Alternating symmetry axis

Alternating symmetry axis (S ) An axis about which a rotation by an angle of 360/n, followed by a reflection across a plane perpendicular to the axis results in an entity that is indistinguishable from (superimposable on) the original. Also called a rotation-reflection axis. See also symmetry axis. 

Rotation-reflection axis See alternating symmetry axis. 

Molecule (13.60) has a three-fold symmetry axis but is devoid of an alternating symmetry axis (i.e. a plane of symmetry or a symmetry centre). It is dissymmetric and therefore optically active. 

Subunits VP2 and VP3 from different pentamers alternate around the threefold symmetry axes like subunits B and C in the plant viruses (Figure 16.12b). Since VP2 and VP3 are quite different polypeptide chains, they cannot be related to each other by strict symmetry, or even by quasi-symmetry in the original sense of the word. To a first approximation, however, they are related by a quasi-sixfold symmetry axis, since the folded structures of the cores of the subunits are very similar. 

Some erystals exhibit a fourth element known as eompound, or alternating symmetry about a rotation-refleetion axis or axis of rotary inversion . 

Figure 19.2 Metal-binding sites in the channel aligned on the three-fold symmetry axis shows binding to three zinc atoms and their symmetrically related subunits the first is in the entrance of the funnel-shaped channel (in cyan), the second is in an alternative position (in blue) and the third is aligned on the three-fold axis (in grey). The overall stoichiometry is seven zinc cations per channel, i.e. 56 zinc cations per molecule. The two representations are with two different orientations part a is aligned on the three-fold axis and part b is perpendicular to the axis. (From Toussaint et al., 2006. Copyright 2006, with permission from Elsevier.)...

Figure 3-23 (A) Stereoscopic a-carbon plot of the cystolic aspartate aminotransferase dimer viewed down its dyad symmetry axis. Bold lines are used for one subunit (subunit 1) and dashed lines for subunit 2. The coenzyme pyridoxal 5 -phosphate (Fig. 3-24) is seen most clearly in subunit 2 (center left). (B) Thirteen sections, spaced 0.1 nm apart, of the 2-methylaspartate difference electron density map superimposed on the a-carbon plot shown in (A). The map is contoured in increments of 2a (the zero level omitted), where a = root mean square density of the entire difference map. Positive difference density is shown as solid contours and negative difference density as dashed contours. The alternating series of negative and positive difference density features in the small domain of subunit 1 (lower right) show that the binding of L-2-methylaspartate between the two domains of this subunit induces a right-to-left movement of the small domain. (Continues)...

Fig. 6. The crystal structure of ice (a) the basic unit, showing the tetrahedral arrangement of four oxygen atoms round any one oxygen (b) the open arrangement of these units as they fit together in ordinary ice(Ih) (c) the alternative positions for the hydrogen atoms, which are represented by the small filled circles, two along each hydrogen bond. (The vertical line, marked with 3 in (a), is a threefold symmetry axis all the vertical lines in (b) coincide with trigonal axes of the ice crystal.)...

Crystalline 1 1 complexes of a few arenes with halogen molecules have been isolated and structurally characterized. As an example, the structure of the n complex C between benzene and bromine is given in Fig. 17 (264). In chains of alternate benzene and Br2 species the bromine atoms are localized on the sixfold symmetry axis of the benzene ring. The bromine-bromine distance of 2.28 A is nearly the same as that observed in the free molecule. The distance from each bromine atom to the adjacent benzene plane is 3.36 A ( 0.30 A less than the sum of the van der Waals radii). The extent of charge transfer is estimated to be 0.06 electrons in the electronic ground state (265), indicating the weakness of n bonding in this and other comparable complexes. 

This result is confirmed when we consider the sensitivity of these results to the various hypotheses, using the alternatives previously described. Changing the surrounding mantle temperature Tx> slightly modifies the temperature profile (because of the scaling to the distance from the symmetry axis to the solidus), but has only a minute effect on voi atid It does change the... 

Alternatively, a chirality invariant nomenclature can be used, in which the two possible conformations of an individual chelate ring in M(en)3 are named lei and ob, respectively, where the central C—C bond of the ring is (approximately) paral/e/ and oWique with respect to the C3 or pseudo-Cs symmetry axis in M(en)5" (13). Thus the four conformers are symbolized as /e/3, leliob, fe/062 and oZ 3, with lelj being equivalent to A(AAA) [or A(55 )]. 

Figure 11.7 Excitation-detection geometries for the determination of the transition strength for (a) Linearly polarized and (b) circularly polarized two-photon excitation. Fluorescence intensity measurements are made at magic angle polarization settings with respect to the quantization (symmetry) axis for the two polarizations. Alternatively, the fluorescence intensity can be constructed from J /V(t) + 2Jh (t) and 2J /(t) + Jn(t) measurements for linear and circular polarizations respectively, (c) Excitation-detection geometry for fluorescence anisotropy measurements following linearly polarized two-photon excitation...

Fig. 17.3. Two alternative descriptions of the AOs containing the two nonbonding electron pairs in EH2. The molecule is lying in the xz plane and the direction of the z-axis has been chosen to coincide with the twofold symmetry axis.

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