Digonal groups

Table 61 Character table of some digonal groups and their double groups...

There exists no uniformity as regards the relations between localized orbitals and molecular symmetry. Consider for example an atomic system consisting of two electrons in an (s) orbital and two electrons in a (2px) orbital, both of which are self-consistent-field orbitals. Since they belong to irreducible representations of the atomic symmetry group, they are in fact the canonical orbitals of this system. Let these two self-consistent-field orbitals be denoted by Cs) and (2p), and let (ft+) and (ft ) denote the two digonal hybrid orbitals defined by... 

Figure 16.9. Location of some of the equivalent points and symmetry elements in the unit cell of space group Pnali. An open circle marked + denotes the position of a general point xyz, the + sign meaning that the point lies at a height z above the xy plane. Circles containing a comma denote equivalent points that result from mirror reflections. The origin is in the top left comer, and the filled digon with tails denotes the presence of a two-fold screw axis at the origin. Small arrows in this figure show the directions of a1 a2, which in an orthorhombic cell coincide with x, y. The dashed line...

An atom, X, using a pair of such sp or digonal hybrid orbitals, will form two equivalent bonds to two other atoms or univalent groups, Y, giving a linear YXY molecule. The gaseous halides (though not the solid compounds) of most of the Group II elements have linear structures which may be attributed to the sp hybridization of the metal atoms. Of course, a completely... 

The hybridization concept indicates some additional aspects of molecular stmcture. The tetrahedral, trigonal, and digonal natures of sp, sp, and sp carbon atoms provide an approximation of bond angles. The idea that tt bonds are formed by the overlap of p orbitals puts some geometrical constraints on structure. Ethene, for example, is planar to maximize p-orbital overlap. Allene, on the other hand, must have the terminal CH2 groups rotated by 90° to accommodate two tt bonds at the central sp carbon. 

The group Fe(CO)4 being isolobal to CH2 (see Sect. 4.4), iron pentacarbonyl may be regarded as an organometallic analog of ketene CH2=C=0 and Eq. (6.5) as comparable to nucleophilic addition of allene-type carbon to the digonal atom. 

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