VB Wave Functions with Localized Atomic Orbitals

1 VB Wave Functions with Localized Atomic Orbitals 

After looking at the VB outputs for the simple two-center/two-electron (2e/2c) bond, let us get used to the theory by applying it to these bonds to start with. A VB determinant is an antisymmetrized wave function that may or may not also be a proper spin eigenfunction. For example, ab in Equation 3.1 is a determinant that describes two spin—orbitals a and b, each having one electron the bar over the b orbital means a (3 spin, and the absence of a bar means an a spin  

A Chemist s Guide to Valence Bond Theory, by Sason Shaik and Philippe C. Hiberty Copyright 2008 John Wiley Sons, Inc. 

While the H—H bond in H2 was considered as purely covalent in Heitler and London s paper (1) (Eq. 3.2 and Structure 1), as we saw in Chapter 2, the exact description of H2 or any homopolar bond OPvB-fuii) involves a small contribution of the ionic structures 3 and 4, which mix by configuration interaction (Cl) in the VB framework. Typically, for homopolar and weakly polar bonds, the weight of the purely covalent structure is 75%, while the ionic structures share the remaining 25%. By symmetry, the wave function maintains an average neutrality of the two bonded atoms (Eq. 3.4). 

For convenience and to avoid confusion, we will symbolize a purely covalent bond between A and B centers as A — B, while the notation A—B will be employed for a composite bond wave function like the one displayed in Equation 3.4. In other words, A—B refers to the real bond while A — B designates its covalent component. 

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