Dihedrals and impropers

Dihedral and improper bonds model the interaction between 4 bonded atoms. They are modeled by an angular spring between the planes formed by the first 3 atoms and the second 3 atoms. The energy for a dihedral or improper between atoms i, j, k, and l is given by

$$E_{\text{d/i}} = k(1+\cos(n \phi + \delta))$$

if n>0 or

$$E_{\text{d/i}} = k{(\phi - \delta)}^2$$

if n=0, where

• k = force constant specified in the parameter file for this bond type
• $\phi$ = calculated angle between the plane formed by atoms i, j, and kand the plane formed by atoms j, k, and l
• n = periodicity of the bond specified in the parameter file for this bond type
• $\delta$ = phase shift specified in the parameter file for this bond type