Right Electron Correlation in the MO and VB Theories

Historically, the first calculation of the electronic structure of a neutral molecule was carried out by Heitler and London [15], who treated H2 using the valence bond (VB) method. In this early paper, the molecular wave function for H2 was considered to be purely covalent, and constructed from the atomic orbitals (AO s) %a and %b of the separate atoms. Dropping the normalization constant hereafter, the wave function is given in equation 1. 

This simple wave function, so called the Heitler-London (HL) wave function, was able to account for about 66% of the bonding energy of H2, and performed a little better than the rival MO method that appeared almost at the same time. 

In the MO framework, The Hartree-Fock wave function Thf takes the form of an anti symmetrized orbital product, which in the case of H2 is the Slater determinant involving the spin-up and spin-down counterparts of the bonding orbital cg, as in eq 2  

The physical constitution of the Hartree-Fock wave function appears most clearly by expanding the MO determinant of eq 2 as a linear combination of determinants constructed from pure AO s, eq 3  

Here the first two determinants are the determinantal form of the Heitler-London function (eq 1), and represent a purely covalent interaction between the atoms. The remaining determinants represent zwitterionic structures, H-H+ and H+H, and contribute 50% to the wave function. The same constitution holds for any interatomic distance. This weight of the ionic structures is clearly too much at equilibrium distance, and becomes absurd at infinite separation where the ionic component is expected to drop to zero. Qualitatively, this can be corrected by including a second configuration where both electrons occupy the antibonding orbital, Gu, i.e. the doubly excited configuration. The more elaborate wave function T ci is shown in eq. 4, where C and C2 are coefficients of the two MO configurations  

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