md.angle

Overview

`Angle`	Constructs the angular bond potential.
`Harmonic`	Harmonic angle potential.
`CosineSquared`	Cosine squared angle potential.
`Table`	Tabulated bond potential.

Details

Angle potentials.

class hoomd.md.angle.Angle

Bases: hoomd.md.force.Force

Constructs the angular bond potential.

Note

Angle is the base class for all angular potentials. Users should not instantiate this class directly.

class hoomd.md.angle.CosineSquared

Bases: hoomd.md.angle.Angle

Cosine squared angle potential.

CosineSquared specifies a cosine squared potential energy between every triplet of particles with an angle specified between them.

\[V(\theta) = \frac{1}{2} k \left( \cos\theta - \cos\theta_0 \right)^2\]

where \(\theta\) is the angle between the triplet of particles. This angle style is also known as g96, since they were used in the gromos96 force field. These are also the types of angles used with the coarse-grained MARTINI force field.

params

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

k (float, required) - potential constant \(k\) \([\mathrm{energy}]\)
t0 (float, required) - rest angle \(\theta_0\) \([\mathrm{radians}]\)

Type: TypeParameter[angle type, dict]

Parameters \(k\) and \(\theta_0\) must be set for each type of angle in the simulation. Note that the value of \(k\) for this angle potential is not comparable to the value of \(k\) for harmonic angles, as they have different units.

Examples:

cosinesq = angle.CosineSquared()
cosinesq.params['polymer'] = dict(k=3.0, t0=0.7851)
cosinesq.params['backbone'] = dict(k=100.0, t0=1.0)

class hoomd.md.angle.Harmonic

Bases: hoomd.md.angle.Angle

Harmonic angle potential.

Harmonic specifies a harmonic potential energy between every triplet of particles with an angle specified between them.

\[V(\theta) = \frac{1}{2} k \left( \theta - \theta_0 \right)^2\]

where \(\theta\) is the angle between the triplet of particles.

params

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

k (float, required) - potential constant \(k\) \([\mathrm{energy} \cdot \mathrm{radians}^{-2}]\)
t0 (float, required) - rest angle \(\theta_0\) \([\mathrm{radians}]\)

Type: TypeParameter[angle type, dict]

Examples:

harmonic = angle.Harmonic()
harmonic.params['polymer'] = dict(k=3.0, t0=0.7851)
harmonic.params['backbone'] = dict(k=100.0, t0=1.0)

class hoomd.md.angle.Table(width)

Bases: hoomd.md.angle.Angle

Tabulated bond potential.

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

Table computes a user-defined potential and force applied to each angle.

The torque \(\tau\) is:

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

and the potential \(V(\theta)\) is:

\[V(\theta) =V_\mathrm{table}(\theta)\]

where \(\theta\) is the angle between the vectors \(\vec{r}_A - \vec{r}_B\) and \(\vec{r}_C - \vec{r}_B\) for particles A,B,C in the angle.

Provide \(\tau_\mathrm{table}(\theta)\) and \(V_\mathrm{table}(\theta)\) on evenly spaced grid points points in the range \(\theta \in [0,\pi]\). Table linearly interpolates values when \(\theta\) lies between grid points. The torque must be specificed commensurate with the potential: \(\tau = -\frac{\partial V}{\partial \theta}\).

params

The potential parameters. The dictionary has the following keys:

V ((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 [angle type, dict]

width

Number of points in the table.

Type: int