Dirac-Fock calculations for the ground states of some small molecules

We present basis-set Dirac-Fock calculations of the ground states of the H₂, HF, HCl, H₂O, NH₃, and CH₄ molecules. Molecular orbitals are constructed by linearly combining four-component spherical spinors centered at the nuclei; the radial dependence of the large component is rⁿ{e}^{{{-}}{ξ}r2}, where n is a non-negative integer determined by the angular quantum numbers, and ξ∈a,ab,{ab}²$,..., where a>0 and b>1 are real numbers; the small component is generated from the large component using the ``strict kinetic balance'' prescription. Our estimates of the ground-state energies of these molecules decrease monotonically as the size of the basis sets used is enlarged. The nonrelativistic (essentially basis-set Hartree-Fock) limits of our calculations are obtained by increasing the speed of light by a few orders of magnitude over its physical value; we are thus able to estimate relativistic corrections in an unambiguous way within the context of our molecular models.