Theory of Infrared Absorption Spectroscopy



Theory of Infrared Absorption Spectroscopy

When infrared radiation is passed through a compound only those frequencies are absorbed which match the vibrational frequencies of the bonds present in the compound. The absorption of  infrared radiation causes the molecules to excite from the ground state to a higher vibrational energy state. As a result, the amplitude of the vibration is increased; the frequency of vibration does net change. The infrared spectrum is obtained by plotting absorbance (A) against frequency or wavelength or wave number. The positions of the absorption bands in the spectrum are expressed either by wavelength (A) in units of micrometer or by wave number ( v) in reciprocal centimeter.

NUMBER OF FUNDAMENTAL VIBRATIONS

The total number of fundamental vibrations in a molecule depends on the number of atoms present in the triatomic or higher molecules. All the molecules arc generally classified into two main classes:  (i) linear (ii) Non- linear. A linear ‘molecule has “3n-5” fundamental vibrational modes whereas a non-linear molecule will have “3n-6” fundamental vibrational modes, n is the number of atoms present in molecule.

SELECTION RULES

(1)  A molecule can have a number of vibrations. Some of these vibrations are associated with the vibrations of individual bonds or functional groups. These are called fundamental vibrations. It is not necessary that every fundamental vibration results in the absorption of infrared radiations. According to the selection rule, “only those vibrations which cause a change in dipole moment and thus produce a fluctuating electric field which interacts with the electromagnetic radiations of matching frequency, results in the absorption of infrared radiations. Such vibrations are called infrared active vibrations. The vibrations which do not cause a change in the dipole moment, will not interact with the infrared radiation and are called infrared inactive vibrations.

(2)  At room temperature, most molecules are in the ground state which is the zeroth vibrational level. The absorption of infrared radiation of the corresponding frequency results in the transition of molecules from the zeroth level to the 1st vibrational level. However, transitions from the zeroth level to the 2nd and 3rd vibrational levels may also occur by the absorption of radiation of the corresponding frequency. This leads to the first and the second overtones that appear at almost twice and thrice the fundamental frequency. Thus a strong absorption at 950 c/m, may be accompanied by a weaker absorption at about 1900 c/m’, due to overtone. Sometimes two fundamental frequencies say v1 and v2 may interact to give combination ( v1 + v2 ) band or difference ( v1 – v2 ) band. The cogibination band arises when absorption by a molecule results in the excitation of two fundamental vibrations simultaneously. This happens when a single photon has precisely the correct energy to excite two vibrations. The difference band arises when absorption of radiation promotes a molecularom the excited state to the 2nd excited state. Thus fundamental absorption at 700c/mand 1000c/m may be accompanied by a weaker absorption at 2700 c/m ( combination band) or at 700 c/m (difference band ).

(3) Stretching vibration of a bond requires more energy than the bending vibration, hence absorbs at a higher frequency. Thus C-H stretching absorption occurs around 300c/m whereas C-H bonding absorption occurs around 1400 c/m .Also the absorption due to the stretching vibration of a double bond occurs at a higher frequency than the similar absorption due ma single bond. The

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TYPICAL INFRARED ABSORPTIONS OF FUNCTIONAL GROUPS
The functional groups of molecules absorb energy with typical infrared wave numbers, which are illustrated in Table.2.3.

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