Space nonsymmorphic

When the symmetry elements are introduced into the possible lattices, the symmorphic elements combine to yield a total of 32 so-called point groups, while inclusion of symmorphic and nonsymmorphic elements leads to the 230 crystallographic space groups. Space groups, symmetry elements, and other aspects of crystal symmetry are tabulated in great detail in the International Tables for Crystallography. ... 

The two types of symmetry transformation considered thus far are the only ones, aside from translations, that occur in a symmorphic space group (composed of rotation and reflection operations). Most molecular crystals, however, belong to nonsymmorphic space groups which contain screw axes and glide planes in addition to pure proper and improper rotations. The space groups C (naphthalene, anthracene) and 75 (a-N2, CO2) are both examples. For a twofold screw axis operation (e.g., axis parallel to ) the rotation is accompanied by a translation composed of half unit cell vectors, (e.g., x + y). Application of such an operation maps one pair of molecules on another pair, neither of them remaining the same ... 

Space Groups of Bravais Lattices. Symmorphic and Nonsymmorphic Space Groups... 

In the next subsection we discuss 73 symmorphic and 157 nonsymmorphic space... 

In the next sections we briefly discuss the 15 crystal structures ordered by space-group index.There are included structures with both symmorphic and nonsymmorphic space groups, the structures with the same Bravais lattice and crystal class but different space groups, structures described by only lattice parameters or by the lattice parameters and free parameters of the Wyckoff positions occupied by atoms. 

Diamond stmcture g. 2.5) is described by nonsymmorphic space group N227 with the face-centered cubic lattice the macroscopic cubic symmetry of this crystal appears as the direct product of the first carbon atom site symmetry group Td and inversion I at the center of C-C bond moving the first carbon to the equivalent second carbon atom in the primitive unit cell. 

The rutile structure (Fig. 2.11) belongs to the PA /rnrirn nonsymmorphic space group. 

For the symmetry directions in the BriUouin zone A(FX), A FL), E (see Fig. 3.2) the small representations of both space groups arep-equivalent to ordinary irreducible representations of point groups C4 ,C3 and C v The notations of these representations are taken from [17]. For symmetry directions on the surface of the BriUouin zone Z XW),S smaU representations of space group are p-equivalent to ordinary irreducible representations of point group C v, for the symmetry direction - to ordinary irreducible representations of group G. For the nonsymmorphic space group... 

The effectiveness of this procedure was demonstrated [201] by way of examples, with reference to four test cases the CH C1 molecule (with symmetry), linear polyacetylene, Uthium bromide with the rocksalt structure (symmorpic space group O ) and crystalline silicon (nonsymmorphic space group O ). SALWFs generated appear well suited for use in the local correlation methods. In future, the symmetrized fitted LWFs can be used to have more a efficient computational procedure of LMP2 calculations. 

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