  We present a new first-principles formalism for calculating forces for
optically excited electronic states using the interacting Green's function
approach with the GW-Bethe Salpeter Equation method. This advance allows for
efficient computation of gradients of the excited-state Born-Oppenheimer
energy, allowing for the study of relaxation, molecular dynamics, and
photoluminescence of excited states. The approach is tested on photoexcited
carbon dioxide and ammonia molecules, and the calculations accurately describe
the excitation energies and photoinduced structural deformations.
