**1. Introduction**

General spectral range of electromagnetic radiation with a wavelength greater than 750 nm (i.e. with the number of wavelength below 13000 cm-1) bears the name of the domain infrared (IR). In this field samples absorb electromagnetic radiation due to transitions of vibration of the structure of molecules, molecular transitions in vibrations crystalline network (if the sample is in the solid state of aggregation) or due to transitions of molecular rotation. Subdomain of spectral wavelengths between 2500 - 50000 nm (respectively the wave numbers 4000 to 200 cm-1) bears the name of the *middle infrared domain.* 

From the point of view of analytical control of medicinal products, this domain is the most used. At the base of absorption is being generated electromagnetic radiation in this area spectral transitions are the vibrations of individual molecules or of crystalline network (if the sample examined is solid). Show effects such transitions caused by the vibrations of individual molecules provides information about molecular structure of the sample examined, and show effects such crystalline network to identify a particular forms of crystallization of the substance of interest.

The most frequent use of the absorption spectrophototometry in the middle infrared field lies in the identification of substances through molecular vibration. The wavelength (i.e, the wave numbers) of the of the absorption band are characteristic chemical identity of the substance in question. The intensity of the absorption bands allows quantitative analysis of the samples but, unlike in the ultraviolet and visible, in the infrared field diffuse radiation is much more refreshing, and for this reason quantitative determination infrared, are affected by notable errors.

From the standpoint of analytical use, the spectra of molecular vibration is enjoying increased popularity in comparison to the study of the crystal latice's vibrations. A molecule may be considered to be a vibrator with more than one degree of freedom, able to execute more modes of vibration. In each mode of vibration every atom in the molecule oscillates about their own position of equilibrium. Such oscillations have different amplitudes for

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Organic Compounds FT-IR Spectroscopy 147

from the environment, then the amount of Ec and Ep remains constant during oscillation. Potential energy is dependent on the single variable of the diatomic system (namely, the deviation of the Δ**r** inter-atomic distance to **r**0) which is variable in time. Potential energy dependence of the Δ**r** (i.e. lengthening the deformation of the diatomic molecule) is

2 2

0

ν*vib*

1 1 ( ) 2 2

In the relationship (2) the coefficient 'k' is *constant of force*, size that characterises the strength of inter-atomic connection in the molecule. On the basis of expression (2) the potential energy of the diatomic assembly, using the mechanics in this quantum mechanics, may

These values of energy 'allowed' shall be calculated on the basis of the expression (3) by

<sup>1</sup> ( ) <sup>2</sup> *En EE h n vib vib c p*

The expression (3) shows that the energy **E**vib (the sume of the kinetic energy **E**c and potential energy **E**p) has a state of vibration allowed to diatomic system depends on the

The lower value of energy (in the fundamental vibration's state diatomic system) is obtained by replacing **n**vib**=** 0 in the relationship (3). In the relationship (3) h is the size Planck constant. (6,626075 x 10-34 Js). If diatomic molecule fundamental changes from the vibration (**n**vib = 0) in the state of vibration excited immediately above (**n**vib = 1), then change of

 ΔEvib(01) = h.ν0 (4) This value to change the vibration energy determines how often (or the number of

In principle, diatomic molecule can pass from the fundamental (**n**vib = 0 ) in a excited state (for example, corresponding **n**vib = 2) but, those quantum transitions in which the number is

Rigorous justification of the rules of selection is treated in detail in literature on the

Preferred frequency (ν0 ), the favorite number of wave **n**vib = 0 to which a small diatomic molecule absorbs radiation (hence to which generates a strip of absorption) as the transition

> 1 1 ; 2 2

 ν

*k k*

*c*

μ=⋅ = ⋅ <sup>⋅</sup> ⋅ ⋅ (5)

π

wavelength) at which diatomic molecule shows preferential absorption of radiation.

changing more than one establishment are prohibited by the rules of selection.

0 0

μ

π

substituting for the number of quantum vibration (**n**vib) integers numbers (0, 1, 2, . .

0

*E k r krr <sup>p</sup>* = ⋅ ⋅Δ = ⋅ ⋅ − (2)

= + =⋅ ⋅ + (3)

expressed, in the harmonic approximation, of the relationship (2).

deduct quantified values ( 'allowed') of diatomic oscillator.

energy Δ**E**vib**(01)** is expressed by the relationship (4).

(01), is expressed quantitatively the relationship (5)

ν

number of vibration quantum **n**vib.

subject.

different atoms of the molecule, but at a certain mode of vibration, each atom in the molecule oscillates with the same frequency. In other words, the frequency of oscillations of the atoms in molecule is characteristic of a particular mode of oscillation of the molecule.

A molecule composed of N atoms has several possible modes of oscillation. In each mode of oscillation (in principle) all the atoms of molecule perform periodic shifts around level position with a frequency of oscillation mode which is a feature of the assembly. Because each of the N atoms can run periodic shifts in 3 perpendicular directions each other, the assembly of N atoms can have 3N ways of motion. But, those displacements that correspond to moving molecule as a whole (not deform the geometry of the molecule) and movements, which correspond to entire molecules rotation about an axis (also without deforming the molecule's geometry), do not represent actual oscillation (associated with actual deformation of the molecule).

These displacements (3 in number) and rotations around the three orthogonal axis (also 3 in number) are eliminated of the total number of atomic movements possible. Therefore, a molecule is, in general, (3N - 6) distinct modes of oscillation and in each of these (3N - 6) modes of oscillation each atom oscillates with frequencies characteristic individual modes of vibration. A special case represents molecules whose structures are linear, because in these cases the inertia of the molecule, in relation to the axis flush by molecule, it is practically zero. For this reason, in the case of a linear molecules consisting of N atoms, the number of modes of vibration is 3N - 5.
