Dihedral angle equivalents

HyperChem uses the improper dihedral angle formed by central atom - neighbor 1 - neighbor 2 - neighbor 3, where the order of neighbors is how they appear in a HIN file. Not all planar atoms customarily have associated improper torsions. The order of atoms is arbitrary but has been consistently chosen by the original authors of the CHARMM force field. The templates contain equivalent CHARMM definitions of improper torsions for amino acids. Improper dihedral angles cannot be defined that do not have a central atom, as is sometimes done in CHARMM calculations. 

Figure 3 Model building by Modeller [31], First, spatial restraints in the form of atomic distances and dihedral angles are extracted from the template stmcture(s). The alignment is used to determine equivalent residues between the target and the template. The restraints are combined into an objective function. Finally, the model for the target is optimized until a model that best satisfies the spatial restraints is obtained. This procedure is technically similar to the one used in structure determination by NMR.

It is typical, for instance, of syndiotactic polystyrene (s-PS) [7-9] and syndiotactic poly- p-methylstyrene (s-PPMS) [10] to present crystalline forms with a transplant conformation of the chains (shown for s-PS in Fig. 1) as well as crystalline forms with sequences of dihedral angles of the kind TTG+G+ (or the equivalent G G TT), corresponding to a s(2/l)2 helical symmetry of the chains (shown for s-PS in Fig. 1). 

In [Ce(N03)5]2 anion, three nitrate ions constitute the equatorial plane and are almost planar with one another and with the Ce atom. The other two nitrates whose terminal N—0 lies very close to the axis passing through the central atom and is normal to the equatorial plane have a dihedral angle of 80° between their planes. All Ce—0 distances are equivalent within the experimental error and these average to a value of 2.58 A. 

A strong dependence was revealed by MNDO calculations (equivalent in this respect to ab initio method) between the dihedral angle of the carbonyl oxygen with respect to the plane of 1,3,2-dithiazolyl radical ring in 1,3,2-thiazolyl esters (35) and spin density on ring S atoms as reflected in ESR experiments (Section 4.12.3.6) <88MRC755>. 

It has only one vibrational mode of low frequency, with a wavenumber v 50 cm. This mode preserves C2 symmetry as the BrCCC dihedral angle oscillates about an equilibrium value of 60°. A wavenumber of 50 cm is equivalent to a wavelength of 2.0 x 10 cm, or a frequency of oscillation v of 1.5 x lO s the reciprocal gives the period of the oscillation, 670 fs, a value quite comparable to the observed coherence (Tc = 680 fs). 

FIGURE 4. The magnitudes of "/hh coupling constants found in aUylmagnesium compounds are consistent with the presence of two rapidly interconverting, equivalent conformers with dihedral angles of ca 30°... 

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