D-orbitals hybridization

It is interesting that a straight line drawn through the tetrahedral radii passes through the metallic radius for calcium this suggests that the metallic bonding orbitals for calcium are sp orbitals, and that those for scandium begin to involve d-orbital hybridization. 

The AO composition of the SOMO can often be deduced from the dipolar hyperfine matrix, particularly when the radical has enough symmetry to restrict possible hybridization. Thus an axial hyperfine matrix can usually be interpreted in terms of coupling to a SOMO composed of a single p- or d-orbital. A departure from axial symmetry may be due to spin orbit coupling effects, if (for example) /) Az and Ax AyxP(gx gy). If the departure from axial symmetry is larger, it is usually caused by d-orbital hybridization. The procedure is best illustrated by examples. 

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. 

The cr-bonding framework in a square-pyramidal species may also be described in terms of an sp d hybridization scheme. The change in spatial disposition of the five hybrid orbitals from trigonal bipyramidal to square-based pyramidal is a consequence of the participation of a different d orbital. Hybridization of s,Px,Py,Pz and dyi yi atomic orbitals generates a set of five sj d hybrid orbitals (Figure 4.7b). 

Explanations for the existence of hypervalent species started with Pauling s proposal of d orbital hybridization [3] where, for example, a set of sp d hybrid orbitals on sulfur was put forward to account for the hexavalence of SFg. Chemical computations [4] ruled out the participation of d atomic orbitals. A later model, the Rundle-Pimentel three-center, four-electron (3c-4e) bonding model [5], does not require d orbital participation and, so, is consistent with chemical computations. Other hypervalency models include the diabatic state model of Dixon and coworkers [6] and the democracy principle of Cooper and coworkers [7]. These various models provide useful insights into some aspects of the electronic structure of hypervalent molecules, but they don t provide an overarching description of these molecules that enables connections to be drawn between hypervalency and related molecular phenomena. 

A (a) polar, fb) nonpolar. 9.3B (a) polar, (b) nonpolar. 9.4A Singly occupied p orbitals from the P atom overlap with j orbitals from H atoms. 9.4B Singly occupied p orbitals from the As atom overlap with s orbitals frx)m H atoms. 9.5A Two of the 4p electrons in Br are promoted to empty d orbitals. The s orbital, aU three p orbitals, and two of the d orbitals hybridize to form six sp d hybrid orbitals. One of the hybrid orbitals contains the lone pair. Each of the remaining hybrid orbitals contains one electron and overlaps with a singly occupied 2p orbital on an F atom. 

F K orbitals that obtains when the p d orbital hybridizes away from F, and... 

PM3/TM is an extension of the PM3 method to include d orbitals for use with transition metals. Unlike the case with many other semiempirical methods, PM3/TM s parameterization is based solely on reproducing geometries from X-ray diffraction results. Results with PM3/TM can be either reasonable or not depending on the coordination of the metal center. Certain transition metals tend to prefer a specific hybridization for which it works well. 

Physical Properties. Sulfur tetrafluoride has the stmcture of a distorted trigonal bipyramid, the sulfur having hybrid sp d orbitals and an unshared electron pair (93). The FSF bond angles have been found to be 101° and 187°, and the bond distances 0.1646 and 0.1545 nm (94). 

It provides electrostatic stabilization of the carbanion formed upon removal of the C-2 proton. (The sf hybridization and the availability of vacant d orbitals on the adjacent sulfur probably also facilitate proton removal at C-2.)... 

Figure Schematic representation of the two components of the ij -Hi-metal bond (a) donation from the filled (hatched) CT-H2 bonding orbital into a vacant hybrid orbital on M (b) jr-back donation from a filled d orbital (or hybrid) on M into the vacant a antibonding orbital of Hj.

C. The structure, which involves two bridging carbonyl groups as shown in Fig. 26.8a, can perhaps be most easily rationalized on the basis of a bent Co-Co bond arising from overlap of angled metal orbitals (d sp hybrids). However, in solution this structure is in equilibrium with a second form (Fig. 26.8b) which has no bridging carbonyls and is held together solely by a Co-Co bond. 

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 hybridization scheme is adopted to match the electron arrangement of the molecule. Valence-shell expansion requires the use of d-orbitals. 

Complexes of d- and /-block metals can be described in terms of hybridization schemes, each associated with a particular shape. Bearing in mind that the number of atomic orbitals hybridized must be the same as the number of hybrid orbitals produced, match the hybrid orbitals sp1d, sp fd , and sp d3f to the following shapes (a) pentagonal bipyramidal ... 

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. 

In the early discussions of hybrid orbitals4,5 it was pointed out that the maximum strength (the maximum value in the bond direction) of a bond orbital formed from completed subshells of orbitals is associated with cylindrical symmetry of the orbital. In order to simplify the analysis of spd hybridization Hultgren5 decided to discuss only orbitals with cylindrical symmetry. He pointed out that no more than three d orbitals with cylindrical symmetry can be formed in a set of five d orbitals, and that each of these three is equivalent to the function d2 (see Table 1), except in orientation. 

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