Dihedral angles definition

Dihedral angle definition. The dihedral angle of atoms A,B,C,D is shown as (A) a positive angle by counter-clockwise rotation of the B-A bond about the B-C bond ... 

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. 

Fig. 9.10 (A) Definition of the dihedral angle d between the spin-pairs ij and k,l. (B) Cross-correlated relaxation can be detected by differences in intensities of the multiplet components of double quantum coherences...

FIGURE 12. Definition of the dihedral angle 1 for a tin-allyl compound. Reproduced by permission of Elsevier Science from Reference 89... 

Figure 6.11 (a) Definition of the dihedral angle, , at a junction of three grain boundaries in a polycrystalline solid, (b) Schematic illustration of the shape of an inclusion phase for different dihedral angles. 

In the cases of the Af-salicylidene (46) and N-benzylidene (47) anilines (15a and 15b), there is less ambiguity arising from thermal motion. For both series of compounds it is believed, on spectroscopic grounds, that the molecules are nonplanar in solution. While there are some crystal phases known in which the molecules retain this conformation (the dihedral angle between the anilino and salicylidenimino planes being of the order of 40°), in others the molecules are definitely planar. In the case of 15a it has been found that there are marked differences in densities and in photochemical and spectroscopic properties between crystals of the two types. 

Fig. 7. Plot of main chain dihedral angles and (see Fig. 5 for definition) experimentally determined for approximately 1000 nonglycine residues in eight proteins whose structures have been refined at high resolution (chosen to be representative of all categories of tertiary structure).

Figure 2.2 Definition and sign convention for dihedral angle ft). The bold lines are the projections of the AB and CD bonds into the bisecting plane. Note that the sign of a> is independent of whether one chooses to view the bisecting plane from the AB side or the CD side...

Fig. 2.14. CH moiety of an sp1 carbon bound to an sp2 carbon, illustrating the definition of the dihedral angle 6.

PROBLEM 7.10.3. The oldest mathematical definition of crystals, Haiiy s law, states that the dihedral angles between crystal faces are constant, if the crystal habit (growth pattern) is the same. Compute the dihedral angle between two general crystal faces (hkl) and (h k l1). 

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