Multi-reference Ab Initio Calculations of 3d Transition-Metal Dimers: Sc2

The problem of calculation of the electronic structure of transition-metal clusters (even dimers) still presents a challenge for computational chemistry. The reason is that the expansion of the ground state wave function on electronic configurations does not contain a principal configuration and a large number of reference configurations must be treated equally. Thus, the multi-reference (MR) approaches are, in general, mandatory. A short description of the MRCI methods is presented. The calculation of Sc-2 at the MRCISD(+Q)/cc-pV5Z level, showed that the its ground state corresponds to a quintet, (5)Sigma(-)(u) in agreement with experiment and previous precise calculations. The triplet (3)Sigma(-)(u) state is located about 1.1 kcal/mol above. We calculated the ground state, X-5 Sigma(-)(u), of the Sc-2 dimer by the MRCISD(+Q) method at the complete basis set (CBS) limit. This is the first MRCISD(+ Q) calculation of 3d transition-metal clusters at the CBS limit. From the Mulliken population analysis and comparison with atomic energies follows that in the ground state Sc-2 dissociates on one Sc in the ground state and the other in the second excited quartet state, F-4(u). The spectroscopic parameters of the ground potential curve, obtained by the Dunham analysis at the valence MRCISD(+ Q)/CBS level, are: R-e = 5.20 bohr, D-e = 50.37 kcal/mol, and e = 234.5 cm(-1). The obtained value for the harmonic frequency agrees very well with the experimental one, e = 239.9 cm(-1). From the indistinguishability of identical atoms in quantum mechanics follows that in spite of an asymmetric dissociation limit for Sc-2, both Sc atoms have the same electron population and it is incorrect to consider them as different. Therefore, the accepted classification of the dimer states should be revised, since some of them are forbidden by the Pauli Exclusion Principle.