Calculation and analysis of exciton couplings via a subsystem formulation of the $GW$-Bethe-Salpeter Equation

Abstract

We present a fragment-based framework for analyzing exciton couplings within the $GW$-Bethe-Salpeter Equation formalism using localized molecular orbitals, and assess how excitonic states in molecular dimers can be decomposed into local and charge-transfer (CT) sectors. Our localization procedure preserves orbital orthonormality via a block-diagonal unitary transformation, enabling a simple and interpretable analysis of excitonic interactions. Using ethylene and pyrene dimers as model systems, we identify key effects of excitonic basis truncation and coupling approximations on excitation energies. We then extend the method to chlorophyll dimers, where weak CT asymmetries emerge due to geometric distortions. This framework offers a tractable route to analyze excitonic behavior in complex systems and paves the way for future fragment-based reconstruction of full exciton coupling matrices in large molecular assemblies.