Vibrational spectroscopy involves photons that induce transitions between vibrational states in molecules and solids, typically in the infrared IR frequency range from 2 to 12 X 10^13 Hz.
Two cases of frequency difference is given by V inc – V emit = Δ N Vº
Δ N = ± 1 is obeyed since the same IR selection rule
V inc > V emit corresponding to a Stokes line
V inc < V emit for an anti-Stokes line.
Infrared active vibrational modes arise from a change in the electric dipole moment µ of the molecule, while Raman active vibrational modes involve a change in the polarizability P = µ ind / E, where the electric vector E of the incident light induces the dipole moment µ ind in the sample. Some vibrational modes are IR active, that is measurable by IR spectroscopy, and some are Raman active.
FTIR and Raman spectroscopy measure the absorption of radiation by high-frequency (ie optical branch) phonon vibrations, and are also sensitive to the presence of particular chemical groups such as hydroxyl (-OH) methyl (-CH3) imido (-NH) and amino (-NH2). Each of these groups absorbs IR radiation at a characteristic frequency, and the actual frequency of absorption varies somewhat with the environment.
What is traditionally considered as Raman scattering of light or Raman spectroscopy, is spectroscopy in which the phonon vibration corresponding to the energy difference of incident light and emitted light, is an optical phonon of the type with a frequency of vibration in the IR region of the spectrum, corresponding to about ~ 400 cm-1, or a frequency of ~ 1.2 x 10^13 Hz. When a low frequency acoustical phonon is involved in the scattering of Raman type, then the process is referred to as Brillon scattering. Acoustic phonons can have frequencies of vibration or energies that are a factor of 1000 less than those of optical phonons. Typical values are ~ 1.5 x 10^10 Hz or ~ 0.5 cm-1. Brillon spectroscopy involves both Stokes and anti-Stokes lines, as does Raman spectroscopy.
For an infinitely long linear NACL lattice each atom vibrates with the same frequency (equation 7.3 page 198). However this is not true for a short chain. The results of calculation of the force constant of the Cl- ion as a function of its distance from the centre of the chain to the end for a 20-ion chain show that except for the end ion, the force constant gradually increases as the ions get closer to the end of the chain. This means the frequencies increase and the amplitudes of vibration decrease as the ions get closer to the end of the linear lattice. Each Cl- ion in the chain has a different force constant and therefore a different vibrational frequency (as do the Na+ ions), unlike the infinite chain. A consequence of this is that a spectroscopic measurement such as by Raman or IR will have broader lines in the nanosized materials compared to the bulk materials (below around 15 nm). The broadening is a result of overlap of lines from the slightly different frequencies of the different atoms or molecules in the materials having nanometer dimensions.
There is an important difference between a one dimensional nanostructure and a two or three dimensional structure. In the one dimensional case the number of atoms or ions at the end of the chain does not change as the chain gets shorter whereas in the higher dimensional nanostructures the number of atoms on the surface increases as the material becomes smaller in the nanometer regime ~ below 10 nm.
Source: Owen F J, Poole C P, The physics and chemistry of nanosolids, pp 66-72, and pp 197-207, WILEY, (2008)