CASSCF model

The conceptual simplicity of the CASSCF model lies in the fact that once the inactive and active orbitals are chosen, the wave function is completely specified. In addition such a model leads to certain simplifications in the computational procedures used to obtain optimized orbitals and Cl coefficients, as was illustrated in the preceding chapters. The major technical difficulty inherent to the CASSCF method is the size of the complete Cl expansion, NCAS. It is given by the so-called Weyl formula, which gives the dimension of the irreducible representation of the unitary group U(n) associated with n active orbitals, N active electrons, and a total spin S ... 

Another extension of the CASSCF model, which has recently been developed, is to introduce several active spaces, and restrict the number of electrons in each subspace in some way. The Restricted Active Space (RAS) model employs five orbital subspaces instead of three ... 

The idea behind the CASSCF model is, of course, not at all new. It was realized very early that full Cl calculations in a valence orbital basis would be a valid model for studies of potential curves, e.g. for the diatomic molecules. Such calculations were already being used 20 years ago for qualitative studies of excited-state potential curves . ... 

The CASSCF model and its implementation into efficient computer programs will be discussed in more detail in the following sections. The main emphasis will, however, not be put on the technical problems concerning the search for efficient MCSCF optimization schemes. A comprehensive discussion of these problems has recently been published in this series . The present contribution will instead concentrate around problems concerning the application of the CASSCF method to different chemieal problems, ranging from accurate calculations of properties of small molecules to studies of the chemical bond in transition-metal compounds. Nevertheless a discussion on the computational strategies developed to obtain a CASSCF wavefunction is necessary and will be given below. However, the main emphasis will be on the... 

CASSCF, like most other MCSCF procedures, is a method which makes it possible to study systems where degeneracies or near-degeneracies occur between different configurations. In such cases the Hartree-Fock model is not a valid zeroth-order approximation. The CASSCF model studies these effects with as little bias as possible, since the only decision made by the user is the selection of the inactive and active orbitals, and of course the AO basis set. The method is not primarily aiming at studies of dynamical correlation effects. 

The Fermi-seas of the Be low-lying states, the corresponding 25, 2p, 35, 3p, id CASSCF model, and the weak bond of... 

The CASSCF model has been developed to make it possible to study situations with near-degeneracy between different electronic configurations and considerable configurational mixing ([3], p. 528). 

Fig. 2 shows the CASSCF potential energy curve for the symmetrical dissociation of H20, using a full-valence active space of six orbitals and eight electrons. For comparison, the figure also contains the FCI and RHF energy curves. Around equilibrium, the differences of the CASSCF and RHF curves from the FCI curve are similar. However, as the bonds are stretched, the RHF model dissociates incorrectly, whereas the CASSCF curve remains parallel to the FCI curve. Thus, the qualitative agreement that the RHF model exhibits around equilibrium has, in the CASSCF model, been extended to all bond distances, making it an ideal method for studies of reactions, at least in a qualitative sense. 

In total, 0.27 electrons are moved from the strongly to the weakly occupied orbitals, thus illustrating the difference in the picture of the bonding that the CASSCF model gives compared to HF. It is interesting to see that quite a redistribution occurs among the 3J-electrons. The... 

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