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 ∼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.