Similarly, arrangements corresponding to angles between 30° and 150° or between −30° and −150° are called clinal (c) and those between 0° and ☓0° or ☑50° and 180° are called periplanar (p). Stereochemical arrangements corresponding to angles between 0° and ☙0° are called syn (s), those corresponding to angles between ☙0° and 180° anti (a). Dihedral angles are used to specify the molecular conformation. As explained above, when two such half-planes intersect (i.e., a set of four consecutively-bonded atoms), the angle between them is a dihedral angle. Every set of three non-colinear atoms of a molecule defines a half-plane. In stereochemistry, a torsion angle is defined as a particular example of a dihedral angle, describing the geometric relation of two parts of a molecule joined by a chemical bond. See also: Alkane stereochemistry and Conformational isomerismįree energy diagram of n-butane as a function of dihedral angle. When the two intersecting planes are described in terms of Cartesian coordinates by the two equationsĪ 1 x + b 1 y + c 1 z + d 1 = 0, which are called the trans, gauche +, and gauche − conformations. The planes of a flying machine are said to be at positive dihedral angle when both starboard and port main planes (commonly called "wings") are upwardly inclined to the lateral axis when downwardly inclined they are said to be at a negative dihedral angle. In higher dimensions, a dihedral angle represents the angle between two hyperplanes. In solid geometry, it is defined as the union of a line and two half-planes that have this line as a common edge. In chemistry, it is the clockwise angle between half-planes through two sets of three atoms, having two atoms in common. A dihedral angle is the angle between two intersecting planes or half-planes.
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