Relativistic corrections, Born-Oppenheimer energies and adiabatic corrections are computed for R < 12.0 bohr for the electronic ground state of the hydrogen molecule. The Born-Oppenheimer potential is slightly lower than ever reported. The problem of linear dependencies in the basis set is removed and the same set is used for all internuclear distances which assures continuity of the results. The radiative corrections are evaluated approximately and-for that purpose-the polarizability of the molecule is also computed. Vibrational energies are computed andcorrected for nonadiabatic effects-compared with experiment for several isotopes. It is argued on the basis of the remaining discrepancies that an improvement in the ab initio nonadiabatic corrections is necessary.

Possible sources of residual errors in the theoretical energies of the hydrogen molecule are investigated. Nonadiabatic corrections are computed for all bound, J≤10 X 1Σg+ ro-vibrational states of the six isotopic hydrogen molecules. The new results improve significantly the overall agreement with accurate experimental transition frequencies. In order to estimate the convergence errors of the Born–Oppenheimer energies generalized James–Coolidge functions with powers of the interelectronic distance, r12, up to 6 are used and the precision of the computations is increased. Except for the equilibrium separation, R=1.4011 bohr, the obtained potential energy curve is lower by a few thousandths of a wave number than any other reported variational result. This lowers the v=0 vibrational levels by 0.009 cm−1 and results in a dissociation energy of H2, D0=36118.069 cm−1.

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.

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