Horizontal mirror

In the Cih point group, there is a one-fold rotation axis plus horizontal symmetry (horizontal mirror). Note also the difference between Cih and... 

These symmetries are then compared with figure 4c which gives the live possible DF symmetries as well as the symmetry elements present in the specimen. The second case is particularly interesting. It corresponds to a two-fold rotation inside a disk (named 1r) due to a horizontal mirror present in the specimen. 

Mirror planes are denoted by the Greek letter a. Mirror planes in a molecule that has an axis of rotation are further classified according to the relative orientation of the axis and the mirror plane. Because it is usual to draw molecules with the principal rotation axis vertical, a mirror plane containing the principal rotation axis is called a vertical mirror and denoted. A mirror plane perpendicular to the rotation axis is called a horizontal mirror and denoted Oh-... 

A stereogram is to be interpreted as a schematic diagram of an object viewed down the principal axis. Horizontal mirror planes and equatorial rotation axes lie in the plane of the diagram. Points in space are designated by x if they lie above the plane of the diagram and by o if they lie below it. 

B = Mortar made of marble C = Spherical vertical mirror and D = Spherical horizontal mirror... 

A = Intense flame of expin B = Successive luminosity C = Image of vertical mirror D = Image of horizontal mirror... 

The drawing of flame shown in Fig 8 may be subdivided into A Intense flame of expln B >= Successive luminosity C = Image of vertical mirror and D = Image of horizontal mirror contml panel. The parameters sensed by the apparatus are displayed on meters or lamps and are expressed as numbers which are arbitrary, but useful for comparing one primer with another. More information about this test is given in Refs I2a 8c 14... 

Linear molecules with a center of symmetry, such as BeF, and all of the X, molecules (Fig. 3.I4e-g), possess a horizontal mirror plane and an infinite number of C2 axes perpendicular to the principal axis and thus have Oxh symmetry. 

Figure 2.8. Stereograms for the six D , T, and O point groups from combinations of proper rotations. Those for the three Cni, point groups from combinations of proper rotations and a horizontal mirror plane [in addition to 2 (m or C, ) and 6 (C3/,) shown in Figure 2.7], Those for the Cm, point groups from combinations of proper rotations and a vertical mirror plane.

C2h c2 axis (perpendicular to the c3h C3 axis and horizontal molecular plane) and a horizontal mirror plane... 

When the temperature is below 193 K, the orthorhomic form further transforms to the hexagonal system in space group D h - P63/mmc. The O2- and Ba2+ ions together form close packed layers and stack in the sequenceABCACB and the Ti4+ ions occupy the octahedral interstices composed only of O2-anions. In this layer stacked structure, the A layers have horizontal mirror symmetry as shown in Fig. 10.4.2(d). Two-thirds of the TiC>6 octahedra share faces to form the Ti2C>9 group, in which the Ti-Ti distance is 267 pm, as represented by a line. This centrosymmetrical crystal is non-ferroelectric. 

The number of classes, equal to 5, is derived considering all the possible conditions for chirotopicity of the catalytic sites corresponding to L. If they are not chirotopic, i.e. if they are achirotopic (e.g. they are bisected by a horizontal mirror plane), there are two possibilities only the two sites are equal (class I catalysts) or different from each other (class II catalysts). If, on the contrary, they are chirotopic, three possibilities exist the two catalytic sites are homotopic (equal) - related by a twofold symmetry axis (class III catalysts), enan-tiotopic - related by a vertical mirror plane (class IV catalysts) or diastereotopic (different from each other) - no symmetry element is present (class V catalysts). As a consequence, only five classes of metallocene catalysts may exist if interconversion among stereoisomers is not taken into account [122]. 

One w-Fold Princinal Rotation Axis C ( Rotation bv 360In Degrees ). Plus Horizontal Mirror Plane... 

One n-Fold Principal Rotation Axis n Cn Axes Perpendicular to C.r Horizontal Mirror Planeffi,... 

Let us take now a more complicated basis, and consider all the nuclear coordinates of HNNH shown in Figure 4-8a. These are the so-called Cartesian displacement vectors and will be discussed in Chapter 5 on molecular vibrations. Let us find the matrix representation of the crh operation (see Figure 4-8b). The horizontal mirror plane leaves all x and y coordinates unchanged while all z coordinates will go into their negative selves. In matrix notation this is expressed in the following way ... 

E = identity operation, C = n-fold proper rotation axis, S = n-fold improper rotation axis, <7h = horizontal mirror plane, <7v = vertical minor plane, <7d = dihedral minor plane, i = inversion center. 

Oy vertical mirn r planes CF f horizontal mirror plane... 

S4 and 8 Sg impiopcr mtatitni axes 3 O), horizontal mirror planes 6 0 dihedral mirror planes... 

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