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

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

2011-05-27

arxiv.org/abs/1105.5435v1

Physics

Quantum Physics

12 pages, 1 figure, 3 tables

Scientific paper

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.

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