Interfacing relativistic and nonrelativistic methods. IV. One- and two-electron scalar approximations

Two approximations for the inclusion of scalar relativistic effects into otherwise nonrelativistic molecular self-consistent field calculations are described, which continue the sequence of approximations from previous work. In the first, the two-electron contributions are confined to those where each small component density is one-center. In the second, the two-electron contributions are approximated by using the bare Coulomb operator, an approach which parallels the Douglas–Kroll–Hess method. The results show that both approximations yield results close to the full two-electron scalar relativistic method, within 0.001 Å in bond lengths and 0.1 kcal/mol in dissociation energies. The approximations also give results which are very similar to those of the Douglas–Kroll–Hess method. The second approximation is similar in cost to the Douglas–Kroll–Hess method and only contains simple operators whose integrals are easy to evaluate.