Spectrum infrared, selection rule

Similar to the case of infrared spectrum, the selection rule for the Raman spectrum is determined by the integral... 

Polyatomic molecules vibrate in a very complicated way, but, expressed in temis of their normal coordinates, atoms or groups of atoms vibrate sinusoidally in phase, with the same frequency. Each mode of motion functions as an independent hamionic oscillator and, provided certain selection rules are satisfied, contributes a band to the vibrational spectr um. There will be at least as many bands as there are degrees of freedom, but the frequencies of the normal coordinates will dominate the vibrational spectrum for simple molecules. An example is water, which has a pair of infrared absorption maxima centered at about 3780 cm and a single peak at about 1580 cm (nist webbook). 

A second, independent spectroscopic proof of the identity of 4 as rans-[Mo(N2)2(weso-prP4) was provided by vibrational spectroscopy. The comparison of the infrared and Raman spectrum (Fig. 7) shows the existence of two N-N vibrations, a symmetric combination at 2044 cm-1 and an antisymmetric combination at 1964 cm-1, indicating the coordination of two dinitrogen ligands. In the presence of a center of inversion the symmetric combination is Raman-allowed and the antisymmetric combination IR allowed. The intensities of vs and vaK as shown in Fig. 2 clearly reflect these selection rules. Moreover, these findings fully agree with results obtained in studies of other Mo(0) bis(dinitrogen)... 

The dipole and polarization selection rules of microwave and infrared spectroscopy place a restriction on the utility of these techniques in the study of molecular structure. However, there are complementary techniques that can be used to obtain rotational and vibrational spectrum for many other molecules as well. The most useful is Raman spectroscopy. 

In polymers the infrared absorption spectrum is generally very simple, considering the large number of atoms that are involved. This simplicity is due to the fact that many of the normal vibrations have almost the same frequency and so appear in the spectrum as one absorption band and, also from the strict selection rules that avoid many of the vibrations from causing absorptions. 

The differences in selection rules between Raman and infrared spectroscopy define the ideal situations for each. Raman spectroscopy performs well on compounds with double or triple bonds, different isomers, sulfur-containing and symmetric species. The Raman spectrum of water is extremely weak so direct measurements of aqueous systems are easy to do. Polar solvents also typically have weak Raman spectra, enabling direct measurement of samples in these solvents. Some rough rules to predict the relative strength of Raman intensity from certain vibrations are [7] ... 

It should also be remembered that the selection rules derived here are relevant to the free molecule and may break down in the liquid or solid state. This is the case, for example, with the electric dipole forbidden 4g transition in ethylene, where v4 is the au torsional vibration shown in Figure 6.23. It is not observed in the infrared spectrum of the gas but is observed weakly in the liquid and solid phases. 

Figure 9.24 shows part of the laser Stark spectrum of the bent triatomic molecule FNO obtained with a CO infrared laser operating at 1837.430 cm-1. All the transitions shown are Stark components of the qP1 8) rotational line of the I,1, vibrational transition, where v, is the N-F stretching vibration. The rotational symbolism is that for a symmetric rotor (to which FNO approximates) for which q implies that AK = 0, P implies that AJ = — 1 and the numbers indicate that K" = 7 and J" = 8 (see Section 6.2.4.2). In an electric field each J level is split into (J + 1) components (see Section 5.2.3), each specified by its value of Mj. The selection rule when the radiation is polarized perpendicular to the field (as here) is AMj = 1. Eight of the resulting Stark components are shown. 

Rigid Molecule Group theory will be given in the main part of this paper. For example, synunetry adapted potential energy function for internal molecular large amplitude motions will be deduced. Symmetry eigenvectors which factorize the Hamiltonian matrix in boxes will be derived. In the last section, applications to problems of physical interest will be forwarded. For example, conformational dependencies of molecular parameters as a function of temperature will be determined. Selection rules, as wdl as, torsional far infrared spectrum band structure calculations will be predicted. Finally, the torsional band structures of electronic spectra of flexible molecules will be presented. 

From the G36 NRG character table, (Table 8), and Table 14, Selection Rules for the electric dipole transitions in the Far Infrared Spectrum of acetone may be easily deduced. They are given in Table 15. 

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