Implementation of the Bethe-Salpeter equation in the TURBOMOLE program.

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.