Torsional rotation

The functional form for dihedral angle (torsional) rotation is identical to that shown in equation (13) on page 175. The barrier heights are in kcal/mol and are in the file pointed to by the Fouri-erTorsion entry for the parameter set in the Registry or the chem. ini file, usually called tor.txt(dbf). If more than one term is... 

Figure 29. Docking of an alkylated base into Z-DNA and torsion of the PAH group, (a, b) Two views of the alkylated base (as determined by X-ray diffraction techniques) docked onto the syn-guanine group in Z-DNA. (c, d) Two views of the same modelling experiment with a torsional rotation of 180 about C6-N6. Note how the curvature of the PAH group conforms to that of the helix. This is a model of the carcinogen lying in a groove of DNA.

D. Rueda, O. V. Boyarkin, T. R. Rizzo, I. Mukhopadhyay, and D. S. Perry, Torsion rotation analysis of OH stretch overtone torsion combination bands in methanol. J. Chem. Phys. 116,... 

R. H. Hunt, W. N. Shelton, F. A. Flaherty, and W. B. Cook, Torsion rotation energy levels and the hindering potential barrier for the excited vibrational state of the OH stretch fundamental band V of methanol. J. Mol. Spectrosc. 192, 277 293 (1998). 

The operation that interconverts stereoisomeric planes can be viewed as a ir rotation of the plane that breaks the bond(s) between the plane and the extraplanar atom(s) and then restores it (or them) in a sterically different way. The axes of this rotation pass through the center of the unsaturated system. As they are infinite in number (46) they cover the plane and in a sense define it. Although several of these axes coincide with bonds, the operation differs profoundly from that characteristic of a line of torsion. Rotation of the plane causes a change in bonding, whereas torsion about a line alters the torsional angles between the ligands that are attached to the terminal atoms of the bond that defines the line. 

Y, and Z are connected by bonds of fixed length joined at fixed valence angles, that atoms W, X, and Y are confined to fixed positions in the plane of the paper, and that torsional rotation 0 occurs about the X-Y bond which allows Z to move on the circular path depicted. If the rotation 0 is "free such that the potential energy is constant for all values of 0, then all points on the circular locus are equally probable, and the mean position of Z, i.e., the terminus of , lies at point z. The mean vector would terminate at z for any potential function symmetric in 0 for any potential function at all, except one that allows absolutely no rotational motion, the vector will terminate at a point that is not on the circle. Thus, the mean position of Z as seen from W is not any one of the positions that Z can actually adopt, and, while the magnitude ll may correspond to some separation that W and Z can in fact achieve, it is incorrect to attribute the separation to any real conformation of the entity W-X-Y-Z. Mean conformations tiiat would place Z at a position z relative to the fixed positions of W, X, and Y have been called "virtual" conformations.i9,20it is clear that such conformations can never be identified with any conformation that the molecule can actually adopt... 

When determining the range of likely helical shapes from intrinsic properties of amylose, this variability in monomer shape is almost as important as hindered rotation about the bonds linking the monomers. This conclusion is supported by conformational analyses of maltose such as shown in Figure 5 of the introductory chapter of this book. There are relatively small ranges (about 40 ) of allowed torsional rotation within one kcal/mol of the minimum (one must correct for the fact that there are two glucose residues in maltose when making such a coiqparison). ... 

In analyzing the conformational properties of carbohydrates, it has often been the practice to consider individual monomer rings to be rigid units, with the only molecular flexibility lying in torsional rotations about the linkage bonds. 

Torsional rotations around single and mulitple bonds are different processes. In a multiple bond a torsional rotation results in the transformation of one isomer into another. In contrast, rotation around single bonds leads to interconversion of conformed (Fig. 2.9). In the latter case, repulsion of the substituents is modeled by van der Waals interaction (see below) and the torsional potential describes the additional electronic component, including distortion of the molecular orbitals and repulsion by the electron clouds. 

It is common practice to describe torsional rotations around single bonds and those around multiple bonds with the same type of potential function but with very different force constants. The function must be able to describe multiple minima. Generally, a Fourier expansion of the torsional angle with only cosine terms is used (Eq. 2.23),... 

The chain conformation of a macromolecule is determined by the torsional angles assumed by the backbone bonds. By convention, the angles 0°, 0° are used to define a trans-trans-planar conformation as shown in Figure 3.9a. Torsion (rotation) of bonds 2 and 4 in Figure 3.9a by 180° generates the cis-trans-plmar conformation (Figure 3.9b). 

In calculating molecular Sis, Burt and Richards allowed intramolecular rotations about the torsional bonds of moving molecules [110], Thus, the number of parameters in the object function was six plus the number of torsional rotations allowed. To exclude conformations with unreasonably large energies, they used a weighted SI in the optimization procedure ... 

Figure 2.151. MacroModel s features include support for a variety of commonly used conformational search methodologies. Using the MacroModel interface integrated within Maestro, the user can automaticly select torsions, rotations, and translations to be explored in a calculation...

According to the classical stereochemical definition, the term conformation describes the different spatial arrangements of atoms in molecules that result solely from torsions (rotations) around single and/or partial double bonds. However in the domain of supramole-cular chemistry, molecular motions arise from the competitive noncovalent interactions between the components. 

ADVANCED STRENGTH OF MATERIALS, J.P. Den Hartog. Superbly written advanced text covers torsion, rotating disks, membrane stresses in shells, much more. Many problems and answers. 388pp. 54 x 84. 65407-9 Pa. 8.95... 

The third term torsion provides the energy associated with torsional rotations. It is generally written as... 

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