Background:
Summary of Methods Used
Simple Example:
Theory
The Vibrations
Research Topics:
Fatty Acid Methyl Esters (FAMEs)
| School of Chemistry |
What are Vibrations?
All molecules are in continual motion.
This motion can be related to all the possible motions of the atoms that make up the molecule and can be classified into three types:
Vibration is often called the internal motion of the molecule since it is possible to define it in such a way as to separate it from translation and rotation. For example, in a true vibration, the centre of mass of the molecule is unmoved (not translated) and there is no net angular momentum as would be associated with rotation. So, the first task in vibrational analysis is to determine the number of vibrational modes of motion for a given molecule.
If the molecule has N atoms then we need 3N displacement coordinates to fully describe all possible motions, i.e. each atom's movement may be described by giving the components of its displacement (from the stable geometry) along the x, y and z directions.
Therefore the sum of the number of modes of translation
So how many translations are there?
Well, the molecule as a whole can move along the x, y or z direction, so there are 3 translations.
How many rotations are there?
for a non-linear molecule: The molecule as a whole can rotate around the x, y or z direction, so there are 3 rotations.
but for a linear molecule: The molecule has only 2 axes around which to rotate, the third is chosen to point along the molecular linear axis. (Rotation about the molecular axis is a combination of electronic orbital and nuclear spin motions and so it is not regarded as part of molecular rotation). So, in this case, there are only 2 rotations.
Therefore;
for a non-linear molecule: of N atoms there will be 3N-6 vibrational modes and
for a linear molecule: of N atoms there will be 3N-5 vibrational modes.
The wavenumber of a bond-stretching vibration is given by:
n = (½pc) Ök/m, where k is the force constant (this measures the stiffness of the bond), and m is the mass of the oscillating atoms. This means that;
- The stronger the bond, the larger the value of k and the higher the stretching vibrational wavenumber - eg triple bonds > double bonds > single bonds.
- Heavier atoms vibrate at lower frequencies (for the same bond strength).
- Bending frequencies are generally lower than stretching frequencies. (kbend < kstretch).
- Symmetric stretching frequencies are generally lower than antisymmetric stretching frequencies.
Selection Rules:
For Infrared Activity:
A vibrational mode can give rise to an absorption of infrared radiation only if the vibration involves a change in the electric dipole moment of the molecule. So, it should be obvious that the vibration of a homonuclear diatomic molecule (e.g. O2, N2, etc.) does not result in infrared absorption.
A polyatomic molecule will possess several vibrations and these may be Infrared active or inactive according to the symmetry of the vibrational mode. The fact that this behaviour is related to the symmetrical structure of the molecule is one reason for the importance of I.R. spectroscopy in chemistry.
For Raman Activity:
A molecule will only display a Raman spectrum if there is a change in the polarizability of the molecule during the vibration. One consequence of this is that although diatomic molecules do not give i.r. spectra they do result in Raman spectra.
According to the Rule of Mutual Exclusion, molecules with a centre of symmetry have no normal modes that are active in both the infrared and the Raman spectrum.
So, what do these vibrations look like? The two pages that follow use the Carbon Dioxide molecule as a simple example of stretching and bending vibrational motion and other vibrations are demonstrated in the pages that describe my research.
