Close relation between quantum interference in molecular conductance and diradical existence

• Published in: Proceedings of the National Academy of Sciences - PNAS Vol. 113; no. 4; pp. E413 - E419
• Main Authors: Tsuji, Yuta, Hoffmann, Roald, Strange, Mikkel, Solomon, Gemma C.
• Format: Journal Article
• Language: English
• Published: United States National Academy of Sciences 26.01.2016; National Acad Sciences
• Series: PNAS Plus
• Subjects: Electrodes; Electrons; Hydrocarbons; Physical Sciences; PNAS Plus; Quantum theory; Theorems; diradicals; determinants; nonbonding orbitals; quantum interference; molecular conductance
• ISSN: 0027-8424; 1091-6490
• DOI: 10.1073/pnas.1518206113

An empirical observation of a relationship between a striking feature of electronic transmission through a π-system, destructive quantum interference (QI), on one hand, and the stability of diradicals on the other, leads to the proof of a general theorem that relates the two. Subject to a number of simplifying assumptions, in a π-electron system, QI occurs when electrodes are attached to those positions of an N-carbon atom N-electron closed-shell hydrocarbon where the matrix elements of the Green’s function vanish. These zeros come in two types, which are called easy and hard. Suppose an N+2 atom, N+2 electron hydrocarbon is formed by substituting 2 CH₂ groups at two atoms, where the electrodes were. Then, if a QI feature is associated with electrode attachment to the two atoms of the original N atom system, the resulting augmented N+2 molecule will be a diradical. If there is no QI feature, i.e., transmission of current is normal if electrodes are attached to the two atoms, the resulting hydrocarbon will not be a diradical but will have a classical closed-shell electronic structure. Moreover, where a diradical exists, the easy zero is associated with a nondisjoint diradical, and the hard zero is associated with a disjoint one. A related theorem is proven for deletion of two sites from a hydrocarbon.