Site of symmetry

Ba -A, with the minor difference that the 8-ring ions are found off the plane at sites of (m) symmetry (see Fig. 1) instead of on the plane with site symmetry man as the calculations assume. Although it is possible that water molecules at 0(5) are responsible for the lower symmetry observed, a Sr2+ ion in dehydrated Srg-A was also located off the plane at a site of symmetry m. 

Figure 124. The molecular structure of Ge(S2COMe)4 the molecule is disposed about a crystallographic site of symmetry 4.

Consider the general equivalent positions of space group P2 /c as shown in Fig. 9.3.4(a). Let position 1 approach the origin of the unit cell in other words, let the coordinates x 0, y 0, and z 0. As this happens, position 4" also approaches the origin, while both 2 and 3 simultaneously approach the center of inversion at (0, 1 /2, 1 /2). When x = 0, y = 0, and z = 0,1 and 4 coalesce into one, and 2 and 3 likewise become the same position. There remain only two equivalent positions (0, 0, 0) and (0, 1/2, 1/2) that occupy sites of symmetry I, and they constitute the special equivalent position 2(a), which is designated as Wyckoff position 2(a). Other sets of special equivalent positions of site symmetry I are obtained by setting x = 1 /2, y = 0, z = 0 x = 0, y = 0,... 

In a molecular crystal, the idealized symmetry of the molecule is often not fully expressed in other words, the molecule occupies a site of lower point symmetry. For example, in the crystal structure of naphthalene, the CsHio molecule (idealized symmetry Z>2h) is located at a site of symmetry I. On the other hand, the hexamethylenetetramine molecule, (CH2)6N4, retains its T symmetry in the crystalline state. Biphenyl, C6H5 —C6H5, which exists in a non-planar conformation with a dihedral angle of 45° (symmetry >2) in the vapor phase, occupies a site of symmetry I in the crystalline state and is therefore completely planar. 

Naphthalene. Since Z = 2, the molecule occupies a site of symmetry I in other words, there is an inversion center in the middle of the C4a-C8a bond. With reference to the atom numbering system shown below, the asymmetric unit can be taken as one of the right (1 1,4a), left (5-8,8a), upper (1,2,7,8,8a) or lower (3,4,4a, 5,6) half of the molecule. Note that the idealized molecular symmetry P>2h of naphthalene is not fully utilized in the solid state, and some of the chemically identical bond distances and bond angles have different measured values. 

Below -65°C, disordered cubic adamantane transforms to an ordered tetragonal form [space group P42 c (no. 114), multiplicity = 8, a-y = 660, ct = 881 pm at — 110°C, Z = 2, molecule occupying site of symmetry 4], The measured C-C bond lengths have a mean value of 153.6(11) pm. The structure of this low-temperature phase, as illustrated in Fig. 9.6.29, is related to that at room temperature in that aj lies along the ab face diagonal of the cubic cell [ axl

Bond lengths (pm) of (a) D6tl (note that in this case the dianion is located at a site of symmetry) and (b) C2v valence tautomers of the rhodizonate dianion. 

The HQ molecule occupies a site of symmetry 2/m, whereas the C60 molecule is highly disordered, with relatively shallow electron-density maxima smeared out tangentially over a sphere of radius 351 pm. 

R3X50,2- Two formula units comprise 3 molecules R2O3, where R may be yttrium or a 4f ion, and 5 molecules X2O3, where X may be Fe, A1 or Ga. The parameter of the cubic unit cell is about 1.24 nm at the R-sites the point symmetry is C2. The X-ions lie at sites of symmetry 31 and S4, in the proportions of 2 3. In YIG, ferric ions occupy these sites with the two moments antiparallel to the three, giving a ferrimagnetic structure with a net moment of 4.96/Tb per formula unit Y3Fe5 0,2. 

The 24 carbon atoms of coronene form three orbits two orbits of six atoms, corresponding to the internal hexagon and to the six atoms on the outer ring that have bonds to the inner ring, and one orbit of the twelve remaining atoms. The elements of the 6-orbit occupy sites of symmetry, based on C, a, ... 

Figure 8 Chemical structure of (a) the adduct formed between trichlorogalhum(in) and triphenylphosphineoxide, ClsGaOPPhs and (b) dimeric aggregate sustained by a sixfold embrace encompassing six C-H- - -jr interactions shown as purple dashed lines. The aggregate in this system is disposed about a crystallographic site of symmetry 3. However, in most examples, such aggregates approximate S3 symmetry.

Dibenzene chromium crystallizes in the cubic space group Pa3, and the chromium atom must occupy a site of symmetry 3 (5e), Assuming an ordered structure, describe the distortion of an idealized molecule with Dsh symmetry that would be consistent with these observations. 

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