# 4.4.1: Chirality

$$\newcommand{\vecs}{\overset { \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$

## Introduction Figure $$\PageIndex{1}$$: Two enantiomers of an amino acid (with side chain R).

Around the year 1847, the French scientist Louis Pasteur provided an explanation for the optical activity of tartaric acid salts. when he carried out a particular reaction, Pasteur observed that two types of crystals precipitated. Patiently and carefully using tweezers, Pasteur was able to separate the two types of crystals. Pasteur noticed that the types rotated the plane polarized by the same amount but in different directions. These two compounds are called enantiomers.

## What is chirality?

A molecule is chiral (or dissymetric) if it is non-superimposable on its mirror image. The two mirror images of a chiral molecule are called enantiomers. Enantiomers have the same physical properties (e.g., melting point, etc.). They differ in their ability to rotate plane polarized light and in their reactivity with other chiral molecules. Due to their ability to rotate plane polarized light, they are referred to as being optically active.

## Using Symmetry to Determine Chirality

There are some general rules of thumb that help determine whether a molecule is chiral or achiral. The point group of the molecule, and the symmetry operations within that point group, can give clues as to whether the molecule is chiral.

##### Symmetry operations of chiral molecules

A chiral molecule cannot posess a plane of symmetry ($$\sigma$$), a center of inversion ($$i$$), or an improper rotation ($$S_n$$). Due to the fact that all groups that lack both $$\sigma$$ and $$i$$ also lack $$S_n$$, a molecule that belongs to any group that lacks $$S_n$$ is chiral.

An example of an inorganic coordination complex is tris(ethylenediamine)coalt(III) (Figure $$\PageIndex{1}$$). Figure $$\PageIndex{1}$$ shows the two enantiomers of tris(ethylenediamine)coalt(III); the $$\Delta$$ and $$\Lambda$$ isomers. Figure $$\PageIndex{2}$$: Two chiral enantiomers of tris(ethylenediamine)coalt(III).

You can visualize the $$\Lambda$$ and $$\Delta$$ isomers by imagining that the ligands around the metal centers are blades of a fan. To push the air toward you, you would need to rotate the $$\Delta$$ isomer clockwise, and the $$\Lambda$$ isomer counter-clockwise. Figure $$\PageIndex{3}$$: Another way of thinking about the chirality of the two chiral enantiomers of tris(ethylenediamine)coalt(III) shown in Figure $$\PageIndex{2}$$. This figure was taken from Structure and Reactivity in Organic, Biological, and Inorganic Chemistry.

Exercise $$\PageIndex{1}$$

Which point groups are possible for chiral molecules?

As a result of the previous discussion, there are a few classes of point groups that lack an improper axis. Those classes are $$C_{1}$$, $$C_{n}$$, and $$D_{n}$$.