The Relationship between Molecular Orbital and Valence Bond Wave Functions

2 The Relationship between Molecular Orbital and Valence Bond Wave Functions 

What is the difference between the MO and VB descriptions of an electronic system, at the simplest level of both theories As we will see, in the cases of le, 3e, and 4e interactions between two centers, there is no difference between the two theories, except for the representations that look different. On the other hand, the two theories differ in their description of the 2e bond. Once again let us take the example of H2, with its two AOs a and b, and examine the VB description first, dropping normalization factors for simplicity. 

Now let us turn to the MO description. Bringing together two hydrogen atoms leads to the formation of two MOs, a and a, respectively bonding and antibonding (Eq. 3.58, dropping normalization constants). 

At the simple MO level, the ground state of H2 is described by LMO, in which the bonding a MO is doubly occupied. Expansion (see Chapter 4 for a general method in the polyelectronic case) of this MO determinant into its AO determinant constituents leads to Equation 3.59 (again dropping normalization constants)  

It follows that mixing the two configurations mo and TD with different coefficients, as in Equation 3.61, will lead to a wave function TMo-ci in which the covalent and ionic components 

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