Geometry#

class quadrupole.geometry.Atom(element: ElementLike, xyz: ArrayLike)#

Bases: object

Class containing the information of a single atom.

Parameters:

elementElementLike: A member of the Element enum, or the atomic symbol/number.
xyzArrayLike of float with length 3: The x-, y-, and z-coordinates of the atom in Ångstrom.

Attributes:

elementElement: A member of the Element enum.
xyzNDArray of float with size 3: The x-, y-, and z-coordinates of the atom in Ångstrom.

class quadrupole.geometry.Geometry(atoms: list[Atom], lat_vec: ndarray[tuple[Any, ...], dtype[float64]] | None = None)#

Bases: object

Class storing the geometric parameters of a molecular geometry or crystal structure.

All quantities should be in Ångstrom.

Parameters:

atomslist[Atom]: The atoms in the geometry.
lat_vecArrayLike of float with shape (3,3), optional: The lattice vectors of the geometry.

Attributes:

atomslist[Atom]: The atoms in the geometry.
lat_vecNDArray of float with shape (3,3), optional: The primitive lattice vectors of the geometry,

Methods

`calc_principal_moments`()	Calculate the principal inertial axes for a given geometry.
`from_cjson`(file)	Read in atoms and potentially crystallographic information from a `.cjson` file.
`from_cube`(file)	Read in and interpret crystallographic information from a CUBE file.
`from_list`(elements, xyzs[, lat_vec])	Create a `Geometry` from a list of elements and an array of coordinates.
`from_orca`(file)	Read in the geometry information from an ORCA output file.
`from_qe_pp`(file)	Read in only the crystallographic information from a Quantum ESPRESSO post-processing file.
`from_xsf`(file)	Read in the crystallographic information from an XSF file.
`from_xyz`(file)	Read in the geometry information from an XYZ file.
`generate_lattice`(bravais_index, cell_params)	Generate a 3x3 unit cell matrix from a Bravais lattice index and a set of cell parameters.

calc_principal_moments()#

Calculate the principal inertial axes for a given geometry.

Returns:

eigenvaluesNDArray: First output of numpy.linalg.eig(inertia_tensor)
eigenvectorsNDArray: Second output of numpy.linalg.eig(inertia_tensor)

property coordinates: ndarray[tuple[Any, ...], dtype[_ScalarT]]#: Get an array of the coordinates with shape (N,3) where N is the number of atoms (len(self)).

property elements: list[Element]#: Get a list of each element in self.

classmethod from_cjson(file: PathLike) → Self#: Read in atoms and potentially crystallographic information from a .cjson file.

classmethod from_cube(file: PathLike) → Self#

Read in and interpret crystallographic information from a CUBE file.

Notes

This function calculates the dimensions of the unit cell by taking the number of grid points and muliplying it by the spacing of the grid points. Due to rounding errors when an external program prints a CUBE file, the cell dimensions can have inaccuracies of +/- 5e-05 angstrom.

classmethod from_list(elements: list[ElementLike], xyzs: ArrayLike, lat_vec: ArrayLike | None = None) → Self#

Create a Geometry from a list of elements and an array of coordinates. Coordinates should be in Ångstrom.

Parameters:

elementslist of ElementLike: A list of either Element members, atomic symbols, or atomic numbers.
xyzsArrayLike of floats with shape (N,3): An N-length sequence of [x, y, z] coordinates.

Examples

>>> elements = [
...     Element.Hydrogen,
...     Element.Ruthenium,
...     Element.Bromine,
... ]
>>> xyzs = np.array([
...     [1.0, 2.0, 3.0],
...     [4.0, 5.0, 6.0],
...     [7.0, 8.0, 9.0],
... ], dtype=np.float64)
>>> geom = Geometry.from_list()
>>> print(geom)
Element     X          Y          Z

H           1.000000   2.000000   3.000000
Ru          4.000000   5.000000   6.000000
Br          7.000000   8.000000   9.000000

classmethod from_orca(file: PathLike) → Self#: Read in the geometry information from an ORCA output file.

classmethod from_qe_pp(file: PathLike) → Self#: Read in only the crystallographic information from a Quantum ESPRESSO post-processing file. (e.g. leaving the &PLOT blank and reading filplot)

classmethod from_xsf(file: PathLike) → Self#: Read in the crystallographic information from an XSF file.

classmethod from_xyz(file: PathLike) → Self#: Read in the geometry information from an XYZ file.

static generate_lattice(bravais_index: int, cell_params: ArrayLike, primitive: bool = False, espresso_like: bool = False) → ndarray[tuple[Any, ...], dtype[float64]]#

Generate a 3x3 unit cell matrix from a Bravais lattice index and a set of cell parameters.

Parameters:

bravais_index{1, 2, 3, -3, 4, 5, -5, 6, 7, 8, 9, -9, 91, 10, 11, 12, -12, 13, -13, 14}: Integer corresponding to the type of Bravais lattice. Described in Bravais Indices.
cell_paramsArrayLike of float with size 6: ArrayLike of cell parameters, in order: (a, b, c, α, β, γ)
primitivebool, default=False: Denote whether supplied cell parameters are for a primitive or a conventional unit cell.
espresso_likebool, default=False: If cell_params are provided in Quantum ESPRESSO format, this should be set to True. Automatically sets primitive to True as well.

Notes

Quantum ESPRESSO format is as follows:

cell_params = (a, b/a, c/a, cos(α), cos(β), cos(γ))

This function will cross-check all Bravais types against the provided cell parameters.

Bravais Indices#

1: Simple Cubic, cP
2: Face-Centered Cubic, cF
3: Body-Centered Cubic, cI
-3: Body-Centered Cubic, cI, Higher Symmetry
4: Simple Hexagonal, hP
5: Rhombohedral, hR, 3-fold symmetry axis c
-5: Rhombohedral, hR, 3-fold symmetry axis <111>
6: Simple Tetragonal, tP
7: Body-Centered Tetragonal, tI
8: Simple Orthorhombic, oP
9: Base-Centered Orthorhombic, oS, c-face
-9: Base-Centered Orthorhombic, oS, alternate alignment
91: Base-Centered Orthorhombic, oS, a-face
10: Face-Centered Orthorhombic, oF
11: Body-Centered Orthorhombic, oI
12: Simple Monoclinic, mP, unique axis c
13: Base-Centered Monoclinic, mS
-13: Base-Centered Monoclinic, mS, unique axis b
14: Simple Triclinic, aP

exception quadrupole.geometry.FileFormatError(message: str)#: Exception raised when a file is improperly formatted.

exception quadrupole.geometry.LatticeError(bravais_index: int, cell_params: ndarray[tuple[Any, ...], dtype[float64]])#: Exception raised when trying to generate lattices with incompatible lattice type and cell parameters.