Cluster expansions

class icet.ClusterExpansion(cluster_space, parameters, metadata=None)[source]

Cluster expansions are obtained by combining a cluster space with a set of effective cluster interactions (ECIs). Instances of this class allow one to predict the property of interest for a given structure.


cluster space that was used for constructing the cluster expansion


effective cluster interactions (ECIs)



The following snippet illustrates the initialization and usage of a ClusterExpansion object. Here, the ECIs are taken to be a list of ones. Usually, they would be obtained by training with respect to a set of reference data:

from import bulk
from icet import ClusterSpace, ClusterExpansion

# create cluster expansion
prim = bulk('Au')
cs = ClusterSpace(prim, cutoffs=[7.0, 5.0],
                  chemical_symbols=[['Au', 'Pd']])
ecis = 14 * [1.0]
ce = ClusterExpansion(cs, ecis)

# make prediction for supercell
sc = prim.repeat(3)
for k in [1, 4, 7]:
    sc[k].symbol = 'Pd'

Gets copy of cluster space on which cluster expansion is based

Return type:ClusterSpace

metadata associated with cluster expansion


orders included in cluster expansion

Return type:List[int]

effective cluster interactions (ECIs)

Return type:List[float]

dataframe containing orbit data and ECIs

Return type:DataFrame

Plot ECIs for given orders, default plots for all orders


Predicts the property of interest (e.g., the energy) for the input structure using the cluster expansion.

Parameters:structure (Union[Atoms, Structure]) – atomic configuration
Returns:property value of predicted by the cluster expansion
Return type:float
print_overview(print_threshold=None, print_minimum=10)[source]

Print an overview of the cluster expansion in terms of the orbits (order, radius, multiplicity, corresponding ECI etc).

  • print_threshold (Optional[int]) – if the number of orbits exceeds this number print dots
  • print_minimum (int) – number of lines printed from the top and the bottom of the orbit list if print_threshold is exceeded
Return type:


prune(indices=None, tol=0)[source]

Removes orbits from the cluster expansion (CE), for which the effective cluster interactions (ECIs; parameters) are zero or close to zero. This commonly reduces the computational cost for evaluating the CE and is therefore recommended prior to using it in production. If the method is called without arguments orbits will be pruned, for which the ECIs are strictly zero. Less restrictive pruning can be achived by setting the tol keyword.

  • indices (Optional[List[int]]) – indices to parameters to remove in the cluster expansion.
  • tol (float) – orbits for which the absolute ECIs is/are within this value will be pruned
static read(filename)[source]

Reads ClusterExpansion object from file.

Parameters:filename (str) – file from which to read

Writes ClusterExpansion object to file.

Parameters:filename (str) – name of file to which to write