High precision variational calculations for the Born-Oppenheimer energies of the ground state of the hydrogen molecule

<jats:p>Born-Oppenheimer approximation Hylleraas variational calculations with up to 7034 expansion terms are reported for the Σg+1 ground state of neutral hydrogen at various internuclear distances. The nonrelativistic energy is calculated to be −1.174475714220(1)hartree at R=1.4bohr, which is four orders of magnitude better than the best previous Hylleraas calculation, that of Wolniewicz [J. Chem. Phys. 103, 1792 (1995)]. This result agrees well with the best previous variational energy, −1.174475714216hartree, of Cencek (personal communication), obtained using explicitly correlated Gaussians (ECGs) [Cencek and Rychlewski, J. Chem. Phys. 98, 1252 (1993); Cencek et al., ibid. 95, 2572 (1995); Rychlewski, Adv. Quantum Chem. 31, 173 (1998)]. The uncertainty in our result is also discussed. The nonrelativistic energy is calculated to be −1.174475931399(1)hartree at the equilibrium R=1.4011bohr distance. This result also agrees well with the best previous variational energy, −1.174475931389hartree, of Cencek and Rychlewski [Rychlewski, Handbook of Molecular Physics and Quantum Chemistry, edited by S. Wilson (Wiley, New York, 2003), Vol. 2, pp. 199–218; Rychlewski, Explicitly Correlated Wave Functions in Chemistry and Physics Theory and Applications, edited by J. Rychlewski (Kluwer Academic, Dordrecht, 2003), pp. 91–147.], obtained using ECGs.</jats:p>