 4 tables, invited contribution to Takeshi Oka Festschrift: Celebrating 45 Years of Astrochemistry, accepted to Jour Phys Chem typos corrected, Introduction and Conclusions are extended