Close relation between quantum interference in molecular conductance and diradical existence
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...
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| Published in | Proceedings of the National Academy of Sciences - PNAS Vol. 113; no. 4; pp. E413 - E419 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
United States
National Academy of Sciences
26.01.2016
National Acad Sciences |
| Series | PNAS Plus |
| Subjects | |
| Online Access | Get full text |
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| Abstract | 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. |
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| AbstractList | 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. An empirical observation of a relationship between a striking feature of electronic transmission through a p-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 p-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. It might seem that the existence of a dramatic diminution in molecular conductance across a hydrocarbon (quantum interference, QI) would be unrelated to the existence of an important class of organic molecules with two electrons in two orbitals, diradicals. However, if you add two carbons to a planar π-electron hydrocarbon, you get a diradical if and only if there is a QI feature in conductance when two electrodes are attached to the molecule at the same sites. When you remove the two carbons where the electrodes are attached, you also generate a diradical. The connection, first empirically observed, is proven. Two kinds of diradicals, with different ground state spin consequences, are also easily distinguished by the relationship. 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 CH 2 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. 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. |
| Author | Hoffmann, Roald Solomon, Gemma C. Strange, Mikkel Tsuji, Yuta |
| Author_xml | – sequence: 1 givenname: Yuta surname: Tsuji fullname: Tsuji, Yuta organization: Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14853 – sequence: 2 givenname: Roald surname: Hoffmann fullname: Hoffmann, Roald organization: Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14853 – sequence: 3 givenname: Mikkel surname: Strange fullname: Strange, Mikkel organization: Nano-Science Center and Department of Chemistry, University of Copenhagen, 2100 Copenhagen Ø, Denmark – sequence: 4 givenname: Gemma C. surname: Solomon fullname: Solomon, Gemma C. organization: Nano-Science Center and Department of Chemistry, University of Copenhagen, 2100 Copenhagen Ø, Denmark |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/26755578$$D View this record in MEDLINE/PubMed |
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| Copyright | Volumes 1–89 and 106–113, copyright as a collective work only; author(s) retains copyright to individual articles Copyright National Academy of Sciences Jan 26, 2016 |
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| Keywords | diradicals determinants nonbonding orbitals quantum interference molecular conductance |
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| Notes | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-1 ObjectType-Feature-2 content type line 23 Author contributions: Y.T. and R.H. designed research; Y.T., M.S., and G.C.S. performed research; Y.T., R.H., M.S., and G.C.S. contributed new reagents/analytic tools; Y.T., R.H., M.S., and G.C.S. analyzed data; and Y.T., R.H., M.S., and G.C.S. wrote the paper. Edited by Ernest Davidson, University of Washington, Seattle, WA, and approved December 4, 2015 (received for review September 12, 2015) |
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| Snippet | An empirical observation of a relationship between a striking feature of electronic transmission through a π-system, destructive quantum interference (QI), on... It might seem that the existence of a dramatic diminution in molecular conductance across a hydrocarbon (quantum interference, QI) would be unrelated to the... An empirical observation of a relationship between a striking feature of electronic transmission through a p-system, destructive quantum interference (QI), on... |
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| Title | Close relation between quantum interference in molecular conductance and diradical existence |
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