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Localized Structures at the Hückel Level, a Hückel-Derived Valence Bond Method

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Applications of Topological Methods in Molecular Chemistry

Part of the book series: Challenges and Advances in Computational Chemistry and Physics ((COCH,volume 22))

Abstract

A simple Hückel Hamiltonian is used and modified to describe localized states, where the electron pairs are confined to bonds between two atoms, or to lone pairs. The electronic delocalization can be considered either as a mixture of these localized states, or through a standard Hückel calculation. The two Hückel-Lewis methods described here attempt to find the coefficients of the mixture, based on energy or overlap consistence with the standard Hückel results. After the description of the two methods, test examples are used to show advantages and drawbacks of the different approaches. In any case, the results are compared to the NBO-NRT approach which is used on the electronic density obtained from standard DFT hybrids calculations such as B3LYP/6-31+G(d). This chapter ends with an introduction to the HuLiS program in which the two methods are implemented.

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Notes

  1. 1.

    Two structures are equivalent when they behave the same and/or when one can be deduced from the other by symmetry.

  2. 2.

    It is the same in the Hückel method: \(\beta\) is negative because the low energy solution is an in-phase interaction and because two adjacent \(p\) orbitals overlap positively.

  3. 3.

    Note here that the \(\tau\) value for the NRT results is defined as the sum of the weights of the \(\pi\)/Lewis resonant structures built from the NBO analysis of the molecular density. The NRT weights given here are renormalized so that the sum of the weights of all considered contributors is equal to 100 %. The same definition will apply in Sect. 13.3.2.

  4. 4.

    Note to the referee: at the moment HuLiS is at http://www.hulis.free.fr but it will migrate soon.

  5. 5.

    The molecule has however to be Hückel-compatible i.e. essentially flat. Methyl substituents are allowed.

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Authors and Affiliations

  1. Aix Marseille Université, Centrale Marseille, CNRS, iSm2, UMR 7313, 13397, Marseille, France

    Yannick Carissan, Nicolas Goudard, Denis Hagebaum-Reignier & Stéphane Humbel

Authors
  1. Yannick Carissan
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  2. Nicolas Goudard
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  3. Denis Hagebaum-Reignier
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  4. Stéphane Humbel
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Corresponding author

Correspondence to Yannick Carissan .

Editor information

Editors and Affiliations

  1. LCC-CNRS, Toulouse, France

    Remi Chauvin

  2. LCC-CNRS, Toulouse, France

    Christine Lepetit

  3. Théorique, UMR 761, Laboratoire de Chimie, Paris, France

    Bernard Silvi

  4. CNRS/UPM, MONARIS UMR 8233 (LADIR + LM2N), Paris, France

    Esmail Alikhani

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Carissan, Y., Goudard, N., Hagebaum-Reignier, D., Humbel, S. (2016). Localized Structures at the Hückel Level, a Hückel-Derived Valence Bond Method. In: Chauvin, R., Lepetit, C., Silvi, B., Alikhani, E. (eds) Applications of Topological Methods in Molecular Chemistry. Challenges and Advances in Computational Chemistry and Physics, vol 22. Springer, Cham. https://doi.org/10.1007/978-3-319-29022-5_13

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