High Precision Variational Calculations for the Born-Oppenheimer Energies of the Ground State of the Hydrogen Molecule

Published

March 1, 2006

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).

Citation

Journal of Chemical Physics

Volume

124

Issue

9

Pub Type

Journals

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Keywords

ground-state energy, Born-oppenheimer energy, Hylleraas method, neutral hydrogen molecule, wave function

Citation

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 14, 2025)