# md.pair.aniso

Overview

 ALJ Anistropic LJ force. AnisotropicPair Base class anisotropic pair force. Dipole Screened dipole-dipole pair forces. GayBerne Gay-Berne anisotropic pair force.

Details

Anisotropic pair forces.

Anisotropic pair force classes apply a force, torque, and virial on every particle in the simulation state commensurate with the potential energy:

$U_\mathrm{pair,total} = \frac{1}{2} \sum_{i=0}^\mathrm{N_particles-1} \sum_{j \ne i, (i,j) \notin \mathrm{exclusions}} U_\mathrm{pair}(r_{ij}, \mathbf{q}_i, \mathbf{q}_j)$

AnisotropicPair applies cuttoffs, exclusions, and assigns per particle energies and virials in the same manner as hoomd.md.pair.Pair

AnisotropicPair does not support 'xplor' shifting mode or the r_on parameter.

class hoomd.md.pair.aniso.ALJ(nlist, default_r_cut=None, mode='none')

Anistropic LJ force.

Parameters

ALJ computes the Lennard-Jones force between anisotropic particles as described in Ramasubramani, V. et. al. 2020. Specifically we implement the formula:

$U(r, r_c) = 4 \varepsilon \left[ \left( \frac{\sigma}{r} \right)^{12} - \left( \frac{\sigma}{r} \right)^{6} \right] + 4 \varepsilon_c \left[ \left( \frac{\sigma_c}{r_c} \right)^{12} - \left( \frac{\sigma_c}{r_c} \right)^{6} \right]$

The first term is the standard center-center interaction between two Lennard-Jones spheres. The second term is a contact interaction computed based on the smallest distance between the surfaces of the two shapes, $$r_c$$. The total potential energy can thus be viewed as the sum of two interactions, a central Lennard-Jones potential and a shifted Lennard-Jones potential where the shift is anisotropic and depends on the extent of the shape in each direction.

Like a standard LJ potential, each term has an independent cutoff beyond which it decays to zero the behavior of these cutoffs is dependent on whether a user requires LJ or Weeks-Chandler-Anderson (WCA)-like (repulsive-only) behavior. This behavior is controlled using the alpha parameter, which can take on the following values:

• 0: All interactions are WCA (no attraction).

• 1: Center-center interactions include attraction, contact-contact interactions are solely repulsive.

• 2: Center-center interactions are solely repulsive, contact-contact interactions include attraction.

• 3: All interactions include attractive and repulsive components.

For polytopes, computing interactions using a single contact point leads to significant instabilities in the torques because the contact point can jump from one end of a face to another in an arbitrarily small time interval. To ameliorate this, the ALJ potential performs a local averaging over all the features associated with the closest simplices on two polytopes. This averaging can be turned off by setting the average_simplices key for the type pair to False.

Specifying only rounding_radii creates an ellipsoid, while specifying only vertices creates a convex polytope (set vertices and faces to empty list to create the ellipsoid).

Example:

nl = hoomd.md.nlist.Cell()
alj = hoomd.md.pair.aniso.ALJ(nl, r_cut=2.5)

cube_verts = [(-0.5, -0.5, -0.5),
(-0.5, -0.5, 0.5),
(-0.5, 0.5, -0.5),
(-0.5, 0.5, 0.5),
(0.5, -0.5, -0.5),
(0.5, -0.5, 0.5),
(0.5, 0.5, -0.5),
(0.5, 0.5, 0.5)];

cube_faces = [[0, 2, 6],
[6, 4, 0],
[5, 0, 4],
[5,1,0],
[5,4,6],
[5,6,7],
[3,2,0],
[3,0,1],
[3,6,2],
[3,7,6],
[3,1,5],
[3,5,7]]

alj.params[("A", "A")] = dict(epsilon=2.0,
sigma_i=1.0,
sigma_j=1.0,
alpha=1,
)
alj.shape["A"] = dict(vertices=cube_verts,
faces=cube_faces,
rounding_radii=1)


The following example shows how to easily get the faces, with vertex indices properly ordered, for a shape with known vertices by using the coxeter package:

Example:

import coxeter

nl = hoomd.md.nlist.Cell()
alj = hoomd.md.pair.aniso.ALJ(nl, r_cut=2.5)

cube_verts = [[-0.5, -0.5, -0.5],
[-0.5, -0.5, 0.5],
[-0.5, 0.5, -0.5],
[-0.5, 0.5, 0.5],
[0.5, -0.5, -0.5],
[0.5, -0.5, 0.5],
[0.5, 0.5, -0.5],
[0.5, 0.5, 0.5]]

cube = coxeter.shapes.ConvexPolyhedron(cube_verts)

alj.params[("A", "A")] = dict(epsilon=2.0,
sigma_i=1.0,
sigma_j=1.0,
alpha=1,
)
alj.shape["A"] = dict(vertices=cube.vertices,
faces=cube.faces,
rounding_radii=1)


Warning

Changing dimension in a simulation will invalidate this force and will lead to error or unrealistic behavior.

params

The ALJ potential parameters. The dictionary has the following keys:

• epsilon (float, required) - base energy scale $$\varepsilon$$ $$[energy]$$.

• sigma_i (float, required) - the insphere radius of the first particle type, $$[length]$$.

• sigma_j (float, required) - the insphere radius of the second particle type, $$[length]$$.

• alpha (int, required) - Integer 0-3 indicating whether or not to include the attractive component of the interaction (see above for details).

• contact_ratio_i (float, optional) - the ratio of the contact sphere radius of the first type with sigma_i. Defaults to 0.15.

• contact_ratio_j (float, optional) - the ratio of the contact sphere radius of the second type with sigma_j. Defaults to 0.15.

• average_simplices (bool, optional) - Whether to average over simplices. Defaults to True. See class documentation for more information.

Type: hoomd.data.typeparam.TypeParameter [tuple [particle_types, particle_types], dict]

shape

The shape of a given type. The dictionary has the following keys per type:

Type: hoomd.data.typeparam.TypeParameter [particle_types, dict]

property type_shapes

The shape specification for use with GSD files for visualization.

This is not meant to be used for access to shape information in Python. See the attribute shape for programatic assess. Use this property to log shape for visualization and storage through the GSD file type.

(Loggable: category=”object”)

Type

list [dict [str, any]]

class hoomd.md.pair.aniso.AnisotropicPair(nlist, default_r_cut=None, mode='none')

Bases: Pair

Base class anisotropic pair force.

Note

AnisotropicPair is the base class for all anisotropic pair forces. Users not not instantiate this class directly.

Parameters
class hoomd.md.pair.aniso.Dipole(nlist, default_r_cut=None, mode='none')

Screened dipole-dipole pair forces.

Parameters

Dipole computes the (screened) interaction between pairs of particles with dipoles and electrostatic charges:

\begin{align}\begin{aligned}U &= U_{dd} + U_{de} + U_{ee}\\U_{dd} &= A e^{-\kappa r} \left(\frac{\vec{\mu_i}\cdot\vec{\mu_j}}{r^3} - 3\frac{(\vec{\mu_i}\cdot \vec{r_{ji}}) (\vec{\mu_j}\cdot \vec{r_{ji}})} {r^5} \right)\\U_{de} &= A e^{-\kappa r} \left(\frac{(\vec{\mu_j}\cdot \vec{r_{ji}})q_i}{r^3} - \frac{(\vec{\mu_i}\cdot \vec{r_{ji}})q_j}{r^3} \right)\\U_{ee} &= A e^{-\kappa r} \frac{q_i q_j}{r}\end{aligned}\end{align}

Note

All units are documented electronic dipole moments. However, Dipole can also be used to represent magnetic dipoles.

Example:

nl = nlist.Cell()
dipole = md.pair.Dipole(nl, default_r_cut=3.0)
dipole.params[('A', 'B')] = dict(A=1.0, kappa=4.0)
dipole.mu['A'] = (4.0, 1.0, 0.0)

params

The dipole potential parameters. The dictionary has the following keys:

• A (float, required) - $$A$$ - electrostatic energy scale (default: 1.0) $$[\mathrm{energy} \cdot \mathrm{length} \cdot \mathrm{charge}^{-2}]$$

• kappa (float, required) - $$\kappa$$ - inverse screening length $$[\mathrm{length}^{-1}]$$

Type: TypeParameter [tuple [particle_type, particle_type], dict]

mu

$$\mu$$ - the magnetic magnitude of the particle local reference frame as a tuple (i.e. $$(\mu_x, \mu_y, \mu_z)$$) $$[\mathrm{charge} \cdot \mathrm{length}]$$.

Type: TypeParameter [particle_type, tuple [float, float, float ]]

class hoomd.md.pair.aniso.GayBerne(nlist, default_r_cut=None, mode='none')

Gay-Berne anisotropic pair force.

Parameters

GayBerne computes the Gay-Berne anisotropic pair force on every particle in the simulation state. This version of the Gay-Berne force supports identical pairs of uniaxial ellipsoids, with orientation-independent energy-well depth. The potential comes from the following paper Allen et. al. 2006.

$\begin{split}U(\vec r, \vec e_i, \vec e_j) = \begin{cases} 4 \varepsilon \left[ \zeta^{-12} - \zeta^{-6} \right] & \zeta < \zeta_{\mathrm{cut}} \\ 0 & \zeta \ge \zeta_{\mathrm{cut}} \\ \end{cases}\end{split}$

where

\begin{align}\begin{aligned}\zeta &= \left(\frac{r-\sigma+\sigma_{\mathrm{min}}} {\sigma_{\mathrm{min}}}\right),\\\sigma^{-2} &= \frac{1}{2} \hat{\vec{r}} \cdot \vec{H^{-1}} \cdot \hat{\vec{r}},\\\vec{H} &= 2 \ell_\perp^2 \vec{1} + (\ell_\parallel^2 - \ell_\perp^2) (\vec{e_i} \otimes \vec{e_i} + \vec{e_j} \otimes \vec{e_j}),\end{aligned}\end{align}

and $$\sigma_{\mathrm{min}} = 2 \min(\ell_\perp, \ell_\parallel)$$.

The cut-off parameter $$r_{\mathrm{cut}}$$ is defined for two particles oriented parallel along the long axis, i.e. $$\zeta_{\mathrm{cut}} = \left(\frac{r-\sigma_{\mathrm{max}} + \sigma_{\mathrm{min}}}{\sigma_{\mathrm{min}}}\right)$$ where $$\sigma_{\mathrm{max}} = 2 \max(\ell_\perp, \ell_\parallel)$$ .

The quantities $$\ell_\parallel$$ and $$\ell_\perp$$ denote the semi-axis lengths parallel and perpendicular to particle orientation.

Example:

nl = nlist.Cell()
gay_berne = md.pair.GayBerne(nlist=nl, default_r_cut=2.5)
gay_berne.params[('A', 'A')] = dict(epsilon=1.0, lperp=0.45, lpar=0.5)
gay_berne.r_cut[('A', 'B')] = 2 ** (1.0 / 6.0)

params

The Gay-Berne potential parameters. The dictionary has the following keys:

Type: TypeParameter [tuple [particle_type, particle_type], dict]

property type_shapes

Get all the types of shapes in the current simulation.

Example

>>> gay_berne.type_shapes
[{'type': 'Ellipsoid', 'a': 1.0, 'b': 1.0, 'c': 1.5}]

Returns

A list of dictionaries, one for each particle type in the system.

(Loggable: category=”object”)