Simple one-electron invariants of molecular chirality

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.