matscipy.calculators.manybody.newmb

Manybody calculator definition.

Functions

ein(*args)

Optimized einsum.

Classes

Manybody(phi, theta, neighbourhood)

Generic two- and three- body interaction calculator.
class matscipy.calculators.manybody.newmb.Manybody(phi: Mapping[int, Phi], theta: Mapping[int, Theta], neighbourhood: Neighbourhood)

Bases: MatscipyCalculator

Generic two- and three- body interaction calculator.

Attributes:
directory
label
name

Methods

Phi()

Define the manybody interaction with pair term ɸ(rᵢⱼ², ξᵢⱼ).

Theta()

Define the three-body term Θ(rᵢⱼ², rᵢₖ², rⱼₖ²).

band_structure()

Create band-structure object for plotting.

calculate(atoms, properties, system_changes)

Calculate properties on atoms.

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 (affine) 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])

Compute hessian.

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 non-affine forces (derivatives w/r reference positions).

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.

sum_ij_pi_ij_n(n, pairs, values_p)

Compute \(\sum_{ij}\pi_{ij|n}\Chi_{ij}\).

sum_ij_sum_X_pi_X_n(n, pairs, triplets, ...)

Compute \(\sum_{ij}\sum_{k\neq i,j}\sum_{X}\pi_{X|n}\Chi_X\).

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

sum_XX_sum_ijk_tau_XX_mn

sum_XY_sum_ijk_tau_XY_mn

sum_X_sum_ijk_tau_ijX_mn

sum_X_sum_ijk_tau_ij_XOR_X_mn

sum_ijk_tau_XY_mn

todict
implemented_properties: List[str] = ['free_energy', 'energy', 'stress', 'forces', 'hessian', 'dynamical_matrix', 'born_constants', 'nonaffine_forces', 'birch_coefficients', 'elastic_constants']

Properties calculator can handle (energy, forces, …)

class Phi

Bases: ABC

Define the manybody interaction with pair term ɸ(rᵢⱼ², ξᵢⱼ).

Methods

__call__(rsq_p, xi_p)

Return ɸ(rᵢⱼ², ξᵢⱼ).

gradient(rsq_p, xi_p)

Return [∂₁ɸ(rᵢⱼ², ξᵢⱼ), ∂₂ɸ(rᵢⱼ², ξᵢⱼ)].

hessian(rsq_p, xi_p)

Return [∂₁₁ɸ(rᵢⱼ², ξᵢⱼ), ∂₂₂ɸ(rᵢⱼ², ξᵢⱼ), ∂₁₂ɸ(rᵢⱼ², ξᵢⱼ)].
abstract gradient(rsq_p, xi_p)

Return [∂₁ɸ(rᵢⱼ², ξᵢⱼ), ∂₂ɸ(rᵢⱼ², ξᵢⱼ)].

abstract hessian(rsq_p, xi_p)

Return [∂₁₁ɸ(rᵢⱼ², ξᵢⱼ), ∂₂₂ɸ(rᵢⱼ², ξᵢⱼ), ∂₁₂ɸ(rᵢⱼ², ξᵢⱼ)].

class Theta

Bases: ABC

Define the three-body term Θ(rᵢⱼ², rᵢₖ², rⱼₖ²).

Methods

__call__(R1_p, R2_p, R3_p)

Return Θ(rᵢⱼ², rᵢₖ², rⱼₖ²).

gradient(R1_p, R2_p, R3_p)

Return [∂₁Θ(rᵢⱼ², rᵢₖ², rⱼₖ²),

hessian(R1_p, R2_p, R3_p)

Return [∂₁₁Θ(rᵢⱼ², rᵢₖ², rⱼₖ²),
abstract gradient(R1_p, R2_p, R3_p)
Return [∂₁Θ(rᵢⱼ², rᵢₖ², rⱼₖ²),

∂₂Θ(rᵢⱼ², rᵢₖ², rⱼₖ²), ∂₃Θ(rᵢⱼ², rᵢₖ², rⱼₖ²)].

abstract hessian(R1_p, R2_p, R3_p)
Return [∂₁₁Θ(rᵢⱼ², rᵢₖ², rⱼₖ²),

∂₂₂Θ(rᵢⱼ², rᵢₖ², rⱼₖ²), ∂₃₃Θ(rᵢⱼ², rᵢₖ², rⱼₖ²), ∂₂₃Θ(rᵢⱼ², rᵢₖ², rⱼₖ²), ∂₁₃Θ(rᵢⱼ², rᵢₖ², rⱼₖ²), ∂₁₂Θ(rᵢⱼ², rᵢₖ², rⱼₖ²)].

__init__(phi: Mapping[int, Phi], theta: Mapping[int, Theta], neighbourhood: Neighbourhood)

Construct with potentials ɸ(rᵢⱼ², ξᵢⱼ) and Θ(rᵢⱼ², rᵢₖ², rⱼₖ²).

classmethod sum_ij_pi_ij_n(n, pairs, values_p)

Compute \(\sum_{ij}\pi_{ij|n}\Chi_{ij}\).

classmethod sum_ij_sum_X_pi_X_n(n, pairs, triplets, values_tq)

Compute \(\sum_{ij}\sum_{k\neq i,j}\sum_{X}\pi_{X|n}\Chi_X\).

classmethod sum_ijk_tau_XY_mn(n, triplets, tr_p, X, Y, values_t)
classmethod sum_XY_sum_ijk_tau_XY_mn(n, triplets, tr_p, values_tXY)
classmethod sum_XX_sum_ijk_tau_XX_mn(n, triplets, tr_p, values_tX)
classmethod sum_X_sum_ijk_tau_ijX_mn(n, triplets, tr_p, values_tX)
classmethod sum_X_sum_ijk_tau_ij_XOR_X_mn(n, triplets, tr_p, values_tX)
calculate(atoms, properties, system_changes)

Calculate properties on atoms.

get_born_elastic_constants(atoms)

Compute the Born (affine) elastic constants.

get_nonaffine_forces(atoms)

Compute non-affine forces (derivatives w/r reference positions).

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.

default_parameters: Dict[str, Any] = {}

Default parameters

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_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)

Compute hessian.

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_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
property name: str
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)
reset()

Clear all information from old calculation.

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)