Formalism Using the Exact Hamiltonian

Let us turn now to the calculation of energetic quantities using exact VB theory by considering the simple case of the H2 molecule. The exact Hamiltonian is of course the same as in MO theory, and is composed in this case of two core terms and a bielectronic repulsion  

Here Q is the energy of a single determinant ab, K is the spin exchange term which will be dealt with later, and S is the overlap integral between the two AOs a and b. 

Plotting the curve as a function of the distance now gives qualitatively 

Examination of the K term in Eq. [22] shows that it is made of a repulsive exchange integral, which is positive but necessarily small (unlike Coulomb two-electron integrals), and of a negative term, given by the product of the overlap S and an integral that is called the resonance integral , which is itself proportional to S. 

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VALENCE BOND FORMALISM USING THE EXACT HAMILTONIAN... 

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