Simple one-electron invariants of molecular chirality

A.V. Luzanov, Dmitry Nerukh

Research output: Contribution to journalArticlepeer-review


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 κ^ naturally emerges as a quantum counterpart of the triple scalar product, involving velocity, acceleration and second acceleration. Averaging κ^ 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.
Original languageEnglish
Pages (from-to)417-435
Number of pages19
JournalJournal of Mathematical Chemistry
Issue number4
Publication statusPublished - 1 May 2007


  • chirality measures
  • differential geometry
  • joint invariants
  • topological matrix
  • high-symmetry chiral systems
  • Berry and Hannay phases


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