Hybrid orbital sp3d2 hybridization

Thus the bonding in sulfur hexafluoride SF6 has for a long time been considered to involve two of the 3d orbitals of sulfur, with the sulfur in a sp3d2 hybridized state 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. 

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). 

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. 

Hybrid orbitals formed two sp three sp2 foursp3 one d five sp3d two d six sp3d2... 

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... 

The difference between d2sp3 and sp3d2 hybrids lies in the principal quantum number of the d orbitals. In d2sp3 hybrids, the principal quantum number of the d orbitals is one less than the principal quantum number of the s and p orbitals. In sp3d2 hybrids, the s, p, and d orbitals have the same principal quantum number. To determine which set of hybrids is used in any given complex, we must know the magnetic properties of the complex. 

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). 

Unlike carbon, the valence shell of the silicon atom has available d orbitals. In many silicon compounds, the d orbitals of Si contribute to the hybrid orbitals and Si forms more than four 2c-2e covalent bonds. For example, Sib s- uses sp3d hybrid orbitals to form five Si-F bonds, and SiF62 uses sp3d2 hydrid orbitals to form six Si-F bonds. 

From the above diagram, we see why the bonds in SFe are called sp3d2 bonds. Mathematical treatment can predict the most stable way of orienting six bonds formed from hybridization of these orbitals the configuration with bond directions toward the comers of a regular octahedron (a polyhedron with eight faces and six corners) may be shown... 

The hybrid orbital type d2sp3 refers to a case in which the d orbitals have a smaller principal quantum number than that of the s and p orbitals (e.g., 3d combined with 4s and 4p orbitals). The sp3d2 hybrid orbital type indicates a case where the s, p, and d orbitals all have the same principal quantum number (e.g., 4s, 4p, and 4d orbitals) in accord with the natural order of filling atomic orbitals having a given principle quantum number. Some of the possible hybrid orbital combinations will now be illustrated for complexes of first-row transition metals. 

The basic idea in this approach is that six atomic orbitals are used to form six hybrid orbitals that are directed toward the corners of an octahedron, the known structure of complexes containing Ti3+. Hybrid orbital types that meet these requirements are d2sp3 and sp3d2. In the case of the Ti3+ ion, two of the 3d orbitals are empty so the dx yi and dzi, the 4s orbital, and the three 4p orbitals can form a set of d2sp3 hybrids. Moreover, the orbitals will be empty as is required for the metal to accept the six pairs of electrons from the six ligands. The electrons in the complex ion [Ti(H20)6]3+ can now be represented as follows ... 

For a complex containing a d4 ion, there are two distinct possibilities. The four electrons may either reside in three available 3d orbitals and a set of d2sp3 orbitals will be formed or else the empty 4d orbitals will be used to form a set of sp3d2 hybrids. The first case would have two unpaired electrons per complex ion, whereas the second would have four unpaired electrons per complex ion. Consequently, the magnetic moment can be used to distinguish between these two cases. An example of a d4 ion is Mn3+, for which two types of complexes are known. The first type of complex is illustrated by [Mn(CN)6]. The orbital population that results after the addition of six cyanide ions to form the complex [Mn(CN)6]3- may be shown as follows ... 

The molecule sulfur hexafluoride SF6 exemplifies one of the most common types of d orbital hybridization. The six bonds in this octahedrally-coordinated molecule are derived from mixing six atomic orbitals into a hybrid set. The easiest way to understand how these come about is to imagine that the molecule is made by combining an imaginary S6+ ion (which we refer to as the S(VI) valence state) with six F ions to form the neutral molecule. These now-empty 3s and 3p orbitals then mix with two 3d orbitals to form the sp3d2 hybrids. 

S(VI) represents the six-coordinated valence state of sulfur, which is considered to have lost its 3s and 3p electrons, making six equivalent sp3d2-hybridized orbitals available for accepting lone pairs contributed by the fluorine atoms. 

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