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

TL;DR

This paper introduces three optimized trial functions for the ground state of the ${ m H}_3^+$ ion, achieving highly accurate energy approximations by including electronic correlation effects.

Contribution

It presents new simple parametric trial functions that incorporate electronic correlation and outperform previous models in accuracy for the ${ m H}_3^+$ ground state.

Findings

Achieved ground state energy estimates with three different trial functions.

Included electronic correlation in the trial functions.

Results agree with the most accurate existing data.

Abstract

Three simple $7-, (7+3)-, 10-$parametric trial functions for the ${\rm H}_3^+$ 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 $E=-1.340 34, -1.340 73, -1.341 59$\,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.