Basis-set completeness profiles in two dimensions

A two-electron basis-set completeness profile is proposed by analogy with the one-electron profile introduced by D. P. Chong (Can J Chem 1995, 73, 79). It is defined as Y(α, β) = ∑m ∑n〈Gα(1)Gβ(2)|(1/r12)| m(1) n(2)〉〈 m(1) n(2)|r12|Gα(1)Gβ(2)〉 and motivated by the expression for the basis-set truncation correction that occurs in the framework of explicitly correlated methods. The two-electron basis-set profiles provide a visual assessment of the suitability of basis sets to describe electron-correlation effects. Furthermore, they provide the opportunity to assess the quality of the basis set as a whole—not only of the individual angular momentum subspaces, as is the case for the one-electron basis-set profiles. The two-electron completeness profiles of the cc-pVXZ (X = D, T, Q), aug-cc-pVTZ, cc-pCVTZ, and SVP-auxiliary basis sets for the carbon atom are presented as illustrative examples. © 2002 John Wiley & Sons, Inc. J Comput Chem 23: 1–6, 2002