Nature of the Configuration-Interaction Method inAb InitioCalculations. I. Ne Ground State

A detailed study of the correlation energy of Ne has been made in order to analyze the nature of the configuration-interaction (CI) method in ab initio calculations. Both the Bethe-Goldstone method of Nesbet and the total-pair-excitation-block method (TPEB) were examined. A series of calculations was made using both "atom-centered" and "shell-centered" basis sets. The most detailed calculations gave - 0.333 a.u. (88%) for the correlation energy by the TPEB method, and - 0.396 a.u. (104%) by the sum-of-the-pairs technique. The difference between these two values is mainly the so-called pair-pair interactions, which have been considered too small to be important to other investigators. A series of perturbation calculations on the triple and quadruple excitations gives ∼ 1.5% of the total correlation energy. A complete CI calculation with a very limited basis set was done on the $p$ block of Ne. The results of this calculation are in agreement with our total-atom calculation, except that now the TPEB calculation gave about 98.5%, and the sum of the pairs about 115% of the complete CI result. The effect on the pair correlation energy of a unitary transformation of the outer-shell occupied self-consistent-field orbitals was also studied. Only a small difference in the results was obtained.