Calculators

ClusterExpansionCalculator

class mchammer.calculators.ClusterExpansionCalculator(structure, cluster_expansion, name='Cluster Expansion Calculator', scaling=None, use_local_energy_calculator=True)[source]

A ClusterExpansionCalculator object enables the efficient calculation of properties described by a cluster expansion. It is specific for a particular (supercell) structure and commonly employed when setting up a Monte Carlo simulation, see Ensembles.

Cluster expansions, e.g., of the energy, typically yield property values per site. When running a Monte Carlo simulation one, however, considers changes in the total energy of the system. The default behavior is therefore to multiply the output of the cluster expansion by the number of sites. This behavior can be changed via the scaling keyword parameter.

Parameters:
  • structure (ase.Atoms) – structure for which to set up the calculator
  • cluster_expansion (ClusterExpansion) – cluster expansion from which to build calculator
  • name (str) – human-readable identifier for this calculator
  • scaling (Union[int, float, None]) – scaling factor applied to the property value predicted by the cluster expansion
  • use_local_energy_calculator (bool) – evaluate energy changes using only the local environment; this method is generally much faster; unless you know what you are doing do not set this option to False
calculate_local_contribution(*, local_indices, occupations)[source]

Calculates and returns the sum of the contributions to the property due to the sites specified in local_indices

Parameters:
  • local_indices (List[int]) – sites over which to sum up the local contribution
  • occupations (List[int]) – entire occupation vector
Return type:

float

calculate_total(*, occupations)[source]

Calculates and returns the total property value of the current configuration.

Parameters:occupations (List[int]) – the entire occupation vector (i.e. list of atomic species)
Return type:float
cluster_expansion

cluster expansion from which calculator was constructed

Return type:ClusterExpansion
structure

atomic structure associated with calculator

Return type:Atoms
sublattices

Sublattices of the calculators structure.

Return type:Sublattices
update_occupations(indices, species)

Updates the occupation (species) of the associated atomic structure.

Parameters:
  • indices (List[int]) – sites to update
  • species (List[int]) – new occupations (species) by atomic number

TargetVectorCalculator

class mchammer.calculators.target_vector_calculator.TargetVectorCalculator(structure, cluster_space, target_vector, weights=None, optimality_weight=1.0, optimality_tol=1e-05, name='Target vector calculator')[source]

A TargetVectorCalculator enables evaluation of the similarity between a structure and a target cluster vector. Such a comparison can be carried out in many ways, and this implementation follows the measure proposed by van de Walle et al. in Calphad 42, 13 (2013) [WalTiwJon13]. Specifically, the objective function \(Q\) is calculated as

\[Q = - \omega L + \sum_{\alpha} \left| \Gamma_{\alpha} - \Gamma^{\text{target}}_{\alpha} \right|.\]

Here, \(\Gamma_{\alpha}\) are components in the cluster vector and \(\Gamma^\text{target}_{\alpha}\) the corresponding target values. The factor \(\omega\) is the radius of the largest pair cluster such that all clusters with the same or smaller radii have \(\Gamma_{\alpha} - \Gamma^\text{target}_{\alpha} = 0\).

Parameters:
  • structure (Atoms) – structure for which to set up calculator
  • cluster_space (ClusterSpace) – cluster space from which to build calculator
  • target_vector (List[float]) – vector to which any vector will be compared
  • weights (Optional[List[float]]) – weighting of each component in cluster vector comparison, by default 1.0 for all components
  • optimality_weight (float) – factor \(L\), a high value of which effectively favors a complete series of optimal cluster correlations for the smallest pairs (see above)
  • optimality_tol (float) – tolerance for determining whether a perfect match has been achieved (used in conjunction with \(L\))
  • name (str) – human-readable identifier for this calculator
calculate_local_contribution(local_indices, occupations)[source]

Not yet implemented, forwards calculation to calculate_total.

Return type:float
calculate_total(occupations)[source]

Calculates and returns the similarity value \(Q\) of the current configuration.

Parameters:occupations (List[int]) – the entire occupation vector (i.e. list of atomic species)
Return type:float
structure

atomic structure associated with calculator

Return type:Atoms
sublattices

Sublattices of the calculators structure.

Return type:Sublattices
update_occupations(indices, species)

Updates the occupation (species) of the associated atomic structure.

Parameters:
  • indices (List[int]) – sites to update
  • species (List[int]) – new occupations (species) by atomic number
mchammer.calculators.target_vector_calculator.compare_cluster_vectors(cv_1, cv_2, orbit_data, weights=None, optimality_weight=1.0, tol=1e-05)[source]

Calculate a quantity that measures similarity between two cluster vecors.

Parameters:
  • cv_1 (ndarray) – cluster vector 1
  • cv_2 (ndarray) – cluster vector 2
  • orbit_data (OrderedDict) – orbit data as obtained by ClusterSpace.orbit_data
  • weights (Optional[List[float]]) – Weight assigned to each cluster vector element
  • optimality_weight (float) – quantity \(L\) in [WalTiwJon13] (see mchammer.calculators.TargetVectorCalculator)
  • tol (float) – numerical tolerance for determining whether two elements are exactly equal
Return type:

float