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Centre of symmetry

Centre of symmetry. A point through which there is reflection to an identical point in the pattern. [Pg.382]

If a molecule has a centre of inversion (or centre of symmetry), i, reflection of each nucleus through the centre of the molecule to an equal distance on the opposite side of the centre produces a configuration indistinguishable from the initial one. Figure 4.4 shows s-trans-buta-1,3-diene (the x refers to trans about a nominally single bond) and sulphur hexafluoride, both of which have inversion centres. [Pg.76]

Fig. 13. Simulated diffraction space of a 10-layer monochiral MWCNT with Hamada indices (40+8/ , 5+k) with / =0,...,9. In (a), (a ) and (02) the initial stacking at ( q was ABAB. whereas in (b), (b[) and (b2) the initial stacking was random, (a) The normal incidence pattern has a centre of symmetry only. (3 )(a2) The cusps are of two different types. The arc length separating the cusps is c (b) The normal incidence pattern now exhibits 2mm symmetry. (b )(b2) The cusps are distributed at random along the generating circles of the evolutes. These sections represent the diffuse coronae referred to in the "disordered stacking model" [17]. Fig. 13. Simulated diffraction space of a 10-layer monochiral MWCNT with Hamada indices (40+8/ , 5+k) with / =0,...,9. In (a), (a ) and (02) the initial stacking at ( q was ABAB. whereas in (b), (b[) and (b2) the initial stacking was random, (a) The normal incidence pattern has a centre of symmetry only. (3 )(a2) The cusps are of two different types. The arc length separating the cusps is c (b) The normal incidence pattern now exhibits 2mm symmetry. (b )(b2) The cusps are distributed at random along the generating circles of the evolutes. These sections represent the diffuse coronae referred to in the "disordered stacking model" [17].
The largest protonated cluster of water molecules yet definitively characterized is the discrete unit lHi306l formed serendipitously when the cage compound [(CyHin)3(NH)2Cll Cl was crystallized from a 10% aqueous hydrochloric acid solution. The structure of the cage cation is shown in Fig. 14.14 and the unit cell contains 4 [C9H,8)3(NH)2aiCUHnOfiiai- The hydrated proton features a short. symmetrical O-H-0 bond at the centre of symmetry und 4 longer unsymmetrical O-H - 0 bonds to 4... [Pg.631]

Spectra of ra 5-Pt35Cl2F and the c/s-isomer show the simpler spectra expected from the trans-isomer (three Pt—F and two Pt—Cl stretches) compared with the m-isomer (four Pt—F and two Pt—Cl stretches). The complexity of the spectrum of the m-isomer is also the result of the lack of a centre of symmetry in the cis-form the selection rules allow all bands to be seen in both the IR and the Raman spectra (in theory, at least). [Pg.184]

The left superscript indicates that the arrangements are all spin triplets. The letter T refers to the three-fold degeneracy just discussed and it is in upper case because the symbol pertains to a many-electron (here two) wavefunction (we use lower-case letters for one-electron wavefunctions or orbitals, remember). The subscript g means the wavefunctions are even under inversion through the centre of symmetry possessed by the octahedron (since each d orbital is of g symmetry, so also is any product of them), and the right subscript 1 describes other symmetry properties we need not discuss here. More will be said about such term symbols in the next two sections. [Pg.37]

The theoretical reason is as follows. Although the placing of the ligands in a tetrahedral molecule does not define a centre of symmetry, the d orbitals are nevertheless centrosymmetric and the light operator is still of odd parity and so d-d transitions remain parity and orbitally Al = 1) forbidden. It is the nuclear coordinates that fail to define a centre of inversion, while we are considering a... [Pg.65]

Now look at octahedral complexes, or those with any other environment possessing a centre of symmetry e.g. square-planar). These present a further problem. The process of violating the parity rule is no longer available, for orbitals of different parity do not mix under a Hamiltonian for a centrosymmetric molecule. Here the nuclear arrangement requires the labelling of d functions as g and of p functions as m in centrosymmetric complexes, d orbitals do not mix with p orbitals. And yet d-d transitions are observed in octahedral chromophores. We must turn to another mechanism. Actually this mechanism is operative for all chromophores, whether centrosymmetric or not. As we shall see, however, it is less effective than that described above and so wasn t mentioned there. For centrosymmetric systems it s the only game in town. [Pg.66]

A mistake often made by those new to the subject is to say that The Laporte rule is irrelevant for tetrahedral complexes (say) because they lack a centre of symmetry and so the concept of parity is without meaning . This is incorrect because the light operates not upon the nuclear coordninates but upon the electron coordinates which, for pure d ox p wavefunctions, for example, have well-defined parity. The lack of a molecular inversion centre allows the mixing together of pure d and p ox f) orbitals the result is the mixed parity of the orbitals and consequent non-zero transition moments. Furthermore, had the original statement been correct, we would have expected intensities of tetrahedral d-d transitions to be fully allowed, which they are not. [Pg.69]

The three-fold degenerate set of p orbitals are labelled tiu t for three-fold, u for odd under inversion through the centre of symmetry). As shown in Fig. 6-6, each metal p orbital matches symmetry with ligand group orbitals comprising just two... [Pg.109]

CCH3 shows the formation of dimers related by a centre of symmetry and close contacts of the cyano groups between neighbouring molecules (see Table 5). The molecules are arranged in layers and overlap more or less with the bicyclohexyl units. [Pg.155]

We have already seen that mesotartaric acid is optically inactive because of internal compensation, although, it contains two asymmetric carbon atoms. We have also seen that the molecule as a whole must be asymmetric for being optically active. Therefore, the best criterion to judge optical activity would be whether molecule is superimposable on its mirror image or not. Now superimposability would lead to optical activity and vice-versa and non-symmetrical molecules are non superimposable. To decide whether a molecule is symmetrical or not, we should first try to know whether it has a plane of symmetry, a centre of symmetry or an alternating axis of symmetry. The presence of any one of these would lead the molecule to be symmetrical and hence to optical inactivity. [Pg.125]

Compounds containing a centre of symmetry are exemplified by those which have three dimensional structures, particularly of ring systems. Let us concentrate on a derivative 2 4 diphenylcyclobutane 1, 3 dicarboxylic acid (IX). [Pg.126]

The centre of the molecule (shown by a thick dot) is the centre of symmetry, because lines drawn on the side and produced an equal distance on the other meet similar points in the molecule. In this connection, it can be mentioned that compounds possessing even numbered rings will have a possibility of having a centre of symmetry and would lead to optical inactivity. [Pg.126]

In 1956 McCasland and Proskow prepared the p.toluenesulphonate of the compound X and found that it has neither a plane nor an centre of symmetry and yet the molecule was superimposable on its mirror image and hence inactive. The molecule owes its symmetry due to the presence of what has been called an alternating axis of symmetry. Rotation of the molecule through 90° along the axis shown produces XI. Observing the latter through a central plane perpendicular to the axis shows that it is identical with X and also coincides with it. [Pg.126]

Any compound with a nonsymmetrical distribution of charge or electron density will possess a permanent dipole moment, /v, whereas a molecule with a centre of symmetry will have no permanent dipole moment. Dipole moment is proportional to the magnitude of the separated charges, z, and also the distance between those charges, l. [Pg.15]

The centre of symmetry (inversion through a point) is represented by 1 and the plane of symmetry (mirror symmetry) by the letter m. The inversion operation... [Pg.99]


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Axes and centres of symmetry

Symmetry centre

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