A Guide to Molecular Properties from the Bethe-Salpeter Equation

The Bethe-Salpeter equation (BSE) combined with the Green's function GW method has successfully transformed into a robust computational tool to describe light-matter interactions and excitation spectra for molecules, solids, and materials from first principles. Thanks to its ability to accurately describe charge-transfer and Rydberg excitations, the GW-BSE already forms an established and cost-efficient alternative to time-dependent density functional theory. This raises the question whether the GW-BSE approach can become a more general framework for molecular properties beyond excitation energies. In this mini-review, we recapitulate recent endeavors along this point in terms of both theoretical and practical developments for quantum chemistry, physical chemistry, and related fields. In doing so, we provide guidelines for current applications to chemical challenges in collaboration with experimentalists as well as to future developments to extended the GW-BSE toolkit.