Torsion function

Torsional function applied to four atoms not connected by consecutive bonds. Often used to enforce planarity in conjugated systems. 

Actually, nonbonding interactions are already included in the torsional term (as gauche-butane interactions) we might have used an ethane-type torsional function and accounted for CH3/CH3 interactions entirely with nonbonded terms. However, in comparing calculated relative energies the torsional term will cancel out. 

It should be pointed out that during torsion the initially planar sections lose their planarity because each of their points experiences a displacement parallel to the z axis. This displacement is proportional (1) to a function jr, called the torsion function, which depends on the position of the point on the section before the deformation is produced, and (2) to the magnitude of the relative rotation between two very close sections, that is, the derivative of a with respect to the z direction. Consequently, the vector displacement has the components... 

For certain cross sections of simple geometry, for example the circular one, closed solutions for the modified torsion function F may be obtained (14). On the other hand, for arbitrary cross sections, such as a rectangular one, it is not possible to find a solution from the boundary equation. In this case, the method of separation of variables is used, and the following solution is proposed. 

Find the torsion function and the torque for a viscoelastic hollow rod of elliptical cross section. 

Some of the interesting features in silanes which are well reproduced by the calculations include the rotational barriers (T7 kcal mole-1 in methylsilane as compared with 2-9 kcal mole-1 in ethane, and correspondingly low numbers for other methyl silanes). While the torsional function about the 2,3-bond in 1-sila-butane looks almost like that in butane, the corresponding function... 

In this aim, the technique developed for determining the acetone far infrared spectrum [4] is adopted. In this, the potential energy surface on which the nuclei are moving is determined, the nuclear motion Schrodinger equation is solved, and from the energy levels, torsional functions and the dielectric moment variations the FIR spectrum is built up. 

Using differential geometry, a curve can be reconstructed from the knowledge of its curvature and torsional functions (the Frenet-Serret formulas). Therefore, these two functions give a concise shape description, provided one associates an everywhere-differentiable curve to the molecular skeleton. This approach has been employed in the analysis of protein shape. Moreover, this technique allows one to represent the dynamics of molecular chains or loops in terms of the deformation of elastic bodies. We return to this point when we discuss a number of purely topological descriptors of molecular curves. 

At present there are discrepancies between the description of internal rotation around bonds in the torsional functions used by various groups. Particularly in the case of TT-conjugated chains, important contributions to the variation in torsional energy arise from the differing interactions between the a and n components of... 

To develop the model, we used the MM4 program starting with cyclohexyl bromide and cyclohexanone, which were previously studied and well-understood systems. In addition to the parameter set from these compounds, we needed a little further information. Specifically, we examined the unit Br-C-C =0. We needed for our model the torsional function that is required to describe that unit, and we also needed any torsion-bend and torsion-stretch interactions that correspond to that torsion. All of these were obtained by studying bromoacetone in the usual way. ... 

The unusual form of the PFOS torsion function for the exo-anomeric component was selected for its ability to fit the inherently asymmetric shape of the rotational energy curves associated with derivatives of tetrahydropyran. Alternative approaches have been employed elsewhere to achieve the same goal (cf. Section 3.2.4). A novel feature of these equations is that, because they were derived as difference functions, they are independent of the force field parameterization and are in principle transferable to other force fields. ... 

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