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.

• Received 11 July 2002

DOI:https://doi.org/10.1103/PhysRevLett.90.076401