DFT and Metal-Metal Bonding: A Dys-Functional Treatment for Multiply Charged Complexes?

Density functional theory (DFT) calculations are reported for 16 binuclear transition-metal complexes. Structural motifs studied include face-shared and edge-shared bioctahedra, carboxylate-bridged "paddlewheel" complexes, and nonbridged dimers possessing direct metal-metal bonds. Most of these structure types are represented both by multiply charged (tri- and tetra-anionic, and tetracationic) and by neutral or singly charged examples. Geometry optimizations for these species, in the vacuum phase, use the "broken-symmetry" approach coupled with nine different DFT methods. We find a clear dichotomy in the performance of different DFT approaches. For the eight neutral or singly charged complexes, orthodox gradient-corrected DFT methods such as BP and PBE perform generally very well in reproducing in vacuo the complex geometries obtained from X-ray crystallographic studies. In contrast, these orthodox approaches fail to reliably mimic the crystalline geometries for more highly charged complexes such as Mo₂Cl ₉^3-, Cr₂(CH₃)₈ ^4-, and Rh₂(NCCH₃)₁₀⁴⁺. Much closer agreement with experimental condensed-phase structures for the multiply charged dinuclear complexes is seen for two " local-density-approximation" approaches, Xα and VWN, and for VWN+B-LYP, an unorthodox combination of the VWN local and B-LYP nonlocal density functionals. The very good performance of the latter approaches arises from an essentially fortuitous cancellation of errors: while the generally overbinding nature of these approaches suggests that they will not reliably describe true gas-phase structures, this overbinding compensates very well for the coulombic distortion expected when complexes are removed from the charge-stabilizing environment of the crystalline or solvated state. We recommend that, as an alternative to the (computationally expensive) incorporation of solvent-field corrections, VWN+B-LYP is the preferred method for structural characterization of triply or more highly charged dinuclear complexes, while orthodox approaches such as PBE perform best for neutral or mildly charged complexes.