Vibrations, bond-bending

In the following compilation the hydrogen bond bending vibrations are given the symbol <5(RXH YR ) rather than <5(XH Y) to avoid confusion with <5XH, These vibrations are related to torsional vibrations of the separate molecules RXH and YR and only occur in the presence of the groups R and R. ... 

The application of Stepanov s theory to intramolecular F bonded systems has been criticized [42], In this case the low frequency vibration described above as vXH Y is also partly constrained by a more nearly harmonic vibration involving skeletal bending motions of the rest of the molecule, and the X, H, and Y atoms are not collinear. These factors would seem to suggest that (I) the vXll Y type of vibration will be of higher frequency than in the usual case (perhaps 200-300 cm"1 rather than 100-200 cm"1) so that the sub-bands will be more widely spaced and may not be recognised as part of the rXH band (2) the motion of the H atom will have less effect on rXY and (3) H-bond bending vibrations may also couple considerably with vXH. The observation of rather smaller frequency shifts for vXR and narrower absorption bands w such cases are in reasonable agreement with this picture,... 

These molecules possess three fundamental vibration frequencies two bond stretching (symmetric and asymmetric and one doubly degenerate bond bending vibration, (Figure 7). The symmetrical... 

The potential energy of a single atom has to account for all the interaction energies with the atoms of the molecule, with those of the zeolite wall, and also for the internal bond bending, vibration, etc. Dual interactions are calculated... 

In an atomic level simulation, the bond stretch vibrations are usually the fastest motions in the molecular dynamics of biomolecules, so the evolution of the stretch vibration is taken as the reference propagator with the smallest time step. The nonbonded interactions, including van der Waals and electrostatic forces, are the slowest varying interactions, and a much larger time-step may be used. The bending, torsion and hydrogen-bonding forces are treated as intermediate time-scale interactions. 

This Schrodinger equation forms the basis for our thinking about bond stretching and angle bending vibrations as well as collective phonon motions in solids... 

Different motions of a molecule will have different frequencies. As a general rule of thumb, bond stretches are the highest energy vibrations. Bond bends are somewhat lower energy vibrations and torsional motions are even lower. The lowest frequencies are usually torsions between substantial pieces of large molecules and breathing modes in very large molecules. 

Table 6.3 lists a number of group vibration wavenumbers for both bond-stretching and angle-bending vibrations. 

A2) In spite of the high individual frequencies, bond length and bond angle vibrations participate in quasi-classical low frequency collective normal modes. Bond angle bending is necessary for the flexibility of five-membered rings, which plays a key role in the polymorphism of nucleic acids. 

The wavenumber of the totally symmetric bending vibration, dsss> of S rings (n = 6, 7, 9, 10, 12), on the other hand, is mainly a function of the ring size and not a function of the quite different bond angles in these molecules, as one may expect. The empirically obtained relation is given by... 

In summary, NIS provides an excellent tool for the study of the vibrational properties of iron centers in proteins. In spectroscopies like Resonance Raman and IR, the vibrational states of the iron centers are masked by those of the protein backbone. A specific feature of NIS is that it is an isotope-selective technique (e.g., for Fe). Its focus is on the metal-ligand bond stretching and bending vibrations which exhibit the most prominent contributions to the mean square displacement of the metal atom. 

Bending vibrations (8) changing bond angles but leaving bond lengths unaltered. 

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