.. _spglib_dataset: Spglib dataset =============== .. contents:: :depth: 2 :local: **At version 1.9.4, SpglibDataset was modified.** The member name ``setting`` is changed to ``choice`` and ``pointgroup_number`` is removed. The dataset is accessible through the C-structure given by :: typedef struct { int spacegroup_number; int hall_number; char international_symbol[11]; char hall_symbol[17]; char choice[6]; double transformation_matrix[3][3]; double origin_shift[3]; int n_operations; int (*rotations)[3][3]; double (*translations)[3]; int n_atoms; int *wyckoffs; char (*site_symmetry_symbols)[7]; int *equivalent_atoms; int *crystallographic_orbits; double primitive_lattice[3][3]; int *mapping_to_primitive; int n_std_atoms; double std_lattice[3][3]; int *std_types; double (*std_positions)[3]; double std_rotation_matrix[3][3]; int *std_mapping_to_primitive; char pointgroup_symbol[6]; } SpglibDataset; .. _dataset_spg_get_dataset_spacegroup_type: Space group type ---------------- ``spacegroup_number`` ^^^^^^^^^^^^^^^^^^^^^^ The space group type number defined in International Tables for Crystallography (ITA). ``hall_number`` ^^^^^^^^^^^^^^^ The serial number from 1 to 530 which are found at `list of space groups (Seto's web site) `_. Be sure that this is not a standard crystallographic defition as far as the author of spglib knows. ``international_symbol`` ^^^^^^^^^^^^^^^^^^^^^^^^^ The (full) Hermann–Mauguin notation of space group type is given by . ``hall_symbol`` ^^^^^^^^^^^^^^^^ The Hall symbol is stored here. ``choice`` ^^^^^^^^^^^ The information on unique axis, setting or cell choices. Symmetry operations -------------------- ``rotations``, ``translations``, and ``n_operations`` ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The symmetry operations of the input unit cell are stored in ``rotations`` and ``translations``. A crystallographic symmetry operation :math:`(\boldsymbol{W}, \boldsymbol{w})` is made from a pair of rotation :math:`\boldsymbol{W}` and translation :math:`\boldsymbol{w}` parts with the same index. Number of symmetry operations is given as ``n_operations``. The detailed explanation of the values is found at :ref:`api_spg_get_symmetry`. .. _dataset_spg_get_dataset_site_symmetry: Wyckoff positions and symmetrically equivalent atoms ----------------------------------------------------- ``n_atoms`` ^^^^^^^^^^^^ Number of atoms in the input unit cell. This gives the numbers of elements in ``wyckoffs`` and ``equivalent_atoms``. ``wyckoffs`` ^^^^^^^^^^^^^ This gives the information of Wyckoff letters by integer numbers, where 0, 1, 2, :math:`\ldots`, represent the Wyckoff letters of a, b, c, :math:`\ldots`. These are assigned to all atomic positions of the input unit cell in this order. Therefore the number of elements in ``wyckoffs`` is same as the number of atoms in the input unit cell, which is given by ``n_atoms``. This is determined from the symmetry of the primitive cell. ``site_symmetry_symbols`` ^^^^^^^^^^^^^^^^^^^^^^^^^^ This gives site-symmetry symbols. These are valid for the standard settings. For different settings and choices belonging to the same space group type, the same set of the symbols is returned. This is determined from the symmetry of the primitive cell. ``equivalent_atoms`` ^^^^^^^^^^^^^^^^^^^^^ This gives the mapping table from the atomic indices of the input unit cell to the atomic indices of symmetrically independent atom, such as ``[0, 0, 0, 0, 4, 4, 4, 4]``, where the symmetrically independent atomic indices are 0 and 4. We can see that the atoms from 0 to 3 are mapped to 0 and those from 4 to 7 are mapped to 4. The number of elements in ``equivalent_atoms`` is same as the number of atoms in the input unit cell, which is given by ``n_atoms``. Symmetry operations found for the input cell are used to determine the equivalent atoms. ``equivalent_atoms`` and ``crystallographic_orbits`` are almost equivalent, but they can be different in a special case as written in :ref:`api_spg_get_symmetry`. ``crystallographic_orbits`` ^^^^^^^^^^^^^^^^^^^^^^^^^^^ **New at version 1.15** This is almost equivalent to ``equivalent_atoms``. But symmetry of the primitive cell is used to determine the symmetrically equivalent atoms. .. _dataset_origin_shift_and_transformation: Transformation matrix and origin shift --------------------------------------- ``transformation_matrix`` and ``origin_shift`` ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ``transformation_matrix`` (:math:`\boldsymbol{P}`) and ``origin_shift`` (:math:`\boldsymbol{p}`) are obtained as a result of space-group-type matching under a set of unique axis, setting and cell choices. These are operated to the basis vectors and atomic point coordinates of the input unit cell as .. math:: ( \mathbf{a}_\mathrm{s} \; \mathbf{b}_\mathrm{s} \; \mathbf{c}_\mathrm{s} ) = ( \mathbf{a} \; \mathbf{b} \; \mathbf{c} ) \boldsymbol{P}^{-1} \;\; \text{and} \;\; \boldsymbol{x}_\mathrm{s} = \boldsymbol{P}\boldsymbol{x} + \boldsymbol{p} \;\;(\mathrm{mod}\; \mathbf{1}), by which the basis vectors are transformed to those of a standardized unit cell. Atomic point coordinates are shifted so that symmetry operations have one of possible standard origins. The detailed definition is presented at :ref:`definitions_and_conventions`. At **versions 1.7.x and 1.8 or before**, the set of ``transformation_matrix`` (:math:`\boldsymbol{P}_\text{old}`) and ``origin_shift`` (:math:`\boldsymbol{p}_\text{old}`) was differently defined from the current definition as follows: .. math:: ( \mathbf{a}_\mathrm{s} \; \mathbf{b}_\mathrm{s} \; \mathbf{c}_\mathrm{s} ) = ( \mathbf{a} \; \mathbf{b} \; \mathbf{c} ) \boldsymbol{P}_\text{old} \;\; \text{and} \;\; \boldsymbol{x}_\mathrm{s} = \boldsymbol{P}^{-1}_\text{old}\boldsymbol{x} - \boldsymbol{p}_\text{old} \;\;(\mathrm{mod}\; \mathbf{1}). .. _dataset_idealized_cell: Standardized crystal structure after idealization -------------------------------------------------- ``n_std_atoms``, ``std_lattice``, ``std_types``, and ``std_positions`` ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The standardized crystal structure after :ref:`idealization ` corresponding to a Hall symbol is stored in ``n_std_atoms``, ``std_lattice``, ``std_types``, and ``std_positions``. These output usually contains the rotation in Cartesian coordinates and rearrangement of the order atoms with respect to the input unit cell. **At versions 1.7.x and 1.8 or before**, the variable names of the members corresponding to those above are ``n_brv_atoms``, ``brv_lattice``, ``brv_types``, and ``brv_positions``, respectively. .. _dataset_std_rotation_matrix: ``std_rotation_matrix`` ^^^^^^^^^^^^^^^^^^^^^^^ **New in version 1.11** Rotation matrix that rotates the standardized crystal structure before idealization :math:`( \mathbf{a}_\mathrm{s} \; \mathbf{b}_\mathrm{s} \; \mathbf{c}_\mathrm{s} )` to that after idealization :math:`( \bar{\mathbf{a}}_\mathrm{s} \; \bar{\mathbf{b}}_\mathrm{s} \; \bar{\mathbf{c}}_\mathrm{s} )` in Cartesian coordinates of the given input unit cell. The rotation matrix :math:`\boldsymbol{R}` is defined by .. math:: ( \bar{\mathbf{a}}_\mathrm{s} \; \bar{\mathbf{b}}_\mathrm{s} \; \bar{\mathbf{c}}_\mathrm{s} ) = ( \boldsymbol{R} \mathbf{a}_\mathrm{s} \; \boldsymbol{R} \mathbf{b}_\mathrm{s} \; \boldsymbol{R} \mathbf{c}_\mathrm{s} ). ``std_mapping_to_primitive`` ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ This is available **at versions 1.10 or later**. This gives a list of atomic indices in the primitive cell of the standardized crystal structure, where the same number presents the same atom in the primitive cell. By collective the atoms having the same number, a set of relative lattice points in the the standardized crystal structure is obtained. Crystallographic point group ----------------------------- ``pointgroup_symbol`` ^^^^^^^^^^^^^^^^^^^^^^ **New in version 1.8.1** .. ``pointgroup_number`` is the serial number of the crystallographic point group, which refers `list of space groups (Seto's web site) `_. ``pointgroup_symbol`` is the symbol of the crystallographic point group in the Hermann–Mauguin notation. There are 32 crystallographic point groups:: 1, -1, 2, m, 2/m, 222, mm2, mmm, 4, -4, 4/m, 422, 4mm, -42m, 4/mmm, 3, -3, 32, 3m, -3m, 6, -6, 6/m, 622, 6mm, -6m2, 6/mmm, 23, m-3, 432, -43m, m-3m Intermediate data in symmetry search ------------------------------------ A primitive cell is searched from the translational symemtry. This primitive cell is given by ``primitive_lattice`` and ``mapping_to_primitive`` below. ``primitive_lattice`` ^^^^^^^^^^^^^^^^^^^^^ **New at version 1.15** Non-standardized basis vectors of a primitive cell in the input cell. ``mapping_to_primitive`` ^^^^^^^^^^^^^^^^^^^^^^^^^ In version 1.10 or later, ``mapping_to_primitive`` is available. This gives a list of atomic indices in the primitive cell of the input crystal structure, where the same number presents the same atom in the primitive cell. By collective the atoms having the same number, a set of relative lattice points in the the input crystal structure is obtained.