Chirality Inherent and Induced: An Algebraic Point of View

Abstract

IUPAC defines chirality as a geometric property of an object. Here we discuss a complementary view of chirality in algebraic terms. This enables us to extend its definition from classical to quantum mechanics. We further infer that classical chirality can only be induced in linear combinations of coherences between quantum states. A current motivation for our approach is the ability to induce chirality in an achiral system by a chiral perturbation, most notably an ultrafast light pulse. The stereodynamics of the electrons will vary rapidly with time. Pumping the electronic states of the hydrogen atom provides an explicit example which is readily visualized. The algebraic definition allows a generalization from a classical, local, to a quantum mechanical, non-local concept of chirality.