We now use a Pauling-like approach to show how hybrid orbitals for a variety of combinations of s, p, and d orbitals may be formulated.10 We assume that the radial dependences of the s, p, d orbitals are similar so that they can be neglected. The angular parts of the orbital wavefunctions are given by the following expressions (in the usual spherical coordinates 9, ) [Pg.372]

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. [Pg.228]

The most common—and perhaps most important—hybrid orbitals are the tetrahdral ones formed by adding one s-, and three p- type orbitals. These can be arranged to form various crystal structures diamond, zincblende, and wurtzite. Combinations of the s-, p-, and d- orbitals allow 48 possible symmetries (Kimball, 1940). [Pg.67]

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.) [Pg.646]

Pauling further extended the sp"dm hybridization approach to the d-block compounds.3 By varying the relative importance of p and d orbitals, Pauling was able to construct hybrid orbitals that rationalized the geometries and magnetic properties of many transition-metal coordination complexes. For example, the square-planar [Pg.363]

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. [Pg.239]

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