Ethylene vibrational energy levels

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. 

The trends in metal ion-ethylene binding energies in Table 5 can be analysed as functions of basis set, theoretical level and metal ion. In contrast to the proton affinity calculation described above where zero-point energy difference contributed more than 6 kcalmoP to the final binding energy (BE) value, the vibrational frequencies in Table 7 show that the electronic energy part of the complex coordination energy will be reduced only by about... 

Table 13-3. Basis set dependence of activation (AEa) and reaction energies (AEr) computed using the B3LYP functional for the concerted gas-phase cycloaddition of ethylene to trans-butadiene [kcal/mol]. All calculations include zero-point vibrational contributions evaluated at the B3LYP/6-311+G(d,p) level.

The shape resonances described in the previous sections have all been associated with tt orbitals. Resonances formed by attachment into the O orbitals of unsubstituted hydrocarbons typically occur at high energy (E > 5 eV) and are usually broader than ir resonances. In compounds in which they are hard to discern in the total cross section, they may appear more readily in the cross sections for vibrational excitation, since direct excitation of vibration is weak, at least for levels which are not allowed optically, and hence the interfering background is small. Such broad 0 resonances, for example, have been observed in methane (42) and ethylene (22) using such measurements. 

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