relentless.model.potential.LennardJones#

class relentless.model.potential.LennardJones(types, name=None)#

Lennard-Jones 12-6 pair potential.

The classic molecular simulation potential:

\[u(r) = 4 \varepsilon\left[\left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^6 \right]\]

where \(r\) is the distance between two particles. The parameters for each \((i,j)\) pair are:

Parameter

Description

Initial

epsilon

Interaction energy \(\varepsilon\).

sigma

Interaction length \(\sigma\).

rmin

Minimum distance cutoff \(r_{\rm min}\). Force is zero and energy is constant for \(r < r_{\rm min}\). Ignored if False.

False

rmax

Maximum distance cutoff \(r_{\rm max}\). Force is zero and energy is constant for \(r > r_{\rm max}\). Ignored if False.

False

shift

If True, shift potential to zero at rmax.

False

For example, setting \(r_{\rm max} = 2^{1/6}\sigma\) and shift=True will give the purely repulsive Weeks–Chandler–Anderson potential that is often used to model nearly hard spheres.

Parameters:

  • types (tuple[str]) – Types.

  • name (str) – Unique name of the potential. Defaults to __u[id], where id is the unique integer ID of the potential.

coeff#

Parameters of the potential for each pair.

Type:

PairParameters

Examples

Standard Lennard-Jones parameters:

>>> u = relentless.potential.pair.LennardJones(('A',))
>>> u.coeff['A','A'].update({'epsilon': 1.0, 'sigma': 1.0, 'rmax': 3.0})
>>> u.energy(('A','A'), 1.0)
0.0
>>> u.force(('A','A'), 2.**(1./6.))
0.0

Methods

derivative(pair, var, r)

Evaluate pair derivative with respect to a variable.

energy(pair, r)

Evaluate pair energy.

force(pair, r)

Evaluate pair force.

from_file(filename[, name])

Create potential from a JSON file.

from_json(data[, name])

Create potential from JSON data.

save(filename)

Save the potential to file as JSON data.

to_json()

Export potential to a JSON-compatible dictionary.

Attributes

count

names

derivative(pair, var, r)#

Evaluate pair derivative with respect to a variable.

The derivative is evaluated using the _derivative() function for all \(u_{0,\lambda}(r)\). The truncation and shifting scheme is applied.

The derivative will be carried out with respect to var for all Variable parameters. The appropriate chain rules are handled automatically. If the potential does not depend on var, the derivative will be zero by definition.

Parameters:

  • pair (tuple[str]) – The pair for which to calculate the derivative.

  • var (Variable) – The variable with respect to which the derivative is calculated.

  • r (float or list) – The pair distance(s) at which to evaluate the derivative.

Returns:

The pair derivative evaluated at r. The return type is consistent with r.

Return type:

float or numpy.ndarray

Raises:

  • ValueError – If any value in r is negative.

  • TypeError – If the parameter with respect to which to take the derivative is not a Variable.

  • ValueError – If the potential is shifted without setting rmax.

energy(pair, r)#

Evaluate pair energy.

The energy is evaluated using the _energy() function for \(u_0(r)\). The truncation and shifting scheme is applied.

Parameters:

  • pair (tuple[str]) – The pair for which to calculate the energy.

  • r (float or list) – The pair distance(s) at which to evaluate the energy.

Returns:

The pair energy evaluated at r. The return type is consistent with r.

Return type:

float or numpy.ndarray

Raises:

  • ValueError – If any value in r is negative.

  • ValueError – If the potential is shifted without setting rmax.

force(pair, r)#

Evaluate pair force.

The force is evaluated using the _force() function for \(f_0(r)\). The truncation and shifting scheme is applied.

Parameters:

  • pair (tuple[str]) – The pair for which to calculate the force.

  • r (float or list) – The pair distance(s) at which to evaluate the force.

Returns:

The pair force evaluated at r. The return type is consistent with r.

Return type:

float or numpy.ndarray

Raises:

ValueError – If any value in r is negative.

classmethod from_file(filename, name=None)#

Create potential from a JSON file.

It is assumed that the JSON file is compatible with the potential type.

Parameters:

  • filename (str) – JSON file to load.

  • name (str or bool or None) – Name of the potential. If a str, name overrides the value in the file. If True, the name in the file is always preserved. If False, the name in the file is always ignored, and a default name is created. If None, the value in the file is used if it is not taken and does not match the default name pattern; otherwise, a new default name is generated.

classmethod from_json(data, name=None)#

Create potential from JSON data.

It is assumed that the data is compatible with the pair potential.

Parameters:

  • data (dict) – JSON data for potential.

  • name (str or bool or None) – Name of the potential. If a str, name overrides the value in the JSON data. If True, the name in the JSON data is always preserved. If False, the name in the JSON data is always ignored, and a default name is created. If None, the value in the JSON data is used if it is not taken and does not match the default name pattern; otherwise, a new default name is generated.

save(filename)#

Save the potential to file as JSON data.

Parameters:

filename (str) – The name of the file to which to save the data.

to_json()#

Export potential to a JSON-compatible dictionary.

The JSON dictionary will contain the id and name of the potential, along with the JSON representation of its coefficients.

Returns:

Potential.

Return type:

dict