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A software update solving the Bethe−Salpeter equation (BSE) is reported for the ESCF module of the TURBOMOLE program for the theoretical description of electronically excited states of atoms and molecules. A resolution-of-the-identity (RI) approximation is used for all two-electron electron-repulsion integrals that are required for solving the equation. Symmetry is utilized for the point group D2h and its subgroups, and the BSE approach can be applied in either a spin-restricted or a spin-unrestricted Kohn−Sham formalism. Triplet as well as singlet excited states of closed-shell atoms and molecules can be treated in the spin-restricted formalism. As a side product, the present software update also allows for the application of the RI approximation to the Hartree−Fock exchange contribution that occurs when a hybrid functional is used in time-dependent density-functional theory. © 2016 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

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(alpha, beta) = sigmam sigman (Galpha(1)Gbeta(2)/(1/r12)/ psim(1)psin(2)) (psim(1)psin(2)/r12/Galpha(1)Gp(2)) and motivated by the expression for the basis-set truncation correction that occurs in the framework of explicitly correlated methods (Galpha is a scanning Gaussian-type orbital of exponent alpha and [psim] 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-pVXZ (X = D, T, Q), aug-cc-pVTZ, cc-pCVTZ, and SVP-auxiliary basis sets for the carbon atom are presented as illustrative examples.