Bonds bending

To gain deeper insights into which constraints are relevant from those which are irrelevant, we follow a given angle individually during the course of the simulation 

Having set the basis of Molecular Dynamics based topological constraint counting, we now review certain results obtained within this new framework. 

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Stretching, bond bending, torsions, electrostatic interactions, van der Waals forces, and hydrogen bonding. Force fields differ in the number of terms in the energy expression, the complexity of those terms, and the way in which the constants were obtained. Since electrons are not explicitly included, electronic processes cannot be modeled. 

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. 

A deformation due to bond bending and stretching which is effectively instantaneous and independent of temperature (ordinary elastic deformation, oe)-... 

The volumes of activation for some additions of anionic nucleophiles to arenediazonium ions were determined by Isaacs et al. (1987) and are listed in Table 6-1. All but one are negative, although one expects — and knows from various other reactions between cations and anions — that ion combination reactions should have positive volumes of activation by reason of solvent relaxation as charges become neutralized. The authors present various interpretations, one of which seems to be plausible, namely that a C — N—N bond-bending deformation of the diazonium ion occurs before the transition state of the addition is reached (Scheme 6-2). This bondbending is expected to bring about a decrease in resonance interaction in the arenediazonium ion and hence a charge concentration on Np and an increase in solvation. 

Arbabi, S Sahimi, M, Elastic Properties of Three-Dimensional Percolation Networks with Stretching and Bond-Bending Eorces, Physical Review B 38, 7173, 1988. 

Although the estimated and actual interhybrid angles agree well in all cases (within 1°), there is evidence of significant bond bending in the actual bond angles (e.g., 6° mismatch in the O—C—P angle). 

As examples of the previous section have shown, bond hybrids are sometimes misaligned with respect to the line of centers between nuclei, a condition described as bond bending. Such bending may be considered to represent the influence of factors other than Bent s rule. In this section we examine the origin and characteristics of bond bending. 

Hyperconjugative interactions (Section 3.4.2) are another factor leading to bond bending. Such interactions are associated with the stereoelectronic influence of more remote bonds or lone pairs, particularly those anti (trans) to the bond of... 

Figure 3.22 Bond bending, A0 = 6>nuciei - 6>nho, in CH2F—NH2 for C—F (circles, solid line), C—Hanti (squares, dotted line), and C—Hsyn (triangles, dotted line) bonds as the amine group is twisted from 0(lp—N—C—F) = 0° to 180° ( lp denotes the bisector of the H—N—H angle).

Figure 3.23 Bond bending in umbrella inversion vibration of NH3 (circles, solid line) and PH3 (squares, dotted line), comparing the lp—A—H umbrella angle for nuclei (0nuciei) and hybrids ( nho)- An inscribed triangle marks the equilibrium geometry for each molecule, and the dashed line marks the limit of perfect orbital...

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