A note about the ground state of the ${\mathrm{H}}_3^{+}$ hydrogen molecular ion

Abstract

Three simple $7-,(7+3)-,10-$parametric trial functions for the ${\mathrm{H}}_3^{+}$ molecular ion are presented. Each of them provides subsequently the most accurate approximation for the Born-Oppenheimer ground state energy among several-parametric trial functions. These trial functions are chosen following a criterion of physical adequacy and includes the electronic correlation in the exponential form $\sim \exp (\gamma r_{12})$, where $\gamma$ is a variational parameter. The Born-Oppenheimer energy is found to be $E=-1.34034,-1.34073,-1.34159$\,a.u., respectively, for optimal equilateral triangular configuration of protons with the equilibrium interproton distance $R=1.65$\,a.u. The variational energy agrees in three significant digits (s.d.) with most accurate results available at present as well as for major expectation values.

12 pages, 1 figure, 3 tables

References in corpus (2)

• 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

Cited by in corpus (1)

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