σ Interference:\nThrough-Space and Through-Bond\nDichotomy

Dividing orbital interactions into through-space (TS)\nand through-bond\n(TB) modes is valuable for understanding various molecular properties.\nIn this paper, we elucidate how the quantum interference phenomenon\nknown as σ interference in electron transport through σ\nsystems arises from TS and TB interactions. We performed electron\ntransport calculations using a combination of density functional theory\nand nonequilibrium Green’s function methods, focusing on ethylenediamine,\na classical molecule that effectively highlights the contrast between\nTS and TB interactions. Our results confirm that destructive σ\ninterference occurs in the <i>syn</i> and <i>gauche</i> conformers of this molecule. To further investigate both TS and\nTB interactions, we employed two analytical methods: the fragment\nmolecular orbital (FMO) method, which captures the effects of both\nTS and TB interactions, and the chemical graph theory method, which\nspecializes in TB interactions. The FMO analysis demonstrated that\nTB interactions lead to the characteristic distribution and energy\nlevel alignment of the frontier orbitals. Additionally, it was clarified\nthat a change in TS interaction, due to a variation in the dihedral\nangle of the molecule, alters the energy gap between these orbitals,\nresulting 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\non the ladder C model, aimed at exploring the topological origin of\nσ interference from the network of TB interactions, revealed\nthat σ interference is caused by the cancellation between the\nwalk associated with geminal interactions (σ-conjugation) and\nthe one related to vicinal interaction (σ-hyperconjugation).\nNotably, it was found that the vicinal interaction, which changes\nsign with the dihedral angle, has a decisive influence on whether\nthis cancellation occurs. These findings clarify that σ interference\narises from the interplay between TS and TB interactions. This insight\nwill be valuable for designing molecular systems that utilize σ\ninterference.