httk.atomistic.asu_structure

A crystal structure held as its asymmetric unit.

An ASUStructure records only the symmetry-distinct sites — the asymmetric unit — plus the space group needed to regenerate the rest. Where a Structure lists every atom in the cell, this lists one representative per orbit as a Wyckoff letter and the values of that position’s free parameters.

Any setting, including non-standard ones. The Wyckoff data is always recorded against the International Tables standard setting, and a SettingTransform carries the change of basis from there to whatever setting the structure is actually in. A setting that appears in no table is representable just as well as a tabulated one: the transform is stored, not looked up. That pairing is what makes the representation lossless for arbitrary settings.

Expansion is exact and needs no tolerance. Reduced coordinates, symmetry operations, Wyckoff parameters, and the setting transform are all exact rationals, and the vendored orbits are complete and pre-deduplicated. So generating the full cell is affine arithmetic over the rationals with an exact equality test at the end — no coordinate grid, no snapping, no neighbour search. Tolerance enters this class only where a measured structure is first recognized as symmetric, never in expansion.

Classes

ASUSite	One symmetry-distinct site: a Wyckoff position, its free parameters, and a species.
ASUStructure	A crystal structure represented by its asymmetric unit.

Module Contents

class httk.atomistic.asu_structure.ASUSite

One symmetry-distinct site: a Wyckoff position, its free parameters, and a species.

wyckoff is a bare letter ("e", not "4e") naming a position of the standard setting, and free_params holds one exact value per degree of freedom of that position — none at all for a fixed position such as an inversion centre. species names one of the owning structure’s species.

Partial occupancy needs nothing special here: it lives in the referenced Species, which already carries a composition.

wyckoff: str

free_params: httk.core.FracVector

species: str

property free_count: int

How many free parameters this site carries.

class httk.atomistic.asu_structure.ASUStructure(cell: httk.atomistic.cell_like.CellLike, spacegroup: httk.atomistic.spacegroup.Spacegroup | int, asu_sites: collections.abc.Sequence[ASUSite], species: collections.abc.Sequence[httk.atomistic.species_like.SpeciesLike], transform: httk.atomistic.setting_transform.SettingTransform | None = None, coordinate_precision: Any = None)

A crystal structure represented by its asymmetric unit.

Holds the cell in the structure’s own setting, the space group as its standard setting, a transform from that standard setting to the structure’s own, one ASUSite per symmetry-distinct site, and the species they name.

property cell: httk.atomistic.cell.Cell

The cell, in the structure’s own setting.

property spacegroup: httk.atomistic.spacegroup.Spacegroup

The space group, as its IT standard setting.

property transform: httk.atomistic.setting_transform.SettingTransform

The change of basis from the standard setting to this structure’s own.

property asu_sites: tuple[ASUSite, Ellipsis]

The symmetry-distinct sites.

property species: tuple[httk.atomistic.species.Species, Ellipsis]

The species referenced by the sites.

property coordinate_precision: fractions.Fraction | None

How precisely the coordinates behind this structure were stated, or None.

Fractional, and expressed in this structure’s own setting — the frame the data arrived in — so it needs no transforming on the way to the expanded sites. Recording it here is what lets an asymmetric unit say how good the data behind it was, rather than leaving that to be guessed again downstream.

It is provenance, never an operating parameter: expansion remains exact and uses no tolerance at all.

property asu: ASUStructure

Self, so a view can recognize a backend that already holds an ASU and pass it through.

property is_standard_setting: bool

Whether the structure is written in the IT standard setting of its space group.

setting() → httk.atomistic.spacegroup.Spacegroup | None

The tabulated setting this structure is written in, or None if untabulated.

A structure in an arbitrary setting is perfectly representable but has no tabulated name; that is the point of storing the transform rather than a setting label.

A transform looked up from the tables remembers which setting it came from, but one that was constructed directly does not, so an equal transform is also matched against the group’s tabulated settings. An identity transform means the structure is in the standard setting, which is of course tabulated — reporting it as nameless would be simply wrong.

expand_sites() → httk.atomistic.sites.Sites

Every site of the unit cell, as exact reduced coordinates in this structure’s setting.

The orbit of each asymmetric-unit site is generated in the standard setting, mapped through the setting transform, wrapped into [0, 1), and deduplicated by exact equality. Deduplication is not a formality: when the transform shrinks the cell — as it does for the seven rhombohedral-axes settings, where det M == 3 — the standard setting’s orbit is three times too large and the surplus points coincide exactly. The opposite case, a transform onto a larger cell, is covered by lattice_cosets().

expand_species_at_sites() → tuple[str, Ellipsis]

The species name occupying each site produced by expand_sites(), in order.

multiplicities() → tuple[int, Ellipsis]

How many cell sites each asymmetric-unit site generates, in order.

Usually the Wyckoff position’s tabulated multiplicity, but not always: a setting transform that changes the cell volume changes the count too, by a factor of three for the rhombohedral-axes settings.

to_structure() → Any

The equivalent full-cell Structure.

Equivalent to UnitcellStructureView(asu_structure); provided as a plain method so the common case needs no knowledge of the view machinery.