Valence bond theory

In chemistry, valence bond theory explains the nature of a chemical bond in a molecule in terms of atomic valencies. Valence bond theory summarizes the rule that the central atom in a molecule tends to form electron pair bonds in accordance with geometric constraints as defined by the octet rule, approximately. Valence bond theory is closely related to molecular orbital theory.

History
In 1916, G.N. Lewis proposed that a chemical bond forms by the interaction of two shared bonding electrons, with the representation of molecules as Lewis structures. In 1927 the Heitler-London theory was formulated which for the first time enabled the calculation of bonding properties of the hydrogen molecule H2 based on quantum mechanical considerations. Specifically, after a long nap one day Walter Heitler figured out how to use Schrödinger’s wave equation (1925) to show how two hydrogen atom wavefunctions join together, with plus, minus, and exchange terms, to form a covalent bond. He then called up his associate Fritz London and they worked out the details of the theory over the course of the night. Later, Linus Pauling used the pair bonding ideas of Lewis together with Heitler-London theory to develop two other key concepts in VB theory: resonance (1928) and orbital hybridization (1930). According to Charles Coulson, author of the noted 1952 book Valence, this period marks the start of “modern valence bond theory”, as contrasted with older valence bond theories, which are essentially electronic theories of valence couched in pre-wave-mechanical terms. Resonance theory was criticized as imperfect by Soviet chemists during the 1950's.

Theory
A valence bond structure is similar to a Lewis structure, however where a single Lewis structure cannot be written, several valence bond structures are used. Each of these VB structures represents a specific Lewis structure. This combination of valence bond structures is the main point of resonance theory. Valence bond theory considers that the overlapping atomic orbitals of the participating atoms form a chemical bond. Because of the overlapping, it is most probable that electrons should be in the bond region. Valence bond theory views bonds as weakly coupled orbitals (small overlap). Valence bond theory is typically easier to employ in ground state molecules.

The overlapping atomic orbitals can differ. The two types of overlapping orbitals are sigma and pi. Sigma bonds occur when the orbitals of two shared electrons overlap head-to-head. Pi bonds occur when two orbitals overlap when they are parallel. For example, a bond between two s-orbital electrons is a sigma bond, because two spheres are always coaxial. In terms of bond order, single bonds have one sigma bond, double bonds consist of one sigma bond and one pi bond, and triple bonds contain one sigma bond and two pi bonds. However, the atomic orbitals for bonding may be hybrids. Often, the bonding atomic orbitals have a character of several possible types of orbitals. The methods to get an atomic orbital with the proper character for the bonding is called hybridization.

VB theory today
Valence bond theory now complements Molecular Orbital Theory (MO theory), which does not adhere to the VB idea that electron pairs are localized between two specific atoms in a molecule but that they are distributed in sets of molecular orbitals which can extend over the entire molecule. MO theory can predict magnetic properties in a straight forward manner, but valence bond theory is more complicated although giving the similar results. Valence bond theory views aromatic properties of molecules as due to resonance between Kekule, Dewar and possibly ionic structures, while molecular orbital theory views it as delocalisation of the π-electrons. The underlying mathematics are also more complicated limiting VB treatment to relatively small molecules. On the other hand, VB theory provides a much more accurate picture of the  reorganization of electronic charge that takes place when bonds are broken and formed during the course of a chemical reaction. In particular, valence bond theory correctly predicts the dissociation of homonuclear diatomic molecules into separate atoms, while simple molecular orbital theory predicts dissociation into a mixture of atoms and ions.

More recently, several groups have developed what is often called modern valence bond theory. This replaces the overlapping atomic orbitals by overlapping valence bond orbitals that are expanded over all basis functions in the molecule. The resulting energies are more competitive with energies where electron correlation is introduced based on a Hartree-Fock reference wavefunction.

Applications of VB theory
An important aspect of the VB theory is the condition of maximum overlap which leads to the formation of the strongest possible bonds. This theory is used to explain the covalent bond formation in many molecules.

For Example in the case of F2 molecule the F - F bond is formed by the overlap of p orbitals of the two F atoms each containing an unpaired electron. Since the nature of the overlapping orbitals are different in H2 and F2 molecules, the bond strength and bond lengths differ between H 2 and F2 molecules.

In a HF molecule the covalent bond is formed by the overlap of 1s orbital of H and 2p orbital of F each containing an unpaired electron. Mutual sharing of electrons between H and F results in a covalent bond between HF.