Symmetry

The Info panel

The symmetry reported depends on the periodicity of the structure:

Structure	Symmetry
crystal (3D)	space group
slab (2D)	layer group
polymer (1D)	the repeat length only, see below
molecule (0D)	point group

The panel also reports the point group, the lattice parameters, the cell volume or area, the density and the formula. All of them are recomputed when the structure is edited.

A polymer’s symmetry is a rod group, and no rod group is named here: the symmetry library the program uses (spglib) implements the 230 space groups and the 80 layer groups, but not the 75 rod groups. A 1D structure is therefore reported by its repeat length and its formula, and its symmetry elements are listed by the point-symmetry analysis below like those of any other structure. A deck written for a polymer uses rod group 1, with every atom listed, which is always valid. Reducing the symmetry of a polymer is refused for the same reason. One-dimensional systems are not otherwise supported; see Not supported yet.

Which cell is described

A space group can be written in several settings, and a crystal computed in a non-standard one has lattice parameters its standard description does not share. The Cell box at the top of the Info panel chooses between the two:

Cell	What the panel reports
As in the file	the cell drawn in the 3D view, with the space group named in that cell’s own setting (P2₁/n)
Standard setting	the conventional standard cell, with the group’s standard symbol (P2₁/c)

The choice is remembered between sessions, and the CRYSTAL input builder starts on it. It applies to crystals only: a slab is always described by its layer group and in-plane cell.

Point symmetry analysis

Cell → Point symmetry analysis lists the symmetry elements of the structure: rotation axes, mirror planes and inversion centres. They are also drawn in the view.

The operators are named in the Schoenflies notation used in chemistry: C₂ to C₆ for rotation axes, S₄ and S₆ for rotoreflection axes, σ for a mirror plane and i for a centre of inversion. Where the group allows it the mirrors are distinguished as σ_h, σ_v and σ_d.

In a crystal each element carries its orientation in lattice terms: an axis by the direction it runs along, as in C₄ ∥ [001], and a mirror by the plane it lies in, as in σ ∥ (110). In a molecule, which has no lattice, both are given as Cartesian directions.

The group itself is reported in its own convention: Hermann–Mauguin for a space or layer group, Schoenflies for a molecular point group.

Reducing the symmetry

A calculation is sometimes run in a symmetry lower than that of the ideal structure: to allow a distortion to relax, to remove a degeneracy, or to converge a particular magnetic state.

The Reduce symmetry… button of the point-symmetry panel removes point-symmetry operators. The subgroups generated by the operators that remain are then listed:

Subgroups that cannot be written in a CRYSTAL deck are listed in grey rather than omitted. Each candidate is verified by reconstruction: the operators are multiplied out and the structure is rebuilt from them, so that a subgroup is offered only if it regenerates the crystal.

The reduction applies to the structure itself. The Info panel reports it under Treated as, and the decks written afterwards use it.

Slabs

The symmetry of a slab is a layer group, one of the 80. The direction normal to the slab is not a lattice vector, and treating the structure as three-dimensional would count the vacuum as one.

The layer group is determined with the aperiodic direction placed along c, as CRYSTAL expects, with the layer centred in the cell, and is verified by rebuilding the slab from it before use. The deck is then written in that layer group, with only the asymmetric unit listed; see CRYSTAL input builder.

Symmetry reduction is not available for slabs, and the dialog reports the reason: a layer group is not a space group.