Centers of symmetry

A point m a molecule is a center of symmetry if any line drawn from it to some element of the structure will when extended an equal distance m the opposite direction encounter an identical element The cyclobutane derivative m Figure 7 4 lacks a plane of symmetry yet is achiral because it possesses a center of symmetry... 

Locate any planes of symmetry or centers of symmetry in each of... 

Furthermore (f) 1 2 dichloroethene has a center of symmetry located at the mid t point of the carbon-carbon double bond This too tells us the molecule is achiral... 

FIGURE 7 4 (a) Struc tural formulas A and B are drawn as mirror images (b) The two mirror images are superimposable by rotating form B 180 about an axis passing through the center of the molecule The cen ter of the molecule is a center of symmetry... 

Any molecule with a plane of symmetry or a center of symmetry is achiral but their absence is not sufficient for a molecule to be chiral A molecule lacking a center of symmetry or a plane of symmetry is likely to be chiral but the supenmposability test should be applied to be certain... 

Section 7 3 A molecule that has a plane of symmetry or a center of symmetry is achi ral as 4 Methylcyclohexanol (Table 7 2) has a plane of symmetry that bisects the molecule into two mirror image halves and is achiral The same can be said for trans 4 methylcyclohexanol... 

IR spectroscopy is an inherently faster method than NMR and an IR spectrum is a superposition of the spectra of the various conformations rather than an average of them When 1 2 dichloroethane is cooled below its freezing point the crystalline matenal gives an IR spectrum consistent with a single species that has a center of symmetry At room temperature the IR spec trum of liquid 1 2 dichloroethane retains the peaks present in the solid but includes new peaks as well Explain these observations... 

Asymmetric (Section 7 1) Lacking all significant symmetry elements an asymmetric object does not have a plane axis or center of symmetry... 

Cation (Section 1 2) Positively charged ion Cellobiose (Section 25 14) A disacchande in which two glu cose units are joined by a 3(1 4) linkage Cellobiose is oh tamed by the hydrolysis of cellulose Cellulose (Section 25 15) A polysaccharide in which thou sands of glucose units are joined by 3(1 4) linkages Center of symmetry (Section 7 3) A point in the center of a structure located so that a line drawn from it to any element of the structure when extended an equal distance in the op posite direction encounters an identical element Benzene for example has a center of symmetry Cham reaction (Section 4 17) Reaction mechanism m which a sequence of individual steps repeats itself many times usu ally because a reactive intermediate consumed m one step is regenerated m a subsequent step The halogenation of alkanes is a chain reaction proceeding via free radical intermediates... 

Only certain types of crystalline materials can exhibit second harmonic generation (61). Because of symmetry considerations, the coefficient must be identically equal to zero in any material having a center of symmetry. Thus the only candidates for second harmonic generation are materials that lack a center of symmetry. Some common materials which are used in nonlinear optics include barium sodium niobate [12323-03-4] Ba2NaNb O lithium niobate [12031 -63-9] LiNbO potassium titanyl phosphate [12690-20-9], KTiOPO beta-barium borate [13701 -59-2], p-BaB204 and lithium triborate... 

Baeyer assigned a cis-form to indigotin, but x-ray crystallographic studies indicated that the dye molecule has a center of symmetry that is only possible if the molecule has a trans-configutation (119). Many derivatives of indigotin have been prepared that would not have been possible if indigotin had a cis-structure, eg, (36) (120). 

Consider for definiteness the antisymmetric case. We choose the origin of the coordinate system in one of the wells, and the center of symmetry has the coordinates Qt,Q-) (fig- 31). Inside the well the classical trajectories are Lissajous figures bordering on the rectangle formed by the lines Q = Q , and Q = —Q , where Q are the turning-point coordinates. 

Center of symmetry in anti staggered conformation of meso-tartaric acid... 

Since the presence of a plane of symmetry in a molecule ensures that it will be achiral, one a q)ro h to classification of stereoisomers as chiral or achiral is to examine the molecule for symmetry elements. There are other elements of symmetry in addition to planes of symmetry that ensure that a molecule will be superimposable on its mirror image. The trans,cis,cis and tmns,trans,cis stereoisomers of l,3-dibromo-rranj-2,4-dimethylcyclobutaijte are illustrative. This molecule does not possess a plane of symmetry, but the mirror images are superimposable, as illustrated below. This molecule possesses a center of symmetry. A center of symmetry is a point from which any line drawn through the molecule encouniters an identical environment in either direction fiom the center of ixnimetry. 

Center of symmetry (Section 7.3) A point in the center of a structure located so that a line drawn from it to any element of the structure, when extended an equal distance in the opposite direction, encounters an identical element. Benzene, for example, has a center of symmetry. 

Symmetriezentrum, n. center of symmetry, symmetrisch, a. symmetrical, S3rmmetric. Symmetrisierung, /. ss mmetrization. sympathetisch, a. sympathetic. 

The two forms differ by the way they pack, a direct result being the different tilt angle of their molecular axis (24" and 30" for the low-temperature and high-temperature form, respectively). Another important difference is the fact that the inversion center of the molecule coincides with a center of symmetry of the unit cell in the HT form, whereas it does not in the LT form 84J. Direct consequences of this feature have not yet been identified. It will be of course of great interest to know what would be its influence on charge transport properties. 

The example of COj discussed previously, which has no vibrations which are active in both the Raman and infrared spectra, is an illustration of the Principle of Mutual Exclusion For a centrosymmetric molecule every Raman active vibration is inactive in the infrared and any infrared active vibration is inactive in the Raman spectrum. A centrosymmetric molecule is one which possesses a center of symmetry. A center of symmetry is a point in a molecule about which the atoms are arranged in conjugate pairs. That is, taking the center of inversion as the origin (0, 0, 0), for every atom positioned at (au, yi, z ) there will be an identical atom at (-a ,-, —y%, —z,). A square planar molecule XY4 has a center of symmetry at atom X, whereas a trigonal planar molecule XYS does not possess a center of symmetry. 

When one of the cartesian coordinates (i.e. x, y, or z) of a centrosymmetric molecule is inverted through the center of symmetry it is transformed into the negative of itself. On the other hand, a binary product of coordinates (i.e. xx, yy, zz, xz, yz, zx) does not change sign on inversion since each coordinate changes sign separately. Hence for a centrosymmetric molecule every vibration which is infrared active has different symmetry properties with respect to the center of symmetry than does any Raman active mode. Therefore, for a centrosymmetric molecule no single vibration can be active in both the Raman and infrared spectrum. 

Earlier in this review, the relationship between the Raman and infrared spectra of molecules possessing high or low symmetry was considered. It was indicated that for molecules possessing a center of symmetry, no vibration is active in both the Raman and infrared spectra. Several adsorbates in this category and one of intermediate symmetry have been studied by laser Raman spectroscopy (Table IX), and most of these spectra are considered in this section. 

The arcsine distribution is a good example of a situation where the notions of center and spread of the distribution must be taken with a grain of salt. The mean of this distribution is obviously located at its center of symmetry, m = 0. Its variance can now be calculated as follows ... 

The subscript g is not used to label the orbitals in a tetrahedral complex because there is no center of symmetry. 

There are, however, differences of opinion regarding the justification of using these K-shell, absorption-edge spectra for assignments to specific oxidation-states (H36). Both symmetry and ligands can affect absorptions by as much as 10 eV, and the absence or presence of a center of symmetry can determine whether a given transition is forbidden or... 

The phase transiton from a paraelectric to a ferroelectric state, most characteristic for the SbSI type compounds, has been extensively studied for SbSI, because of its importance with respect to the physical properties of this compound (e.g., J53, 173-177, 184, 257). The first-order transition is accompanied by a small shift of the atomic parameters and loss of the center of symmetry, and is most probably of a displacement nature. The true structure of Sb4S5Cl2 106), Bi4S5Cl2 194), and SbTel 108,403) is still unknown. In contrast to the sulfides and selenides of bismuth, BiTeBr 108) and BiTel (JOS, 390) exhibit a layer structure similar to that of the Cdl2 structure, if the difference between Te, Br, and I (see Fig. 36) is ignored. 

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