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Organic Chemistry: Orbitals

Valence Bond Theory


Problems: Valence Bond Theory

So far we've presented a straightforward view of covalent bonding as the sharing of electrons between two atoms. However, we have yet to answer questions such as these: How are electrons shared? What orbitals do shared electrons reside in? Can we say anything about the energies of these shared electrons? Our task now is to extend the orbital scheme that we've developed for atoms to describe bonding in molecules.

Introduction to Valence Bond Theory

Valence bond theory (VB) is a straightforward extension of Lewis structures. Valence bond theory says that electrons in a covalent bond reside in a region that is the overlap of individual atomic orbitals. For example, the covalent bond in molecular hydrogen can be thought of as result of the overlap of two hydrogen 1 s orbitals.

Figure %: Two hydrogen 1 s orbitals overlap to form a covalent bond.

Molecular Geometry

In order to understand the limitations of valence bond theory, first we must digress to discuss molecular geometry, which is the spatial arrangement of covalent bonds around an atom. A very simple and intuitive approach, the Valence Shell Electron Pair Repulsion (VSEPR) model, is used to explain molecular geometry. VSEPR states that electron pairs tend to arrange themselves around an atom in such a way that repulsions between pairs are minimized. /PARGRAPH For instance, VSEPR predicts that carbon, which has a valence of four, should have a tetrahedral geometry. This is the observed geometry of methane ( CH 4 ). In such an arrangement, each bond about carbon points to the vertices of an imaginary tetrahedron, with bond angles of 109.5 degrees, which is the largest bond angle that can be attained between all four bonding pairs at once. Similarly, the best arrangement for three electron pairs is a trigonal planar geometry with bond angles of 120 degrees. The best arrangement for two pairs is a linear geometry with a bond angle of 180 degrees.

Figure %: Optimal spatial arrangements for 4, 3, and 2 electron pairs around an atom.

The VSEPR scheme includes lone pairs as well as bonded pairs. Since lone pairs are closer to the atom, they actually take up slightly more space then bonded pairs. However, lone pairs are "invisible" as far as the geometry of the atom is concerned. For instance, ammonia ( CH 3 ) has three C-H bonded pairs and one lone pair. These four electrons will, like methane, occupy a tetrahedral arrangement. Since lone pairs take more space, the H-N-H bond angle is reduced from 109.5 degrees to about 107 degrees. The geometry of ammonia is trigonal pyramidal rather than tetrahedral since the lone pair is not included. By similar reasoning, water has a bent geometry with a bond angle of about 105 degrees.

Figure %: Geometries of methane, ammonia, and water.

Note that multiple bonds don't affect the VSEPR scheme. A double or triple bond is considered no more repulsive than a single bond.

Hybrid Orbitals

The Valence Bond model runs into problems as soon as we try to take molecular geometries into account. The tetrahedral geometry of methane is clearly impossible if carbon uses its 2s and 2p orbitals to form the C-H bonds, which should yield bond angles of 90 degrees.

Figure %: The discrepancy between the spatial arrangement of the atomic orbitals of carbon and the geometry of methane.

Chemists invoke the concept of hybridization to explain this discrepancy. Under this concept, to accommodate the geometry of molecules, atomic orbitals modify themselves to become hybrid orbitals of the suitable geometry. For instance, to attain a tetrahedral arrangement the carbon undergoes sp 3 hybridization: the 2s orbital and three 2p orbitals become four sp 3 hybrid orbitals. Note that the total number of orbitals is conserved, but the orientation and energy of the orbitals have changed.

Figure %: Hybridization of s and p orbitals into sp 3 hybrid orbitals.

Orbital View of Multiple Bonding

Single covalent bonds can be explained by the VB model as the result of a head-on overlap between atomic orbitals. In some cases, these may be hybrid orbitals. Such head-on overlap is a sigma bond ( σ bond), so-called because of the bond's cylindrical symmetry. Only one σ bond can exist between two given atoms. How, then, are double and triple bonds formed?

The answer lies in the fact that p -orbitals are capable of overlapping sideways in what is called a pi bond ( Π bond). Π bonds are weaker than σ bonds because sideways overlap is not as effective as head-on overlap. For example, a C-C σ bond has a typical bond energy of 80 kcal/mol, but the C-C Π bond energy is usually around 60 kcal/mol.

Consider ethylene, which has a C=C double bond. Each carbon has three bonds in the VSEPR scheme, so each carbon has a trigonal planar geometry. To accommodate this geometry each carbon undergoes sp 2 hybridization. The 2 s orbital and two of the 2 p orbitals hybridize to form three sp 2 hybrid orbitals. The last p -orbital of each carbon atom remains unhybridized. These unhybridized p -orbitals overlap with one another to form the necessary Π -bond.

Figure %: Hybridization into sp 2 orbitals and Π bond formation in ethylene.

Triple bonds are formed in a similar process. In acetylene, the C-C triple bond is actually one σ bond and two Π bonds. Each carbon undergoes sp hybridization. The two unhybridized p -orbitals on each carbon form two orthogonal Π -bonds.

Figure %: Hybridization into sp orbitals and bonding in acetylene.

The Valence Bond Model: Conclusions

The valence bond model provides a simple and useful framework through which we mayunderstand covalent bonding. However it has several drawbacks. First, when using this model it is difficult to say anything about the energies of electrons. A more serious drawback of the VB model is its assumption that electrons are localized to specific atoms. In fact electrons are commonly delocalized to several atoms, as described by resonance structures. The Molecular Orbital model, while more complex, addresses both of these issues.

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