# Dihedral

1. 1. Proper Dihedrals
1. 1.1. Periodic Dihedrals
2. 1.2.
3. 1.3. Ryckaert-Bellemans Dihedrals
4. 1.4. Improper Dihedrals

A dihedral angle is the angle that occurs between two planes defined by four atoms.

## Proper Dihedrals

A proper dihedral consists of four atoms, joined linearly through bonds.  These dihedrals can be represented either by a periodic or Ryckaert-Bellemans potential.

### Periodic Dihedrals

A periodic dihedral is represented by a cosine function of the form

```Vd(φijkl) = kφ(1 + cos(nφ - φs))
```

### Ryckaert-Bellemans Dihedrals

The form of a Ryckaert-Bellemans dihedral is given as

```Vrb(φijkl) = ΣCn(cos(ψ))n
```

The above expression is evaluated for values of n from 0 to 5, and ψ is given as φ - 180°. Note that the OPLS force field uses a modified form of a Ryckaert-Bellemans dihedral, a Fourier function.

### Improper Dihedrals

An improper dihedral is used to keep planar groups (like rings) planar.  This dihedral type can also be used to prevent interconversion of stereocenters.