Mirror glide plane

In an infinite Fischer projection, chirality is not consistent with the presence of the following elements of reflective synunetry (41, 46, 254) d, mirror plane containing the chain axis m, an infinite number of mirror planes perpendicular to the chain axis and/or c, mirror glide plane containing the chain axis. For... 

The elements of mirror symmetry d, m, and c can be removed in different ways, resulting in different classes of chiral polymers. Plane d containing the polymer chain is eliminated by the presence, in the main chain, of tertiary carbon atoms —CHR—), or of quaternary atoms with different substituents (—CR R"—), or with equal chiral substituents (—CR R —). Mirror glide plane c does not exist in isotactic structures, nor in syndiotactic ones in which the substituents are chiral and of the same configuration, 75 (33, 263). The perpendicular planes, m, are eliminated by the presence of chiral substituents of the same sign in syndiotactic, 75 (33, 263) or isotactic structures, 76 (263) or if the two directions of the chain are rendered nonreflective. This last condition can be realized in different ways some of which follow (264) ... 

The stereocenters in all three stereoregular polymers are achirotopic. The polymers are achiral and do not possess optical activity. The diisotactic polymers contain mirror planes perpendicular to the polymer chain axis. The disyndiotactic polymer has a mirror glide plane of symmetry. The latter refers to superposition of the disyndiotactic structure with its mirror image after one performs a glide operation. A glide operation involves movement of one structure relative to the other by sliding one polymer chain axis parallel to the other chain axis. 

All four diisotactic polymers (cis and trans, erythro and threo) are chiral and possess optical activity. Each of the four disyndiotactic polymers possesses a mirror glide plane and is achiral. For symmetric 1,4-disubstituted 1,3-butadienes (R = R ), only the cis and transthreo-diisotactic structures are chiral. Each of the erythrodiisotactic and threodisyndiotactic polymers has a mirror glide plane. Each of the erythrodisyndiotactic polymers has a mirror glide plane. 

It is important to note that high molecular weight trans-isotactic poly(methy-lene-1,3-cyclopentane) contains no mirror or mirror glide planes of symmetry and is thus chiral by virtue of its main chain stereochemistry (it exhibits optical activity) this is in contrast to high molecular weight polypropylene and other poly(a-olefin)s, which contain an effective mirror plane perpendicular to the molecular axis in the middle of the molecule and are thus achiral [30,497],... 

In addition we studied a defective (111) surface ofc-ZrOj built up from the 2x2 supercell. Owing to the mirror/glide plane in the centre of the c-Zr02(l 11) slab (see section 2.2.2) a defect was constructed on both surfaces of the slab, resulting in a defect density of 9=0.25 ML per surface. In the current paper, we consider the neutral oxygen defect, created according to ... 

The 3-D periodic boundary conditions employed by VASP and CASTEP imply that the surfaces are modelled as repeated slabs, separated by a pseudo-vacuum . In the current investigation a pseudo vacuum of -10-15 A has been applied, depending on the system under investigation. All slabs (including our CR98 calculations) are modelled with two equivalent surfaces, due to symmetry Le. each slab contains a mirror/glide plane in the middle. To keep the symmetry restrictions introduced for the clean surfaces, the metal adlayers were deposited on both surfaces of the slab. 

A very special case among optically active dienes is given by chiral allenes. Polymerization of (-)-(R)-2,3-pentadiene by organometallic transition metal derivatives [59] gives an optically active crystalline polymer to which the structure reported in Table XVI has been assigned. In fact that structure is the only linear structure not possessing symmetry planes or mirror glide planes. 

Cyclic monomers are a special class of prochiral monomer from the viewpoint of asymmetric polymerization [4, 13]. Symmetrically substituted cyclic olefins can give erythro cfz-isotactic polymers which are nonchiral because they possess a mirror glide plane on the contrary the threo-di-isotdictic polymer can be optically active due to the lack of the above symmetry elements. Unsymmetrically disubstituted cyclic olefins give both erythro- and threo-di-hoi2iCi c polymers which are chiral and which can then be obtained in optically active form by asymmetric induction polymerization (Scheme 11). 

EUO can be built using building units composed of 14T atoms two 1-5-1 units (one T 14-unit bold in Figure 1). The two-dimensional PerBU is obtained when T14-units, related along a by a mirror glide plane perpendicular to b and along 6 by a rotation of 180° about c, are connected into the ab layer as shown in Figure 1. (Compare with the PerBUs in IWV, NES and NON.)... 

These include rotation axes of orders two, tliree, four and six and mirror planes. They also include screM/ axes, in which a rotation operation is combined witii a translation parallel to the rotation axis in such a way that repeated application becomes a translation of the lattice, and glide planes, where a mirror reflection is combined with a translation parallel to the plane of half of a lattice translation. Each space group has a general position in which the tln-ee position coordinates, x, y and z, are independent, and most also have special positions, in which one or more coordinates are either fixed or constrained to be linear fimctions of other coordinates. The properties of the space groups are tabulated in the International Tables for Crystallography vol A [21]. 

Orthorhombic symmetry mm2 comprises two mirror planes perpendicular to each other, which automatically generates a twofold axis along the line of intersection. This point symmetry applies to all noncentrosymmetric orthorhombic crystals that have mirror or glide planes such as those of space groups Pna2t and Pca2,. 

Inversion centre Mirror plane Glide plane... 

Same as mirror plan, but followed by a translation of half the unit cell parallel to the plane glide planes are not relevant in macromolecular crystallography due to the chirality of the biological building blocks... 

First, it is necessary to define the structure. The structure of a planar zig-zag polyethylene chain is shown in Fig. 2, together with its symmetry elements. These are C2 — a two-fold rotation axis, C — a two-fold screw axis, i — a center of inversion, a — a mirror plane, and og — a glide plane. Not shown are the indentity operation, E, and the infinite number of translations by multiples of the repeat (or unit cell) distance along the chain axis. All of these symmetry operations, but no others, leave the configuration of the molecule unchanged. 

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 displacement by in the first row and fourth column comes from the mirror reflection in the plane at x = 1/4. The A in the second and third rows of the fourth column are the components of the diagonal glide. The location of the transformed point is that marked by a comma (,) and M>+. The MR of the operation (rry A 0 0)[xyz], when the axial glide plane lies at y=lA, is... 

The symmetry elements, proper rotation, improper rotation, inversion, and reflection are required for assigning a crystal to one of the 32 crystal systems or crystallographic point groups. Two more symmetry elements involving translation are needed for crystal structures—the screw axis, and the glide plane. The screw axis involves a combination of a proper rotation and a confined translation along the axis of rotation. The glide plane involves a combination of a proper reflection and a confined translation within the mirror plane. For a unit cell... 

Major axes are indicated by positive numbers for Cn and barred numbers, 2, 3, etc., for improper axes of rotation. Screw axes are indicated by subscripts such as 2i, 32, etc. A 4i screw axis involves translation of 1 /4 upward for an anticlockwise rotation, 42 involves translation by 1/2 (2/4), an 43 involves translation by 3/4. Mirror planes (m) and glide planes are indicated by letters, using the letters corresponding to translation by the fractions along a particular direction as follows... 

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