Comparison of the MO and VB Theories

Let us compare the molecular-orbital and valence-bond treatments of the H2 ground state. 

If tj a symbolizes an atomic orbital centered on nucleus a, the spatial factor of the imnormalized LCAO-MO wave function for the H2 ground state is 

What is the physical significance of the terms The last two terms have each electron in an atomic orbital centered on a different nucleus. These are covalent terms, corresponding to equal sharing of the electrons between the atoms. The first two terms have both electrons in AOs centered on the same nucleus. These are ionic terms, corresponding to the chemical structures 

How can we remedy this Since H2 is nonpolar, chemical intuition tells us that ionic terms should contribute substantially less to the wave function than covalent terms. The simplest procedure is to omit the ionic terms of the MO function (13.108). This gives 

Although interelectronic repulsion causes the electrons to avoid each other, there is some probability of finding both electrons near the same nucleus, corresponding to an ionic structure. Therefore, instead of simply dropping the ionic terms from (13.108), we might try 

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