Treating charge-neutral excitations using geminal-screened electron-hole interaction kernel in the Bethe-Salpeter and TDDFT formulations

The electron-hole or quasiparticle representation plays a central role in describing electronic excitations in many-electron systems. Accurate determination of the electron-hole interaction kernel remains a significant challenge for precise calculations of optical properties in both GW+BSE and TDDFT formalism. The inclusion of unoccupied states has long been recognized as the leading computational bottleneck that limits the application of this approach for large finite systems. In this work, we present the geminal-screened electron-hole interaction kernel (GSIK) method that avoids using unoccupied states to construct the electron-hole interaction kernel. Using diagrammatic techniques, we demonstrate that an infinite-order summation of a subset of particle-hole diagrams that appear in MBPT can be expressed as a renormalized two-body operator in real-space representation. The GSIK was combined with both BSE and linear-response TDDFT methods to calculate excitation energies and exciton binding energies (where applicable) in atoms, molecules, clusters, and quantum dots.