md.dihedral¶

Overview

`Dihedral`	Base class dihedral force.
`Harmonic`	Periodic dihedral force.
`Periodic`	Periodic dihedral force.
`OPLS`	OPLS dihedral force.
`Table`	Tabulated dihedral force.

Details

Dihedral forces.

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 ( |_| ).

class hoomd.md.dihedral.Dihedral¶

Bases: Force

Base class dihedral force.

Dihedral is the base class for all dihedral forces.

Warning

This class should not be instantiated by users. The class can be used for isinstance or issubclass checks.

class hoomd.md.dihedral.Harmonic¶

Bases: Periodic

Periodic dihedral force.

Deprecated since version v3.7.0: Use Periodic.

class hoomd.md.dihedral.OPLS¶

Bases: Dihedral

OPLS dihedral force.

OPLS computes forces, virials, and energies on all dihedrals in the simulation state with:

\[U(\phi) = \frac{1}{2}k_1 \left( 1 + \cos\left(\phi \right) \right) + \frac{1}{2}k_2 \left( 1 - \cos\left(2 \phi \right) \right) + \frac{1}{2}k_3 \left( 1 + \cos\left(3 \phi \right) \right) + \frac{1}{2}k_4 \left( 1 - \cos\left(4 \phi \right) \right)\]

\(k_n\) are the force coefficients in the Fourier series.

params¶

The parameter of the OPLS bonds for each particle type. The dictionary has the following keys:

k1 (float, required) - force constant of the first term \([\mathrm{energy}]\)
k2 (float, required) - force constant of the second term \([\mathrm{energy}]\)
k3 (float, required) - force constant of the third term \([\mathrm{energy}]\)
k4 (float, required) - force constant of the fourth term \([\mathrm{energy}]\)

Type: TypeParameter [dihedral type, dict]

Examples:

opls = dihedral.OPLS()
opls.params['A-A-A-A'] = dict(k1=1.0, k2=1.0, k3=1.0, k4=1.0)

class hoomd.md.dihedral.Periodic¶

Bases: Dihedral

Periodic dihedral force.

Periodic computes forces, virials, and energies on all dihedrals in the simulation state with:

\[U(\phi) = \frac{1}{2}k \left( 1 + d \cos\left(n \phi - \phi_0 \right) \right)\]

params¶

The parameter of the harmonic bonds for each dihedral type. The dictionary has the following keys:

k (float, required) - potential constant \(k\) \([\mathrm{energy}]\)
d (float, required) - sign factor \(d\)
n (int, required) - angle multiplicity factor \(n\)
phi0 (float, required) - phase shift \(\phi_0\) \([\mathrm{radians}]\)

Type: TypeParameter [dihedral type, dict]

Examples:

harmonic = dihedral.Harmonic()
harmonic.params['A-A-A-A'] = dict(k=3.0, d=-1, n=3, phi0=0)
harmonic.params['A-B-C-D'] = dict(k=100.0, d=1, n=4, phi0=math.pi/2)

class hoomd.md.dihedral.Table(width)¶

Bases: Dihedral

Tabulated dihedral force.

Parameters: width (int) – Number of points in the table.

Table computes computes forces, virials, and energies on all dihedrals in the simulation given the user defined tables \(U\) and \(\tau\).

The torque \(\tau\) is:

\[\tau(\phi) = \tau_\mathrm{table}(\phi)\]

and the potential \(U(\phi)\) is:

\[U(\phi) = U_\mathrm{table}(\phi)\]

Provide \(\tau_\mathrm{table}(\phi)\) and \(U_\mathrm{table}(\phi)\) on evenly spaced grid points points in the range \(\phi \in [-\pi,\pi]\). Table linearly interpolates values when \(\phi\) lies between grid points. The torque must be specificed commensurate with the potential: \(\tau = -\frac{\partial U}{\partial \phi}\).

params¶

The potential parameters. The dictionary has the following keys:

U ((width,) numpy.ndarray of float, required) - the tabulated energy values \([\mathrm{energy}]\). Must have a size equal to width.
tau ((width,) numpy.ndarray of float, required) - the tabulated torque values \([\mathrm{force} \cdot \mathrm{length}]\). Must have a size equal to width.

Type: TypeParameter [dihedral type, dict]

width¶

Number of points in the table.

Type: int