principia_materia.translation_group.crystal_ftg module

class principia_materia.translation_group.crystal_ftg.CrystalFTG(vec, atoms, supa=None, orbitals=None, lattice_coordinate=True, pg=None, tol=1e-06)

Bases: Crystal

A crystal structure with a finite translation group (FTG).

Here we define a finite translation group by mapping the infinite translation group of the crystal with periodic boundary condition. This boundary condition is defined with a supercell.

Parameters:

vec (array of float, shape(dim, dim)) – The lattice vectors.
atoms (dict of str as keys and array of float as values) – A dictionary of names of atoms and their positions. The positions are in lattice coordinate if lattice_coordinate == True, otherwise they are in cartesian coordinate.
supa (array of int, shape(dim, dim)) – The supercell matrix.
orbitals (str or array of str) – Orbital names to assign to the atoms.
lattice_coordinate (bool, optional, default to True) – If True, the coordinate in input variable atoms is in Cartesian coordinates.
pg (str or a PointGroup object) – The point group of the lattice.
tol (float, optional, default to 1.0E-6) – Tolerance.

as_primitive()

Return a copy of the object with the current structure as the primitive cell and supa equal to identity.

Returns:: new – An CrystalFTG object with the current vec, atoms, orbitals, pg and tol, supa set to identity.
Return type:: CrystalFTG

property atoms: A dictionary of atoms and their positions.

copy()

Return a copy of the object.

Returns:: new – A copy of the object itself.
Return type:: CrystalFTG

find_atoms(positions)

Find the indices of atoms of that have identical positions within a translation.

If an atom is not found, in return index will be -1.

Parameters:

positions (array of float, shape (dim, ) or (N, dim)) – Positions of atoms to be found. If input shape is (dim, ), it will be reshaped into (1, dim) and N = 1.

Returns:

atoms_index (array of int, shape (N, )) – The indices of atoms.
translation (array of int, shape (N, dim)) – The translation that will take the atoms in the crystal to the input atom position.

classmethod from_primitive(primitive, supa)

Construct CrystalFTG from Crystal and a supercell.

Parameters:

primitive (Crystal) – The Crystal object of a primitive cell.
supa (array of int, shape(dim, dim)) – The supercell matrix.

Returns:

new – The produced CrystalFTG object.

Return type:

CrystalFTG

get_basis_at_q(qpoint)

Compute the basis vectors of the primitive cell orbitals at a q-point.

The input q-point has to fit in the supercell.

Parameters:: qpoint (array of Fraction, shape(dim, )) – A q-point.
Returns:: basis – The dictionary of the basis vectors of the primitive cell orbitals.
Return type:: dict with tuple(int, str) as keys and array of complex, shape(natoms, dim) as values

get_wigner_seitz_cell(center)

Find atoms in the Wigner Seitz (WS) cell at a given center.

Parameters:

center (array of float, shape(self.dim)) – The coordinate of the center of the WS cell in lattice coordinate.

Returns:

ws_cell_translation (array of int, shape(N, self.dim)) – The primitive translation vector of the WS atom. N is the total number of the atoms in the WS cell.
ws_cell_atoms (array of int, shape(N)) – The index of the WS atom in the primitive cell.
ws_cell_weights (array of float, shape(N)) – The weight of the WS atom.

property invsupa: The inverse of the supercell matrix.

property orbitals: A list of all orbitals of atoms in the cluster.

rotate(rotation)

Rotate atoms (in place).

Parameters:: rotation (arrat of floats, shape(dim, dim)) – The rotation matrix in column convention.

shift_atom(atom_index, shift)

Shift an atom.

Parameters:

atom_index (int) – Index of the atom to shift.
shift (float or array of float, shape(dim, )) – The shift amount.

property species_names: A list of names of species.

property supa: The supercell matrix.

property supa_atoms_map: The atom indices of the supercell atoms with respect to their corresponding atoms in primitive cell.

property supa_translations: The translation vectors of the supercell atoms with respect to their corresponding atoms in primitive cell.

to_dict(): Return a dictionary containing key information about the CrystalFTG object.

property tol: Error tolerance.

principia_materia.translation_group.crystal_ftg.get_crystal_ftg_io_wrapper(title='CrystalFTG'): YAML data wrapper for CrystalFTG class.