Valence bond theory orbital hybridization schemes

Covalent bonds in polyatomic molecules and ions are formed by the overlap of hybrid orbitals, or of hybrid orbitals with unhybridized ones. Therefore, the hybridization bonding scheme is still within the framework of valence bond theory electrons in a molecule are assumed to occupy hybrid orbitals of the individual atoms. 

For molecular species with other than linear, trigonal planar or tetrahedral-based structures, it is usual to involve d orbitals within valence bond theory. We shall see later that this is not necessarily the case within molecular orbital theory. We shall also see in Chapters 14 and 15 that the bonding in so-called hypervalent compounds such as PF5 and SFg, can be described without invoking the use of J-orbitals. One should therefore be cautious about using sp"d hybridization schemes in compounds of />-block elements with apparently expanded octets around the central atom. Real molecules do not have to conform to simple theories of valence, nor must they conform to the sp"d" schemes that we consider in this book. Nevertheless, it is convenient to visualize the bonding in molecules in terms of a range of simple hybridization schemes. 

Despite its successes, the application of valence bond theory to the bonding in polyatomic molecules leads to conceptual difficulties. The method dictates that bonds are localized and, as a consequence, sets of resonance structures and bonding pictures involving hybridization schemes become rather tedious to establish, even for relatively small molecules (e.g. see Figure 4.10c). We therefore turn our attention to molecular orbital (MO) theory. 

When we considered how valence bond theory can be used to describe the bonding in BH3, CH4 and NH3, we used appropriate hybridization schemes such that bonds known to be structurally equivalent would be equivalent in the bonding scheme. One hybrid orbital contributed to each localized X—H (X = B, C or N) bond. On the other hand, the results of MO theory indicate that the bonding character is delocalized. Moreover, in each of BH3, NH3 and CH4, there are two different types of bonding MO a unique MO involving the 2s atomic orbital of the central atom, and a degenerate set of two (in BH3 and NH3) or three (in CH4) MOs involving the 2p atomic orbitals of the central... 

For a high-spin octahedral complex such as [FeFg], the five 3d electrons occupy the five 3d atomic orbitals (as in the free ion shown above) and the two d orbitals required for the sp d hybridization scheme must come from the Ad set. With the ligand electrons included, valence bond theory describes the bonding as follows leaving three empty Ad atomic orbitals (not shown) ... 

The hybridization scheme in valence bond theory is a very useful concept for chemists since it permits a localized view of the bonding. The most general method for generating hybridized orbitals is based on defining a bond wavefunction (a linear combination of atomic orbitals) in a specific bond direction (usually the z-axis direction). Then the second and subsequent hybrids are obtained by a rotation transformation. Orthogonality conditions are then used to evaluate the hybrid coefficients. These bond wavefunctions are defined as equivalent because they differ from one another only by a rotation. Generally, the first bond wavefunction is... 

Molecules such as NHj and HjO etc. are described in terms of an inequivalent hybridization scheme based on sp in valence bond theory. The construction of hybridized orbitals in such molecules is different from that developed above. The tetrahedral molecule XAY3 (3) provides a useful starting point. Since the hyl is distinguished from hy2, hy3 and hy4, the symmetry-adapted linear combinations of these hybrids cannot be generated in terms of the spherical harmonic expansion in Eq. (1). But they can be derived as follows ... 

The structures discussed in the sections 2-4 are referred to as spherical polyhedra since their hybridization schemes can be either exactly or very closely described in terms of the spherical harmonic methodology developed above. In summary the orbitals describing these polyhedra based on the Valence Bond Theory can be classified into three types ... 

The sp hybridization scheme corresponds to trigonal-planar electron-group geometry and 120° bond, as in BF3. Note again that in the hybridization schemes of valence bond theory, the number of orbitals is conserved that is, in an sp hybridized atom there are still four orbitals three sp hybrids and an unhybridized p orbital. 

Bonding in acetylene, C2H2, is similar to that in C2H4, but with these differences The Lewis structure of C2H2 features a triple covalent bond, H—C=C—H. The molecule is linear, as found by experiment and as expected from VSEPR theory. A hybridization scheme to produce hybrid orbitals in a linear orientation is sp. The valence-shell orbital diagrams representing sp hybridization are... 

To describe hybridization schemes that correspond to the 5- and 6-electron-group geometries of VSEPR theory, we need to go beyond the s and p subshells of the valence shell, and traditionally this has meant including d-orbital contributions. We can achieve the five half-filled orbitals of phosphorus to account for the five P—Cl bonds in PCI5 and its trigonal-bipyramidal molecular geometry through the hybridization of the s, three p, and one d orbital of the valence shell into five sp d hybrid orbitals. 

In the previous section, we emphasized that hybridization of some or all of the valence atomic orbitals of the central atom in an XY species provided a scheme for describing the X—Y f7-bonding. In, for example, the formation of sp, sp and sp d hybrid orbitals, some p or d atomic orbitals remain unhybridized and, if appropriate, may participate in the formation of TT-bonds. In this section we use the examples of C2H4, HCN and BF3 to illustrate how multiple bonds in polyatomic molecules are treated within VB theory. Before considering the bonding in any molecule, the ground state electronic configurations of the atoms involved should be noted. 

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