relentless.model.potential.AnglePotential#

class relentless.model.potential.AnglePotential(keys, params, container=None, name=None)#

Abstract base class for an angle potential.

The angle potential is defined by the angle between three bonded particles. The angle between particles \(i\), \(j\), and \(k\) is defined as:

\[\theta_{ijk} = \arccos\left(\frac{\mathbf{r}_{ij} \cdot \mathbf{r}_{jk}}{|\mathbf{r}_{ij}||\mathbf{r}_{jk}|}\right)\]

where \(\mathbf{r}_{ij}\) and \(\mathbf{r}_{jk}\) are the vectors from particle i to particle j and from particle j to particle k, respectively. \(\theta\) is bound between \(0\) and \(\pi\).

Methods

derivative(type_, var, theta)

Evaluate derivative with respect to a variable.

energy(key, x)

Evaluate potential energy.

force(key, x)

Evaluate force magnitude.

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.

abstract energy(key, x)#

Evaluate potential energy.

Parameters:

  • key – Key parametrizing the potential in coeff.

  • x (float or list) – Potential energy coordinate.

Returns:

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

Return type:

float or numpy.ndarray

abstract force(key, x)#

Evaluate force magnitude.

The force is the (negative) magnitude of the x gradient.

Parameters:

  • key – Key parametrizing the potential in coeff.

  • x (float or list) – Potential energy coordinate.

Returns:

The force evaluated at x. The return type is consistent with x.

Return type:

float or numpy.ndarray

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