**3. Potential energy dependence of the inter atomic distance of a diatomic molecule in Morse potential energy approximation**

In inharmonic approximation of the vibration of diatomic molecules of the selection rule, relating to the variation in **n**vib allowed for the quantum number, it is not so strict as in the case described harmonics. The model does not exclude the possibility inharmonic transitions between the status of vibration to which variation **n**vib quantum number to be 2,3 , etc. , in practice IR spectrophotometry.

Transitions associated with variations in higher than the unit are called harmonics of the upper fundamental transition (i.e., the transition that starts at the same lower status, but for which Δ**n**vib = 1 ).

The appearance of the absorption bands assigned to upper harmonics inherent in spectra are observed frequently in IR (especially in the case polyatomic molecules), but as a rule occur with intensities that are smaller than corresponding fundamental bands.

Strips of the upper harmonics associated with fundamental tape appear at frequencies (or wave numbers) which are approximately multiples whole frequency (or the wave-number) fundamental.

Another practical consequence of the inharmonicity of vibration of molecules is the rise of the inter-combination bands in the IR absorption spectra.

These bands of absorptions are observed at frequencies equal to the sum or the difference between two frequencies or fundamental frequency of a fundamental and a harmonic one. By cause of bands of combination appear various normal modes of oscillation of the molecule. The high harmonics and the bands of combination in IR absorption spectra cause considerably complications in their interpretation.

Organic Compounds FT-IR Spectroscopy 151

The vibrating atoms in a molecule polyatomic can be described as a function of internal coordinates instead of cartesian coordinates. Such are eliminated those movements which correspond translations to atoms and rotation molecule without deformation. Internal coordinates of a molecules polyatomic can be defined in different ways. How to define the most frequently involves the covalent connection between pairs of atoms connect (lab for atoms a and b), Angles between connections covalent) binding centered on an atom common (αabc for atoms a and c bound by common atom (b) and diedral angles θabcd (the angle of the plans P and R containing three connections between four **atoms covalent)** 

Each vibration mode of the molecule can be described as a time-dependent periodic variation of all the internal coordinates. For a specific molecular structure, consisting of N atoms, the whole structure runs ((3N-6) or (3N-5)) modes of preferential oscillations, involving in (3N-6) (or (3N-5)) ways the internal coordinates of the molecule. These "preferential" types of oscillations represent the normal oscillations of the molecule. In each normal type of oscillation, all the internal coordinates of the molecule oscillate at a common

In each normal mode of oscillation, the internal coordinates are involved in varying degrees. For a normal oscillation is characteristic of the internal coordinate of the molecule (e.g., a covalent bond length) is more involved than the others, then it may be said (with some tolerance) that normally oscillation that the respective oscillation type is characteristic for

Figure 3 represents the fine vibration structure of the fundamental electronic state and of the first excited electronic states, for the case of a hypothetical triatomic molecule. This type of molecule has 3·3-6=3 normal vibration modes. Oscillation modes are also represented in Figure 3, indicating the direction and the direction of the relative shift of the individual atoms in one of the half period of oscillation. Each electronic state consists in a number of vibration states characterized by the vibration quantum numbers **nvib**. For each normal way

**binding) (Figure 2).**

Fig. 2. Define Internal coordinates l , α and θ

frequency (in principle), specific for that type of oscillation.

the respective internal coordinate (e.g., the length of the covalent bond).
