Octahedral hybrid orbitals

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. 

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. 

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

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... 

A persistent feature of qualitative models of transition-metal bonding is the supposed importance of p orbitals in the skeletal hybridization.76 Pauling originally envisioned dsp2 hybrids for square-planar or d2sp3 hybrids for octahedral bonding, both of 50% p character. Moreover, the 18-electron rule for transition-metal complexes seems to require participation of nine metal orbitals, presumably the five d, one s, and three p orbitals of the outermost [( — l)d]5[ s]1[ p]3 quantum shell. 

RuC1(CO)2(PBu 2P-To1)]2 0.047 Ru—Ru distance is much shorter than other Ru or Ru° polymers. This fact, together with nonplanarity of Cl bridge system, suggests a bent Ru—Ru bond (formed by overlap of essentially octahedral hybrid orbitals). 1... 

Show that for a molecule of octahedral symmetry the a-bonding hybrid orbitals on the central atom are composed of six atomic orbitals s, p , pv, pa, ds , and... 

Most hybridizations result in equivalent hybrid orbitals, i.e., all the hybrid orbitals are identical in composition (% s and % p character) and in spatial orientation with respect to each other. They have very high symmetries, culminating in tetrahedral and octahedral symmetry. In the case of dsp hybrid orbitals, the resulting... 

In symmetries lower than cubic the (/-orbitals mix with the donor atom s—p hybrid orbitals to varying extents in molecular orbitals of appropriate symmetry. However, the mixing is believed to be small and the ligand field treatment of the problem proceeds upon the basis that the effective d-orbitals still follow the symmetry requirements as (/-orbitals should. There will be separations between the MOs which can be reproduced using the formal parameters appropriate to free-ion d-orbitals. That is, the separations may be parameterized using the crystal field scheme. Of course, the values that appear for the parameters may be quite different to those expected for a free ion (/-orbital set. Nevertheless, the formalism of the CFT approach can be used. For example, for axially distorted octahedral or tetrahedral complexes we expect to be able to parameterize the energies of the MOs which house the (/-orbitals using the parameter set Dq, Ds and Dt as set out in Section 6.2.1.4 or perhaps one of the schemes defined in equations (11) and (12). 

Construct wave functions for six equivalent octahedral (d2sp3) hybrid orbitals, using dX2 y2, d, s, px, py, and pz valence orbitals. 

FIGURE 7.13 Thesixsp3d2 hybrid orbitals and their octahedral geometry. 

In octahedral complexes, the metal ion uses either sp3d2 or d2sp3 hybrid orbitals. To see the difference between these two kinds of hybrids, let s consider... 

Because [V(NH3)g]3+ is octahedral, the V3+ ion must use either d2sp3 or sp3d2 hybrid orbitals in accepting a share in six pairs of electrons from the six NH3 ligands. The preferred hybrids are d2sp3 because several 3d orbitals are vacant and d2sp3 hybrids have... 

Valence bond theory describes the bonding in complexes in terms of two-electron, coordinate covalent bonds resulting from the overlap of filled ligand orbitals with vacant metal hybrid orbitals that point in the direction of the ligands sp (linear), sp3 (tetrahedral), dsp2 (square planar), and d2sp3 or sp3d2 (octahedral). 

The valence bond model constructs hybrid orbitals which contain various fractions of the character of the pure component orbitals. These hybrid orbitals are constructed such that they possess the correct spatial characteristics for the formation of bonds. The bonding is treated in terms of localised two-electron two-centre interactions between atoms. As applied to first-row transition metals, the valence bond approach considers that the 45, 4p and 3d orbitals are all available for bonding. To obtain an octahedral complex, two 3d, the 45 and the three 4p metal orbitals are mixed to give six spatially-equivalent directed cfisp3 hybrid orbitals, which are oriented with electron density along the principal Cartesian axes (Fig. 1-9). 

Figure 1-9. The construction of six d2spi hybrid orbitals from six atomic orbitals for use in an octahedral complex.

Molecular orbitals. Overlap of certain atomic orbitals of the metal and ligand atoms in a coordination site leads to the formation of molecular orbitals. In octahedral coordination, a-bonds are formed by the overlap of hybrid orbitals... 

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