Five versions of CIBS (corrections to an incomplete basis set) theory are used to compute first and second corrections to Roothaanndash;Hartreendash;Fock energies via expansion of a given basis set. Version one is an order by order perturbation approximation which neglects virtual orbitals; version two is a full CIBS expansion which neglects virtual orbitals; version three is an order by order perturbation approximation which includes virtual orbitals; version four is a full CIBS expansion which includes orthogonalization to virtual orbitals but neglects virtual orbital coupling terms; and version five is a full CIBS expansion with inclusion of coupling to virtual orbitals. Results are presented for the atomic and molecular systems He, Be, H2, LiH, Li2, and H2O. Version five is shown to produce a corrected Hartreendash;Fock energy which is essentially in agreement with a comparable SCF result using the same expanded basis set. Versions one through four yield varying degrees of agreement; however, it is evident that the effect of the virtual orbitals must be included. From the results, CIBS version five is shown to be a viable quantitative procedure which can be used to expand or to study the use of basis sets in quantum chemistry.
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