Excited-State Forces, Relaxation, and Higher-Order Derivatives from Ab Initio Many-Body Perturbation Theory

We present a computationally tractable approach to obtain derivatives of the excitation energy in materials of any dimension from first principles within the highly accurate GW plus Bethe-Salpeter equation (GW-BSE) formulation of many-body perturbation theory (MBPT). Our approach is based on finite-difference calculations and interpolation techniques that can efficiently yield first- and higher-order energy derivatives. This allows one to obtain, from the same method, both excited-state forces and the vibrational spectrum of an optically excited material, including excitonic contributions to the Born effective charges. We demonstrate how to predict the atomic structure of the excited states of molecular excitations, exciton-polarons, self-trapped excitons, Stokes shifts, and photocatalytic equilibria. We present results for the structure and vibrational spectrum of a photoexcited benzene molecule in the spin-triplet configuration and self-trapped exciton in SiO2 as examples of prototypical calculations. Due to the good scalability of underlying MBPT calculations, we anticipate that this approach can be used to predict the excited-state dynamics in structurally complex materials.