The ground state of the ${\mathrm{H}}_3^{+}$ molecular ion: physics behind

Abstract

Five physics mechanisms of interaction leading to the binding of the ${\mathrm{H}}_3^{+}$ 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${}_2$-molecule plus proton (two variational parameters), H${}_2^{+}$-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 $\sim \exp (\gamma r_{12})$, where $\gamma$ 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${}_2$-molecule plus proton (ten variational parameters), provides the total energy at the equilibrium of $E=-1.3432$\ a.u. The superposition of three mechanisms: generalized Guillemin-Zener plus (H${}_2$ -molecule plus proton) plus (H${}_2^{+}$ -ion plus H) (fourteen parameters) leads to the total energy which deviates from the best known BO energy to $\sim 0.0004$\ 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.

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

References in corpus (3)

• Charged Hydrogenic, Helium and Helium-Hydrogenic Molecular Chains in a Strong Magnetic Field
• The $H_3^{+}$ molecular ion in a magnetic field in linear parallel configuration
• A note about the ground state of the ${\mathrm{H}}_3^{+}$ hydrogen molecular ion

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• Static field-gradient polarizabilities of small atoms and molecules in finite temperature
• The molecule ${\mathrm{H}}_2$ in a strong magnetic field revisited
• Partial separability of the Schroedinger equation combined with a Jastrow factor