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Simple One-electron Invariants of Molecular Chirality

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Pseudoscalar measures of electronic chirality for molecular systems are derived using the spectral moment theory applied to the frequency-dependent rotational susceptibility. In this scheme a one-electron chirality operator \(\hat{\kappa}\) naturally emerges as a quantum counterpart of the triple scalar product, involving velocity, acceleration and second acceleration. Averaging\(\hat{\kappa}\) over an electronic state vector gives rise to an additive chirality invariant (κ-index), considered as a quantitative measure of chirality. A simple computational technique for quick calculation of the κ-index is developed and various structural classes (cyclic hydrocarbons, cage-shaped systems, etc.) are studied. Reasonable behaviour of the chirality index is demonstrated. The chirality changes during the β-turn formation in Leu-Enkephalin is presented as a useful example of the chirality analysis for conformational transitions.

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Authors and Affiliations

  1. STS “Institute for Single Crystals”, National Academy of Sciences, Kharkov, 61001, Ukraine

    A. V. Luzanov

  2. Unilever Centre for Molecular Informatics, Department of Chemistry, Cambridge University, Cambridge, CB2 1EW, UK

    Dmitry Nerukh

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  1. A. V. Luzanov
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  2. Dmitry Nerukh
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Correspondence to A. V. Luzanov.

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Luzanov, A.V., Nerukh, D. Simple One-electron Invariants of Molecular Chirality. J Math Chem 41, 417–435 (2007). https://doi.org/10.1007/s10910-006-9087-8

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  • DOI: https://doi.org/10.1007/s10910-006-9087-8

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