Atomic hybrids and bonding geometry

It should be pointed out that in searching for the best possible hybrids and bonding pattern, the NBO program makes no use of molecular geometry information. 

The extracted Natural Hybrid Orbitals (NHOs) are therefore not simply encoded forms of the molecular shape, as envisioned in valence shell electron pair repulsions (VSEPR)-type caricatures of hybridization theory. Instead, the NHOs represent optimal fits to the ESS-provided electronic occupancies (first-order density matrix elements cf. V B, p. 21ff) in terms of known angular properties of basis AOs. Thus, the NHOs predict preferred directional characteristics of bonding from angular patterns of electronic occupancy, and the deviations (if any) between NHO directions and the actual directions of bonded nuclei give important clues to bond strain or bending that are important descriptors of molecular stability and function. 

The original concept of main-group valence hybrids refers simply to quantum mechanical mixing ( superposition ) of the four atomic valence orbitals (s, p, py, p ) to form four directed hybrid orbitals (hi, h2, h3,114) that are variationally superior for chemical bonding mathematically. 

Because the s orbital is isotropic, the direction of h,- is determined solely by its p-orbital mixing. Just as p, p, p point in the respective directions (x, y, z) of unit vectors along the Cartesian axes, so does each new h,-point in a unique direction given by a unit vector d, (see Fig. 4.4). If we define a hybridization parameter A,- for each h,-as the ratio of squared p-type to s-type contributions  

The normalized p, orbital pointed in the d, direction is given by the corresponding linear combination  

---

In this structure, there are three sigma bonds and one pair of nonbonding electrons. Four hybrid orbitals are required, implying sp3 hybridization and tetrahedral geometry around the nitrogen atom, with bond angles of about 109.5°. The resulting structure is much like that of methane, except that one of the sp3 hybrid orbitals is occupied by a lone pair of electrons. 

The hybridization and bond angles of a simple carbanion also resemble those of an amine. The carbon atom is sp3 hybridized and tetrahedral. One of the tetrahedral positions is occupied by an unshared lone pair of electrons. Figure 4-16 compares the orbital structures and geometry of ammonia and the methyl anion. 

Hybridization and Resulting Geometry Orbitals Used by Each C Atom Bonds Formed by Each C Atom Example... 

The Universal Force Field, UFF, is one of the so-called whole periodic table force fields. It was developed by A. Rappe, W Goddard III, and others. It is a set of simple functional forms and parameters used to model the structure, movement, and interaction of molecules containing any combination of elements in the periodic table. The parameters are defined empirically or by combining atomic parameters based on certain rules. Force constants and geometry parameters depend on hybridization considerations rather than individual values for every combination of atoms in a bond, angle, or dihedral. The equilibrium bond lengths were derived from a combination of atomic radii. The parameters [22, 23], including metal ions [24], were published in several papers. 

One more hybridization scheme is important m organic chemistry It is called sp hybridization and applies when carbon is directly bonded to two atoms as m acetylene The structure of acetylene is shown m Figure 2 18 along with its bond distances and bond angles Its most prominent feature is its linear geometry... 

This nitrogen atom has three bonds and one lone pair, so it is sp hybridized, just as we would expect. The lone pair occupies an sp hybridized orbital, and the nitrogen atom has trigonal pyramidal geometry, just as we saw in the previous section. But now consider the nitrogen atom in the following compound ... 

Using Valence Bond (VB) theory, the central atoms of the molecules with formulas AB2U2 and AB3U should undergo sp3 hybridized with predicted bond angles of 109.5°. If no hybridization occurs, bonds would be formed by the use of p orbitals. Since the p orbitals are oriented at 90° from each other, the bond angles would be 90°. Note that hybridization is only invoked if the actual molecular geometry data indicate that it is necessary. 

Table 3.8 summarizes the geometries, atomic charges, and a ah NBO parameters (ionicity and hybridization) for the first three members of each family of elements in groups 13-17. Figures 3.16(a)-(e) show corresponding contour plots of valence bond (oah left) and antibond (aAn - right) NBOs for all these species. 

---