Elementary Theory of Vibrational Spectroscopy

The decomposition of coupled harmonic oscillators into a collection of independent oscillators is known as a normal mode expansion and the independent oscillators are called normal modes. Normal modes are defined as modes of vibration where the respective atomic motions of the atoms are in harmony , i.e., they all reach their maximum and minimum displacements at the same time. These normal modes can be expressed in terms of bond stretches and angle deformation (termed internal coordinates) and can be calculated by using a procedure called normal coordinate analysis. 

Our primary interest is in determining the structure of polymers so we need to understand the molecular basis of vibrational spectroscopy as a structural tool (a.4). The vibrational energy levels can be calculated from first principles by using a technique called normal coordinate analysis (a.5), and as a result some of the factors influencing spectra have been discovered. 

A normal vibrational mode in a molecule may give rise to resonant IR absorption (or emission) of electromagnetic radiation only when the transition is induced by the interaction of the electric vector, E, of the incident beam with the electric dipole moment, Pi, of the molecule. That is, the dynamic dipole moment of the ith normal mode, 8pi/8qj or Pi, is nonzero. The intensity of the transition is proportional to the square of the transition dipole moment, i.e., the matrix element of the electric dipole moment operator between the two quantised vibrational levels involved. 

Vibrational techniques are particularly sensitive to the structure of the macromolecules. A vast literature exists from which group frequencies have been correlated with structural components of the molecules (a.6). 

Raman scattering is envisaged as the process of reradiation of scattered light by dipoles induced (P) in the molecules by the incident light and modulated by the vibrations of the molecules (a.3). In normal Raman scattering by molecules in isotropic media, the dipoles are simply those that result from the action of the electric field component, E, of the incident light on the molecules, 

---