Umbrella motion

Figure 2.11 A plot of the potential energy function V = kx2 + be cusing appropriate values of b and c, to describe the umbrella motion in ammonia...

The CD axis now corresponds to the symmetry axis of CZ3 and is described by the unit vector s. The umbrella motion of the CZ3 group and its rotation is described by two internal angles , the angle between a CZ bond and the symmetry axis S, and the rotation angle 2 of CZ3 about S. The angles (px and are also known as the... 

Certain particular failures should be noted. The frequency of the out-ofplane symmetric vibration of CH3 was found to be too low for all the DFT methods. The same is also true for the three ab initio methods. For the umbrella motion of NH3, too high a value is found by all methods. For the symmetric bending vibration of C2H2, all of the theoretical values except HF are too low. 

For the molecule PF5, we could find no evidence of turnstile rotation for PF5, and concluded that umbrella motion was highly improbable. 

Fig. 7 HREELS of the methylated Si(in). HREELS incident electron energy 2.84 eV, incident angle = exit angle = 60° from the surface normal. The full width at half maximum of inelastic peak = 7.6 meV. 2944 cm C—H stretching, 1423 cm CHj umbrella motion, 1268 cm CH3 asymmetric bending, 1099 cm Si—O stretching in Si02, 789 cm CH3 rocking,...

An example of an activation barrier is provided by the ammonia umbrella motion (Figure 4.10). The motion of the nitrogen atom through the plane of the three hydrogens is related to a comparatively low activation barrier. 

FIGURE 4.10 Umbrella motion vibration in the ammonia molecule. 

Figure 3-15. Example of a dynamical situation of a polyme ylene chain -(CH2)n- which contains defects consisting of CDt groups and of CH3 units at either ends. The motion of CD2 rocking occurs in a gap and does not couple with the host lattice, thus generating localized modes on the contrary the frequencies of both external deformation and umbrella motions of the CH3 group occur in the frequency range spanned by the dispersion curves of the host lattice coupling takes place and resonance modes are generated.

Here R, r and are the translational coordinate, pseudo vibration coordinate and umbrella motion coordinate, respectively, j, and L are the rotational angular momentum of CH4, the projection operator of j along the 2-axis in the body-fixed (BF) frame and the orbital angular momentum. 

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