Valence bond theory
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The valence bond theory considers that the overlapping atomic orbitals of the participating atoms form a chemical bond. Due to 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 be of different types. There are two different types of overlapping orbitals: sigma and pi. Sigma bonds occur when the orbitals of two shared electrons overlap co-axially. Pi bonds occur when two orbitals overlap but do not do so on the axes (i.e. the side-to-side overlap of p-orbitals). 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 consist of one sigma bond, double bonds consist of one sigma bond and one pi bond, and triple bonds consist of one sigma bond and two pi bonds.
However, the atomic orbitals for bonding may not be "pure" atomic orbitals directly from the solution of the Schrödinger equation. 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 (also spelled hybridisation). Hybridization can only occur when electrons need to be promoted to the next energy level.
Valence bond theory has been extended to Molecular Orbital Theory, which explains this hybridization as linear combinations of the wavefunctions associated with each atom involved.
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.

