σ Interference: Through-Space and Through-Bond Dichotomy

Dividing orbital interactions into through-space (TS) and through-bond (TB) modes is valuable for understanding various molecular properties. In this paper, we elucidate how the quantum interference phenomenon known as σ interference in electron transport through σ systems arises from TS and TB interactions. We performed electron transport calculations using a combination of density functional theory and nonequilibrium Green's function methods, focusing on ethylenediamine, a classical molecule that effectively highlights the contrast between TS and TB interactions. Our results confirm that destructive σ interference occurs in the <i>syn</i> and <i>gauche</i> conformers of this molecule. To further investigate both TS and TB interactions, we employed two analytical methods: the fragment molecular orbital (FMO) method, which captures the effects of both TS and TB interactions, and the chemical graph theory method, which specializes in TB interactions. The FMO analysis demonstrated that TB interactions lead to the characteristic distribution and energy level alignment of the frontier orbitals. Additionally, it was clarified that a change in TS interaction, due to a variation in the dihedral angle of the molecule, alters the energy gap between these orbitals, resulting in the manifestation of σ interference in the <i>syn</i> and <i>gauche</i> conformers, but not in the <i>trans</i> conformer. The chemical graph theory analysis based on the ladder C model, aimed at exploring the topological origin of σ interference from the network of TB interactions, revealed that σ interference is caused by the cancellation between the walk associated with geminal interactions (σ-conjugation) and the one related to vicinal interaction (σ-hyperconjugation). Notably, it was found that the vicinal interaction, which changes sign with the dihedral angle, has a decisive influence on whether this cancellation occurs. These findings clarify that σ interference arises from the interplay between TS and TB interactions. This insight will be valuable for designing molecular systems that utilize σ interference.