dihedral

Dihedral force classes apply a force and virial on every particle in the simulation state commensurate with the potential energy:

\[U_\mathrm{dihedral} = \sum_{(i,j,k,l) \in \mathrm{dihedrals}} U_{ijkl}(\phi)\]

Each dihedral is defined by an ordered quadruplet of particle tags in the hoomd.State member dihedral_group. HOOMD-blue does not construct dihedral groups, users must explicitly define dihedrals in the initial condition.

In the dihedral group (i,j,k,l), \(\phi\) is the signed dihedral angle between the planes passing through (\(\vec{r}_i, \vec{r}_j, \vec{r}_k\)) and (\(\vec{r}_j, \vec{r}_k, \vec{r}_l\)).

Dihedral force classes assign 1/4 of the potential energy to each of the particles in the dihedral group:

\[U_m = \frac{1}{4} \sum_{(i,j,k,l) \in \mathrm{dihedrals}} U_{ijkl}(\phi) [m=i \lor m=j \lor m=k \lor m=l]\]

and similarly for virials.

Important

There are multiple conventions pertaining to the dihedral angle in the literature. HOOMD-blue utilizes the convention where \(\phi = \pm \pi\) in the anti-parallel stretched state ( /\/ ) and \(\phi = 0\) in the parallel compact state ( |_| ).

Classes

• Dihedral
• OPLS
• Periodic
• Table