Vibrational energy levels individual molecules

When IR and Raman spectroscopic techniques are used in combination, the resuits are much greater than with the use of either technique individually. The combined use of IR and Raman spectroscopy extracts most of the obtainable information (silent, or optically inactive, modes and extremely weak modes are not detected). The complementary nature of the IR and Raman data has important practical applications. This complementary nature arises from the differences in selection rules governing the vibrational energy levels. For molecules with a center of symmetry (there are identical atoms on either side of the center of symmetry), no vibrational frequencies are common to the IR and Raman spectra. This principle is called the mutual exclusion principle. Although symmetry might be considered important for low-molecular-weight substances like ethylene and benzene (both of which have a center of symmetry), polymers are not usually expected to have a center of symmetry. Polyethylene has a center of symmetry, and the observed IR and Raman lines do not coincide in frequency (see Fig. 5.1). Theory predicts that eight modes for polyethylene are active in the Raman while only five in the infrared. 

Once you have calculated an ab initio or a semi-empirical wave function via a single point calculation, geometry optimization, molecular dynamics or vibrations, you can plot the electrostatic potential surrounding the molecule, the total electronic density, the spin density, one or more molecular orbitals /i, and the electron densities of individual orbitals You can examine orbital energies and select orbitals for plotting from an orbital energy level diagram. 

Intermolecular lateral interactions and resulting collectivized vibrations of individual adsorbed molecules greatly add to the complexity of description for local vibrational excitations in adsorbates. Fig. 4.5 schematically demonstrates that these interactions on a simple planar lattice of adsorbed molecules which vibrate with high (toh) and low (co/) frequencies lead to the emergence of the corresponding energy bands, with energy levels classified by the wave vector K. 

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