LCAO local-spin-density and Xα calculations for Cr₂ and Mo₂

Abstract

Broken-symmetry (C _∞v ) LCAO local-spin-density calculations using gaussian basis sets have been performed for Cr₂ and Mo₂ using five different approximations for the exchange and correlation potentials. The Xα potential is found to be inadequate. The correlated potentials of von Barth and Hedin, Gunnarsson and Lundqvist, Janak, Moruzzi and Williams, and Vosko, Wilk and Nusair all yield the same essential physics. The calculated bond lengths with these potentials are in near perfect agreement with experiment. The agreement for the dissociation energy is less good. The ‘best’ local potential (VWN) overestimates the binding energy by 55 per cent for Cr₂ and 19 per cent for Mo₂. The calculations indicate that Cr₂ and Mo₂ have equilibrium distances and binding energies which are close to those of a hypothetical hexuple bond, but vibrational properties which are drastically different. The large anharmonicities (and the proper dissociation of the molecules to high-spin atoms) are ultimately due to the rapid localization of the δ orbitals near R _e, followed by a more gradual localization of the other orbitals as R increases. The electron spins are arranged in an antiferromagnetic fashion in these localized orbitals which yields the nearest possible one-electron (‘single determinant’) approximation to the observed ¹Σ⁺ _g ground state.