Comment on “Is the Antiresonance in Meta-Contacted Benzene Due to the Destructive Superposition of Waves Traveling Two Different Routes around the Benzene Ring”

Sýkora, Rudolf; Novotný, Tomáš

doi:10.1021/acs.jpcc.7b07120

Cited by 5 publications

(7 citation statements)

References 3 publications

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“…As for the interpretation of destructive quantum interference through the pristine benzene ring, the relationship G 13 ( E ) ∝ cos k = 0 at k ( E ) = π/2 is derived in ref (this derivation is described in eqs 9, 12, 29, 30, and 34 of ref ). We agree with the authors of ref that the analysis in ref showing G 13 ( E ) ∝ cos k and T ( E ) ∝ |1 + e ikL | 2 indeed gives 0 when k = π/2 and L = 2. Therefore, we are not saying that G meta = 0 as derived by ref is incorrect since the meta -case does indeed give zero values.…”

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confidence: 93%

mentioning

confidence: 97%

“…The recent comment by Sykora et al on the work of Nozaki et al pointed out that the phase shifts between two independent pathways through a meta -contacted benzene calculated in Figures 4f,g of ref include erroneous shifts and that the phase shift should instead be π. This statement in ref is correct, and there was an error in the calculation of the phase shift in ref , which is discussed in more detail below. Nevertheless, this does not invalidate the central argument made in ref , i.e., that the “intuitive interpretation” breaks down under certain conditions and is thus not generally applicable, as discussed below.…”

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confidence: 97%

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Reply to Comment on “Is the Antiresonance in Meta-Contacted Benzene Due to the Destructive Superposition of Waves Traveling Two Different Routes around the Benzene Ring?”

Nozaki

Toher

2017

J. Phys. Chem. C

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confidence: 93%

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confidence: 97%

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confidence: 97%

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Reply to Comment on “Is the Antiresonance in Meta-Contacted Benzene Due to the Destructive Superposition of Waves Traveling Two Different Routes around the Benzene Ring?”

Nozaki

Toher

2017

J. Phys. Chem. C

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“…Further debate ensued. 45,46 If one wants to understand QI effects, it may also make sense to use the formalism of Feynman paths. 47 QI features might be interpreted as the consequence of the interference between electron wave-functions through different Feynman paths.…”

Section: State Of the Art In The Theory Of Qimentioning

confidence: 99%

“…Thus, they argued that the analogy between the classical double-slit experiment and QI is not correct. Further debate ensued. , …”

Section: State Of the Art In The Theory Of Qimentioning

confidence: 99%

Quantum Interference, Graphs, Walks, and Polynomials

Tsuji

Estrada

Movassagh³

et al. 2018

Chem. Rev.

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In this paper we explore quantum interference 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 orHückel 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 cancelled by others, leading to another class of quantum interference. For non-alternant hydrocarbons, the finite Green's function expansion may include both even and odd powers. Nevertheless, QI can in some circumstances come about for non-alternants, 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. And we introduce a perturbation theory for transmission as well as some potentially useful infinite power series expansions of the Green's function.

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Conductance zeros in complex molecules and lattices from the interference set method

2021

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Comment on “Is the Antiresonance in Meta-Contacted Benzene Due to the Destructive Superposition of Waves Traveling Two Different Routes around the Benzene Ring”

Cited by 5 publications

References 3 publications

Reply to Comment on “Is the Antiresonance in Meta-Contacted Benzene Due to the Destructive Superposition of Waves Traveling Two Different Routes around the Benzene Ring?”

Reply to Comment on “Is the Antiresonance in Meta-Contacted Benzene Due to the Destructive Superposition of Waves Traveling Two Different Routes around the Benzene Ring?”

Quantum Interference, Graphs, Walks, and Polynomials

Conductance zeros in complex molecules and lattices from the interference set method

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