Hi!

The activity of a mode can be deduced from the symmetry of the molecule/cristal you are looking. A molecule or a cristal belong to a point group symetry.

If you know the group, you know the active modes.

However calculating the intensities is complex and needs some quantum mecanics...

In one word: for ir, you need to vary the dipolar moment during vibration to be active. For raman it is the variation of the polarisability tensor...

My system Raman Active Modes are Ag,B1g,B2g,B3g as well IR active modes are B1u,B2u,B3u.I want to represent these modes in phonon spectrum. How It could be I am asking......

- Is your question "I want to label the bands I observe at some measured frequency in my IR and Raman spectra ?"

There is one example here by considering polarized/depolarized Raman bands:

http://faculty.uscupstate.edu/llever/Chem%20542/ShortCl2O4/GroupTheor.htm

Firstly, each phonon has different frequency at different q points (q is the phonon wave vector). To be able to identify the frequencies at a specific q point, momentum should be conserved, so:

ki=ks+q (ki,ks, being the incident and scattered light wave vector, respectively)

So for example for the Gamma point (q=0), ki=ks , forward scattering should be performed.

At each q point, the system has #atoms*3 degrees of freedom and frequencies. The symmetry of the modes can be found from the character table. In the last column of the character table, the symmetries are given in terms of Cartesian system and rotations. What do they mean? It means that the incident and the scattered wave should have the same symmetry; for example if the function for A1 irreducible representation(irrep) in c3v point group is x^2, it means the polarization of the incident and scattered wave should both be parallel to x, while in the E irrep, function xy means that incident and scattered weaves should have x and y polarization or vice versa.

Given that, we can assign the modes to each irrep.

How do we know if the modes are TO or LO?

We know that the dipole moment vector is along the vibration direction of the atoms, that means if dipole moment is parallel to the propagation direction q, the mode is LO and it is TO if the two vectors are perpendicular.

I hope it helps.