Torsion angle convention

Torsion-Angle Conventions Referenced to the Phosphodiester Backbone... 

Note The formal lUPAC-IUB Commission on Biochemical Nomenclature convention for the definition of the torsion angles polypeptide chain (Biochemistry 9 3471-3479, 1970) is different from that used here, where the atom serves as the point of reference for both rotations, but the result is the same. (Irving Gas)... 

Editors footnote The convention adopted in polymer chemistry (21)—t for bond angle, 6 for torsion angle—will be used in this article. It is opposite to the usage commonly adopted by crys-tallographers and others in the description of small molecules. 

Floiy (155) and other American writers use the opposite convention making 8 = 0° for the trans or anti conformation. As a result the numerical values of the torsion angles reported here are often different from those reported in the original literature. Differences are found in the formulas involving trigonometrical functions and in the appearance of energy maps. Specific conventions are used for vinyl polymers. 

FIGURE 12. The Winkler-Dunitz convention for quantifying pyramidaUty at nitrogen (xn) and twist about the C—N bond (t) as functions of torsion angles coi — C04 in an RCON(X)Y amide... 

A helical unit is inherently chiral. Its chirality sense or helicity can assume two values that correspond to the sign of the torsional angle. Although the definition of the sign is arbitrary (sec Section 1.1.1.). a universal scientific convention2 is followed (Klyne Prelog convention) ... 

An additional five torsion angles are needed to specify the backbone conformation of a polynucleotide. According to the convention adopted by the IUB the six angles are desig-... 

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). 

Convention for torsion angles 0° when bonds A-B and C-D arecvs clockwise rotation of bond C-D relative to A-B is positive. 

Figure 8 Building a molecular model based on internal geometries (bond lengths /, bond angles 6, and torsional angles ). Each subsequent atom is added to the framework with respect to earlier situated atoms. The convention in many programs is that the x Cartesian axis is the horizontal axis on the computer screen, the y axis is vertical, and the z axis comes out of the computer screen toward the user.

Other than in the preceding section, the matrix D must now relate the increments of symmetrically equivalent internal (or bond) coordinates with the increment of the respective base internal coordinate. Let us return to the example, Eq. 56, and let the matrix D, as depicted there, be a portion of the whole matrix D. The row and column headings of each 3x3 block of D for a particular atom now specify the increments of bond length Ar, bond angle Atp, and dihedral (or torsional) angle AO used for the attachment of this atom to the chain, instead of the increments of Cartesian coordinates of the atom. It is assumed that the description by internal coordinates has been chosen for the best possible preservation of molecular symmetry. The three symmetrically equivalent atoms a, a, and a" will then be attached to an interatomic bond along thejr-axis (or, by convention, to an equivalent... 

Figure 6.13 The torsion angle sign convention and the effect of rotation, reflection and inversion operations on the sign.

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