Hybrid orbitals, construction

Use the four-step procedure described earlier. Begin with the Lewis structure for the molecule, and then identify the appropriate hybrid orbitals. Construct a a bond framework, and complete the bonding picture by assembling the bonds from the unhybridized p orbitals. 

Therefore, in order for boron to form a 77-bond perpendicular to the molecular plane to each of the chlorine atoms, it must use three hybrid orbitals constructed from one AO which belongs to V and a pair of AOs which belong to r Table 11-2.2 shows that only the following orbitals meet these requirements ... 

Figure 7.23 Examples of sp hybrid orbitals constructed from AOs which belong to the same irreducible representation, (a) AOs of the same energy would contribute equally to give degenerate hybrids, (b) When the energy separation between s and p states is larger, the hybrid orbitals are no longer equivalent. The grey spot in the hi orbital indicates the position of the nucleus, showing that mixing in 0.1 p has polarized the s-orbital.

The isotropic interaction This concerns exclusively s-type orbitals or orbitals with partial s character (such as hybrid orbitals constructed from s-type... 

The hybrid orbitals, constructed by the combination of atomic orbitals, can be represented in a similar way (Fig. 1.5). Only the two sp-hybrid orbitals are shown but the trigonal sp - and tetrahedral sp hybrid orbitals have similar shapes. In each case the large bonding lobes have the same sign, taken as positive. 

Starting from hybrid orbitals, it is possible to construct bond orbitals by using normalized combinations. For every couple of hybrids pointing to each other along a bond direction, a bond-antibond pair can be obtained2 ... 

The promotion of electrons will occur if, overall, it leads to a lowering of energy by permitting the formation of more bonds. Hybrid orbitals are constructed on an atom to reproduce the electron arrangement characteristic of the experimentally determined shape of a molecule. 

Any hybrid orbital is named from the atomic valence orbitals from which It Is constmcted. To match the geometry of methane, we need four orbitals that point at the comers of a tetrahedron. We construct this set from one s orbital and three p orbitals, so the hybrids are called s p hybrid orbitais. Figure 10-8a shows the detailed shape of an s p hybrid orbital. For the sake of convenience and to keep our figures as uncluttered as possible, we use the stylized view of hybrid orbitals shown in Figure 10-8Z). In this representation, we omit the small backside lobe, and we slim down the orbital in order to show several orbitals around an atom. Figure 10-8c shows a stylized view of an s p hybridized atom. This part of the figure shows that all four s p hybrids have the same shape, but each points to a different comer of a regular tetrahedron. 

Each carbon atom has a steric number of 2, indicating that acetylene is a linear molecule and that sp hybrid orbitals can be used to construct the bonding orbital framework. Figure 10-24a shows the a bonding system of acetylene. 

These compounds are often referred to as hypervalent. The apical bonds in a trigonal bipyramid are described by molecular orbitals constructed from a p-orbital on the central atom and o-bonding orbitals (p- or sp hybrid) on the apical ligands. The molecular orbitals can be drawn as ... 

For example, we can construct hi and h2, two hybrid orbitals for describing the bonds in the water molecule, by taking the two combinations... 

Hybridization does not in general predict the equilibrium geometry. On the contrary, the construction of appropriate hybrid orbitals relies on a given or predetermined, geometry. 

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... 

We shall now construct two concentrated spd hybrid orbitals that are equivalent, orthonormal, and have maximum concentration of electron density in their respective bonding directions. We can choose any arbitrary direction for the two bond hybrids that we construct. The judicious choice for the direction of the first bond hybrid is along the z axis, because only one of the five d-orbital functions (dz2) can contribute to a bond in this direction. The largest value of the angular part of the first hybrid function (i.e., the maximum concentration of electron density) along the z axis for a chosen spM hybrid orbital hi is insured by choosing both the p and d components to lie along the z direction,... 

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