There is a group theory table for all point groups which defines the simmetry behaviour of every vibration of a molecule belonging to that point group. There are four possible letters: A, B, E, T that assign a vibration to a particular irreducible representation in a particular point group. A and B mean that the vibration is singly degenerate. E means that is doubly degenerate, and T triply degenerate.

When radiation interacts with a lattice it induces vibrations in the whole lattice, that can be longitudinal(L) or Transversal (T) and that can be low in energy (Acoustic) or high in energy (Optic).

There is a group theory table for all point groups which defines the simmetry behaviour of every vibration of a molecule belonging to that point group. There are four possible letters: A, B, E, T that assign a vibration to a particular irreducible representation in a particular point group. A and B mean that the vibration is singly degenerate. E means that is doubly degenerate, and T triply degenerate.

When radiation interacts with a lattice it induces vibrations in the whole lattice, that can be longitudinal(L) or Transversal (T) and that can be low in energy (Acoustic) or high in energy (Optic).

with addition of Anna's comment........

Degrees of freedom of lattice = 3n, n = no. of atoms per unit cell. Out of 3n, there are 3 acoustic branch and 3n-3 are optical branch. Depending on direction of vibration , this modes again classified into Longitudinal modes (LA, LO) and Transverse modes (TA, TO). Again, this vibrations may be in-plane(i) of out-of-plane(o), based on this, vibrations are iTO, oTO,iTA etc........

From phonon dispersion curve, you can identify the modes.

just go through the "vibrational modes of linear mono- and di- atomic chain"

Thank you very much! but if you would elaborate few things like as, How to identify longitudinal or transverse modes from Raman data? is there any method or any trick which gives the information about its direction?

Yes. I'm not expert on that area but from phonon dispersion curve, you can tell this. at k=0 and 2(pi), w=0 for accoustic bands. Higher frequency corresponds to Longitudinal mode and lowers are transverse mode for that specific branch. To clear it, I attached phonon dispersion curve of graphene, look on that.

If you know high and low frequency relative permittivities of the system, LO and TO modes can be calculated directly from Lydanne-Sachs-Teller relation. These modes, are normally size independent. With size reduction, a surface optic mode (SO) appears in between these modes (typically, at the left asymmetric part of LO mode) which can be probed using Klein's equation. However, I do not know how the irreducible representation scheme can be linked to all these standard modes. Please write if someone has worked on it.

If it can be usefull, I would like to add some about the notation Ag or Bg or Eg. As it has been before said, Group Theory applied to molecular vibrations uses a notation in which a one-dimensional (which describes a non-degenerate mode) representations are denoted by A or B, a two-dimensional representations (which decribe a doubly degenerate) with E, and three-dimensional representations (which decrobes a doubly degenerate) with T. If a one-dimensional vibration modes is symmetric respect to the principal symmetry axis Cn, the mode is denoted by A. It means that the matrix describing the rotatio@n of the molecule around the Cn axis has a trace = 1. But If a one-dimensional vibration modes is anti-symmetric respect to the principal symmetry axis Cn, the mode is denoted by B. It means that the matrix describing the rotation of the molecule around the Cn axis has a thace = -1.

On the other hand, no matter the degeneration of the mode, a subsript in the respective letter 1 or 2 is used, depending on the mode is symmetric or anti-symmetric with respect to a rotation around a two-fold axis (C2) normal to Cn.

Finnlally, another subscript “g” or “u” accompanies to 1 o 2, depending on the mode is symmetric or anti-symmetric with respect to the inversión of coordinate.

Excuse me Dr.F.R.Perez, F. R. Pérez

The question now is HOW can we identify that the mode is A or B or E is there is a specific equation coming form the group theory that can be used to identifiy each raman peak?

Thanks in advance F. R. Pérez