Symmetry designator, site

The Wyckoff symbol is a short designation it consists of a numeral followed by a letter, for example 8/. The cipher 8 states the multiplicity, that is, the number of symmetry-equivalent points in the unit cell. The / is an alphabetical label (a, b,c,...) according to the sequence of the listing of the positions a is always the position with the highest site symmetry. 

This region of the spectrum for MnOf dissolved in anhydrous NaClO is shown in Fig. 4. The site symmetry of the tetrahedral ions in this lattice is CW- The degenerate levels should be completely split in this symmetry, the symmetries Of the resulting states (in CV) and the polarization of the transitions rendered allowed by the perturbation are given in Table V. As indicated in this table a T state in a field of symmetry Ctv should show absorption with electric vector parallel to the b and c axes, for an E state absorption with electric vector parallel to the a axis, the direction of the twofold axis at position of the ion. The spectrum in the region II (Teltow s designation) corresponds precisely to what one would expect from a T state. ... 

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,... 

Fig. 10. Theoretical shifts in the energies of the d orbital states of a d ion with four equivalent ligands (Ds = 765 cm-1 Dt = 444 cm-1) as the structure of the site is varied from tetrahedral (fi = 54.7°) to square planar (fi = 90°). The symmetry designation (and the corresponding half-filled d orbital) of each state are a1(dz2) b d. ) e(d,j, d ) b d,) (from Ref. 35)...

The trigonal planar complexes of the MX3 type, whether of the lanthanide or of the transition metal series, have a particular significance. In an amendment to the crystal field intensity theory, designed to accommodate the hypersensitive f—f transitions, the addition of the first-rank spherical harmonics, Yim to the ligand field was proposed in order to form, with the dipole operator, an effective quadrupole operator within the 4f shell i). Crystal field potentials of the Yim form are restricted, however, to metal complexes with a permanent dipole moment, that is, to the site symmetries Cpv and their subgroups ), and the proposal does not account for the relatively large oscillator strengths of the quadrupole-allowed d—d or f—f transitions of... 

The cobalt atoms in Fig. 14.1 are stereogenic and the site symmetries are C2v and D4h, for (A) and (B), respectively. The term stereogenic center is at present used to designate a coordinated atom that was formerly called an asymmetric atom [2],... 

The crystallographic sites of nonframework cations in the structures of zeolite A (LTA) and zeolites X and Y (FAU) are indicated in Fig. 22 where their coordination to the framework is shown in the lower part. Their nomenclature, sites per unit cell, site symmetry and location are summarized in Table 3. Note that the SI position in LTA is equivalent to site SII in FAU and will be further designated as SIA. 

The site symmetry of a bond containing a representative atom of an equivaloit set 0 is a subgroup of die molecular point group G. If die representative atom is designated by a the respective polar tensor will have nine elements of the type 3p /9Xr ( ) where n = x, y, z. The following rule determines the structure of die 3><3 tensor if die p component and coordinate belong to the same symmetiy species of the site subgroup, the respective derivatives will differ from zero. In all other cases the elements will vanish. 

Each bond polarizability tensor is a 3 x3 square matrix which, in die case of an ordinaiy Raman experiment, has six independent elements. If, however, a special set of local bond Cartesian axes is chosen, the bond polarizability tensor can be presented in a simple diagonal form. Thus, the number of parameters characterizing electro-optica] properties of each molecular bond can be reduced to three. A local bond Cartesian system can be defined as follows (1) One of the coordinate axes is directed along the bond its unit vector is denoted by e lk) (2) The other two axes are chosen in such a w that they are perpendicular to the longitudinal vector and, at die same time, are at right angle one to another. Their particular orientation in space depends on the bond site symmetry. The respective unit vectors can be designated as e2W and e3(k). 

Table 11.5 lists many of the commonly used restriction endonucleases and their recognition sites. Because these sites all have twofold symmetry, only the sequence on one strand needs to be designated. 

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