Natural transition orbital in the fragment molecular orbital method with application to characterizing exciton states

Characterization and visualization of electronically excited states are essential for understanding photophysical and photochemical processes in condensed molecular systems. Here, we present a procedure to reconstruct the total transition density matrix (TDM) using the fragment molecular orbital (FMO) method. The application of the natural transition orbital (NTO) analysis to the total TDM allows us to define descriptors that quantify the collectivity and orbital delocalization of excited states. We show that the FMO-based procedure can reasonably reproduce the TDM and NTOs from conventional calculations. Applying the approach to pentacene clusters, we demonstrate that the descriptors successfully distinguish Frenkel exciton and Wannier-Mott exciton states. Furthermore, we investigate how the cluster size and dielectric screening effects shape the spatial characteristics of the excited states. In particular, we demonstrate that the dielectric screening effect reduces exciton binding energies and promotes Wannier-Mott-like character without strongly affecting the absorption maxima. These results highlight the applicability of the FMO-based framework for analyzing excited-state wave functions in complex molecular systems.