Lagrangian Z-vector approach to Bethe–Salpeter analytic gradients: Assessing approximations

Abstract

We present an implementation of excited-state analytic gradients within the Bethe–Salpeter equation formalism using an adapted Lagrangian Z-vector approach with a cost independent of the number of perturbations. We focus on excited-state electronic dipole moments associated with the derivatives of the excited-state energy with respect to an electric field. In this framework, we assess the accuracy of neglecting the screened Coulomb potential derivatives, a common approximation in the Bethe–Salpeter community, as well as the impact of replacing the GW quasiparticle energy gradients by their Kohn–Sham analogs. The pros and cons of these approaches are benchmarked using both a set of small molecules for which very accurate reference data are available and the challenging case of increasingly extended push–pull oligomer chains. The resulting approximate Bethe–Salpeter analytic gradients are shown to compare well with the most accurate time-dependent density-functional theory (TD-DFT) data, curing in particular most of the pathological cases encountered with TD-DFT when a nonoptimal exchange–correlation functional is used.