Electronic structure of trigonal-planar transition-metal-imido complexes: Spin-state energetics, spin-density profiles, and the remarkable performance of the OLYP functional

We have carried out a detailed multifunctional density functional theory study of first-row transition-metal (Cr to Cu)beta-diketiminato ("nacnac") imido and oxo complexes. All the complexes studied exhibit essentially the same d-orbital energy ordering, which is a(1) (d(x)(2)-(2)(z)) <= a(2) (d(xy)) <= a(1) (d(y2)) < b(2) (d(yz)) < b(1) (d(xz)), where the metal-imido vector is identified with the z axis and metal-N3 plane is identified with the xz plane. A curious aspect of this orbital ordering is that the metal dx(2)-z(2) orbital, one of whose lobes points directly at the imido nitrogen, is considerably lower in energy than the d pi orbitals. We have determined that the remarkable stability of the d(o)-type orbitals owes largely to the way these orbitals hybridize or "shape-shift" as a result of the absence of ligands trans or equatorial with respect to the imido (or oxo) group. Of the many functionals examined, OLYP and OPBE, based on the Handy-Cohen OPTX exchange functional, appear to provide the best overall description of the spin-state energetics of the various complexes. In particular, these two functionals predict an S = 3/2 ground state for Fe(III) nacnac imido complexes and an S = 0 ground state for Co( III) nacnac imido complexes, as observed experimentally. In contrast, classic pure functionals such as PW91 predict S = 1/2 ground states or at best equienergetic S = 1/2 and S = 3/2 states for the Fe(III) imido complexes, while hybrid functionals such as B3LYP and O3LYP predict S = 1 or 2 ground states for the Co(III) nacnac imido complexes.