The importance of symmetry in chemistry

Introduction

Symmetry is everywhere- in snowflakes, flowers and even art. Chemistry is no different and  the symmetrical properties of a molecule often dictate its behaviour. From interpreting  spectra, to predicting reaction pathways and understanding bonding, symmetry shapes all  chemical disciplines.  

1. Symmetry in spectroscopy

Firstly, understanding the symmetry of molecules is essential in a range of characterisation techniques.

In ¹H NMR spectroscopy, the number of peaks seen in a spectrum correspond to the  number of unique chemical environments. For example, dibenzylidene acetone has a  plane of symmetry and a rotational axis (C₂) through the centre of the carbonyl. This  explains why the spectrum only has 5 different proton environments.  

In IR spectroscopy, infrared radiation is absorbed by a molecule causing stretching and  bending of bonds when they vibrate. The total number of vibrational modes can be  predicted using:  

• 3N – 5 rule for linear molecules  

• 3N – 6 rule for non-linear molecules (where N = no. of atoms) 

However, only vibrations which cause a change in dipole moment are seen in IR spectra.  This explains why CO₂ only shows 3 main absorption peaks, despite having 4 vibrational  modes.  

2. Symmetry in reaction mechanisms

Considering the symmetry of molecules also helps chemists predict the stereochemical  outcome of organic reactions. A common example is the E2 elimination of a  halogenoalkane, where an alkene is formed via elimination of a halogen. 

For an E2 elimination to occur, the H and the leaving group must be 180^°from each other, in  an ‘anti-periplanar’ conformation. To predict which groups, have this relationship, Newman  projections are used to easily assign and rotate bonds. A Newman projection is a  perspective of a molecule, typically by imagining you are looking down a specific C-C bond. See Figure 3.

3. Symmetry in bonding

Lastly, considering the symmetry of a molecule is vital for understanding Molecular Orbital  (MO) Theory. MO theory explains how covalent bonding occurs by considering the  symmetry elements of the valence orbitals.

For example, in H₂, the two valence 1s orbitals are completely symmetric and therefore can  overlap effectively to form a σ molecular orbital. However, in HF, the introduction of 2p  orbitals means the shape and symmetry has changed. The 2p_x and 2p_y orbitals can no  longer overlap with the 1s H orbital as their symmetries are incompatible.  

Using this information, a MO diagram can be constructed to show how the orbitals  combine, explaining why H₂ has a single bond. In essence, symmetry determines which  orbitals can ‘match up’ to form bonds. See Figure 4.

Conclusion

Symmetry influences every aspect of chemistry and is frequently employed to rationalise  observed molecular characteristics. While sometimes overlooked, considering the  symmetry of a molecule underpins any chemistry undertaken across industry and  academia. If you enjoyed this article, future articles could build on this topic by introducing  Group Theory and showing how you can predict an entire vibrational spectrum, or the  molecular geometry of a compound based entirely on its symmetry.

Written by Antony Lee

REFERENCES

S. Civis, M. Ferus, A. Knizek, in The Chemistry of CO₂ and TiO₂: From Breathing Minerals  to Life on Mars, ed. S. Civis, M. Ferus, A. Knizek, Springer Nature, Switzerland, 1^st edn.,  2019, vol. 1, ch. 1, pp. 1-7

A. Burrows, J. Holman, S. Lancatser, T. Overton, A. Parsons, G. Pilling, G. Price, in  Chemistry³, Oxford University Press, Oxford, 3^rd edn., 2017, ch.4, pp. 172-219