ccu.structure.symmetry

Symmetry-related functions and classes.

This class defines the Transformation class and useful subclasses (Rotation, Translation, Reflection, and Inversion)

Example

>>> from ase import Atoms
>>> from ccu.structure.symmetry import check_symmetry, Rotation
>>> rotation1 = Rotation(90, [0, 0, 1])
>>> co = Atoms("CO", positions=[[0, 0, 0], [1, 0, 0]])
>>> rotated = rotation1(co)
>>> rotated.positions
array([[0.000000e+00, 0.000000e+00, 0.000000e+00],
      [6.123234e-17, 1.000000e+00, 0.000000e+00]])
>>> check_symmetry(rotation1, co)
False
>>> h2 = Atoms("HH", positions=[[0, 0, 0], [1, 0, 0]])
>>> rotation2 = Rotation(180, [0, 0, 1])
>>> check_symmetry(rotation2, h2)
True

class ccu.structure.symmetry.Inversion(point: Iterable[float] | None = None)

Bases: Transformation

An inversion operation.

This Transformation represents the inverson of coordinates through a point.

Variables:

point – A length 3, 1D ndarray that represents the inversion point.

Instantiate an Inversion.

Parameters:

point – A length 3 iterable of floats that represents the inversion point.

_abc_impl = <_abc._abc_data object>

_is_protocol = False

class ccu.structure.symmetry.Reflection(point: Iterable[float] | None = None, norm: Iterable[float] | None = None)

Bases: Transformation

A reflection operation.

This Transformation represents the reflection of coordinates through a plane.

Variables:

• point – A length 3, 1D ndarray that represents a point on the reflection plane.

• norm – A length 3, 1D ndarray that represents a vector normal to the reflection plane.

Create a reflection operation.

Parameters:

• point – A length 3 iterable of floats that represents a point on the reflection plane. Defaults to the origin.

• norm – A length 3 iterable of floats that represents a vector normal to the reflection plane. Defaults to the positive z-axis.

_abc_impl = <_abc._abc_data object>

_is_protocol = False

class ccu.structure.symmetry.Rotation(angle: float = 0.0, axis: Iterable[float] | None = None)

Bases: Transformation

A rotation operation.

Variables:

• angle – A float specifying a rotation angle in degrees.

• axis – A numpy.ndarray representing the axis of rotation.

Create a rotation operation.

Parameters:

• angle – The angle of rotation. Defaults to 0.0.

• axis – The axis of rotation. Defaults to the positive z-axis.

_abc_impl = <_abc._abc_data object>

_is_protocol = False

as_matrix() → NDArray[np.floating]

The rotation matrix of the symmetry operation.

class ccu.structure.symmetry.Transformation(*args, **kwargs)

Bases: Protocol

A protocol for structural transformations.

In general, implementers of this protocol should preserve the info dictionary of Atoms objects; however, if changes are made to the chemical composition, metadata should be updated as well.

_abc_impl = <_abc._abc_data object>

_is_protocol = True

class ccu.structure.symmetry.Translation(direction: Iterable[float] | None = None)

Bases: Transformation

A reflection operation.

This Transformation represents the reflection of coordinates through a plane.

Variables:

direction – A length 3, 1D ndarraythat represents a translation.

Create a reflection operation.

Parameters:

direction – A length 3, 1D ndarraythat represents a translation. Defaults to the zero vector.

_abc_impl = <_abc._abc_data object>

_is_protocol = False

ccu.structure.symmetry.check_symmetry(transform: Transformation, structure: Atoms, tol: float = 0.05) → bool

Check if a structure is symmetric with respect to a transformation.

Parameters:

• transform – The Transformation with respect to which structure will be checked for symmetry.

• structure – An Atoms object.

• tol – A float specifying the absolute tolerance for positions. Defaults to 5e-2.

Returns:

A bool indicating whether or not the given structure possesses the symmetry with respect to the given Transformation subject to the specified tolerance.