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Valence Bond Method

The quantum mechanical description of Lewis electron pair bond is known as valence bond method. It was developed by Heitler and London in 1927 and later extended by Pauling and Slater in 1931. In the approach, it is assumed that

(i)    Atoms maintain their individuality.
(ii)    The bond is formed due to the interaction of valence electrons as the atoms approach each other, i.e., the inner atomic orbital form each atom forming the bond are undisturbed.
(iii)    When they form a bond, only valence electrons form each bonded atom lose their identity.
(iv)    The stability of the bond is accounted by the fact that the electrons forming the bond between two atoms undergo exchange between them.

This method is based on two theorems which are stated as:

(i)    If Ψ and ΨB are the wave functions for two isolated independent atoms, with energies EA and EB, respectively, then the total wave function Ψ of the system can written as a product of the wave functions of the two atoms
                                                                  Ψ = ΨA ΨB    
and energy of the system by                
                                                                 E = EA + EB
(ii)    If a system can be represented by a number of wave functions such as Ψ1, Ψ2, Ψ3,.........then the true wave function Ψ can be obtained by tacking a linear combination of all wave functions.

   Ψ = N (c1Ψ1+ c2 Ψ2+ c3 Ψ3+....)

where N is the normalization constant and c1,c2,c3....., are the coefficients indicating the weight to each of the Ψn's . They are so adjusted as to give a state of lowest energy. The squares of the coefficients may be taken as a measure of the weights of each wave function to the total wave function.

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