Glide plane of symmetry

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. 

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],... 

It is to be noted that each amide group in the chain (neglecting the side chains) may be described as obtained from the preceding one by the operation of a glide plane of symmetry. Because of this, side chains of L-amino... 

So far we have discussed the macroscopic symmetry elements that are manifested by the external shape of the three-dimensional patterns, that is, crystals. They can be studied by investigating the symmetry present in the faces of the crystals. In addition to these symmetry elements there are two more symmetry elements that are related to the detailed arrangements of motifs (atoms or molecules in actual crystals). These symmetry elements are known as microscopic symmetry elements, as they can only be identified by the study of internal arrangement of the motifs. As X-ray or electron diffraction can reveal the internal structures, these symmetry arrangements can only be identified by X-ray, Electro or Neutron diffraction. Obviously, they are not revealed in the external shape of the pattern. These symmetry elements are classified as microscopic symmetry elements. There are two such types of synunetry elements (i) glide plane of symmetry and (ii) screw axis of synunetry. 

Glide plane of symmetry It is a combination of reflection and translation of the motif. It is explained by Fig. 5.1. Figure 5.2 shows simple pattern of a glide plane. 

Hermann-Mauguin symbol of glide plane of symmetry ... 

Now one particular ball will have glide plane of symmetry on the same plane the ball exists, but will also have a glide plane up the plane in three-dimensional arrangements of the balls. The different layers arranged one over other are manifested by different colors. 

Planes of symmetry. Planes through which there is reflection to an identical point in the pattern. In a lattice there may be a lateral movement parallel to one or more axes (glide plane). 

In referring to any particular space-group, the symbols for the symmetry elements are put together in a way similar to that used for the point-groups. First comes a capital letter indicating whether the lattice is simple (P for primitive), body-centred (I for inner), side-centred (A, B, or C), or centred on all faces (F). The rhombohedral lattice is also described by a special letter R. Following the capital letter for the lattice type comes the symbol for the principal axis, and if there is a plane of symmetry or a glide plane perpendicular to it, the two symbols... 

In a similar way, it can be shown that if a crystal has a plane of symmetry perpendicular to its b axis, the Patterson function has maxima along the 6 axis of the cell (the line 0, y, 0, in Fig. 229) which indicate the distance of atoms from the plane of symmetry. For a glide plane perpendicular to b, with a translation c/2, the distance of atoms from this plane are indicated by maxima along the line 0, y,... 

A crystal can have additional symmetry based on rotation plus translation elements. The combination of a rotation axis and a translation is a screw axis (e.g. a 2X screw axis involves a 180° rotation and translation by half a unit cell dimension). The combination of a mirror plane and a translation is a glide plane. These symmetry elements lead to systematic absences in a diffraction pattern e.g. for a 2i axis in the c... 

I, 25e, 25g=2Cs, Sl=i, 3C2, and 3a (glide plane). These elements are exactly the same as those of the point group Ds, although the last element is a glide plane rather than a plane of symmetry in a single molecule. 

A particular crystal system has some definite number of point groups and for this monoclinic system it has symmetry operations like 2, m, and 2/m, that is, twofold rotation, a mirror plane, and twofold with mirror plane of symmetries. Now, for three-dimensional crystal the possible symmetry elements will include also screw axes and glide planes, and when screw axes and glide planes are added to the point group of symmetries for this system, we can say that different possibilities that may exist are 2, 2i, m, c, 2/m, 2i/m, 2/c, and 2j/c. Now each of these symmetry groups are repeated by lattice translation of the Bravais lattices of that system. As monoclinic system has only primitive P and C, all the symmetry possibilities may be associated with both P and C. Therefore, if they are worked out, they come out to be 13 in number and they are Pm, Pc, Cm, Cc, P2, P2i, C2, P2/m, P2i/m, C2/m, P2/c, P2i/c, C2/c, etc. 

Labeling the 4 tt crystal orbitals at high symmetry point M in the Brillouin zone, using their symmetry with respect to the 4 screw axis and the c glide plane of the unit cell, there are fourcombinations p, (SS), (AA),... 

Table 6-1. C2(l molecular poinl group. The electronic stales of the flat T6 molecule are classified according lo the lwo-1 old screw axis (C2). inversion (/). and glide plane reflection (o ) symmetry operations. The A and lt excited slates transform like translations Oi along the molecular axes and are optically allowed. The Ag and Bg stales arc isoniorphous with the polarizability tensor components (u), being therefore one-photon forbidden and Iwo-pholon allowed.

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