Mutual interdependence of spin crossover and metal-metal bond formation in M2Cl9(3-) (M = Fe, Ru, Os)

Measuring Metal-Metal Communication in a Series of Ketimide-Bridged [Fe2]6+ Complexes

Reaction of Fe(acac)3 with 3 equiv of Li[N═C(R)Ph] (R = Ph, tBu) results in the formation of the [Fe2]6+ complexes, [Fe2(μ-N═C(R)Ph)2(N═C(R)Ph)4] (R = Ph, 1; tBu, 2), in low to moderate yields. Reaction of FeCl2 with 6 equiv of Li(N═C13H8) (HN═C13H8 = 9-fluorenone imine) results in the formation of [Li(THF)2]2[Fe(N═C13H8)4] (3) in good yield. Subsequent oxidation of 3 with ca. 0.8 equiv of I2 generates the [Fe2]6+ complex, [Fe2(μ-N═C13H8)2(N═C13H8)4] (4), along with free fluorenyl ketazine. Complexes 1, 2, and 4 were characterized by 1H NMR spectroscopy, X-ray crystallography, 57Fe Mössbauer spectroscopy, and SQUID magnetometry. The Fe-Fe distances in 1, 2, and 4 range from 2.803(7) to 2.925(1) Å, indicating that no direct Fe-Fe interaction is present in these complexes. The 57Fe Mössbauer spectra for complexes 1, 2, and 4 are all consistent with the presence of symmetry-equivalent high-spin Fe3+ centers. Finally, all three complexes exhibit a similar degree of antiferromagnetic coupling between the metal centers (J = -26 to -30 cm-1), as ascertained by SQUID magnetometry.

Metal-Metal Bonding in Trinuclear, Mixed-Valence [Ti3X12](4-) (X = F, Cl, Br, I) Face-Shared Complexes

Metal-metal bonding in structurally characterized In4Ti3Br12, comprising linear, mixed-valence d(1)d(2)d(1) face-shared [Ti3Br12](4-) units with a Ti-Ti separation of 3.087 Å and strong antiferromagnetic coupling (Θ = -1216 K), has been investigated using density functional theory. The antiferromagnetic configuration, in which the single d electron on each terminal Ti(III) (d(1)) metal center is aligned antiparallel to the two electrons occupying the central Ti(II) (d(2)) metal site, is shown to best agree with the reported structural and magnetic data and is consistent with an S = 0 ground state in which two of the four metal-based electrons are involved in a two-electron, three-center σ bond between the Ti atoms (formal Ti-Ti bond order of ∼0.5). However, the unpaired spin densities on the Ti sites indicate that while the metal-metal σ interaction is strong, the electrons are not fully paired off and consequently dominate the ground state antiferromagnetic coupling. The same overall partially delocalized bonding regime is predicted for the other three halide [Ti3X12](4-) (X = F, Cl, I) systems with the metal-metal bonding becoming weaker as the halide group is descended. The possibility of bond-stretch isomerism was also examined where one isomer has a symmetric structure with identical Ti-Ti bonds while the other is unsymmetric with one short and one long Ti-Ti bond. Although calculations indicate that the latter form is more stable, the barrier to interconversion between equivalent unsymmetric forms, where the short Ti-Ti bond is on one side of the trinuclear unit or the other, is relatively small such that at room temperature only the averaged (symmetric) structure is likely to be observed.

A new local density functional for main-group thermochemistry, transition metal bonding, thermochemical kinetics, and noncovalent interactions

We present a new local density functional, called M06-L, for main-group and transition element thermochemistry, thermochemical kinetics, and noncovalent interactions. The functional is designed to capture the main dependence of the exchange-correlation energy on local spin density, spin density gradient, and spin kinetic energy density, and it is parametrized to satisfy the uniform-electron-gas limit and to have good performance for both main-group chemistry and transition metal chemistry. The M06-L functional and 14 other functionals have been comparatively assessed against 22 energetic databases. Among the tested functionals, which include the popular B3LYP, BLYP, and BP86 functionals as well as our previous M05 functional, the M06-L functional gives the best overall performance for a combination of main-group thermochemistry, thermochemical kinetics, and organometallic, inorganometallic, biological, and noncovalent interactions. It also does very well for predicting geometries and vibrational frequencies. Because of the computational advantages of local functionals, the present functional should be very useful for many applications in chemistry, especially for simulations on moderate-sized and large systems and when long time scales must be addressed.

Benchmarking approximate density functional theory for s/d excitation energies in 3d transition metal cations

Holthausen has recently provided a comprehensive study of density functional theory for calculating the s/d excitation energies of the 3d transition metal cations. This study did not include the effects of scalar relativistic effects, and we show here that the inclusion of scalar relativistic effects significantly alters the conclusions of the study. We find, contrary to the previous study, that local functionals are more accurate for the excitation energies of 3d transition method cations than hybrid functionals. The most accurate functionals, of the 38 tested, are SLYP, PBE, BP86, PBELYP, and PW91.

Periodic trends in metal–metal interactions in face-shared [M2Cl9]z−systems

The periodic trends in metal-metal interactions in even-electron and mixed-valence [M2Cl9]z- face-shared systems, involving transition metals in Groups 4 to 8 and electronic configurations ranging from d1d1 through to d5d5 and from d1d2 through to d4d5, have been investigated by calculating metal-metal bonding and spin polarization (exchange) effects using density functional theory. These two terms are in opposition to one another and their relative difference determines the extent to which the metal-based electrons are delocalized and thus the degree of metal-metal bonding. Remarkably strong linear correlations between the two terms, and between each term and the square of the spin density on the metal centres, have been obtained for all group and period series considered, and are discussed in terms of their dependence on the metal orbital properties and electron density.

Metal−Metal Interactions in Mixed-Valence [M2Cl9]2- Species: Electronic Structure of d1d2 (V, Nb, Ta) and d4d5 (Fe, Ru, Os) Face-Shared Systems

The molecular and electronic structures of mixed-valence d1d2 (V, Nb, Ta) and d4d5 (Fe, Ru, Os) face-shared [M2Cl(9)]2- dimers have been calculated by density functional methods in order to investigate metal-metal bonding in this series. General similarities are observed between d1d2 and d4d5 systems and can be considered to reflect the electron-hole equivalence of the individual d1-d5 and d2-d4 configurations. The electronic structures of the dimers have been analyzed using potential energy curves for the broken-symmetry and other spin states resulting from the d1d2 and d4d5 coupling modes. In general, a spin-doublet (S = 1/2) state, characterized by delocalization of the metal-based electrons in a metal-metal bond with a formal order of 1.5, is favored in the systems containing 4d and 5d metals, namely, the Nb, Ta, Ru, and Os dimers. In contrast, the calculated ground structures for [V2Cl9]2- and [Fe2Cl9]2- correspond to a spin-quartet (S = 3/2) state involving weaker coupling between the metal centers and electron localization. In the case of [Ru2Cl9]2-, both the spin-doublet and spin-quartet states are predicted to be energetically favored suggesting that this species may exhibit double-minima behavior. A comparison of computational results across the (d1d1, d1d2, d2d2) [Nb2Cl9]z- and [Ta2Cl9]z- and (d4d4, d4d5, d5d5) [Ru2Cl9]z- and [Os2Cl9]z- series has revealed that, in all four cases, the shortening of the metal-metal distances correlates with an increase in formal metal-metal bond order.

Density Functional Investigation of Metal−Metal Interactions in Mixed-Valence d2d3 (Cr, Mo, W) and d3d4 (Mn, Tc, Re) Face-Shared [M2Cl9]2- Systems

The molecular and electronic structures of mixed-valence face-shared (Cr, Mo, W) d(2)d(3) and (Mn, Tc, Re) d(3)d(4) [M(2)Cl(9)](2-) dimers have been calculated by density functional methods in order to investigate metal-metal bonding in this series. The electronic structures of these systems have been analyzed using potential energy curves for the broken-symmetry and other spin states arising from the d(2)d(3) and d(3)d(4) coupling modes. In (d(2)d(3)) [Mo(2)Cl(9)](2-) and [W(2)Cl(9)](2-), the global minimum has been found to be a spin-doublet state characterized by delocalization of the metal-based electrons in a multiple metal-metal bond (with a formal bond order of 2.5). In contrast, weak coupling between the metal centers and electron localization are favored in (d(2)d(3)) [Cr(2)Cl(9)](2-), the global minimum for this species being a ferromagnetic S = 5/2 state with a relatively long Cr-Cr separation. The (d(3)d(4)) [Re(2)Cl(9)](2-) system also exhibits a global minimum corresponding to a metal-metal bonded spin-doublet state with a formal bond order of 2.5, reflecting the electron-hole equivalence between d(2)d(3) and d(3)d(4) configurations. Double minima behavior is predicted for (d(3)d(4)) [Tc(2)Cl(9)](2-) and [Mn(2)Cl(9)](2-) due to two energetically close low-lying states (these being S = 3/2 and S = 5/2 states for the former, and S = 5/2 and S = 7/2 states for the latter). A comparison of computational results for the d(2)d(2), d(2)d(3), and d(3)d(3) [W(2)Cl(9)](z-) series and the d(3)d(3), d(3)d(4), and d(4)d(4) [Re(2)Cl(9)](z-) series indicates that the observed trends in metal-metal distances can only be rationalized if changes in both the strength of sigma bonding and metal-metal bond order are taken into consideration. These two factors act conjointly in the W series but in opposition to one another in the Re series. In the case of the [Cr(2)Cl(9)](z-) and [Mn(2)Cl(9)](z-) dimers, the metal-metal bond lengths are significantly shorter for mixed-valence (d(2)d(3) or d(3)d(4)) than d(3)d(3) systems. This result is consistent with the fact that some degree of metal-metal bonding exists in the former (due to partial delocalization of a single sigma electron) but not in the latter (where all metal-based electrons are completely localized).

Density Functional Investigation of Metal−Metal Interactions in d4d4 Face-Shared [M2Cl9]3- (M = Mn, Tc, Re) Systems

The molecular and electronic structures of the d(4)d(4) face-shared [M(2)Cl(9)](3)(-) (M = Mn, Tc, Re) dimers have been calculated by density functional methods in order to investigate metal-metal bonding in this series. The electronic structures of these systems have been analyzed using potential energy curves for the broken-symmetry and other spin states arising from the various d(4)d(4) coupling modes, and closed energy cycles have been utilized to identify and quantify the parameters which are most important in determining the preference for electron localization or delocalization and for high-spin or low-spin configurations. In [Tc(2)Cl(9)](3)(-) and [Re(2)Cl(9)](3)(-), the global minimum has been found to be a spin-triplet state arising from the coupling of metal centers with low-spin configurations, and characterized by delocalization of the metal-based electrons in a double (sigma and delta(pi)) bond with a metal-metal separation of 2.57 A. In contrast, high-spin configurations and electron localization are favored in [Mn(2)Cl(9)](3)(-), the global minimum for this species being the ferromagnetic S = 4 state with a rather long metal-metal separation of 3.43 A. These results are consistent with metal-metal overlap and ligand-field effects prevailing over spin polarization effects in the Tc and Re systems, but with the opposite trend being observed in the Mn complex. The ground states and metal-metal bonding observed for the d(4)d(4) systems in this study parallel those previously found for the analogous d(2)d(2) complexes of V, Nb, and Ta, and can be rationalized on the basis that the d(4)d(4) dimer configuration is the hole equivalent of the d(2)d(2) configuration.

Influence of the ligand on the coupling between the metal-based electrons in face-shared [M2X9]3- (M = Mo, W; X = F, Cl, Br, I) systems

Orbital overlap and spin polarization effects in Mo and W [M(2)X(9)](3)(-) halide and in [M(2)X'(3)X' '(6)](3)(-) mixed-halide systems have been investigated by means of density-functional calculations performed on the S = 0, S = 3, and reference states of these species. For the regular [M(2)X(9)](3)(-) systems, a strong linear correlation between the two factors has been obtained, and decreasing trends in both the overlap energy and the spin polarization energy upon descending the halide group have been observed. These trends can be related to the changes in the size and covalency of the ligands and in the nature of the metal-bridge interaction. For the mixed-ligand [M(2)X'(3)X' '(6)](3)(-) systems, important deviations (from the behavior of the regular systems), which are apparently the result of particular structural and energetic characteristics, have been observed.

Cl(3)V(mu-S(CH(3))(2))(3)VCl(3)(2)(-): a first-row, face-shared bioctahedral complex with multiple metal-metal bonding

Density functional theory calculations have been used to investigate the structure and bonding of the d(3)d(3) bioctahedral complexes X(3)V(mu-S(CH(3))(2))(3)VX(3)(2)(-) (X = F(-), Cl(-), OH(-), SH(-), NH(2)(-)). According to geometry optimizations using the broken-symmetry approach and the VWN+B-LYP combination of density functionals, the halide-terminated complexes have a V-V bond order of approximately 2, while complexes featuring OH(-), SH(-), or NH(2)(-) as terminal ligands exhibit full triple bonding between the vanadium atoms. The tendency toward triple bonding in the latter complexes is consistent with an increased covalency of the vanadium-ligand bonds, and the influence of bond covalency is apparent also in the tendency for V-V bond elongation in the complexes with OH(-) and NH(2)(-) terminal ligands. Detailed examination of the composition of molecular orbitals in all of the thioether-bridged V(II) complexes substantiates the conclusion that the strong antiferromagnetic coupling which we have determined for these complexes (-J > 250 cm(-)(1)) is due to direct bonding between metal atoms rather than superexchange through the bridging ligands. As such, these V(II) complexes comprise the first apparent examples of multiple metal-metal bonding in first-transition-row, face-shared dinuclear complexes and are therefore of considerable structural and synthetic interest.

Factors affecting metal-metal bonding in the face-shared d(3)d(3) bioctahedral dimer systems, MM'Cl(9)(5-) (M, M' = V, Nb, Ta)

Density functional theory (DFT) calculations have been used to investigate the d(3)d(3) bioctahedral complexes, MM'Cl(9)(5-), of the vanadium triad. Broken-symmetry calculations upon these species indicate that the V-containing complexes have optimized metal-metal separations of 3.4-3.5 A, corresponding to essentially localized magnetic electrons. The metal-metal separations in these weakly coupled dimers are elongated as a consequence of Coulombic repulsion, which profoundly influences (and destabilizes) the gas-phase structures for such dimers; nevertheless, the intermetallic interactions in the V-containing dimers involve significantly greater metal-metal bonding character than in the analogous Cr-containing dimers. These observations all show good agreement with existing experimental (solid state) results for the chloride-bridged, face-shared dimers V(2)Cl(9)(5-) and V(2)Cl(3)(thf)(6)(+). In contrast to the V-containing dimers, complexes featuring only Nb and Ta have much shorter intermetallic distances (approximately 2.4 A) consistent with d-electron delocalization and formal metal-metal triple bond formation; again, good agreement is found with available experimental data. Calculations on the complexes V(2)(mu-Cl)(3)(dme)(6)(+), Nb(2)(mu-dms)(3)Cl(6)(2-), and Ta(2)(mu-dms)(3)Cl(6)(2-), which are closely related to compounds for which crystallographic structural data exist, have been pursued and provide an insight into the intermetallic interactions in the experimentally characterized complexes. Analysis of the contributions from d-orbital overlap (E(ovlp)) stabilization, as well as spin polarization (exchange) stabilization of localized d electrons (E(spe)), has also been attempted for the MM'Cl(9)(5-) dimers. While E(ovlp) clearly dominates over E(spe) as a stabilizing factor in those dimers containing only Nb and Ta metal atoms, detailed assessment of the competition between E(ovlp) and E(spe) for V-containing dimers is obstructed by the instability of triply bonded V-containing dimers against Coulombic explosion. On the basis of the periodic trends in E(ovlp) versus E(spe), the V-triad dimers have a greater propensity for metal-metal bonding than do their Cr-triad or Mn-triad counterparts.

FeMo cofactor of nitrogenase: a density functional study of states M(N), M(OX), M(R), and M(I)

The M(N) S = (3)/(2) resting state of the FeMo cofactor of nitrogenase has been proposed to have metal-ion valencies of either Mo(4+)6Fe(2+)Fe(3+) (derived from metal hyperfine interactions) or Mo(4+)4Fe(2+)3Fe(3+) (from Mössbauer isomer shifts). Spin-polarized broken-symmetry (BS) density functional theory (DFT) calculations have been undertaken to determine which oxidation level best represents the M(N) state and to provide a framework for understanding its energetics and spectroscopy. For the Mo(4+)6Fe(2+)Fe(3+) oxidation state, the spin coupling pattern for several spin state alignments compatible with S = (3)/(2) were generated and assessed by energy and geometric criteria. The most likely BS spin state is composed of a Mo3Fe cluster with spin S(a) = 2 antiferromagnetically coupled to a 4Fe' cluster with spin S(b) = (7)/(2). This state has a low DFT energy for the isolated FeMoco cluster and the lowest energy when the interaction with the protein and solvent environment is included. This spin state also displays calculated metal hyperfine and Mössbauer isomer shifts compatible with experiment, and optimized geometries that are in excellent agreement with the protein X-ray data. Our best model for the actual spin-coupled state within FeMoco alters this BS state by a slight canting of spins and is analogous in several respects to that found in the 8Fe P-cluster in the same protein. The spin-up and spin-down components of the LUMO contain atomic contributions from Mo(4+) and the homocitrate and from the central prismane Fe sites and muS(2) atoms, respectively. This qualitative picture of the accepting orbitals for M(N) is consistent with observations from Mössbauer spectra of the one-electron reduced states. Similar calculations for the Mo(4+)4Fe(2+)3Fe(3+) oxidation state yield results that are in poorer agreement with experiment. Using the Mo(4+)6Fe(2+)Fe(3+) oxidation level as the most plausible resting state, the geometric, electronic and energetic properties of the one-electron redox transition to the oxidized state, M(OX), catalytically observed M(R) and radiolytically reduced M(I) states have also been explored.