Combination of approximate spin‐projection and spin‐restricted calculations based on ONIOM method for geometry optimization of large biradical systems

In this article, we combine the approximate spin projection (AP) and the spin-restricted (R) calculations based on ONIOM method for a geometry optimization of large biradical systems such as polynuclear metal complexes. This two-layer quantum mechanics/quantum mechanics′ (QM/QM′) (AP/R) method treats atoms of an inner layer around the spin sources with the AP method, whereas the whole atoms including the peripheral ligands are calculated by the R method. The AP/R method is applied for the geometry optimizations of chromium(II) ions in Cr2(O2CCH3)4(OH2)2 (1) and Cr2{O2CPh(CHMe2)3}4 (2) complexes that involve quadruple CrCr bonds. The optimized structural parameters indicate that the error of the two-layer combination is smaller than 0.01 A in the optimized CrCr bond length on both complexes. The error is only 12.3% of the spin contamination error and 1.7% of the static correlation correction in the complex 1. The error of the two-layer combination in a total energy is also estimated to be lower than 1 kcal mol−1 in both complexes. © 2012 Wiley Periodicals, Inc.