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 〈 G α (1) G β (2)∣(1/ r 12 )∣Ψ m (1)Ψ n (2)〉〈Ψ m (1)Ψ n (2)∣ r 12 ∣ G α (1) G β (2)〉 and motivated by the expression for the basis‐set truncation correction that occurs in the framework of explicitly correlated methods ( G α is a scanning Gaussian‐type orbital of exponent α and {Ψ m } is the orthonormalized one‐electron basis under study). 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‐pV X Z ( X =D, T, Q), aug‐cc‐pVTZ, cc‐pCVTZ, and SVP‐auxiliary basis sets for the carbon atom are presented as illustrative examples. © 2002 Wiley Periodicals, Inc. J Comput Chem 23: 420–425, 2002