How many vibrational modes are there for a given molecular species

How many vibrational modes are there for a given molecular species  

Vibrational spectroscopy is concerned with the observation of the degrees of vibrational freedom, the number of which can be determined as follows. The motion of a molecule containing n atoms can conveniently be described in terms of the three Cartesian axes the molecule has 3n degrees of freedom which together describe the translational, vibrational and rotational motions of the molecule. 

Infrared and Raman spectroscopies are both concerned with the study of molecular vibrations, and while IR spectroscopy is used routinely in the practical laboratory, Raman spectroscopy is a more specialized technique. When radiation of a particular frequency, v (usually from a laser source), falls on a molecule, some radiation is scattered. The scattered radiation is of two types  

The selection rules for Raman and IR active vibrations are different. A vibrational mode is Raman active if the polarizability of the molecule changes during the vibration. Changes in polarizability (for Raman spectra) are not as easy to visualize as changes in electric dipole moments (for IR spectra) and in most cases it is necessary to use group theory to determine whether or not a mode will be Raman active. 

A combination of IR and Raman spectroscopic data is often of great use. Molecules with a centre of symmetry are 

The translational motion of a molecule (i.e. movement through space) can be described in terms of three degrees of freedom relating to the three Cartesian axes. If there are 3n degrees of freedom in total and three degrees of freedom for translational motion, it follows that there must be (3n — 3) degrees of freedom for rotational and vibrational motion. For a non-linear molecule there are three degrees of rotational freedom, but for a linear molecule, there are 

An early success of Raman spectroscopy was in 1934 when Woodward reported the spectrum of mercury(I) nitrate. After the assignment of lines to the [N03] ion, a line at 169 cm remained which he assigned to the stretching mode of the Hg-Hg bond in [Hg2]. This was one of the 

Part of the apparatus at the Combustion Research Facility, Livermore, USA, in which Raman spectroscopy is used to measure ambient flame pressure. 

Number of degrees of vibrational freedom for a non-linear molecule = 3m — 6 (3.5) 

For example, from eq. 3.6, the linear CO2 molecule has four normal modes of vibration and these are shown in Fig. 3.11. Two of the modes are degenerate-, i.e. they possess the same energy and could be represented in a single diagram with the understanding that one vibration occurs in the plane of the paper and another, identical in energy, takes place in a plane perpendicular to the first. 

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