Excited state properties from the Bethe–Salpeter equation: State-to-state transitions and spin–orbit coupling

The formalism to calculate excited state properties from the GW–Bethe–Salpeter equation (BSE) method is introduced, providing convenient access to excited state absorption, excited state circular dichroism, and excited state optical rotation in the framework of the GW–BSE method. This is achieved using the second-order transition density, which can be obtained by solving a set of auxiliary equations similar to time-dependent density functional theory (TD-DFT). The proposed formulation therefore leads to no increase in the formal computational complexity when compared to the corresponding ground state properties. We further outline the calculation of fully relaxed spin–orbit coupling matrix elements within the GW–BSE method, allowing us to include perturbative corrections for spin–orbit coupling in aforementioned properties. These corrections are also extended to TD-DFT. Excited state absorption and perturbative spin–orbit coupling corrections within GW–BSE are evaluated for a selected set of molecular systems, yielding promising results.