Symmetry element complex

In Section 4.2.1 it will be pointed out that hydrogen peroxide (Figure 4.1 la) has only one symmetry element, a C2 axis, and is therefore a chiral molecule although the enantiomers have never been separated. The complex ion [Co(ethylenediamine)3], discussed in Section 4.2.4 and shown in Figure 4.11(f), is also chiral, having only a C3 axis and three C2 axes. 

The mathematical expression of N(6, q>, i//) is complex but, fortunately, it can be simplified for systems displaying some symmetry. Two levels of symmetry have to be considered. The first is relative to the statistical distribution of structural units orientation. For example, if the distribution is centrosymmetric, all the D(mn coefficients are equal to 0 for odd ( values. Since this is almost always the case, only u(mn coefficients with even t will be considered herein. In addition, if the (X, Y), (Y, Z), and (X, Z) planes are all statistical symmetry elements, m should also be even otherwise = 0 [1]. In this chapter, biaxial and uniaxial statistical symmetries are more specifically considered. The second type of symmetry is inherent to the structural unit itself. For example, the structural units may have an orthorhombic symmetry (point group symmetry D2) which requires that n is even otherwise <>tmn = 0 [1], In this theoretical section, we will detail the equations of orientation for structural units that exhibit a cylindrical symmetry (cigar-like or rod-like), i.e., with no preferred orientation around the Oz-axis. In this case, the ODF is independent of t/z, leading to n — 0. More complex cases have been treated elsewhere [1,4]... 

For a nucleus sharing all the molecular symmetry elements (e.g., the metal nucleus in a mononuclear complex), the hyperfine matrix is subject to the same... 

During the study of inorganic chemistry, the structures for a large number of molecules and ions will be encountered. Try to visualize the structures and think of them in terms of their symmetry. In that way, when you see that Pt2+ is found in the complex PtCl42 in an environment described as D4h, you will know immediately what the structure of the complex is. This "shorthand" nomenclature is used to convey precise structural information in an efficient manner. Table 5.1 shows many common structural types for molecules along with the symmetry elements and point groups of those structures. 

The ground state spectrum in Figure 5 exhibits the typical features of the Raman spectrum of a bipyridine complex (40,51,52). Seven relatively intense peaks dominate the spectrum. These may be approximately described as the seven symmetric C-C and C-N stretches expected of bipyridine in any point group wherein the two pyridine rings are related by a symmetry element. 

With the structure assumed above for the Cr—C6H5X system, the common symmetry element is the cr (xz) plane although the n orbitals of the arene moiety are conveniently classified according to their local C2v symmetry as above, the symmetry classification in the complex is with respect to cr and is given in Table IX. 

The type of arrangement of pattern-units is called the space-lattice . Secondly, the group of atoms forming a pattern-unit—the group of atoms associated with each lattice point—may have certain symmetries, and some of these symmetries cause further systematic absences of certain types of reflections from the diffraction pattern. The complex of symmetry elements displayed by the complete arrangement is known as the space-group. ... 

In fact, even approximate cubic symmetry seems to be rare for lanthanoid or actinoid element complexes.50 In low symmetry the number of crystal field parameters necessary to account for the system can be quite large. On the other hand, the spectra of lanthanoid complexes contain many... 

The interpretation of vibrational spectra is dependent on a correct assessment of the symmetry properties of the adsorbed species themselves and of their vibrational modes. Several general accounts have been given of the classification of vibrations of adsorbed species in terms of the symmetry elements associated with a surface complex (89, 90). 

One simple practical method of assessing the possibility of the existence of non-superimposable mirror images, particularly with complex structures, is to construct models of the two molecules. The property of chirality may alternatively be described in terms of the symmetry elements of the molecule. If there is a lack of all elements of symmetry (i.e. a simple axis, a centre, a plane, or an n-fold alternating axis) the chiral molecule is asymmetric, and will possess two non-superimposable mirror image structures (e.g. 2a and 2b). If, however, the molecule possesses a simple axis of symmetry (usually a C2 axis) but no other symmetry elements, the chiral molecule is dissymmetric. Thus 4a and 4b are dissymmetric and the simple C2 axis of symmetry, of for example 4a, is shown below. If the molecule possesses a centre of symmetry (C.) or a plane of symmetry (alternating axis of symmetry (S ), the mirror images of the molecule are superimposable and the molecule is optically inactive. These latter three symmetry elements are illustrated in the case of the molecule 4c. 

The simplest symmetry operations and elements needed to describe unitcell symmetry are translation, rotation (element rotation axis), and reflection (element mirror plane). Combinations of these elements produce more complex symmetry elements, including centers of symmetry, screw axes, and glide planes (discussed later). Because proteins are inherently asymmetric, mirror planes and more complex elements involving them are not found in unit cells of proteins. All symmetry elements in protein crystals are translations, rotations, and screw axes, which are rotations and translations combined. 

The structure of the tetranitro derivative was confirmed by X-ray diffraction in the solid state, this compound does not possess any symmetry element. The conformation of the calixarene structure is less symmetrical than for calix[4]arene(bis crown-6). The nitro groups appear to strongly modify the usual conformation of this calixarene, and a decrease in the preorganization toward cesium complexation can be expected. 

Compound B has no symmetry element in the planar conformation. C-5 is a chiral center, and the protons of each CH2 group are diastereotopic pairs. Each proton of the pair has its own chemical shift. The H-4 proton adjacent to the chiral center is distinctly separated, but the H-3 protons are not, at 300 MHz. Each proton of a diastereotopic pair couples geminally with the other and independently (different coupling constants) with the vicinal protons to give complex multiplets. 

In addition, the reader may realize that axis of rotation can still be present in some chiral Cp-metal complexes (e.g., a C2 axis in the enantiomeric forms in 22 and 23, a C5 axis in 24). With rotation axes present the systems are not asymmetric, only dissymmetric (i.e., lacking mirror symmetry). This is, however, sufficient to induce the existence of enantiomeric forms (218). Moreover, it is known from numerous examples that chiral ligands with C2 symmetry can provide for a higher stereoselectivity in (transition metal-catalyzed) reactions than comparable chiral ligands with a total lack of symmetry. The effect is explained by means of a reduced number of possible competing diastereomeric transition states (218). Hence, rotational symmetry elements may be advantageous for developing useful Cp-metal-based catalytic systems. 

Complex molecules may not possess any symmetry elements, or if they do, the localizations of the electrons can so distort the electron cloud that its symmetry bears little relation to the molecular symmetry. In such cases it may be best to revert to a description of states in terms of the individual orbitals. As an example, we will consider formaldehyde, although a molecule as simple as this is probably best described by the group-theoretical term symbol of the last paragraph. The last filled orbitals in H2CO can easily be shown to be. ..(jtco)2 (no)2, where no represents the nonbonding orbital on the O atom and the two electrons in it are the lone pair. The first unfilled orbitals in formaldehyde are the tt 0 and rr o antibonding orbitals. Promotion of one... 

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