Breathing vibrations

Figure 6.13 Illustration of (a) rocking, (b) twisting, (c) scissoring and (d) wagging vibrations in a CH2 group. Also shown are (e) the torsional vibration in ethylene, (f) the ring-breathing vibration in benzene and (g) the inversion, or umbrella, vibration in ammonia...

Fig. 56. Contour plots of (a) shaking and (b) breathing vibrations coupled to hindered rotation around the three-fold axis. The MEP is shown.

From (6.31) it follows that coupling contributes to the Fg potential, even if the latter term is absent from the bare potential. Both shaking and breathing vibrations promote tunneling, but in... 

This explains the enhanced reactivity of D2 species toward water vapor compared to the structures responsible for the D1 and 430 cm 1 bands (Figure 7), which are assigned to ring breathing vibrations of unstrained four-membered and higher order rings, respectively. 

Dielectric constant of the medium n = Refractive index of the medium (Ae) = Charge transferred from one reactant to another /t and ff = jth normal mode force constants in the reactants and products respectively. Breathing vibrations are often employed and / = mean of the breathing force constants. 

A<7j = change in equilibrium value of the jth normal coordinate, and when breathing vibrations are employed... 

Many triazoles have been reported to have strong absorption bands in the region 1150-900 cm, which may be due to ring breathing vibrations. 

Fig. 12. Ligand-field potential curves of a Cr3+ ion in an octahedral field. Splittings are as in Figure 11, and Q is the breathing vibrational mode. Dq = Dqx s 1200 cm-1 at Q = 6eq(M2).

The infrared spectra of the mono-terpyridyl complexes have been analyzed. Sinha [307, 330—332] has found the breathing vibration of... 

Azo compounds. These compounds exhibit stretching of the —N=N— bond giving rise to only weak absorption near 1600 cm-1, which is shifted to lower frequency by conjugation. In aromatic compounds the band is generally masked by the aromatic ring breathing vibrations. 

Fig. 6.12. A Typical CARS signal trajectory revealing the particle number fluctuations of 110-nm polystyrene spheres undergoing free Brownian diffusion in water. The epi-detected CARS contrast arises from the breathing vibration of the benzene rings at 1003cm 1. B Measured CARS intensity autocorrelation function for an aqueous suspension of 200-nm polystyrene spheres at a Raman shift of 3050 cm-1 where aromatic C-H stretch vibrations reside. The corresponding translational diffusion time, td, of 20 ms is indicated. (Panel B courtesy of Andreas Zumbusch, adapted from [162])...

From (7.32) it follows that coupling contributes to the V6 potential even if the latter term is absent in the bare potential U(d>). Both shaking and breathing vibration promote tunneling, but in a different way. Shaking makes the effective barrier narrower, while breathing lowers it. Similar to Section 4.2, we define a parameter that characterizes the relative modulation of the barrier by breathing modes (C = 0) ... 

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