Approximately spin-projected geometry optimization method and its application to di-chromium systems

A geometry optimization method based on Yamaguchi’s approximate spin projection (AP) procedure is presented. This method, which can eliminate the effect of spin contamination from the broken-symmetry (BS) solution, is applied to the Cr dimer model and the Cr2(O2CCH3)4(OH2)2 complex. The optimized Cr–Cr distance corresponding to the energy minimum of the AP potential curve within 0.008 Å demonstrates the validity of this method. The optimized geometry of the Cr(II) ions in Cr2(O2CCH3)4(OH2)2 indicates that the spin contamination elongates the quadruple bonds between the Cr(II) ions more than 0.1 Å. The results show that the effect of spin contamination in the structure optimized by the BS method is not negligible.