Hybrid octahedral

The remaining p-orbitals (one on each carbon) form the pi orbital. In ethyne, sp hybridization occurs to give two hybrid orbitals on each atom with lobes pointing along the axis. The two remaining p-orbitals on each carbon form two pi orbitals. Hybrid atomic orbitals can also involve d-orbitals. For instance, square-planar complexes use sp d hybrids octahedral complexes use sp if. 

The chemistry of Cr(III) in aqueous solution is coordination chemistry (see Coordination compounds). It is dominated by the formation of kineticaHy inert, octahedral complexes. The bonding can be described by Ss]] hybridization, and HteraHy thousands of complexes have been prepared. The kinetic inertness results from the electronic configuration of the Cr ion (41). This type of orbital charge distribution makes ligand displacement and... 

We need six orbitals to accommodate six electron pairs around an atom in an octahedral arrangement, as in SF6 and XeF4, and so we need to use two d-orbitals in addition to the valence s- and p-orbitals to form six sp3d2 hybrid orbitals (Fig. 3.18). These identical orbitals point toward the six corners of a regular octahedron. 

FIGURE 3.18 One of the six sp d1 hybrid "S-orbitals, and their six directions, that may be formed when el-orbitals are available 2 and we need to account for an octahedral o arrangement of electron pairs. 

FIGURE 16.36 I1ie tear-shaped objects are representations of the six ligand atomic orbitals that are used to build the molecular orbitals of an octahedral complex in ligand field theory. They might represent s- or p-orbitals on the ligands or hybrids of the two. 

For elements adjacent to the noble gases the principal orbitals used in bond formation are those formed by hybridisation of the s and p orbitals. For the transition elements there are nine stable orbitals to be taken into consideration, which in general are hybrids of five d orbitals, one s orbital, and three p orbitals. An especially important set of six bond orbitals, directed toward the comers of a regular octahedron, are the d2sps orbitals, which are involved in most of the Werner octahedral complexes formed by the transition elements. 

A transargononic structure for sulfur, with six bonds formed by sp3d2 hybrid orbitals, was suggested for sulfur in the octahedral molecule SF6 long ago, and also for one of the sulfur atoms, with ligancy 6, in binnite (Pauling and Neuman, 1934). Some transargononic structures of metal sulfides have been proposed recently by Franzen (1966). 

A molecule with a steric number of 6 requires six hybrid orbitals arranged in octahedral geometry. In Chapter 9, sulfur hexafluoride appears as the primary example of a molecule with a steric number of 6 (Figure ). Six equivalent orbitals for sulfur can be constmcted for the inner sulfur atom by combining the 3. S, the three 3 p,... 

An inner atom with a steric number of 6 has octahedral electron group geometry and can be described using S p d hybrid orbitals. 

With a steric number of 6, xenon has octahedral electron group geometry. This means the inner atom requires six directional orbitals, which are provided by an. s p d hybrid set. Fluorine uses its valence 2 p orbitals to form bonds by overlapping with the hybrid orbitals on the xenon atom. The two lone pairs are on opposite sides of a square plane, to minimize electron-electron repulsion. See the orbital overlap view on the next page. 

XANES spectroscopy shows that a narrow and intense pre-edge peak at 4967 eV, due to the Is 3pd electronic transition involving Ti atoms in tetrahedral coordination, is present in well-manufactured TS-1 (Fig. 2c). Conversely this electronic transition of Ti(IV) species in Ti02 (anatase or rutile) is characterized by a very low intensity due to the small pd hybridization in octahedral symmetry. Indeed the transitions l2g are symmetrically forbidden in the case of octahedral coordination of Ti (IV), but the transition Ai T2 is allowed in the case of tetrahedral coordination of Ti(IV), as in the case of [Ti04] units [52,58-61,63,68]. 

Figure 2. Diagrams showing the directions of the maxima of octahedral sp3d2 and trigonal bipyramidal and square pyramidal sp3d hybrid orbitals.

The Ni octahedra derive their stability from the interactions of s, p, and d electron orbitals to form octahedral sp3d2 hybrids. When these are sheared by dislocation motion this strong bonding is destroyed, and the octahedral symmetry is lost. Therefore, the overall (0°K) energy barrier to dislocation motion is about COCi/47r where = octahedral shear stiffness = [3C44 (Cu - Ci2)]/ [4C44 + (Cu - C12)] = 50.8 GPa (Prikhodko et al., 1998), and the barrier = 4.04 GPa. The octahedral shear stiffness is small compared with the primary stiffnesses C44 = 118 GPa, and (Cn - C12)/2 = 79 GPa. Thus elastic as well as plastic shear is easier on this plane than on either the (100), or the (110) planes. 

For metal ions having configurations d°, d1, d1, or d. there will always be two of the d orbitals empty to form a set of d2sp3 hybrids. Therefore, we expect complexes of these metal ions to be octahedral in which the hybrid orbital type is d2sp3. If we consider Cr3+ as an example, the formation of a complex can be shown as follows ... 

When the number of electrons in the d orbitals is four, as in the case of Mn3+, there exists more than one possible type of hybrid orbital. For example, if the electrons remain unpaired in the d orbitals, there is only one orbital in the set that is empty. As a result, if an octahedral complex is formed, making... 

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