Equivalence between MO and VB Based Wave Functions

The unitary group invariance of the hamiltonian assures that its exact eigenvalue spectrum is invariant to a unitary transformation of the basis. It means that a full Cl calculation must provide the same eigenvalues (many-electron energy states) as a full VB calculation. However, at intermediate levels of approximation, this equivalence is not straightforward. In this section we will sketch out the main points of contact between MO and VB related wave functions. 

The most simple and well known equivalence holds for the special case of two electrons in two orbitals, described by GVB(pp) and CASSCF(2,2) wave functions for covalent bonds [41]. When the bond has a mixed ionic-covalent character, the CASSCF(2,2) description is able to account approximately for this effect due to the presence of an extra ionic configuration. This problem is exactly replicated in a larger scale when 

Formally, all these wave functions, VB or MO based, can be reproduced at the GMS level. When using one structure, the GMS wave 

In this section we will review briefly some of the recent applications of the GMS wave function. A previous review [45] covers most of the early applications of the GMS wave function. Our main goal is to illustrate some of the new ideas presented in the last section, using the most recent applications and some earlier but not unpublished material. 

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