Cluster space

ClusterSpace

class hiphive.ClusterSpace(prototype_structure, cutoffs, config=None, cluster_filter=None, **kwargs)

Primitive object for handling clusters and force constants of a structure.

Parameters:

• prototype_structure (ase.Atoms) – prototype structure; spglib will be used to find a suitable cell based on this structure unless the cell is already a primitive cell.

• cutoffs (list or Cutoffs) – cutoff radii for different orders starting with second order

• cluster_filter (ClusterFilter) – accepts a subclass of hiphive.filters.BaseClusterFilter to further control which orbits to include.

• config (Config object) – a configuration object that holds information on how the cluster space should be built, e.g., values for tolerances and specifications regarding the handling of acoustic sum rules; if config is not given then the keyword arguments that follow below can be used for configuration.

• acoustic_sum_rules (bool) – If True the aucostic sum rules will be enforced by constraining the parameters.

• symprec (float) – numerical precision that will be used for analyzing the symmetry (this parameter will be forwarded to spglib)

• length_scale (float) – This will be used as a normalization constant for the eigentensors

Examples

To instantiate a ClusterSpace object one has to specify a prototype structure and cutoff radii for each cluster order that should be included. For example the following snippet will set up a ClusterSpace object for a body-centered-cubic (BCC) structure including second order terms up to a distance of 5 A and third order terms up to a distance of 4 A.

>>> from ase.build import bulk
>>> from hiphive import ClusterSpace
>>> prim = bulk('W')
>>> cs = ClusterSpace(prim, [5.0, 4.0])

property acoustic_sum_rules

True if acoustic sum rules are enforced

Type:

bool

property atom_list

atoms inside the cutoff relative to the of the center cell

Type:

BiMap

property cluster_list

clusters possible within the cutoff

Type:

BiMap

property cutoffs

cutoffs used for constructing the cluster space

Type:

Cutoffs

get_n_dofs_by_order(order)

Returns number of degrees of freedom for the given order.

Parameters:

order (int) – order for which to return the number of dofs

Returns:

number of degrees of freedom

Return type:

int

get_parameter_indices(order)

Returns a list of the parameter indices associated with the requested order.

Parameters:

order (int) – order for which to return the parameter indices

Returns:

list of parameter indices associated with the requested order

Return type:

list(int)

Raises:

ValueError – if the order is not included in the cluster space

property length_scale

normalization constant of the force constants

Type:

float

property n_dofs

number of free parameters in the model

If the sum rules are not enforced the number of DOFs is the same as the total number of eigentensors in all orbits.

Type:

int

property orbit_data

detailed information for each orbit, e.g., cluster radius and atom types.

Type:

list(dict)

property orbits

orbits associated with the lattice structure.

Type:

list(Orbit)

property permutations

lookup for permutation references

Type:

list(numpy.ndarray)

property primitive_structure

structure of the lattice

Type:

ase.Atoms

print_orbits()

Prints a list of all orbits.

print_tables()

Prints information concerning the underlying cluster space to stdout,including, e.g., the number of cluster, orbits, and parameters by order and number of bodies.

read()

Reads a cluster space from file.

Parameters:

f (str or file object) – name of input file (str) or stream to load from (file object)

property rotation_matrices

symmetry elements (3x3 matrices) representing rotations

Type:

list(numpy.ndarray)

property spacegroup

space group of the lattice structure obtained from spglib

Type:

str

property symprec

symprec value used when constructing the cluster space

Type:

float

property translation_vectors

symmetry elements representing translations

Type:

list(numpy.ndarray)

write(fileobj)

Writes cluster space to file.

The instance is saved into a custom format based on tar-files. The resulting file will be a valid tar file and can be browsed by by a tar reader. The included objects are themself either pickles, npz or other tars.

Parameters:

fileobj (str or file-like object) – If the input is a string a tar archive will be created in the current directory. Otherwise the input must be a valid file like object.

property wyckoff_sites

wyckoff sites in the primitive cell

Type:

list

Cutoffs

class hiphive.cutoffs.BaseClusterFilter

Base cluster filter class.

This filter simply accepts all proposed clusters. A proper subclass must implement the same methods.

setup(atoms)

The filter is passed the environment of the primitive cell.

Parameters:

atoms (ase.Atoms) – non-pbc primitive cell plus neighboring atoms

class hiphive.cutoffs.CutoffMaximumBody(cutoff_list, max_nbody)

Specify cutoff-list plus maximum body

Usefull when creating e.g. 6th order expansions but with only 3-body interactions.

Parameters:

• cutoff_list (list) – list of cutoffs for order 2, 3, etc. Must be in decresing order

• max_nbody (int) – No clusters containing more than max_nbody atoms will be generated

class hiphive.cutoffs.Cutoffs(cutoff_matrix)

This class maintains information about the cutoff configuration, i.e. which clusters will be included (=”inside cutoff”). It also encapsulates functionality that is used e.g., during cluster space construction.

Here, n-body refers to number of atoms in a cluster. For example the cluster (0011) is a two-body cluster of fourth order and the cluster (123) is a three-body cluster of third order.

Parameters:

cutoff_matrix (numpy.ndarray) – the matrix element ij provides to the cutoff for order j+2 and nbody i+2; elements with i>j will be ignored

property cutoff_matrix

copy of cutoff matrix

Type:

numpy.ndarray

get_cutoff(order, nbody)

Returns cutoff for a given body and order.

Parameters:

• order (int)

• nbody (int)

Raises:

• ValueError – if order is not in orders

• ValueError – if nbody is not in nbodies

• ValueError – if nbody is larger than order

Return type:

float

property max_cutoff

maximum cutoff

Type:

float

property max_nbody

maximum body

Type:

int

max_nbody_cutoff(nbody)

Return maximum cutoff for a given body.

max_nbody_order(nbody)

Returns maximum order for a given body

property max_order

maximum order

Type:

int

property nbodies

allowed bodies

Type:

list(int)

property orders

allowed orders

Type:

list(int)

read()

Reads an instance from file.

Parameters:

fileobj (file-like object) – input file to read from

to_filename_tag()

Simple function turning cutoffs into a string to be used in e.g. filenames.

write(fileobj)

Writes instance to file.

Parameters:

fileobj (file-like object) – file-like object to which the cutoffs will be written to

hiphive.cutoffs.estimate_maximum_cutoff(atoms, max_iter=11)

Estimates the maximum possible cutoff given the atoms object

Parameters:

• atoms (ase.Atoms) – structure used for checking compatibility with cutoff

• max_iter (int) – number of iterations in binary search

hiphive.cutoffs.is_cutoff_allowed(atoms, cutoff)

Checks if atoms is compatible with cutoff

Parameters:

• atoms (ase.Atoms) – structure used for checking compatibility with cutoff

• cutoff (float) – cutoff to be tested

Returns:

True if cutoff compatible with atoms object, else False

Return type:

bool