Introduction of a New Theory for the Calculation of Magnetic Coupling Based on Spin–Flip Constricted Variational Density Functional Theory. Application to Trinuclear Copper Complexes which Model the Native Intermediate in Multicopper Oxidases

We have introduced a new method for the calculation of spin-exchange between weakly interacting electron spins on different metal centers. The method is based on spin-flip constricted variational density functional theory (SF-CV-DFT). The application of SF-CV-DFT to two trinuclear systems [Cu3(L)(μ3-O)](4+) and [(L')3]Cu3(μ-OH)3](3+) revealed that SF-CV-DFT affords exchange coupling constants that are similar to the values obtained by the traditional broken-symmetry (BS) scheme for the same functional. The BHandHLYP functional affords for both systems the best fit to experiment and results from high-level theory in the case of BS-DFT as well as SF-CV(2)-DFT. All methods and functionals predict [Cu(L)(μ3-O)](4+) to be ferromagnetic and the [(L')3Cu3(μ-OH)3](3+) system to be antiferromagnetic. The SF-CV(2)-DFT method is not only able to evaluate exchange coupling constants, it can in addition calculate the full multiplet spectrum with complete use of spatial symmetry. Further, in its restricted formulation, calculations can be carried out with use of full spin-symmetry without spin-contamination.