Donor-Acceptor Strength from the Real-Space-Partitioning of One Particle Transition Density Matrix

Orbital analysis is a fundamental tool for studying excited states in organic molecules; however, it is not particularly efficient at describing excitonic states, crucial for designing materials with specific optical and electronic properties. Recently, a method was proposed to connect the exciton model with the orbital picture by analyzing the one-particle transition density matrix (1TDM). Following this idea, we present a new approach to partition the 1TDM based on the Quantum Theory of Atoms in Molecules (QTAIM), which provides a real-space description of the electronic structure. This QTAIM-based partitioning is applied to eight donor-π-acceptor (D-π-A) systems. The results reveal a clear relationship between the chemical nature of molecular fragments and their associated charge-transfer numbers. To visualize this relationship, we introduce a charge-transfer-number matrix representation that explicitly shows how each fragment contributes to the excitation. This analysis directly reveals the push-pull character of the electronic transitions in these compounds. Furthermore, a consistent relationship is observed between the strength of the donor group and the spatial distribution of the hole density, and the strength of the acceptor group with the spatial distribution of the electron density. This relationship is quantitatively confirmed using a set of ten para-substituted benzoic acids, where the topological hole and electron densities show clear correlations with Hammett constants. Overall, this work establishes meaningful connections between donor/acceptor strength, hole/electron densities, and the information encoded in the 1TDM, offering a topologically grounded perspective for the analysis of excitons.