Molecular Chirality and Chiral Parameters

TL;DR

This paper explores the fundamental symmetry principles of molecular chirality, showing that chiral measures are pseudoscalars involving three-point correlations, and discusses how molecular handedness depends on the property observed, with implications for liquid crystal behavior.

Contribution

It introduces a comprehensive framework for understanding molecular chirality through chiral parameters and their relation to symmetry and macroscopic properties like cholesteric pitch.

Findings

Chiral measures are pseudoscalars involving three-point correlations.

Molecules have an infinite set of chiral parameters with varying signs.

Handedness depends on the property observed, not an absolute characteristic.

Abstract

The fundamental issues of symmetry related to chirality are discussed and applied to simple situations relevant to liquid crystals. We show that any chiral measure of a geometric object is a pseudoscalar (invariant under proper rotations but changing sign under improper rotations) and must involve three-point correlations which only come into play when the molecule has at least four atoms. In general, a molecule is characterized by an infinite set of chiral parameters. We illustrate the fact that these parameters can have differing signs and can vanish at different points as a molecule is continuously deformed into its mirror image. From this it is concluded that handedness is not an absolute concept but depends on the property being observed. Within a simplified model of classical interactions, we identify the chiral parameter of the constituent molecules which determines the macroscopic pitch of cholesterics.