One of the oldest forms of spectroscopy uses the infrared region of the electromagnetic spectrum. In order to understand IR spectroscopy, we must first consider the motion of atoms in molecules.
Atoms in a molecule do not maintain fixed positions with respect to each other, but actually vibrate back and forth about an average value of interatomic distance with a certain frequency. Think of a child on a swing. The frequency of the back and forth motion can be found by counting the number of swings in a minute. If the child is pushed on the swing when the frequency of pushing matches the frequency of the swinging the child swings higher (greater amplitude) but the frequency remains the same. Organic molecules absorb infrared radiation when the frequency of IR radiation is synchronized with a natural vibration frequency of the molecule. When IR radiation is absorbed, the molecule begins to vibrate with a greater amplitude (but with the same frequency), and thus the molecule has gained energy.
Activity One
Students will investigate the factors affecting the frequency of oscillation of a swing. (See Investigation 1) Teachers should note that the only factor that should affect the frequency of the swing is the length of the swing, therefore, swings of different lengths should be made available. If swings of different lengths are not available the activity can be modified to use pendulums constructed with strings of different lengths.
A molecule can have the following types of motions: (1) translation of the entire molecule, which can be regarded as translation of the center of mass, (2) rotation of the molecule as a framework around its center of mass, (3) vibrations of the individual atoms within the framework, which occur in such a way that the center of mass does not change position and the framework does not rotate. The number of degrees of freedom of a particle equals the number of coordinates required to specify its position in space. A molecule has as many degrees of freedom as the total degrees of freedom of its individual atoms. Each atom has three degrees of freedom corresponding to the Cartesian coordinates (x,y,z) necessary to describe its position relative to other atoms in the molecule. For a molecule composed of n atoms there are 3n degrees of freedom associated with the momentum coordinates. For nonlinear molecules, three degrees of freedom describe rotation and three describe translation; the remaining 3n-6 degrees of freedom are vibrational degrees of freedom or fundamental vibrations. Linear molecules have 3n-5 vibrational degrees of freedom, for only two degrees of freedom are required to describe rotation. Fundamental vibrations involve no change in the center of mass of the molecule.
The ability of a compound to absorb IR energy depends on a net change in the dipole moment occurring when the molecule vibrates. Whether or not such a change occurs depends on the distribution of electrical charges in the molecule. The carbon monoxide molecule can be thought of as a carbon atom joined to an oxygen atom by means of a compressible bond. The carbon has six electrons surrounding its nucleus and oxygen has eight. During a vibration a change in the charge distribution occurs, this appears to the incident IR radiation as an oscillating charge. It is this oscillating charge that the light interacts with. When the frequency of the radiation matches the frequency of the oscillating charge the IR radiation is absorbed. Consequently, carbon monoxide shows an absorption band in the IR region at the frequency corresponding to the vibrational frequency of the nuclei. There is no net change in the dipole moment during the vibration of homonuclear molecules such as O2, N2, and H2, and these molecules do not absorb IR radiation. The ability of a molecule to absorb radiation during a particular vibration depends on its electrical geometry.
The water molecule consists of three atoms and is nonlinear; therefore, it should produce three fundamental vibrations. The three fundamental vibrations of the water molecule can be depicted as symmetrical stretching, asymmetrical stretching, and scissoring. (See Figure 1) The carbon dioxide molecule also consists of three atoms but is linear, therefore, it has four fundamental vibrations: symmetrical stretching, asymmetrical stretching, scissoring in the x-y plane, and scissoring perpendicular to the x-y plane. (See Figure 2) The symmetrical stretching vibration in carbon dioxide is inactive in the infrared since it produces no change in the dipole moment of the molecule. The bending vibrations are equivalent, and are the resolved components of bending motion oriented at any angle to the internuclear axis; they have the same frequency and are said to be doubly degenerate. Some sets of vibrations are degenerate, they are identical in frequency but in perpendicular directions and these multiple vibrations only result in one infrared absorption band being seen in the spectrum. In addition, bands of low intensity may occur as overtones. As a result, the infrared spectrum of an organic compound is usually rather complex. Computer software like MacSpartan or PC Spartan can be used to show the students a model of the vibrations possible for a number of molecules.
The vibrational motion is quantized. At room temperature most of the molecules in a given sample will be in the lowest vibrational state. Absorption of light of the appropriate energy allows the molecule to become excited to a higher vibrational level. In general, such absorption of an infrared light quantum can occur only if the dipole moment of the molecule is different in the two vibrational levels. The variation of the dipole moment with the change in interatomic distance during the vibration corresponds to an oscillating electric field that can interact with the oscillating electric field associated with electromagnetic radiation. The requirement that absorption of a vibrational quantum be accompanied by a change in dipole moment is known as a selection rule. Such a vibrational transition is said to be infrared-active. Vibrational transitions that do not result in a change of dipole moment of the molecule during vibration are not observed directly and are referred to as infrared-inactive transitions. The greater the change in dipole moment the stronger the infrared absorption. This explains why the groups whose components differ considerably in electronegativity show stronger absorption bands.
There are two types of molecular vibrations: stretching and deformations. A stretching vibration is a rhythmical movement along the bond axis such that the interatomic distance is increasing or decreasing. A deformation may consist of a change in bond angle between bonds with a common atom (much like a pair of scissors opening and closing) or the movement of a group of atoms with respect to the remainder of the molecule without movement of the atoms in the group with respect to one another. For example, twisting, rocking, and torsional vibrations involve a change in bond angles with reference to a set of coordinates arbitrarily set up within the molecule.
Each of these vibrational modes has a natural frequency of motion. This natural frequency is determined by the mass of the atoms bonded and for stretching of a single bond the strength of the bond. The larger masses have a lower frequency and the stronger bonds have a higher frequency.
If we attach a small mass to a large, loose spring it would bounce with a certain frequency, let’s arbitrarily say 50 per minute. If we put a larger mass on the same spring the natural rate of motion would be less, maybe 30 per minute. If we keep that same large mass but replace the spring with a tighter one the mass will bounce with a higher frequency, maybe 40 per minute.
Activity Two
Students will explore the effects of mass and bond nature on vibration frequency using a mass on a spring as a model. (See Investigation 2)
The frequency of vibration of various masses on the same spring will be measured by displacing the mass from its equilibrium position and counting the number of oscillations in 30 seconds. The number of oscillations multiplied by two will give the number of vibrations per minute or the frequency. Students should conclude that the frequency of vibration is inversely related to the mass of the object. The greater the mass the lower the frequency. The effect of bond nature on vibration frequency will be tested by keeping the mass constant and varying the number of springs or the spring strength and measuring the frequency of vibration in the same way as before. Teachers should note that the frequency is proportional to the square root of the spring constant (k) divided by the mass (m).
Activity Three
For real molecules, or covalent bonds within larger molecules, the natural frequency follows the same trends. The O-H bond has a higher frequency of vibration than the O-C bond has since the average mass, calculated as (m1m2 )/(m1+m2), of the atoms is less for OH. The O=C bond has a higher frequency than the O-C bond has since the double bond is stronger than a single bond.
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Students will be asked to predict the relative frequencies of vibration for isolated bonds by applying the relationships between mass and frequency and spring strength and frequency that they determined in activity one to organic molecules. (See Worksheet 1 and Worksheet 2)
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