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Single-Molecule Electronics pp 165–190Cite as

Orbital Rule for Electron Transport of Molecular Junctions

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Abstract

Constructive and destructive interference are typical features of electron transport in molecular junctions, which appear as parabolic curves and sharp dips of transmission functions, respectively. To understand the quantum interference properties in molecular junctions, the Green’s function method with tight-binding models was adopted, and the quantum interference was analyzed in terms of orbitals, which leads to an efficient orbital rule for qualitative predictions of electron transport in molecular junctions. A minimum model, a two-site tight-binding model, was used to explain the orbital rule for electron transport without ambiguity. The orbital bases in tight-binding models are typically atomic orbitals, and thus the tight-binding model can be easily extended to larger molecules by simply adding atomic sites. As the next example, a three-site triangular tight-binding model was introduced. The quantum interference that appears in the three-site model can be easily understood using the orbital rule. With regard to the orbital bases as molecular orbitals, the triangular tight-binding model could efficiently explain the destructive interference recently observed in a large molecular unit. In the final part, we also examine the applicability of the orbital rule for molecular spin systems including spin-flip processes.

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Notes

  1. 1.

    The so-called measurement problem in quantum mechanics is still not resolved; therefore, we cannot deny the presence of any suspicious interactions between two propagating states that are separated by large distances. The term interaction used in this chapter denotes an apparent interaction that is explicitly represented in Hamiltonian.

  2. 2.

    According to their three-site model, the hopping parameters between sites 1 and 3 (2 and 3) are also positive, whereas \(\Lambda _{\mathrm{x}}\)-junction is negative for these. However, it was confirmed that the intrinsic property (anti-resonance) in the \(\Lambda _{\mathrm{x}}\)-junction was not sensitive to the sign of the 1–3 and 2–3 hopping parameters. The key parameter for the anti-resonance is the sign for hopping between sites 1 and 2 because the key factor is the orbital exchange between \(\varepsilon _{1}\) and \(\varepsilon _{2}\) from \(\Lambda _{\mathrm{a}}\) to \(\Lambda _{\mathrm{x}}\)

  3. 3.

    The explanations for the neglected incoherent processes given in this part are originally from Ref. [24]. However, there is a typographical error in Eq. (21) of Ref. [24]; the equations shown here in this section are correct.

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Acknowledgements

T.T. sincerely thanks Prof. Kazunari Yoshizawa for contributions and support toward the development of the orbital rule, and Drs. Masakazu Kondo, Aleksandar Staykov, Daijiro Nozaki, Yuta Tsuji, and Xinqian Li for their extensional applications of the orbital rule. This research was supported by Grants-in-Aid for Scientific Research (Innovative Areas “π−System Figuration: Control of Electron and Structural Dynamism for Innovative Functions”) from the Japan Society for the Promotion of Science and Grant-in-Aid for Young Scientists (B) and from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan.

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  1. Materials Research Center for Element Strategy, Tokyo Institute of Technology, Tokyo, Japan

    Tomofumi Tada

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  1. Tomofumi Tada
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Correspondence to Tomofumi Tada .

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  1. Dept of Chemistry Grad. Sch of Sci & Eng, Tokyo Institute of Technology, Tokyo, Tokyo, Japan

    Manabu Kiguchi

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Tada, T. (2016). Orbital Rule for Electron Transport of Molecular Junctions. In: Kiguchi, M. (eds) Single-Molecule Electronics. Springer, Singapore. https://doi.org/10.1007/978-981-10-0724-8_7

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