Significant contributions of second-order exchange terms in GW electron-hole interaction kernel for charge-transfer excitations

The GW electron-hole interaction kernel, which includes two second-order exchange terms in addition to the first-order direct and exchange terms considered in the conventional GW + Bethe-Salpeter method, is applied to 10 two-molecular systems and six thermally activated delayed fluorescence (TADF) molecules in which inter- and intramolecular charge transfer excitations are expected to occur. The contributions of the two second-order exchange terms are almost zero for intermolecular charge transfer excitations and similar to 0.75 eV for intramolecular charge transfer excitations according to our exciton analysis method with exciton wave functions. For TADF molecules, we found that the second-order exchange terms are more significant than the first-order exchange terms, and the contributions-even for local-type and delocalized-type excitations-are not negligibly small. We revealed that the two second-order exchange terms are proportional to the molecular size, the exciton binding energy, and the electron-hole overlap strength for intramolecular charge-transfer excitations. We believe that our findings are indispensable for further considerations of the GW method in the future.