Valence bond theory tetrahedral

The concepts of directed valence and orbital hybridization were developed by Linus Pauling soon after the description of the hydrogen molecule by the valence bond theory. These concepts were applied to an issue of specific concern to organic chemistry, the tetrahedral orientation of the bonds to tetracoordinate carbon. Pauling reasoned that because covalent bonds require mutual overlap of orbitals, stronger bonds would result from better overlap. Orbitals that possess directional properties, such as p orbitals, should therefore be more effective than spherically symmetric 5 orbitals. 

FIGURE 3.14 Each C H bond in methane is formed by the pairing of an electron in a hydrogen U-orbital and an electron in one of the four sp hybrid orbitals of carbon. Therefore, valence-bond theory predicts four equivalent cr-bonds in a tetrahedral arrangement, which is consistent with experimental results. 

How does valence bond theory describe the electronic structure of a polyatomic molecule, and how does it account for molecular shape Let s look, for example, at a simple tetrahedral molecule such as methane, CH4. There are several problems to be dealt with. 

Valence bond theory describes the bonding in complexes in terms of two-electron, coordinate covalent bonds resulting from the overlap of filled ligand orbitals with vacant metal hybrid orbitals that point in the direction of the ligands sp (linear), sp3 (tetrahedral), dsp2 (square planar), and d2sp3 or sp3d2 (octahedral). 

The bond angle in H2O (104.5°) is closer to the tetrahedral value (109.5°) than to the 90° angle that would result from bonding by pure 2p atomic orbitals on O. Valence bond theory therefore postulates four sp hybrid orbitals centered on the O atom two to participate in bonding and two to hold the two unshared pairs. 

In Figure 4.6b we illustrate how the tetrahedral structure of CH4 relates to a cubic framework. This relationship is important because it allows us to describe a tetrahedron in terms of a Cartesian axis set. Within valence bond theory, the bonding in CH4 can conveniently be described in terms of an sp valence state for C, i.e. four degenerate orbitals, each containing one electron. Each hybrid orbital overlaps with the li atomic orbital of one H atom to generate one of four equivalent, localized 2c-2e C—H (T-interactions. 

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. 

According to valence bond theory, what set of orbitals is used by a Period 4 metal ion in forming (a) a square planar complex (b) a tetrahedral complex ... 

Hybridization. Finally, what does valence bond theory say about the atomic orbitals demanded by VSEPR For example, though the regions occupied by sets of electrons having a tetrahedral arrangement around a central atom make angles of 109.5° to one another, valence p-orbitals are at 90° angles. 

SECTION 9.5 To extend the ideas of valence-bond theory to polyatomic molecules, we must envision mixing s, p, and sometimes d orbitals to form hybrid orbitals. The process of hybridization leads to hybrid atomic orbitals that have a large lobe directed to overlap with orbitals on another atom to make a bond. Hybrid orbitals can also accommodate nonbonding pairs. A particular mode of hybridization can be associated with each of three common electron-domain geometries (linear = sp trigonal planar = sp -, tetrahedral = sp ). 

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 ... 

More than anyone else it has been Linus Pauling (b. 1901) who has been responsible for the development and application of the valence bond theory. In the early 1930s he deduced from quantum mechanics the tetrahedrally directed valencies of carbon, and he introduced the concept of the hybridisation of atomic orbitals. He introduced the idea of resonance as the quantum-mechanical counterpart of mesomerism. The wavefiinction for the molecule must contain terms for all possible structures, and the molecule is said to resonate between them. In 1933 Pauling described the benzene molecule as a resonance hybrid between the two Kekule structures and the three possible Dewar structures (Figure 11.22). 

The C—H bonds in methane, CH4, are described by valence bond theory as the overlapping of each sp hybrid orbital of the carbon atom with Is orbitals of hydrogen atoms (see Figure 10.22Q. Thus, the bonds are arranged tetrahedrally, which is... 

Pauling s valence bond theory is likewise of only limited value in its application to transition metal complexes. In the VBT, the ligand electrons are accommodated in hybrid orbitals localized on the central metal. The orbitals of interest for transition metals are the nd, n -f 1), n + l)p, and n + )d. An octahedral configuration arises from d sp hybridization of the metal orbitals, while dsp hybridization gives the square planar structure and sp hybridization results in a tetrahedral geometry. 

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