relentless.model.potential.HarmonicCosineAngle#

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

Harmonic cosine angle potential.

\[u(\theta) = \frac{k}{2} (\cos \theta - \cos \theta_0)^2\]

where \(\theta\) is the angle between three bonded particles. The parameters for each type are:

Parameter

Description

k

Spring constant \(k\).

theta0

Minimum-energy angle \(\theta_0\).
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 type.

Type:

AngleParameters

Examples

Cosine Squared Angle:

>>> u = relentless.potential.angle.HarmonicCosineAngle(("A",))
>>> u.coeff["A"].update({'k': 1000, 'theta0': 1})

Methods

derivative(type_, var, theta)

Evaluate derivative with respect to a variable.

energy(type_, theta)

Evaluate angle energy.

force(type_, theta)

Evaluate angle 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(type_, var, theta)#

Evaluate derivative with respect to a variable.

The derivative is evaluated using the _derivative() function for all \(u_{0,\lambda}(theta)\).

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:

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

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

  • theta (float or list) – The angle(s) at which to evaluate the derivative.

Returns:

The angle derivative evaluated at theta. The return type is consistent with theta.

Return type:

float or numpy.ndarray

Raises:

  • ValueError – If any value in theta is not between 0 and pi.

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

energy(type_, theta)#

Evaluate angle energy.

force(type_, theta)#

Evaluate angle force.

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