Accurate Adiabatic Treatment of the Ground State of the Hydrogen Molecule

TLDR

Accurate ground‑state energies of H₂ were obtained by expanding wavefunctions in elliptic coordinates with explicit interelectronic distance, using 54‑term (0.4–3.7 a₀) and 80‑term (0.5–2.0 a₀) expansions and incorporating relativistic and diagonal nuclear‑motion corrections. At equilibrium the best total energies are –1.1744701 a.u.

Abstract

Accurate ground-state energies of the hydrogen molecule have been computed using wavefunctions in the form of expansions in elliptic coordinates and including explicitly the interelectronic distance. The computations have been made with 54-term expansions (0.4≤R≤3.7) and with 80-term expansions (0.5≤R≤2.0). For the equilibrium internuclear distance, the best total energies obtained in the two cases are —1.1744701 a.u. and —1.1744746 a.u., respectively, the corresponding binding energies being 38 291.8 and 38 292.7 cm—1. Employing the 54-term wavefunctions, the relativistic corrections and the diagonal corrections for nuclear motion have been computed for several internuclear distances. For equilibrium their contributions to the binding energy have been found to be —0.526 and 4.947 cm—1, respectively. Thus the final theoretical binding energy for H2 amounts to 38 297.1 cm—1 and is a little larger than the experimental value 38 292.9±0.5 cm—1. The discrepancy may be due to the adiabatic approximation.