matscipy.calculators.pair_potential.calculator

Simple pair potential.

Classes

`BeestKramerSanten`(A, B, C, cutoff)	Beest, Kramer, van Santen (BKS) potential.
`CutoffInteraction`(cutoff)	Pair interaction potential with cutoff.
`FeneLJCut`(K, R0, epsilon, sigma)	Finite extensible nonlinear elastic(FENE) potential for a bead-spring polymer model.
`LennardJones84`(C1, C2, C3, C4, cutoff)	Function form of a 8-4 Lennard-Jones potential, used to model the structure of a CuZr.
`LennardJonesCut`(epsilon, sigma, cutoff)	Functional form for a 12-6 Lennard-Jones potential with a hard cutoff.
`LennardJonesLinear`(epsilon, sigma, cutoff)	Function form of a 12-6 Lennard-Jones potential with a soft cutoff The energy and the force are shifted at the cutoff.
`LennardJonesQuadratic`(epsilon, sigma, cutoff)	Functional form for a 12-6 Lennard-Jones potential with a soft cutoff.
`PairPotential`(f[, cutoff])

class matscipy.calculators.pair_potential.calculator.CutoffInteraction(cutoff)

Bases: ABC

Pair interaction potential with cutoff.

Attributes:

cutoff: Physical cutoff distance for pair interaction.

Methods

`__call__`(r, qi, qj)	Compute interaction energy.
`derivative`([n])	Return specified derivative.
`first_derivative`(r, qi, qj)	Compute derivative w/r to distance.
`get_cutoff`()	Get cutoff.
`second_derivative`(r, qi, qj)	Compute second derivative w/r to distance.

__init__(cutoff): Initialize with cutoff.

property cutoff: Physical cutoff distance for pair interaction.

get_cutoff(): Get cutoff. Deprecated.

abstract first_derivative(r, qi, qj): Compute derivative w/r to distance.

abstract second_derivative(r, qi, qj): Compute second derivative w/r to distance.

derivative(n=1): Return specified derivative.

class matscipy.calculators.pair_potential.calculator.LennardJonesCut(epsilon, sigma, cutoff)

Bases: CutoffInteraction

Functional form for a 12-6 Lennard-Jones potential with a hard cutoff. Energy is shifted to zero at cutoff.

Attributes:

cutoff: Physical cutoff distance for pair interaction.

Methods

`__call__`(r, *args)	Compute interaction energy.
`derivative`([n])	Return specified derivative.
`first_derivative`(r, *args)	Compute derivative w/r to distance.
`get_cutoff`()	Get cutoff.
`second_derivative`(r, *args)	Compute second derivative w/r to distance.

__init__(epsilon, sigma, cutoff): Initialize with cutoff.

first_derivative(r, *args): Compute derivative w/r to distance.

second_derivative(r, *args): Compute second derivative w/r to distance.

property cutoff: Physical cutoff distance for pair interaction.

derivative(n=1): Return specified derivative.

get_cutoff(): Get cutoff. Deprecated.

class matscipy.calculators.pair_potential.calculator.LennardJonesQuadratic(epsilon, sigma, cutoff)

Bases: CutoffInteraction

Functional form for a 12-6 Lennard-Jones potential with a soft cutoff. Energy, its first and second derivative are shifted to zero at cutoff.

Attributes:

cutoff: Physical cutoff distance for pair interaction.

Methods

`__call__`(r, *args)	Return function value (potential energy).
`derivative`([n])	Return specified derivative.
`first_derivative`(r, *args)	Compute derivative w/r to distance.
`get_cutoff`()	Get cutoff.
`second_derivative`(r, *args)	Compute second derivative w/r to distance.

__init__(epsilon, sigma, cutoff): Initialize with cutoff.

first_derivative(r, *args): Compute derivative w/r to distance.

second_derivative(r, *args): Compute second derivative w/r to distance.

property cutoff: Physical cutoff distance for pair interaction.

derivative(n=1): Return specified derivative.

get_cutoff(): Get cutoff. Deprecated.

class matscipy.calculators.pair_potential.calculator.LennardJonesLinear(epsilon, sigma, cutoff)

Bases: CutoffInteraction

Function form of a 12-6 Lennard-Jones potential with a soft cutoff The energy and the force are shifted at the cutoff.

Attributes:

cutoff: Physical cutoff distance for pair interaction.

Methods

`__call__`(r, *args)	Return function value (potential energy).
`derivative`([n])	Return specified derivative.
`first_derivative`(r, *args)	Compute derivative w/r to distance.
`get_cutoff`()	Get cutoff.
`second_derivative`(r, *args)	Compute second derivative w/r to distance.

__init__(epsilon, sigma, cutoff): Initialize with cutoff.

first_derivative(r, *args): Compute derivative w/r to distance.

second_derivative(r, *args): Compute second derivative w/r to distance.

property cutoff: Physical cutoff distance for pair interaction.

derivative(n=1): Return specified derivative.

get_cutoff(): Get cutoff. Deprecated.

class matscipy.calculators.pair_potential.calculator.FeneLJCut(K, R0, epsilon, sigma)

Bases: LennardJonesCut

Finite extensible nonlinear elastic(FENE) potential for a bead-spring polymer model. For the Lennard-Jones interaction a LJ-cut potential is used. Due to choice of the cutoff (rc=2^(1/6) sigma) it ensures a continous potential and force at the cutoff.

Attributes:

cutoff: Physical cutoff distance for pair interaction.

Methods

`__call__`(r, *args)	Compute interaction energy.
`derivative`([n])	Return specified derivative.
`first_derivative`(r, *args)	Compute derivative w/r to distance.
`get_cutoff`()	Get cutoff.
`second_derivative`(r, *args)	Compute second derivative w/r to distance.

__init__(K, R0, epsilon, sigma): Initialize with cutoff.

first_derivative(r, *args): Compute derivative w/r to distance.

second_derivative(r, *args): Compute second derivative w/r to distance.

property cutoff: Physical cutoff distance for pair interaction.

derivative(n=1): Return specified derivative.

get_cutoff(): Get cutoff. Deprecated.

class matscipy.calculators.pair_potential.calculator.LennardJones84(C1, C2, C3, C4, cutoff)

Bases: CutoffInteraction

Function form of a 8-4 Lennard-Jones potential, used to model the structure of a CuZr. Kobayashi, Shinji et. al. “Computer simulation of atomic structure of Cu57Zr43 amorphous alloy.” Journal of the Physical Society of Japan 48.4 (1980): 1147-1152.

Attributes:

cutoff: Physical cutoff distance for pair interaction.

Methods

`__call__`(r, *args)	Compute interaction energy.
`derivative`([n])	Return specified derivative.
`first_derivative`(r, *args)	Compute derivative w/r to distance.
`get_cutoff`()	Get cutoff.
`second_derivative`(r, *args)	Compute second derivative w/r to distance.

__init__(C1, C2, C3, C4, cutoff): Initialize with cutoff.

first_derivative(r, *args): Compute derivative w/r to distance.

second_derivative(r, *args): Compute second derivative w/r to distance.

property cutoff: Physical cutoff distance for pair interaction.

derivative(n=1): Return specified derivative.

get_cutoff(): Get cutoff. Deprecated.

class matscipy.calculators.pair_potential.calculator.BeestKramerSanten(A, B, C, cutoff)

Bases: CutoffInteraction

Beest, Kramer, van Santen (BKS) potential.

Buckingham:: Energy is shifted to zero at the cutoff.

References

1. Van Beest, G. J. Kramer and R. A. Van Santen, Phys. Rev. Lett. 64.16 (1990)

Attributes:

cutoff: Physical cutoff distance for pair interaction.

Methods

`__call__`(r, *args)	Compute interaction energy.
`derivative`([n])	Return specified derivative.
`first_derivative`(r, *args)	Compute derivative w/r to distance.
`get_cutoff`()	Get cutoff.
`second_derivative`(r, *args)	Compute second derivative w/r to distance.

__init__(A, B, C, cutoff): Initialize with cutoff.

first_derivative(r, *args): Compute derivative w/r to distance.

second_derivative(r, *args): Compute second derivative w/r to distance.

property cutoff: Physical cutoff distance for pair interaction.

derivative(n=1): Return specified derivative.

get_cutoff(): Get cutoff. Deprecated.

class matscipy.calculators.pair_potential.calculator.PairPotential(f, cutoff=None)

Bases: MatscipyCalculator

Attributes:

directory
label

Methods

`band_structure`()	Create band-structure object for plotting.
`calculate`(atoms, properties, system_changes)	Calculate system properties.
`calculate_numerical_forces`(atoms[, d])	Calculate numerical forces using finite difference.
`calculate_numerical_stress`(atoms[, d, voigt])	Calculate numerical stress using finite difference.
`calculate_properties`(atoms, properties)	This method is experimental; currently for internal use.
`check_state`(atoms[, tol])	Check for any system changes since last calculation.
`get_birch_coefficients`(atoms)	Compute the Birch coefficients (Effective elastic constants at non-zero stress).
`get_born_elastic_constants`(atoms)	Compute the Born elastic constants.
`get_dynamical_matrix`(atoms)	Compute dynamical matrix (=mass weighted Hessian).
`get_elastic_constants`(atoms[, cg_parameters])	Compute the elastic constants at zero temperature.
`get_hessian`(atoms[, format, divide_by_masses])	Calculate the Hessian matrix for a pair potential.
`get_magnetic_moments`([atoms])	Calculate magnetic moments projected onto atoms.
`get_non_affine_contribution_to_elastic_constants`(atoms)	Compute the correction of non-affine displacements to the elasticity tensor.
`get_nonaffine_forces`(atoms)	Compute the non-affine forces which result from an affine deformation of atoms.
`get_property`(name[, atoms, allow_calculation])	Get the named property.
`get_stress_contribution_to_elastic_constants`(atoms)	Compute the correction to the elastic constants due to non-zero stress in the configuration.
`get_stresses`([atoms])	the calculator should return intensive stresses, i.e., such that stresses.sum(axis=0) == stress
`read`(label)	Read atoms, parameters and calculated properties from output file.
`reset`()	Clear all information from old calculation.
`set`(**kwargs)	Set parameters like set(key1=value1, key2=value2, ...).
`set_label`(label)	Set label and convert label to directory and prefix.

calculation_required
export_properties
get_atoms
get_charges
get_default_parameters
get_dipole_moment
get_forces
get_magnetic_moment
get_potential_energies
get_potential_energy
get_stress
read_atoms
todict

implemented_properties: List[str] = ['energy', 'free_energy', 'stress', 'forces', 'hessian', 'dynamical_matrix', 'nonaffine_forces', 'birch_coefficients', 'nonaffine_elastic_contribution', 'stress_elastic_contribution', 'born_constants', 'elastic_constants']: Properties calculator can handle (energy, forces, …)

default_parameters: Dict[str, Any] = {}: Default parameters

name = 'PairPotential'

__init__(f, cutoff=None): Construct calculator.

reset(): Clear all information from old calculation.

calculate(atoms, properties, system_changes): Calculate system properties.

band_structure(): Create band-structure object for plotting.

calculate_numerical_forces(atoms, d=0.001)

Calculate numerical forces using finite difference.

All atoms will be displaced by +d and -d in all directions.

calculate_numerical_stress(atoms, d=1e-06, voigt=True): Calculate numerical stress using finite difference.

calculate_properties(atoms, properties): This method is experimental; currently for internal use.

calculation_required(atoms, properties)

check_state(atoms, tol=1e-15): Check for any system changes since last calculation.

property directory: str

discard_results_on_any_change = False: Whether we purge the results following any change in the set() method.

export_properties()

get_atoms()

get_birch_coefficients(atoms)

Compute the Birch coefficients (Effective elastic constants at non-zero stress).

Parameters:: atoms (ase.Atoms) – Atomic configuration in a local or global minima.

get_born_elastic_constants(atoms)

Compute the Born elastic constants.

Parameters:: atoms (ase.Atoms) – Atomic configuration in a local or global minima.

get_charges(atoms=None)

get_default_parameters()

get_dipole_moment(atoms=None)

get_dynamical_matrix(atoms): Compute dynamical matrix (=mass weighted Hessian).

get_elastic_constants(atoms, cg_parameters={'M': None, 'atol': 1e-05, 'callback': None, 'maxiter': None, 'rtol': 1e-05, 'x0': None})

Compute the elastic constants at zero temperature. These are sum of the born, the non-affine and the stress contribution.

Parameters:

atoms (ase.Atoms) – Atomic configuration in a local or global minima.
cg_parameters (dict) –
Dictonary for the conjugate-gradient solver.

x0: {array, matrix}
Starting guess for the solution.

rtol/atol: float, optional
Tolerances for convergence, norm(residual) <= max(rtol*norm(b), atol).

maxiter: int
Maximum number of iterations. Iteration will stop after maxiter steps even if the specified tolerance has not been achieved.

M: {sparse matrix, dense matrix, LinearOperator}
Preconditioner for A.

callback: function
User-supplied function to call after each iteration.

get_forces(atoms=None)

get_hessian(atoms, format='sparse', divide_by_masses=False)

Calculate the Hessian matrix for a pair potential. For an atomic configuration with N atoms in d dimensions the hessian matrix is a symmetric, hermitian matrix with a shape of (d*N,d*N). The matrix is in general a sparse matrix, which consists of dense blocks of shape (d,d), which are the mixed second derivatives. The result of the derivation for a pair potential can be found e.g. in: L. Pastewka et. al. “Seamless elastic boundaries for atomistic calculations”, Phys. Rev. B 86, 075459 (2012).

Parameters:

atoms (ase.Atoms) – Atomic configuration in a local or global minima.
format ("sparse" or "neighbour-list") – Output format of the hessian matrix.
divide_by_masses (bool) – if true return the dynamic matrix else hessian matrix
Restrictions
----------
systems (This method is currently only implemented for three dimensional)

get_magnetic_moment(atoms=None)

get_magnetic_moments(atoms=None): Calculate magnetic moments projected onto atoms.

get_non_affine_contribution_to_elastic_constants(atoms, eigenvalues=None, eigenvectors=None, pc_parameters=None, cg_parameters={'M': None, 'atol': 1e-05, 'callback': None, 'maxiter': None, 'rtol': 1e-05, 'x0': None})

Compute the correction of non-affine displacements to the elasticity tensor. The computation of the occuring inverse of the Hessian matrix is bypassed by using a cg solver.

If eigenvalues and and eigenvectors are given the inverse of the Hessian can be easily computed.

Parameters:

atoms (ase.Atoms) – Atomic configuration in a local or global minima.
eigenvalues (array) – Eigenvalues in ascending order obtained by diagonalization of Hessian matrix. If given, use eigenvalues and eigenvectors to compute non-affine contribution.
eigenvectors (array) – Eigenvectors corresponding to eigenvalues.
cg_parameters (dict) –
Dictonary for the conjugate-gradient solver.

x0: {array, matrix}
Starting guess for the solution.

rtol/atol: float, optional
Tolerances for convergence, norm(residual) <= max( rtol*norm(b), atol).

maxiter: int
Maximum number of iterations. Iteration will stop after maxiter steps even if the specified tolerance has not been achieved.

M: {sparse matrix, dense matrix, LinearOperator}
Preconditioner for A.

callback: function
User-supplied function to call after each iteration.
pc_parameters (dict) –
Dictonary for the incomplete LU decomposition of the Hessian.

A: array_like
Sparse matrix to factorize.

drop_tol: float
Drop tolerance for an incomplete LU decomposition.

fill_factor: float
Specifies the fill ratio upper bound.

drop_rule: str
Comma-separated string of drop rules to use.

permc_spec: str
How to permute the columns of the matrix for sparsity.

diag_pivot_thresh: float
Threshold used for a diagonal entry to be an acceptable pivot.

relax: int
Expert option for customizing the degree of relaxing supernodes.

panel_size: int
Expert option for customizing the panel size.

options: dict
Dictionary containing additional expert options to SuperLU.

get_nonaffine_forces(atoms)

Compute the non-affine forces which result from an affine deformation of atoms.

Parameters:: atoms (ase.Atoms) – Atomic configuration in a local or global minima.

get_potential_energies(atoms=None)

get_potential_energy(atoms=None, force_consistent=False)

get_property(name, atoms=None, allow_calculation=True): Get the named property.

get_stress(atoms=None)

get_stress_contribution_to_elastic_constants(atoms)

Compute the correction to the elastic constants due to non-zero stress in the configuration. Stress term results from working with the Cauchy stress.

Parameters:: atoms (ase.Atoms) – Atomic configuration in a local or global minima.

get_stresses(atoms=None): the calculator should return intensive stresses, i.e., such that stresses.sum(axis=0) == stress

ignored_changes: Set[str] = {}: Properties of Atoms which we ignore for the purposes of cache

property label

read(label)

Read atoms, parameters and calculated properties from output file.

Read result from self.label file. Raise ReadError if the file is not there. If the file is corrupted or contains an error message from the calculation, a ReadError should also be raised. In case of succes, these attributes must set:

atoms: Atoms object: The state of the atoms from last calculation.
parameters: Parameters object: The parameter dictionary.
results: dict: Calculated properties like energy and forces.

The FileIOCalculator.read() method will typically read atoms and parameters and get the results dict by calling the read_results() method.

classmethod read_atoms(restart, **kwargs)

set(**kwargs)

Set parameters like set(key1=value1, key2=value2, …).

A dictionary containing the parameters that have been changed is returned.

Subclasses must implement a set() method that will look at the chaneged parameters and decide if a call to reset() is needed. If the changed parameters are harmless, like a change in verbosity, then there is no need to call reset().

The special keyword ‘parameters’ can be used to read parameters from a file.

set_label(label)

Set label and convert label to directory and prefix.

Examples:

label=’abc’: (directory=’.’, prefix=’abc’)
label=’dir1/abc’: (directory=’dir1’, prefix=’abc’)
label=None: (directory=’.’, prefix=None)

todict(skip_default=True)