Naming of httk₂ structural classes¶

Overview¶

Geometrical information	Anonymous occupation	Assigned species
None	`Formulatype`	`ChemicalFormula`
Wyckoff (± representative/discriminator)	`Prototype`	`Protostructure`
Exact geometry	`Structuretype`	`Structure`

The middle row is represented by exactly two structural families. Prototype stores anonymous PrototypeOccupation values; Protostructure stores assigned WyckoffOccupation values. Either may be base-only, or may additionally carry an exact fundamental-domain representative, an assigned discriminator, or both — the optional refinements that pin a specific geometrical class.

Details¶

The naming of the structural classes in httk starts from:

A crystal structure, Structure, has both precise geometry (atomic coordinates and cell parameters) and species information (chemical elements and may have, e.g., isotopes, oxidation states, etc.).

Structures can be given a “geometrical classification” representing less precise geometrical information. This notion is adopted from the related (but not identical) concept of isoconfigurational structures for which the geometrical constraint is: “the crystallographic point configurations (crystallographic orbits) and their geometrical interrelationships are similar” [https://doi.org/10.1107/S0108767307038081]. Specifically, we adopt this idea with the more specific meaning that two structures have the same “geometrical classification” if there exists a representation of them in the same spacegroup and setting (origin, orientation and cell choice; but usually disregarding enantiomorphs) where the same species occupy the same Wyckoff positions with similar values for all Wyckoff degrees of freedom (i.e., “similar point configurations”) in a unit cell where the cell parameters have similar values modulo an overall scaling factor. The exact degree of similarity has to be defined by numerical cutoff parameters. In httk₂ this cutoff-based geometrical class is not a separate structural family; it refines a Protostructure (or its anonymous counterpart Prototype) through an optional exact representative — a standard-setting fundamental-domain value that holds one exact realization of the class — and/or an assigned discriminator string. Two such values are compared at a chosen tolerance through the similar method, which measures the continuous distance between their representatives (see Similarity, below).

Removing that cutoff-based refinement leaves the higher-level classification that avoids the numerical cutoff by classifying only by the spacegroup, the occupied Wyckoff positions, and the species that occupy them. We use the prefix “Proto” for this. Hence:

A protostructure, Protostructure, is a structural representation specifying only the spacegroup (also distinguishing enantiomorphs), the occupied Wyckoff positions, and the species that occupy them.

These classifications still distinguish the two members of an enantiomorphic pair through their space groups, as stated above. A structure’s canonicalization (canonicalize, canonical_asu) preserves chirality by default; the canonical Protostructure/Prototype key is instead built from the chirality-normalized result (canonical_asu(preserve_chirality=False), or normalize_chirality applied to a chirality-preserved result), so the two members of an enantiomorphic pair share one canonical label even though the classes can still tell them apart.

We can take the weaker geometrical representation one step further, down to:

A chemical formula, ChemicalFormula, represents the structure only in terms of composition of the elements. The “Normalized Formula” gives the composition only in relative terms; any other unit cell representation can be condensed into a formula.

Going in another direction, one can strip the absolute meaning of the chemical species and classify occupation only in terms of equivalent and non-equivalent species (the sites carry placeholder/equivalence assignments — a template into which real species may later be filled in). We mark this anonymous-occupation direction with the suffix “-type”. Hence:

A structuretype, Structuretype, has precise geometry but only an abstract representation that indicates which sites are occupied by equivalent species, i.e., an anonymous occupation template (and where the order of assignments is not regarded as relevant). It is the anonymous-occupation counterpart of Structure.

Following the same naming to a less precise geometrical classification takes us to:

A prototype, Prototype, is the anonymous-occupation counterpart of Protostructure: a structural representation based only on the spacegroup, the occupied Wyckoff positions, and their occupation template. Following the “-type” scheme systematically it would be a templatetype, but the more commonly used prototype is the already-established name for this, so that is the one we adopt. (“Templatetype” is only a prose explanation of where Prototype sits in the scheme; there is no such code name or alias.) A Prototype may likewise carry an exact fundamental-domain representative (a FundamentalDomainTemplate) and/or a discriminator to pin a geometrical class.

The word “Template” itself survives only for the exact fundamental-domain anonymous values that serve as class anchors and ASU keys — FundamentalDomainTemplate and ASUTemplate — not for the exact anonymous family as a whole, which is Structuretype.

To cover a couple of other related names and explain how they differ:

Isopointal structures: account for the spacegroup (with or without distinguishing enantiomorphic groups) and the same complete Wyckoff sequence, including repeated independent occupations but excluding the chemical identity of the occupying atoms.
Isoconfigurational structures: isopointal structures further distinguished by geometrical classification (i.e., similarities in atomic coordinates and cell parameters, but sometimes with further requirements), however still described by colorless occupation.
AFLOW labels: very similar to httk prototypes, except occupations are ordered by occupying element symbol, making the AFLOW labels different for, e.g., ZrO₂ (A2B_oP12_29_2a_a) and FeS₂ (AB2_oP12_29_a_2a).
Extended AFLOW labels: an extension of three digits is added to describe geometrical similarity (-001, -002, …), bringing them closer to discriminator-carrying prototypes.
Decorated AFLOW labels: AFLOW labels are sometimes used with a “decoration” to indicate chemical species, although there does not seem to be one universal endorsed format. These decorations take AFLOW labels closer to httk protostructures.

Similarity¶

The similar methods compare the discrete space group and occupied Wyckoff positions first. Discriminators conflict when both are present and differ. If both values carry representatives, their continuous distance is the total Cartesian atom travel from the public structure_delta function. It maps the structures into a common subgroup and setting, pairs compatible Wyckoff orbits, and sums shortest periodic travel using each endpoint’s own cell. It is not a label comparison or a content-id comparison. A missing representative leaves the continuous portion unspecified rather than fabricating a distance.

Labels¶

The prototype notation is shared by the middle-row families. Anonymous labels render class groups as A, B, and so on. Assigned labels append the real species names after :. The discriminator remains separate, so two values can render the same label while remaining unequal and having different content identities. See Material-information levels for the full grammar, the httk-vs-AFLOW comparison, and the Pearson-symbol and parser rules.

Storage migration¶

The only middle-row storage identities are atomistic_prototype and atomistic_protostructure; their registry records are atomistic-prototype and atomistic-protostructure in the prototypes and protostructures families. Optional representatives and discriminators are projected into the canonical identity. Stores built with the retired four-class layout or its table names must be rebuilt; old registry keys are intentionally not accepted.