A maximal subgroup of a space group. More...

#include <subgroup.h>

Public Member Functions
bool	is_translationengleiche () const

bool	is_klassengleiche () const

std::string	to_string () const
	The 3x4 matrix [P \| p] as an ITA-style string, e.g. "a-b,a+b,c".

Public Attributes
int	parent {0}
	Space group number of the parent.

int	subgroup {0}
	Space group number of the subgroup.

int	index {1}
	The index [G:H].

SubgroupType	type {SubgroupType::Translationengleiche}

Mat3	basis_transform {Mat3::Identity()}
	Basis change; columns are the new basis vectors in terms of the old.

Vec3	origin_shift {Vec3::Zero()}
	Origin shift, in fractional coordinates of the parent cell.

Detailed Description

A maximal subgroup of a space group.

The relation is described by the subgroup's space group number, the index [G:H], and the transformation to the subgroup's standard setting: a basis change \(P\) (columns are the new basis vectors in terms of the old) and an origin shift \(p\), following the International Tables convention

\[ (a', b', c') = (a, b, c) P, \qquad x' = P^{-1}(x - p) \]

Note: \(\det P \ne 1\) in general, and it is not equal to the index either. Both the parent and the subgroup are given in their conventional (possibly centred) cells, so

\[ \det P = \text{index} \times \frac{\text{centring of } H}{\text{centring of } G} \]

For example P2 (2 operations) has a klassengleiche subgroup C2 (4 operations) at index 2, with \(\det P = 4\); and a centred parent may transform to a primitive cell, giving \(\det P < 1\). The invariant that always holds, counting symmetry operations per unit volume, is

\[ n_G \cdot \det P = n_H \cdot \text{index} \]

so the naive \(|H| \cdot \text{index} = |G|\) is not a valid check.

Member Function Documentation

◆ is_klassengleiche()

bool occ::crystal::MaximalSubgroup::is_klassengleiche ( ) const

inline

◆ is_translationengleiche()

bool occ::crystal::MaximalSubgroup::is_translationengleiche ( ) const

inline

◆ to_string()

std::string occ::crystal::MaximalSubgroup::to_string ( ) const

The 3x4 matrix [P | p] as an ITA-style string, e.g. "a-b,a+b,c".

Member Data Documentation

◆ basis_transform

Mat3 occ::crystal::MaximalSubgroup::basis_transform {Mat3::Identity()}

Basis change; columns are the new basis vectors in terms of the old.

◆ index

int occ::crystal::MaximalSubgroup::index {1}

The index [G:H].

◆ origin_shift

Vec3 occ::crystal::MaximalSubgroup::origin_shift {Vec3::Zero()}

Origin shift, in fractional coordinates of the parent cell.

◆ parent

int occ::crystal::MaximalSubgroup::parent {0}

Space group number of the parent.

◆ subgroup

int occ::crystal::MaximalSubgroup::subgroup {0}

Space group number of the subgroup.

◆ type

SubgroupType occ::crystal::MaximalSubgroup::type {SubgroupType::Translationengleiche}

The documentation for this struct was generated from the following file:

/home/runner/work/occ/occ/include/occ/crystal/subgroup.h

Public Member Functions

Public Attributes