The present status of ab initio computations for atomic and molecular wave functions is analyzed in this paper, with special emphasis on the work done at the IBM Research Laboratory, San Jose. The Roothaan-Hartree-Fock method has been described in detail for atomic systems. A systematic tabulation of atomic Hartree-Fock functions has been made available in an extended supplement to this paper. Techniques for computing many-center, two-electron matrix elements have been discussed for Slater or Gaussian basis sets. It is concluded that the two possibilities are comparable in efficiency. We have advanced a few suggestions for the extension of the self-consistent field technique to macromolecules. The validity of the suggestions have not been tested.

Following the Bethe and Salpeter formalism, the relativistic correction has been discussed and illustrated with numerical results for closed-shell atoms. A brief analysis of the relativistic correction for molecular systems shows that the relativistic effects cannot be neglected in ionic systems containing third-row atoms.

The correlation energy is discussed from an experimental starting point. The relativistic and Hartree-Fock energies are used for determining the correlation energy for the elements of the first three periods of the atomic system. A preliminary analysis of the data brings about a “simple pairing” model. Data from the third period force us to consider the “simple pairing” model as a first-order approximation to the “complex pairing” model. The latter model is compared with the geminals method and limitations of the latter are pointed out.

A semiempirical model, where use is made of a pseudopotential that represents a coulomb hole, is advanced and preliminary results are presented. This model gives reason to some hope for the practical formulation of a Coulomb-Hartree-Fock technique where the correlation effects are accounted for and the one-particle approximation is retained.