Stretching vibrations normal mode limit

Initially excited In the normal mode that Is predominately a CO stretch In the small displacement limit. The curves show the energy In each of the three vibrational normal modes averaged over an ensemble of 50 trajectories. This ensemble was chosen using a method developed by Hase and co-workers (21). Each trajectory In the ensemble was chosen so that both the normal mode which Is predominately CS stretch (about 80% CS character) as well as the bend normal mode have zero point energy. The normal modes were resolved in the usual way (22) and the energy In each normal mode Is defined as E (P + u Q ), where (o Is the frequency of the normal... 

A model atom approximation is permitted if all of the stretching vibrations of the molecule are ascribed to the local-mode limit. In the normal-mode limit, using the effective Hamiltonian of the whole molecule is preferable, as was shown in the example of CH3CI and CH3F. 

The fitted and calculated vibrational frequencies and normal mode composition factors corresponding to the 17 most important NIS bands are presented in Table 5.9. It is evident that the vibrational peaks in the calculated NIS spectrum are typically 0-30 cm lower than to the experimental values. In the calculated NIS spectra, there are two small peaks at 635 and 716 cm (Fig. 5.14b) that are not visible in the experimental spectrum. According to the normal mode calculations these are Fe-N-N and Fe-O-C deformation vibrations. Small admixtures of Fe-N and Fe-O stretching modes account for the calculated nonzero normal mode composition factors. Although the calculated relative intensities are slightly above detection limit dictated by the signal-to-noise ratio, they are determined by values of pea which are very small (0.028 and 0.026 for the peaks at 635 and 716 cm ). They must be considered to be within the uncertainties of the theoretical... 

The procedure of interpreting data concerning the molecule OPCl is described as an example. Fig. 4.4-3 shows the infrared spectrum of matrix-isolated OPCl with the two stretching vibrations at 1237.7 ( /(PO)) and at 489.4 cm (z/(PCl)). The deformation mode, of much lower intensity, lies at 308.0 cm. By using the precursor P OCl3, the absorptions are shifted to 1211.8, 484.7, and 298.0 cm respectively. These data confirmed the assignment of vibrations and the assumed sequence of the atoms O-P-Cl. Furthermore, by means of a normal coordinate analysis it was possible to limit the bond angle to a value of 105°, which is in accordance with the results of quantum-mechanical calculations. 

CD measurements penetrate to lower frequencies, the fundamental difficulty mentioned above does not appear to be a serious limitation since large effects are still observed this might be due to the fact that deformation coordinates, which can generate much larger vibrational optical activity than stretch coordinates, start to make significant contributions to the normal modes. Several recent reviews discuss infrared CD and ROA from a unified standpoint5 8). 

If the Hamiltonian now contains the Casimir operators of both G, and G[, which do not commute, then the labels of neither provide good quantum numbers. Of course, in general such a Hamiltonian has to be diagonalized numerically. In this way one can proceed to break the dynamical symmetries in a progressive fashion. In (61) all the quantum numbers of G, up to G remain good. If we add another subalgebra beside Gz only those quantum numbers provided by G, on will be conserved, etc. In applications, the different chains are found to correspond to different limiting cases such as the normal versus the local mode limits for coupled stretch vibrations (99). 

Figure 2.1. Schematic stretching vibrational energy levels for the water molecule. The levels on the left side represent the normal mode Umit and are indicated with quantum numbers Vi, 1)3. The levels on the right side represent the local mode limit, and they are labeled with the quantum numbers m,n. The true energy levels are shown in the center of diagram. From reference 53. Reproduced by permission from Elsevier Science B.V.

Because the C—H stretching modes exhibit the characteristics of good group frequencies, this collection of vibrations is found to occur over a relatively narrow wavenumber range of about 130 cm (2970-2840 cm ). Indeed, in the normal series the individual peaks occur within ranges as narrow as 5 cm. This is, of course, a rather limited number of substances. 

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