Journal of Mathematical Chemistry

, Volume 41, Issue 4, pp 417–435 | Cite as

Simple One-electron Invariants of Molecular Chirality

Article

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.

Keywords

chirality measures differential geometry joint invariants topological matrix high-symmetry chiral systems 

AMS subject classification

81Q70 differential-geometric methods including holonomy Berry and Hannay phases etc. or 92E10 molecular structure (graph-theoretic methods, methods of differential topology, etc) 

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.STS “Institute for Single Crystals”National Academy of SciencesKharkovUkraine
  2. 2.Unilever Centre for Molecular Informatics, Department of ChemistryCambridge UniversityCambridgeUK

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