Why we describe Raman modes At perticular wave number by E1 or A1,A2 or other If E1 say at 645cm^{-1}, Why we cannot describe A1 at this wave number. How we write the representation at perticlar wave number. Please reply.
These labels refer to the representation of the molecular point group. The vibrational ground state always transforms as A1 and the excited state with one vibrational quantum transforms as some representation of the molecular symmetry group, e.g. E1. Then the excitation of one quantum of this vibration corresponds to an energy difference ##\Delta E=E_\mathrm{E1}-E_\mathrm{A1}=hc \tilde{\nu} ## where ##\tilde{\nu}## is the wavenumber of the Raman transition.
Actually i am discussing about the space group symmetry of crystalline material how this mode assign for this name i.e, E1,A1, at particular wave number. Why these mods name come and what terminology behind this.Please clarify
In crystalline media, the labels refer to the representation of the little group pertaining to the wavevector k. In Raman spectroscopy k=0, and that little group is identical to the crystallographic point group. The labels of the irreducible representations depend on the point group and are standardized. You have to look them up. For example A is a one-dimensional representation, E two dimensional and T three dimensional. In Raman spectroscopy they refer to the symmetry of the vibration being exited. One quantum of vibration has a fixed energy, hence the asignment of a symmetry label to a wavelength.
Ok Sir i agree with you...But For my System Aluminium Nitride There Are Number of mode in which A1,E1,E2 are raman active and E1 at 624 cm^{-1} and A1 546 cm^{-1}, Why E1 cannot written at the place of 546 and A1 at 624???
I think the representation can be worked out experimentally from the polarisation and intensity of the incident and scattered light. For details you should have a look at some book on IR and Raman spectroscopy.