arXiv:1105.5435v1 [quant-ph] 27 May 2011 A note about the ground state of the H + 3 hydrogen molecular ion J. C. Lopez Vieyra, ∗ A.V. Turbiner, † and H. Medel ‡ Instituto de Ciencias Nucleares, Universidad Nacional Aut´ onoma de M´ exico, Apartado Postal 70-543, 04510 M´ exico, D.F., Mexico (ΩDated: May 25, 2011) Abstract Three simple 7−, (7+3)−, 10−parametric trial functions for the 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 ∼ exp (γr 12 ), where γ 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 configu- ration 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. * Electronic address: vieyra@nucleares.unam.mx † Electronic address: turbiner@nucleares.unam.mx ‡ Electronic address: medel@nucleares.unam.mx 1