### 抜粋

In this paper, we explore quantum interference (QI) in molecular conductance from the point of view of graph theory and walks on lattices. By virtue of the Cayley-Hamilton theorem for characteristic polynomials and the Coulson-Rushbrooke pairing theorem for alternant hydrocarbons, it is possible to derive a finite series expansion of the Green's function for electron transmission in terms of the odd powers of the vertex adjacency matrix or Hückel matrix. This means that only odd-length walks on a molecular graph contribute to the conductivity through a molecule. Thus, if there are only even-length walks between two atoms, quantum interference is expected to occur in the electron transport between them. However, even if there are only odd-length walks between two atoms, a situation may come about where the contributions to the QI of some odd-length walks are canceled by others, leading to another class of quantum interference. For nonalternant hydrocarbons, the finite Green's function expansion may include both even and odd powers. Nevertheless, QI can in some circumstances come about for nonalternants from cancellation of odd- and even-length walk terms. We report some progress, but not a complete resolution, of the problem of understanding the coefficients in the expansion of the Green's function in a power series of the adjacency matrix, these coefficients being behind the cancellations that we have mentioned. Furthermore, we introduce a perturbation theory for transmission as well as some potentially useful infinite power series expansions of the Green's function.

元の言語 | 英語 |
---|---|

ページ（範囲） | 4887-4911 |

ページ数 | 25 |

ジャーナル | Chemical Reviews |

巻 | 118 |

発行部数 | 10 |

DOI | |

出版物ステータス | 出版済み - 5 23 2018 |

### All Science Journal Classification (ASJC) codes

- Chemistry(all)

## フィンガープリント Quantum Interference, Graphs, Walks, and Polynomials' の研究トピックを掘り下げます。これらはともに一意のフィンガープリントを構成します。

## これを引用

*Chemical Reviews*,

*118*(10), 4887-4911. https://doi.org/10.1021/acs.chemrev.7b00733