Dear Yehya Boureghda,

The molecule can vibrate in different ways, and each way is called a vibrational mode.

Assignments mean you refer the observed peak in the spectrum to the possible correct modes.

The basic information in Wikipedia could help you

https://en.wikipedia.org/wiki/Infrared_spectroscopy

Best Regards

Dear Abdu Saeed ,

Thank you for the answer,

The vibration modes are, stretching, deformation..., associated to the bond between the atoms. However, Assignments is still unclear, because I found many researchers refer the assignments to specific molecules (lipids, proteins, sugar..), other authors merge the vibration mode and assignments.

Hi @Yehya Boureghda,

For any complex system with N atoms we have 3N-6 (non linear) or 3N-5 (linear) degrees of freedom that constitute the vibrational motion. Some of these are Raman active some are IR active. For the centrosymmetric molecules these modes never superpose. In complex system, we have different vibrational modes correspond to different type of atomic movements. These modes are generally characterized by the symmetry analysis in group theory. On the other hand, assistants are the short hand notation to indicate which atom (or group of atoms like benzene ring) is moving (stretching, bending etc) in a particular way.

Thanks.

Arka

Arka Bandyopadhyay Thank you

As mentioned above when you have a molecule with N atoms, you get 3N-6 (non-linear) or 3N-5 (linear) vibrational degrees of freedom, i.e. everything that is not a rotational or translational motion of the molecule as hole. Each normal mode is a linear combination of the cartesian displacements of each atom, in a way that when you consider only small displacements from the equilibrium position (the potential contains no higher terms than quadratic) a transformation to the normal mode coordinates diagonalizes both the kinetic and the potential energy (then, all normal modes are orthogonal). The normal modes are collective motions of ALL atoms in a molecule with a fix frequency but different phase and amplitude; and each mode has a certain symmetry associated with it, and that is why we use group theory to predict if these modes are IR and/or Raman active. The characteristic frequency of each normal mode is experimentally observable as a line position on the infrared spectra.

The assignment is the process of matching an observed frequency with a normal mode. Many times assignments are made to functional groups, as opposed to collective movements of ALL atoms. For example you might read that the CO stretch is about 1600 cm-1. This is just a normal mode where amplitudes are much higher for the set of atoms in the functional group than in the rest of the molecule.