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# Infrared Spectroscopy

Infrared Spectroscopy is the analysis of infrared light interacting with a molecule. This can be analyzed in three ways by measuring absorption, emission and reflection. The main use of this technique is in organic and inorganic chemistry. It is used by chemists to determine functional groups in molecules. IR Spectroscopy measures the vibrations of atoms, and based on this it is possible to determine the functional groups.5 Generally, stronger bonds and light atoms will vibrate at a high stretching frequency (wavenumber).

### Introduction

The use of infrared spectroscopy began in the 1950's by Wilbur Kaye. He had designed a machine that tested the near-infrared spectrum and provided the theory to describe the results. Karl Norris started using IR Spectroscopy in the analytical world in the 1960's and as a result IR Spectroscopy became an accepted technique. There have been many advances in the field of IR Spec, the most notable was the application of Fourier Transformations to this technique thus creating an IR method that had higher resolution and a decrease in noise. The year this method became accepted in the field was in the late 1960's.4

### Theory

Infrared light imposed on a molecule will not create electronic transitions but it does contain enough energy to interact with a molecule causing vibrational and rotational changes. For example, the molecule can absorb the energy contained in the incident light and the result is a faster rotation or a more pronounced vibration. The possible rotations are around the axis of symmetry for a given molecule or either of the two perpendicular axis'. Vibrations can be in the form of a bend or a stretch for each bond. Illustrated below are possible vibrational motions for a three atom molecule (all are in the plane unless explicitly stated):

(+ means out of screen and - is into screen)

The set of equations below accounts for only one absorption but experimental studies found that there were multiple peaks for each individual molecule. Quantum Mechanics describes the different absorption maxima as Jth level vibrational states that account for these other frequencies observed. There are 3N-5 vibrational states for linear molecules and 3N-6 vibrational states for non-linear molecules where N is the number of atoms.  For more information, see vibrational modes.

$F = -ky$

$dE = - Fdy$

$\displaystyle \int_{0}^{E} dE = \int_{0}^{y} kydy$

This equation describes the potential energy of the vibration

$E = \frac{1}{2}ky^2$

Because

$F = ma$

$m\dfrac{d^2y}{dt^2} = -ky$

This equation describes the periodic vibrational motion

$y = Acos(2\pi v_{\mu}t)$

Where

$\mu$ = the reduced mass

$\dfrac{d^2y}{dt^2} = -4\pi^2 v_{\mu}^{2} Acos(2\pi v_{\mu}t)$

Therefore,

$v_{\mu} = \dfrac{1}{2\pi} \sqrt{\dfrac{k}{\mu}}$

This is for the natural frequency of oscillation.

### Instrument

The components of an IR machine are the IR source, beam splitter, monochromator, a transducer, an analog to digital converter and a digital machine to quantify the readout.1 The IR light exits the source and becomes split into to beams, one to be directed to the sample the other to a reference. The intensity of the beam is measured by the intensity emitted divided by the intensity observed, also known as the Transmittance. All frequencies are measured in wavenumber, cm-1. To make a sample with a liquid, the liquid is placed between two pure salt sheets of NaCl and for a solid it is pressure pressed with KBr to incorporate both into one sheet. The reason for using salt to suspend the molecule is because the salt structures form a lattice that is strongly ionically bonded and will not absorb IR light because it lacks the vibrational capability.3 The Background scan or reference tends to be air.

Below 1500 cm-1 the spectra have very high sensitivity and this region is known as the fingerprint region where C-C bond stretching and bending motions overlap, making it difficult to predict functional groups.5 For more specific bond stretch frequencies see Characteristic Absorption Frequencies in IR Spectra.

### References

1. D. A. Skoog, F. J. Holler, S. R. Crouch. Principles of Instrumental Analysis, 6th ed. Belmont, CA. Thomson Higher Education. 2007.
2. D. A. McQuarrie, J. D. Simon. Physical Chemistry A Molecular Approach. Sausalito, Ca. University Science Books. 1997.
3. D. L. Pavia, G. M. Lampman, G. S. Kriz. Introduction to Organic Laboratory Techniques A Microscale Approach 4th Edition. Belmont, Ca. The Thomson Corporation. 2007.
4. F. E. Barton II. Theories and Principles of Near-Intrared Spectroscopy. Spectroscopy Europe 14/1. 2002.
5. Vollhardt, K. Peter C., and N. Schore. Organic chemistry structure and function. New York: W.H. Freeman, 2007.

### Problems

1. If the wavenumber associated with a vibration is equal to 2.3 x 103calculate the spring constant for SiO.
2. At what wavelength does a carbon - carbon double bond usually appear on an IR spectrum?
3. What functional groups are present in the spectrum below?

### Contributors

• Mustafa Rupawalla, Harpreet Singh, Randeep Johl, Korey Reid, Molly Mulleague
15:50, 17 Feb 2014

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