Introducing appropriate criteria for the choice of such an orbital transformation, which need not be unitary, we are able to obtain alternative representations of exactly the same wavefunction, but based instead on nonorthogonal orbitals, such as those that are more characteristic of VB approaches. The initial main motivation was to be able to use modern VB language to extract highly visual interpretations of correlated electronic structure, whilst avoiding the need to carry out actual VB calculations, which were traditionally perceived to be somewhat more expensive.
Particularly for systems with few active electrons, a fully-variational spin-coupled generalized valence bond (SCGVB) wavefunction based on a single product of N singly-occupied nonorthogonal orbitals, tends to be only slightly inferior to the corresponding many-configuration 'N electrons in N orbitals' CASSCF wavefunction. As such, an obvious criterion for choosing the general orbital transformation in such a case is to maximize the overlap of the full wavefunction with a subcomponent of SCGVB form. The result is of course exactly the same wavefunction, except that it is now represented in terms of orbitals that closely resemble those from fully-variational modern VB calculations. Furthermore, all of the CI coefficients that are not associated with the VB-like subcomponent tend to be very small. The program can deal with a fairly wide choice of 'target' for the chosen subcomponent, and uses an efficient iterative strategy (involving analytic first and second derivatives) for optimizing the orbital transformation.
Perhaps the most obvious alternative criterion for the choice of orbital transformation is to minimize the difference between the energy of the full wavefunction and that of the chosen subcomponent. This 'energy criterion' is computationally slightly more demanding than the 'overlap criterion' described above, but not prohibitively so. Furthermore, having embedded the 'energy criterion' CASVB transformation within the iterations that would ordinarily be used to optimize (say) a CASSCF wavefunction, we may now use the CASVB program in MOLCAS to carry out a wide variety of fully-variational modern VB calculations for ground and excited states.