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High Precision Variational Calculations for the Born-Oppenheimer Energies of the Ground State of the Hydrogen Molecule
Published
Author(s)
James S. Sims, Stanley A. Hagstrom
Abstract
Born-Oppenheimer approximation Hylleraas (Hy) variational calculations with up to 7034 expansion terms are reported for the singlet sigma g+ ground state of neutral hydrogen at various internuclear distances. The nonrelativistic energy is calculated to be -1.1744 7571 4220(1)hartree at R = 1.4 bohr, which is 4 orders of magnitude better than the best previous Hylleraas calculation, that of Wolniewicz. This result agrees well with the best previous variational energy, -1.1744 7571 4216 hartree, of Cencek\, obtained using Explicitly Correlated Gaussians (ECG). The uncertainty in our result is also discussed. The nonrelativistic energy is calculated to be -1.1744 7593 1399(1)hartree at the equilibrium R = 1.4011 bohr distance. This result also agrees well with the best previous variational energy, -1.1744 7593 1389 hartree, of Cencek and Rychewski\citeRy:03,Ry:03a}, obtained using Explicitly Correlated Gaussians (ECG).
Sims, J.
and Hagstrom, S.
(2006),
High Precision Variational Calculations for the Born-Oppenheimer Energies of the Ground State of the Hydrogen Molecule, Journal of Chemical Physics, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=150389
(Accessed October 9, 2025)