The valence bond theory was developed by W.Heitler and F.London in 1927. Then it was further amended by the Linus Pauling and J.C. Slater. For this Linus Pauling get the Chemistry Nobel Prize in 1954.
Valence bond theory is based on wave mechanical expression of the Lewis concept to explain chemical bonding. The main focus is on atomic orbitals which combine to give individual chemical bond. This theory includes only the atoms not the whole molecule.
We explain this theory by following example:
Formation of a Hydrogen atom:
Let us consider the two hydrogen atoms. The two hydrogen atoms are denoted as A and B. Both the atoms are apart from each other i.e. there is no interaction between them.
Now let us suppose ø A be the wave function of the hydrogen atom A and øB be the wave function of the hydrogen atom B. when both the atoms are combined to form hydrogen molecule, then the Combined wave equation For the hydrogen molecule i.e. H2 will be given by:
Ø = ø A (1) ø B (2)
Where 1 and 2 numbers denote the two electrons. For calculating the energy of each hydrogen atom Schrodinger wave equation is used. Schrodinger wave equation can be written as:
Ĥø = Eø
Ĥ represents the Hamiltonian operator
E represents the potential energy of the hydrogen atom.