A variety of results are reported for the ground state ($X{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$) of the hydrogen molecule. They include improved Born-Oppenheimer calculations, a study of the convergence of energies with basis-set size, adiabatic calculations, and the first successful ab initio nonadiabatic calculation. The latter, which treats ${\mathrm{H}}_2$ as a four-body problem, leads us to predict that the dissociation energy of ${\mathrm{H}}_2$ is 36117.92 ${\mathrm{cm}}^{-1\mathrm{}}$. This value may be compared with 36 117.8±0.4 ${\mathrm{cm}}^{-1\mathrm{}}$ (the value derived from the experimental ionization potential), with 36118.6±0.5 ${\mathrm{cm}}^{-1\mathrm{}}$ (the value derived from the experimental vibrational levels of the $B{}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ state), or with 36118.3 ${\mathrm{cm}}^{-1\mathrm{}}$ (the upper-bound value derived from the experimental absorption limit).

• Received 17 November 1977

DOI:https://doi.org/10.1103/PhysRevA.18.1846