Vibration rocking

The effect of the AK = 1 selection rule, compared with AK = 0 for an transition, is to spread out the sets of P, Q, and R branches with different values of K. Each Q branch consists, as usual, of closely spaced lines, so as to appear almost line-like, and the separation between adjacent Q branches is approximately 2 A — B ). Figure 6.29 shows such an example, E — A band of the prolate symmetric rotor silyl fluoride (SiH3F) where Vg is the e rocking vibration of the SiH3 group. The Q branches dominate this fairly low resolution specttum, those with AK = - -1 and —1 being on the high and low wavenumber sides, respectively. 

Figure 1 illustrates the IR spectra of NBR and HNBR samples with different concentrations of residual double bonds [11]. The CN stretching vibration is observed at 2222 cm in NBR and HNBR. The peak at 1440 cm is for C—H deformation of —CH2— groups. The =C—H out of plane deformations of trans, vinyl, and cis double bonds are observed at 970 cm", 920 cm", and 730 cm", respectively. These peak absorbances decrease gradually, and a new peak at 723 cm" appears on the spectrum of HNBR for—CH2— rocking vibration [when (CH2)n n > 4] [11,78]. The CN stretching vibration is taken as an internal standard and the... 

Figure 9. Calculated normal modes of the two key bands of the TT and GT forms of the bmim" cation. The arrows indicate vibrational amphtudes of atoms. The CH2 rocking vibration of the Cg methylene group are surrounded by a circle.

Figure 3. Structures of PuRs and PjRj as examples for substituted polyanions. The IR spectra of the compounds PyiMme ) with M = Si, Ge, Sn, and Pb show the nearly unchanged fundamental vibrations of the Py skeleton (black-filled), the shifts of v(P-M) (black star), and of f(M-C ) (white star), and the CH rocking vibrations (not marked).

Figure 12.8 Calculated normal modes of key bands of the AA and GA forms of the [C4CiIm]+ cation. The arrows indicate vibrational amplitudes of atoms. The C8 methylene group is surrounded by a circle. Obviously it appears that the CH2 rocking vibration is coupled to the ring modes only for the GA conformer, thereby lowering the frequencies. (Adapted from Hamaguchi, H., and Ozawa, R., Adv. Chem. Phys., 131, 85-104,2005. With permission.)...

The band resulting from the methylene rocking vibration (p CH2), in which all of the methylene groups rock in phase, appears near 720 cm-1 for straight-chain alkanes of seven or more carbon atoms. This band may appear as a doublet in the spectra of solid samples. In the lower members of the w-alkane series, the band appears at somewhat higher frequencies. 

Assignments have been made for a few of the more prominent and reliable in-plane bending vibrations. The vinyl group absorbs near 1416 cm-1 because of a scissoring vibration of the terminal methylene. The C—H rocking vibration of a cis-disubstituted alkene occurs in the same general region. 

An interesting comparison can be made on the basis of the hydrogen distribution of the three macerals. The aromatic hydrogen content (%H.r) has been calculated from the total area of the infrared absorption between 11 and 14 n (aromatic HCC rocking vibrations) (6). The aliphatic hydrogen content (% H.i) has been derived from the absorption of the aliphatic H-C stretching vibration between 3.3 and 3.6 m (7). The values found for the three macerals under investigation are reported in Table II, columns 3 and 4. 

The geometry of the vinylidene molecule is such that the MEP coincides with the direction of the CH2 rocking vibration. The two hydrogen atoms are initially equivalent, so there are two equivalent paths of decay, and the potential along MEP corresponding to this picture can be modeled by a polynomial ... 

It is assumed that the degrees of freedom of TCad include vibrations that are close to the vibrations of the noninteracting B and A/s/, two surface-restricted rotations corresponding to the soft rocking vibrations of B in AB/s/, and rB free rotations similar to the rotations of free B as a whole, where... 

Here, ez roc is the zero-point energy of the two soft rocking vibrations mentioned above cot the frequency of the normal mode of AB/s/ corresponding to the reaction coordinate a, aa/s/> and aB the Helmholtz free energies of the internal degrees of freedom of AB/s/, A/s/, and B amc the Helmholtz free energy of the two soft rocking vibrations mentioned above. 

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