The Concept of Chirality from a Mathematical Perspective

In this chapter, we explain the concept of chirality from a mathematical perspective. We begin with the history of chirality in the field of mathematics known as knot theory. A knot is a closed loop in space which cannot be deformed into a plane, and a link is a collection of loops which together cannot be deformed into a plane. If a knot or link cannot be deformed into its mirror image, then it is considered topologically chiral. The chapter explains how knot polynomials and linking numbers can be used to show that a knot or link is topologically chiral. It then explores the difference between topological chirality and chemical chirality and introduces intrinsic chirality, which is the strongest type of chirality. A structure is intrinsically chiral, regardless of its spatial orientation, it cannot be deformed into its mirror image. Finally, we present techniques to show that a structure is intrinsically chiral. Throughout the chapter, we use molecular structures to illustrate the concepts.