Dihedral Angle

A dihedral angle is the angle between two planes (1). This is determined as the angle formed by normal lines to each plane, as shown in Figure  1. When the rotation about a single bond in a molecule is being measured, eg, the rotation about the peptide NCa bond, it is preferred nomenclature to use the conventions described for torsion angles . Unlike torsion angles, it is possible to determine the dihedral angle between the planes defined by any two groups of three atoms, whether they are bonded together or not. If any four atoms are specified in order: atom-1, atom-2, atom-3, atom-4, the dihedral angle is measured between the plane containing atom-1, atom-2, and atom-3 and the plane containing atom-2, atom-3, and atom-4. If the four atoms are not sequentially bonded, this dihedral angle may be referred to as an “improper dihedral” or “improper torsion” (2). 

Figure 1. The dihedral angle F is the angle between the two planes defined by atoms 1, 2, and 3 and atoms 2, 3, and 4, respectively. The angle is determined as the angle between lines perpendicular to each plane.

References

1.   Oxford English Dictionary, 2nd ed. (1989) Clarendon Press, Oxford. 

2. B. R. Brooks et al. (1983) J. Comp. Chem. 4, 187–217.