Vibration /vibrations bond-stretching

Molecular mechanics calculations use an empirically devised set of equations for the potential energy of molecules. These include terms for vibrational bond stretching, bond angle bending, and other interactions between atoms in a molecule. All of these are summed up as follows ... 

Velocity-modulated allosteric regulation, V, ,-TYPE ALLOSTERIC SYSTEM VENOM EXONUCLEASE Venom phosphodiesterase, PHOSPHODIESTERASES VESICLE TRANSPORT IN CELLS Vibrational bond stretching mode,... 

Stationary point geometries on Bi So and Tj surfaces are presented in Figure 4.14. The crystal structure of t-Bi shows it to be strictly planar, eliminating phenyl-vinyl torsion toward planarity as a crucial NVET reaction coordinate. The authors emphasized that while experiment and theory support the initial proposition that double-bond torsion is the key reaction coordinate enabling NVET to stilbenes, as multidimensional surfaces are involved, other vibrations, including bond stretching, will also contribute. 

The simplest molecular vibrations are bond stretchings. Besides stretching, there are other vibrational modes, for instance vibrations of changing the angle between bonds. Let us analyze the vibrations of a molecule of water. As shown in the next scheme, there are two vibrational modes for bond stretching Vi and V2 and one vibrational mode for the angle change V3. 

Hence, the shape of the mountain pass is representative of the entropy changes along the reaction coordinate. The entropy changes are in turn related to changes in vibrational states (bond stretches, bends, wags, etc.) of the molecular structures. If vibrations (degrees of... 

Rubahn, H. G. and K. Bergmann (1990). The effect of laser-induced vibrational bond stretching in atom-molecule collisions. Ann. Rev. Phys. Chem. 41, 735. 

The vibrational form can be described by specifying the relative amplitudes of the Cartesian displacements of each mass (Fig. 7). The vibration can also be described in terms of the relative changes in the internal coordinates of the molecule, namely, changes in the bond lengths and bond angles. For example, in Fig. 7 the CO2 molecule has two bonds in one vibration, both bonds stretch at the same time (inphase stretch), whereas in another vibration one bond stretches while the other bond contracts (out-of-phase stretch). There are two mutually perpendicular bending vibrations that have the same frequency. 

Figure 1, Coordinates used for describing the dynamics of a) H -I- H2 (6) NOCl, (c) butatriene, (a), (b) Are Jacobi coordinates, where and are the dissociative and vibrational coordinates, respectively, (c) Shows the two most important normal mode coordinates, Qs and Q a, which are the torsional and central C—C bond stretch, respectively.

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. 

In this article we describe an extension of SISM to a system of molecules for which it can be assumed that both bond stretching and angle bending describe satisfactorily all vibrational motions of the molecule. The SISM presented here allows the use of an integration time step up to an order of magnitude larger than possible with other methods of the same order and complexity. 

For the model Hamiltonian used in this study it was assumed that the bond stretching and angle i)ending satisfactorily describe all vibrational motions... 

SISM for an Isolated Linear Molecule An efficient symplectic algorithm of second order for an isolated molecule was studied in details in ref. [6]. Assuming that bond stretching satisfactorily describes all vibrational motions for linear molecule, the partitioned parts of the Hamiltonian are... 

Intensive use of cross-terms is important in force fields designed to predict vibrational spectra, whereas for the calculation of molecular structure only a limited set of cross-terms was found to be necessary. For the above-mentioned example, the coupling of bond-stretching (f and / and angle-bending (B) within a water molecule (see Figure 7-1.3, top left) can be calculated according to Eq. (30). 

Figure 7-13. Cross-terms combining internal vibrational modes such as bond stretch, angle bend, and bond torsion within a molecule.

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

When the above analysis is applied to a diatomic species such as HCl, only k = 0 is present since the only vibration present in such a molecule is the bond stretching vibration, which has a symmetry. Moreover, the rotational functions are spherical harmonics (which can be viewed as D l, m, K (Q,< >,X) functions with K = 0), so the K and K quantum numbers are identically zero. As a result, the product of 3-j symbols... 

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. 

Even with this simple model it is clear that if one of the nuclei is given a sudden displacement it is very likely that the whole molecule will undergo a very complicated motion, a Lissajous motion, consisting of a mixture of angle-bending and bond-stretching. The Lissajous motion can always be broken down into a combination of the so-called normal vibrations of the system which, in the Lissajous motion, are superimposed in varying proportions. 

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

Table 6.3 Typical bond-stretching and angle-bending group vibration wavenumbers co...

Just as group vibration wavenumbers are fairly constant from one molecule to another, so are their intensities. For example, if a molecule were being tested for the presence of a C—F bond there must be not only an infrared absorption band due to bond-stretching at about 1100 cm but also it must be intense. A weak band in this region might be attributable to another normal mode. 

Figure 9.29 shows that the most important inducing vibration is V14/ a b2u vibration involving stretching and contracting of alternate C-C bonds in the ring. Using Table A.32 in Appendix A for the 14q transition, Equation (9.24) becomes... 

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