Legitimate calculation of first-order molecular properties in the case of limited CI functions. Dipole moments

Abstract

Two alternative definitions for the calculation of first-order properties from limited CI functions are discussed. It is argued that computing the first-order properties by the differentiation of the perturbed CI energy is more appropriate than using the Hellmann—Feynman theorem. The energy derivative definition of the first-order properties corrects the Hellmann—Feynman results for an incomplete variational treatment of the perturbation effects. The additional term which is referred to as the Brillouin correction is computed for the dipole moments of FH, H 2O, NH 3 and CO using the CI functions involving single and double substitutions with respect to the HF determinant. It is shown that the Brillouin correction gives a substantial contribution to the dipole moment of the CO molecule. This indicates that it may be fortuitous that some data previously calculated from CI functions by using the Hellmann—Feynman theorem are close to the experimental value. The structure of the Brillouin correction is analysed in terms of the diagrammatic expansion of the correlation corrections to the first-order properties. Additionally, some rough estimates of the influence of the unlinked diagrams are obtained by computing the so-called corrections due to Davidson and Siegbahn.