Fully Analytic Nuclear Gradients for the Bethe-Salpeter Equation

The Bethe-Salpeter equation (BSE) formalism, combined with the GW approximation for ionization energies and electron affinities, is emerging as an efficient and accurate method for predicting optical excitations in molecules. In this Letter, we present the first derivation and implementation of fully analytic nuclear gradients for the BSE@G₀W₀ method. Building on recent developments for G₀W₀ nuclear gradients, we derive analytic nuclear gradients for several BSE@G₀W₀ variants. We validate our implementation against numerical gradients and compare excited-state geometries and adiabatic excitation energies obtained from different BSE@G₀W₀ variants with those from state-of-the-art wave function methods.