The normal modes of a molecule must belong to one of the symmetry species of the molecular point group, and this proves to be a highly convenient method of classifying them, allowing rapid prediction of the form of the vibrational spectra of the molecule. The determination of the symmetry species of the normal modes is […]

## Normal Modes of Vibration

Vibrations in molecules can be excited by the application of radiation at the same frequency as the vibration itself. This gives rise to spectroscopic methods of studying molecular structure, which depend upon being able to predict or at least rationalise the vibrations that are observed. Symmetry considerations play an important role in this. Note that […]

## Applications of Symmetry to Integrals

One of the most useful applications of symmetry is to the evaluation of various integrals. It is possible with many integrals that are commonly encountered in chemistry to use symmetry arguments to tell whether an integral must necessarily be zero. We will consider a general integral of the product of two functions f1 and f2: […]

## Interpretation of a Character Table

The characters of the identity operation, E, reveal the degeneracy of the orbitals of each symmetry species. Thus in a C3v molecule any a1 or a2 orbital is non-degenerate. Any doubly degenerate pair of orbitals in a C3v molecule must be labeled e, as the only symmetry species with a character greater than one is […]

## Character Tables

The symmetry properties of orbitals in polyatomic molecules are denoted by symmetry labels, which look like a, a1, b, e etc. These labels indicate the behaviour of the orbitals in a molecule under the symmetry operations of the point group to which the molecule belongs. This can be illustrated by a hypothetical example: We will […]

## Polar and Chiral Molecules

There are some conclusions that may be drawn about a molecule as soon as its point group has been identified: A polar molecule is one which possesses a permanent electric dipole moment. A molecule belonging to a group Cn can only have a dipole moment parallel to the rotational axis. This is because the symmetry […]

## Key for Assignment of Point Groups

1 Is the molecule linear? Yes- Go to 2 No- Go to 3 2 Does it have a centre of inversion? Yes- Belongs to D∞h No- Belongs to C∞v 3 Does it have three or more different Cn axes with n > 2? Yes- Go to 4 No- Go to 5 4 Does it have […]

## Point Groups

The name of the group to which a molecule belongs is determined by the symmetry elements it possesses. Grouping together molecules with the same symmetry elements will automatically group together molecules of the same shape eg CX4 where X = H, F, Cl, Br or I; as long as the four X groups are identical, […]

## Introduction to Symmetry

The symmetry properties of molecules and orbitals are extremely useful in a consideration of their properties. In order to explore the symmetry of an object in a rigorous mathematical fashion, we need to introduce various terms to describe the concepts we shall encounter: A symmetry operation is any action that may be carried out upon […]

## Electron Spin Resonance (ESR) Spectroscopy

This is a spectroscopic technique related to NMR that makes use of the fact that electrons also have an intrinsic spin angular momentum. For electrons, the spin quantum number, S, is equal to ½. This number specifies the magnitude of the total spin angular momentum for an electron to have the numerical value / 2 […]