Symmetrization of the VB Wavefunction

In VB theory, all electrons are assigned to localized two-centered bonds, lone pairs and impaired components. Each collective pattern of such components constitutes a VB structure. The corresponding VB structure function can be expressed as , namely, a bonded tableau (BT) state as mentioned before. The wavefunction for the whole system is defined as the superposition of all possible VB structure functions 

Usually, an individual VB structure assembled from the localized bonding components does not share the point group symmetry of the molecule anymore. However, the overall VB wavefunction, PVB, should retain the same symmetry properties as the MO wavefunction (in the sense of full Cl, they are in fact identical). Therefore, TVs can be classified by an irreducible representation associated with a given point group. In order to sort vFra by symmetry, a project operator can be introduced as follows  

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