Inexpensive determinations of valence virtual MOs for CI calculations

Abstract

The full treatment of the non-dynamical correlation energy (i.e. the correlation within a shell of valence occupied and virtual MOs) is hihgly desirable since it is strongly shape and distance dependent, and ensures a proper dissociation into the HF ground state of the free atoms. The ideal way to achieve this goal is the valence CAS SCF procedure, which is rapidly very expensive. The present paper tries to define valence virtual MOs to perform full CAS CI or to use them in other approximate CI expansions. Very limited MC SCF procedures involving a few pair-wise excitations are sufficient to generate well-defined valence MOs. One may sometimes use virtual valence MOs from the upper valence multiplet but in many cases this procedure fails, the high-spin arrangement tending to avoid the σ bond region where it becomes too repulsive. The projection of the SCF atomic orbitals of the free atom in the virtual molecular space (Levy's PAO) is very efficient; this procedure may be improved by a proper definition of the hybridized AOs, i.e. the linear combination of the AOs which are most occupied in the molecular Fock space. The MOs defined from these four procedures prove to give CAS CI energies which are very close to the CAS SCF result, at a very low price. On the contrary, the usual improved virtual MOs defined from SCF calculations of the cation, or with an increased nuclear charge to compensate the excess repulsion of the Fock operator, fail to define valence virtual MOs even if they concentrate the spatial extension of the lowest virtual MOs. The quality of our MO sets is compared at the valence CAS CI level and through the convergence of the iterative multireference second-order Møller-Plesset CIPSI algorithm. Three comparisons concern a triply bonded molecule (N 2), an non-Lewis structure (Na 4), and an intermolecular complex Cu…CO, which is proved to be weakly bound. To obtain reliable potential curves in selected CI algorithms, it is recommended to give an (almost) constant physical meaning to all MOs.