On the nature of homo- and hetero-dinuclear metal-metal quadruple bonds - Analysis of the bonding situation and benchmarking DFT against wave function methods

Homo- and hetero-dimetallic (d-d)(8) analogues of the formally quadruply bonded [Re2Cl8](2-) system with the general formula [MM'Cl-8](x) (M, M' = Tc, Re, Ru, Os, Rh, Ir and x = -2, -1, 0, +1, +2) have been calculated with the density functional theory (DFT) functionals SVWN, BLYP, BP86, PBE, OLYP, OPBE, HCTH, B3LYP, O3LYP, X3LYP, BH&HLYP, TPSS, VSXC, TPPSh, and ab initio methods (CASPT2, CCSD(T)) using basis sets of triple-zeta quality. The performance of the functionals for the description of the metal-metal bond distance and the bond dissociation energy as well as the singlet-triplet gap was evaluated with respect to ab initio data at the CASPT2 level. Generally, the generalized gradient approximation (GGA) functionals, BLYP, BP86, and PBE, show good performance in the description of the metal-metal bond distance and for the dissociation energy. Hybrid functionals are not to be used for compounds of the type discussed here as they lead to increasingly too short and too weak bonds with the amount of exact exchange included. All functionals underestimate the singlet-triplet gap, with the GGA functionals BLYP, BP86, PBE being the closest to the CASPT2 values. The bonding situations of the [MM'Cl-8](x) compounds were analyzed at the DFT level (BP86) using the natural bond orbital (NBO) method and the energy decomposition analysis. The M-M bond in homodimetallic compounds, [MMCl8](x), becomes weaker from group 7 to group 8 to group 9 metals and the bond is weaker for 4d metal systems than for 5d transition metal compounds. The M-M bonds have approximately 50% covalent and 50% electrostatic character and the covalent contribution is dominated by the p orbitals, whereas the delta orbitals do not contribute significantly to the covalent bonding. Heterodimetallic systems, [MM'Cl-8](x), have significantly stronger metal-metal bonds than the homodimetallic compounds. This comes from weaker Pauli repulsion and stronger electrostatic attraction. The most stable heterodimetallic bonds are observed for 5d-5d metal pairs.