Reparameterization of hybrid functionals based on energy differences of states of different multiplicity

Low-spin/high-spin energy splittings for Fe(II) transition-metal complexes - particularly in weak ligand fields - cannot be well described by density functional methods, Different density functionals yield results which differ by up to 1 eV in transition-metal complexes with sulfur-rich first coordination spheres. We attribute this failure to the fact that the high-spin state is systematically favoured in Hartree-Fock-type theories, because Fermi correlation is included in the exact exchange, while Coulomb correlation is not. We thus expect that the admixture of exact exchange to a given density functional will heavily influence the energy splitting between states of different multiplicity. We demonstrate that the energy splitting depends linearly on the coefficient of exact exchange admixture. This remarkable result is found for all the Fe(II) S complexes studied. From this observation we conclude in connection with experimental results that Becke's 20% admixture should be reduced to about 15% if meaningful energetics are sought for transition-metal compounds. We rationalize that this reduction by 5% will not affect the quality of the hybrid functional since we arrive at a slightly modified functional, which lies between the pure density functional and the hybrid density functional, which both give good results for "standard" systems.