Dihedral Angle

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dihedral angle

[dī′hē·drəl ‚aŋ·gəl]
(mathematics)
The angle between two planes; it is said to be zero if the planes are parallel; if the planes intersect, it is the plane angle between two lines, one in each of the planes, which pass through a point on the line of intersection of the two planes and are perpendicular to it.

Dihedral Angle

 

a figure formed in space by two half-planes emanating from a single straight line and also the portion of space bounded by these half-planes (see Figure 1).

Figure 1.

The half-planes are called the faces of the dihedral angle and their common straight line the edge. The dihedral angle is measured by the linear angle, that is, the angle α between two perpendiculars to the edge that emanate from one point and that lie in the different faces or, in other words, the angle formed by the intersection of the dihedral angle and a plane perpendicular to the edge.

References in periodicals archive ?
Table-4: Some values such as bond lengths, bond angles and dihedral angles obtained by PM3, AM1 and MNDO with HyperChem-8 computational programs.
The values presented in the table 2 this are of different dihedral angles, For all the compounds, the calculations B3LYP / 6-31G (d, p) predict that the dihedral angles are generally close to zero for 01, 145[degrees] in average for 02 and [theta]3 to a mean value equal to 20[degrees].
Choose a point in the saddle-shaped weld; dihedral angle of the point on saddle weld is the angle between the cylinder's tangent plane through this point and the pipe's tangent plane.
Although the molecules differ from each other by their moieties bonded to the imidazole rings, the bond lengths, the bond angles, and the dihedral angles belong to the ring, and its immediate vicinity are in good agreement with each other and with the corresponding X-ray diffractometer (XRD) results of previously investigated similar molecule 1,3-bis(acetamide) imidazol-3-ium bromide which was crystallized successfully [22].
Table 1 shows the bond length and dihedral angle in gas and solvent (THF), respectively.
The supplementary materials for this work contain Figures S1 to S4, where are displayed the vibrational spectra (S1-S2), a section of the polymeric structure of LISZn2 (S3), and dihedral angles of the LISZn2 complex (S4).
Caption: Figure 6: Dihedral angles of ToCDS protomers in crystals I, II, III, and IV.
Initial analyses were conducted by considering all non-Gly/nonPro residues in all types of structures in recent protein structure ensembles (Data 1.6 and Data 1.2 for bond and dihedral angles, resp.; see Methods for details), as Pro and Gly frequently display peculiar structural properties at geometry level [9, 29].
We now show that all dihedral angles are submutliples of [pi].
An ideal polytope P is called Coxeter if the dihedral angles of edges of P are submultiples of [pi].
SAR studies of the ten synthetic molecules demonstrated that the three-dimensional shape of the t-Bu attached side chain significantly affects the potent neurotoxicity of 1: the bulkiness of the C9-substituent and the specific dihedral angle of the C7-C8 bond strongly correlated to potent cytotoxicity, and truncation of the terminus induced activity loss.
These instances have different sequence's lengths and different number of variables (dihedral angles).