Structures¶
Preparing structures for training¶
hiphive provides some utility functions for handling training :structures.
For example get_displacements
can be used to calculate the displacements of atoms given a reference
structure accounting while accounting for periodic boundary conditions.
In cases where the ordering/indexing of atoms in the training structures
differs from the reference structure, one can use find_permutation
which finds the permutation that
reorderes the training structures to match the reference.
The function prepare_structures
combines these two functions together and adds displacements and forces as
arrays to the structures such that they can be added directly a
StructureContainer
.

hiphive.utilities.
get_displacements
(atoms, atoms_ideal, cell_tol=0.0001)[source] Returns the the smallest possible displacements between a displaced configuration relative to an ideal (reference) configuration.
Notes
assumes periodic boundary conditions in all directions
 Parameters
atoms (
Atoms
) – configuration with displaced atomsatoms_ideal (
Atoms
) – ideal configuration relative to which displacements are computedcell_tol (
float
) – cell tolerance; if cell missmatch more than tol value error is raised
 Return type

hiphive.utilities.
find_permutation
(atoms, atoms_ref)[source] Returns the best permutation of atoms for mapping one configuration onto another.
 Parameters
atoms (
Atoms
) – configuration to be permutedatoms_ref (
Atoms
) – configuration onto which to map
Examples
After obtaining the permutation via
p = find_permutation(atoms1, atoms2)
the reordered structureatoms1[p]
will give the closest match toatoms2
. Return type
List
[int
]

hiphive.utilities.
prepare_structures
(structures, atoms_ideal, calc=None)[source] Prepares a set of structures in the format suitable for adding them to a
StructureContainer
.structures should represent a list of supercells with displacements while atoms_ideal should provide the ideal reference structure (without displacements) for the given structures.
The structures that are returned will have their positions reset to the ideal structures. Displacements and forces will be added as arrays to the atoms objects.
If no calculator is provided, then there must be an ASE SinglePointCalculator <ase.calculators.singlepoint> object attached to the structures or the forces should already be attached as arrays to the structures.
If a calculator is provided then it will be used to compute the forces for all structures.
Example
The following example illustrates the use of this function:
db = connect('dft_training_structures.db') training_structures = [row.toatoms() for row in db.select()] training_structures = prepare_structures(training_structures, atoms_ideal) for s in training_structures: sc.add_structure(s)
 Parameters
structures (
List
[Atoms
]) – list of input displaced structuresatoms_ideal (
Atoms
) – reference structure relative to which displacements are computedcalc (
Optional
[SinglePointCalculator
]) – ASE calculator used for computing forces
 Returns
 Return type
list of prepared structures with forces and displacements as arrays
StructureContainer¶
hiphive organizes the data for training and testing in a socalled
:structure container, which provides methods for adding and accessing these
:data. The structure container is essentially a collection of
:FitStructure
objects, each of which comprises an original atomic
:configuration along :with its representation in clusters and reference
:forces.

class
hiphive.
StructureContainer
(cs, fit_structure_list=None)[source]¶ This class serves as a container for structures as well as associated fit properties and fit matrices.
 Parameters
cs (ClusterSpace) – cluster space that is the basis for the container
fit_structure_list (list(FitStructure)) – structures to be added to the container

add_structure
(atoms, **meta_data)[source]¶ Add a structure to the container.
Note that custom information about the atoms object may not be stored inside, for example an ASE
SinglePointCalculator
will not be kept. Parameters
atoms (ase.Atoms) – the structure to be added; the Atoms object must contain supplementary peratom arrays with displacements and forces
meta_data (dict) – dict with meta_data about the atoms

property
cluster_space
¶ copy of the cluster space the structure container is based on
 Type

property
data_shape
¶ tuple of integers representing the shape of the fit data matrix
 Type
tuple

get_fit_data
(structures=None)[source]¶ Return fit data for structures. The fit matrices and target forces for the structures are stacked into NumPy arrays.
 Parameters
structures (list, tuple) – list of integers corresponding to structure indices. Defaults to None and in that case returns all fit data available.
 Returns
stacked fit matrices, stacked target forces for the structures
 Return type

static
read
(fileobj, read_structures=True)[source]¶ Restore a StructureContainer object from file.
 Parameters
f (str or file object) – name of input file (str) or stream to load from (file object)
read_structures (bool) – if True the structures will be read; if False only the cluster space will be read
FitStructure¶

class
hiphive.structure_container.
FitStructure
(atoms, fit_matrix, **meta_data)[source]¶ This class holds a structure with displacements and forces as well as the fit matrix.
 Parameters
atoms (ase.Atoms) – supercell structure
fit_matrix (numpy.ndarray) – fit matrix, N, M array with N = 3 * len(atoms)
meta_data (dict) – any meta data that needs to be stored in the FitStructure

property
displacements
¶ atomic displacements
 Type

property
fit_matrix
¶ the fit matrix
 Type

property
forces
¶ forces
 Type

static
read
(fileobj, read_fit_matrix=True)[source]¶ Read a OrientationFamily instance from a file.
 Parameters
fileobj (str or file object) – name of input file (str) or stream to read from (file object)
read_fit_matrix (bool) – whether or not to read the fit_matrix
 Returns
 Return type
FitStructure instance
Structure generation¶
This module enables the generation of structures with displacements that can be used to generate reference forces.

hiphive.structure_generation.
generate_mc_rattled_structures
(atoms, n_configs, rattle_std, d_min, seed=42, **kwargs)[source] Returns list of Monte Carlo rattled configurations.
Rattling atom i is carried out as a Monte Carlo move that is accepted with a probability determined from the minimum interatomic distance \(d_{ij}\). If \(\min(d_{ij})\) is smaller than \(d_{min}\) the move is only accepted with a low probability.
This process is repeated for each atom a number of times meaning the magnitude of the final displacements is not directly connected to rattle_std.
Warning
Repeatedly calling this function without providing different seeds will yield identical or correlated results. To avoid this behavior it is recommended to specify a different seed for each call to this function.
Notes
The procedure implemented here might not generate a symmetric distribution for the displacements kwargs will be forwarded to mc_rattle (see user guide for a detailed explanation)
 Parameters
atoms (ase.Atoms) – prototype structure
n_structures (int) – number of structures to generate
rattle_std (float) – rattle amplitude (standard deviation in normal distribution); note this value is not connected to the final average displacement for the structures
d_min (float) – interatomic distance used for computing the probability for each rattle move
seed (int) – seed for setting up NumPy random state from which random numbers are generated
n_iter (int) – number of Monte Carlo cycles
 Returns
generated structures
 Return type
list of ase.Atoms

hiphive.structure_generation.
generate_rattled_structures
(atoms, n_structures, rattle_std, seed=42)[source] Returns list of rattled configurations.
Displacements are drawn from normal distributions for each Cartesian directions for each atom independently.
Warning
Repeatedly calling this function without providing different seeds will yield identical or correlated results. To avoid this behavior it is recommended to specify a different seed for each call to this function.
 Parameters
atoms (ase.Atoms) – prototype structure
n_structures (int) – number of structures to generate
rattle_std (float) – rattle amplitude (standard deviation of the normal distribution)
seed (int) – seed for setting up NumPy random state from which random numbers are generated
 Returns
generated structures
 Return type
list of ase.Atoms

hiphive.structure_generation.
generate_phonon_rattled_structures
(atoms, fc2, n_structures, temperature)[source] Returns list of phononrattled configurations.
Configurations are generated by superimposing harmonic phonon eigenmodes with random amplitudes and phase factors consistent with a certain temperature.
Let \(\boldsymbol{X}_{ai}\) be the phonon modes indexed by atom \(a\) and mode \(i\), \(\omega_i\) the phonon frequencies, and let \(0 < Q_i \leq 1\) and \(0 \leq U_i < 1\) be uniformly random numbers. Then
\[\boldsymbol{R}_a = \boldsymbol{R}^0_a + \left<\frac{k_B T}{m_a} \right>^{1/2} \sum_i \frac{1}{\omega_i} \boldsymbol{X}_{ai} \sqrt{2 \ln Q_i} \cos(\pi \omega_i U_i)\]See: West and Estreicher, Physical Review Letters 96, 115504 (2006)
 Parameters
atoms (ase.Atoms) – prototype structure
fc2 (numpy.ndarray) – second order force constant matrix, with shape (3N, 3N) or (N, N, 3, 3). The conversion will be done internally if.
n_structures (int) – number of structures to generate
temperature (float) – temperature in Kelvin
 Returns
generated structures
 Return type
list(ase.Atoms)