Overview of CASVB

As is well known, CASSCF wavefunctions are invariant to general (i.e. nonunitary) linear transformations of the active orbitals. As such, we may seek alternative, but equivalent, representations in which a small number of configurations are dominant. This is achieved in our case by means of efficient computational schemes for carrying out exactly the transformations of full-CI spaces induced by nonunitary transformations of orbital spaces [9]. 

In its simplest form, the CASVB approach may be used simply to generate representations of a CASSCF wavefunction 4 CAS in which a single- or multiconfiguration modem-VB component 4,VB is dominant. Writing 

This procedure is relatively inexpensive and, with suitable choices of the general form of 4/vb, it is fairly robust. An obvious alternative is to minimize the energy quantity Ew defined according to 

By its very nature, minimization of En is more expensive than the maximization of S, because it requires the construction of quantities corresponding to applications of the hamiltonian operator, but this may be achieved by adapting the efficient procedures already available in various CASSCF codes. It turns out, however, that the two sets of orbital representations tend to be rather similar, and so maximization of tends to be preferred. In either case, the actual optimization uses reliable Newton-Raphson-like procedures that utilize first and second derivatives. 

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