Efficient Implementation of Analytical Nuclear Forces within the Bethe-Salpeter Equation: Applications to Point Defects in Solids

First-principles studies of electronic excited states using the GW-Bethe-Salpeter equation (GW-BSE) play an important role in understanding the excitonic and optical properties of condensed systems. However, most calculations are restricted to fixed ionic positions, limiting the exploration of phenomena associated with excitation-induced structural changes, such as self-trapped excitons and vibrationally resolved optical spectra. Efficient implementation of excited-state analytical nuclear forces is key to overcoming this limitation. While excited-state analytical forces are available in the WEST code within the time-dependent density functional theory (TDDFT) framework [1], in some cases, their accuracy may be limited by approximate exchange-correlation functionals, particularly in heterogeneous systems with defects and interfaces. In this talk, I will present an efficient implementation of excited-state analytical nuclear forces within the BSE formalism based on the extended Lagrangian approach, which enables the study of excited-state structural relaxation in systems containing hundreds of atoms. I will also discuss results for point defects in semiconductors and compare them with those obtained at the TDDFT level.

[1] Y. Jin, V. W.-z. Yu, M. Govoni, A. C. Xu, and G. Galli, J. Chem. Theory Comput. 19, 8689-8705 (2023).