Potential-Energy Curves for the X 1Σ g+, b 3Σ u+, and C 1Π u States of the Hydrogen Molecule

Abstract

Previous calculation of the ground-state energy of H2 has been extended to include large internuclear distances and accurate potential-energy curve for 0.4≤R≤10.0 a.u. is presented. For 0.4≤R≤4.0 a.u. expectation values of several operators have also been calculated. The calculation was made using a wavefunction in the form of an expansion in elliptic coordinates. The wavefunction depends on the interelectronic distance but, in contrast to the James—Coolidge expansion, is flexible enough to describe properly the dissociation of the molecule. Extensive calculations have also been made for the repulsive 3Σu+ state (1.0≤R≤10.0) and for the 1Πu state (1.0≤R≤10.0). In the former case a van der Waals minimum has been found at R=7.85 a.u. and 4.3 cm−1 below the dissociation limit. For the 1Πu state the computed binding energy De=20 490.0 cm−1 and the equilibrium internuclear distance Re=1.0330 Å are in a satisfactory agreement with the experimental values De=20 488.5 cm−1 and Re=1.0327 Å. In this case a van der Waals potential maximum has been found to occur at R=9.0 a.u. and 105.5 cm−1 above the dissociation limit. Preliminary results for the 1Σu+ state at R≈Re are also given.