Structure and bonding in binuclear metal carbonyls from the analysis of domain averaged fermi holes. 2. Fe2(CO)8(2-) and Fe2(CO)8

The nature of the bonding interactions in individual isomeric structures of the above carbonyls was studied using the analysis of domain averaged Fermi holes (DAFH). The main focus was directed on the confrontation of the picture of the bonding resulting from this analysis with the predictions of empirical 18-electron rule. This rule assumes, namely, the presence of direct metal-metal bond(s) for both carbonyls, but the detailed insights provided by the DAFH analysis show that the straightforward association of metal-metal bond with the favorable electron count only is too simplistic, and provided the actual structure of individual isomeric species is not taken into account, the predictions of this rule may fail. This is, e.g., the case of the C(2v) isomer of the carbonylate anion [Fe2(CO)8](2-) where the DAFH analysis denies the existence of direct metal-metal bond similarly as in the case the isoelectronic Co2(CO)8. Similar discrepancies between the predictions of the 18-electron rule and DAFH analysis were found also in the case of the C(2v) isomer of the neutral Fe2(CO)8 carbonyl, where the DAFH analysis detects the presence of a single bent Fe-Fe bond rather than the double bond anticipated by the 18-electron rule.     

Analytic models of domain-averaged Fermi holes: a new tool for the study of the nature of chemical bonds

Simple analytical models are introduced that significantly enhance the ability to understand and rationalise the nature of bonding interactions depicted by domain-averaged Fermi hole (DAFH) analysis. The examples presented show that besides shedding new light on the role of electron-sharing in ordinary two-centre two-electron (2c-2e) chemical bonds that are well represented by the classical Lewis model, the proposed approach also provides interesting new insights into the nature of bonding interactions that go beyond the traditional Lewis paradigm. This is, for example, the case of 3c-2e multicentre bonding, but a straightforward extension of the approach also reveals for direct metal-metal bonding the existence of a completely new type of bonding interaction that involves the mutual exchange of electrons between the lone pairs on adjacent metal atoms.     

Integration of electron density and molecular orbital techniques to reveal questionable bonds: the test case of the direct Fe-Fe bond in Fe2(CO)9

The article illustrates the advantages of partitioning the total electron density rho(rb), its Laplacian (inverted Delta)2 rho(rb), and the energy density H(rb) in terms of orbital components. By calculating the contributions of the mathematically constructed molecular orbitals to the measurable electron density, it is possible to quantify the bonding or antibonding character of each MO. This strategy is exploited to review the controversial existence of direct Fe-Fe bonding in the triply bridged Fe2(CO)9 system. Although the bond is predicted by electron counting rules, the interaction between the two pseudo-octahedral metal centers can be repulsive because of their fully occupied t(2g) sets. Moreover, previous atoms in molecules (AIM) studies failed to show a Fe-Fe bond critical point (bcp). The present electron density orbital partitioning (EDOP) analysis shows that one sigma bonding combination of the t(2g) levels is not totally overcome by the corresponding sigma* MO, which is partially delocalized over the bridging carbonyls. This suggests the existence of some, albeit weak, direct Fe-Fe bonding.     

Binuclear homoleptic manganese carbonyls: Mn2(CO)x (x = 10, 9, 8, 7)

The unsaturated homoleptic manganese carbonyls Mn(2)(CO)(n)() (n = 7, 8, 9) are characterized by their equilibrium geometries, thermochemistry, and vibrational frequencies using methods from density functional theory (DFT). The computed metal-metal distances for global minima range from 3.01 A for the unbridged Mn(2)(CO)(10) with a Mn-Mn single bond to 2.14 A for a monobridged Mn(2)(CO)(7) formulated with a metal-metal quadruple bond. The global minimum for Mn(2)(CO)(9) has a four-electron bridging mu-eta(2)-CO group and a 2.96 A Mn-Mn distance suggestive of the single bond required for 18-electron configurations for both metal atoms. This structure is closely related to an experimentally realized structure for the isolated and structurally characterized stable phosphine complex [R(2)PCH(2)PR(2)](2)Mn(2)(CO)(4)(mu-eta(2)-CO). An unbridged (OC)(4)Mn-Mn(CO)(5) structure for Mn(2)(CO)(9) has only slightly (<6 kcal/mol) higher energy with a somewhat shorter metal-metal distance of 2.77 A. For Mn(2)(CO)(8) the lowest energy structure is a D(2)(d)() unbridged structure with a 2.36 A metal-metal distance suggesting the triple bond required for the favored 18-electron configuration for both metal atoms. However, the unbridged unsymmetrical (CO)(3)Mn-Mn(CO)(5) structure with a metal-metal bond distance of 2.40 A lies only 1 to 3 kcal/mol above this global minimum. The lowest energy structure of Mn(2)(CO)(7) is an unbridged C(s)() structure with a short metal-metal distance of 2.26 A. This is followed energetically by another C(s)() unbridged Mn(2)(CO)(7) structure with a somewhat longer metal-metal distance of 2.38 A.     

Electron-structure calculations and bond order analysis using density functional theory of cationic dinuclear arene ruthenium complexes

The structure and nature of the metal-metal bonding interaction in the cationic complexes [(eta6-C6Me6)2Ru2(mu2-H)3]+ (1), [(eta6-C6Me6)2Ru2(mu2-H)2(mu2-1,4-SC6H4Br)]+ (2), [(eta6-C6Me6)2Ru2(mu2-H)(mu2-1,4-SC6H4Br)2]+ (3), and [(eta6-C6Me6)2Ru2(mu2-1,4-SC6H4Br)3]+ (4) have been studied at the density functional theory (DFT) level using molecular orbital (MO) theory, bond order (BO) analysis, bond decomposition energy (BDE), electron localization function (ELF), and Laplacian of the density methods. The results show that there is no direct bond between the two ruthenium atoms in 1-4, the MO interaction within the diruthenium backbone being stabilized by the bridging ligands. For complex 1, the ELF clearly shows that the bond within the diruthenium backbone is through the three bridging hydride ligands, which act as a sort of glue by forming three-center two-electron bonds characterized by (Ru, H, Ru) basins with 1.8 e mostly located in the H atomic basin.     

The molecular structures of H2Os3(CO)10, H(SC2H5)Os3(CO)10 and (OCH3)2Os3(CO)10

X-ray crystallographic analyses of H₂Os₃(CO)₁₀, H(SC₂H₅)Os₃(CO)₁₀ and (OCH₃)₂Os₃(CO)₁₀ are reported. Although hydrogen atom positions have not been located, the essential isostructural nature of the three commplexes establishes the hydride ligands as bridging two metal atoms, separated by 2.670 Å, with a formal bond order of two; the bridging hydrido- and thiolato-ligands span an osmium---osmium bond of length 2.863 Å and formal bond order one; the two μ-methoxy ligands bridge two metal atoms separated by 3.078 Å which, by simple 18 electron rule counting, has a metal---metal bond order of zero. Some general comments are made on the structures of polynuclear transition metal carbonyls.     

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.     

Quasi－aromaticity in Cluster Chemistry Ⅱ． Localized Molecular Orbital Studies on 〔Co_6（CO）_（14）〕~（4－） and 〔Ni_2Co_4（CO）_（14）〕~（2－） Cluster Anions

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Electronic Structure of [Ta(5)(NH)(4)Cl(17)](6-): A Cluster with a Distorted Square Pyramidal Ta(5) Core

We report approximate molecular orbital calculations on the [Ta(5)(NH)(4)Cl(17)](6-) cluster synthesized by Simon and Meyer. The cluster is based on a "flattened" square pyramid of tantalum atoms, basal bridging imides, and terminal chlorides. This cluster was of interest to us due to the unusual presence of imide ligands, the distorted nature of the metal core, and the possible resemblance to B(5)H(9). Our calculations indicate that metal-metal bonding is limited to Ta(apical)-Ta(basal) bonding, with no significant bonding between the basal metal atoms. The imide ligands, which bridge the base of the pyramid, were found to have a significant amount of capping character. The metal-metal bonding orbitals have some unusual features due to the pyramid's distortion. Additionally, the flattened nature of the pyramid leads to an interesting energy ordering of the metal-metal bonding orbitals.     

Insertion of a bis(phosphine)platinum group into the S-S bond of Mn(2)(CO)(7)(mu-S(2))

The reaction of Mn(2)(CO)(7)(mu-S(2)), 1, with Pt(PPh(3))(2)(PhC(2)Ph) yielded the new complex, Mn(2)(CO)(6)Pt(PPh(3))(2)(mu(3)-S)(2), 3, by loss of CO and insertion of a Pt(PPh(3))(2) group into the S-S bond of 1. Complex 3 was characterized crystallographically and was found to consist of an open Mn(2)Pt cluster with one Mn-Mn bond, 2.8154(14) A, one Mn-Pt bond, 2.9109(10) A, and two triply bridging sulfido ligands. Compound 3 reacts with CO to form adduct Mn(2)(CO)(6)(mu-CO)Pt(PPh(3))(2)(mu(3)-S)(2), 4. Compound 4 also contains an open Mn(2)Pt cluster with two triply bridging sulfido ligands but has only one metal-metal bond, Mn-Mn = 2.638(2) A. Under nitrogen, compound 4 readily loses CO and reverts back to 3.     

Electronic structure of [(CpCr)[(CO)3M]]mu-Cot (M = Cr, Fe): a theoretical study

The electronic structure of two cyclooctatetraene-bridged dinuclear first-row transition metal complexes of the type [(CpM)[(CO)3M']]mu-Cot (M = Cr; M' = Fe (1), Cr (2)) was investigated by complete active space self-consistent field (CASSCF) calculations. In this context the differences in the binding capabilities of the complex fragments CpM and (CO)3M are discussed on the basis of extended Huckel molecular orbital (MO) calculations. The geometries used for the CASSCF calculations for complex 1 were obtained from the crystal structure. For 2 a model structure was established by geometry optimization using density functional methods. The CASSCF results agree well with the experimental findings and provide insight into the binding situation of the two compounds. Complex 1 can be regarded as being composed of a chromocene-like subunit CpCr(eta5-C5H5) and the fragment (CO)3Fe(eta3-C3H3). A direct metal-metal bond is found, involving one initially singly occupied orbital of each fragment, leading to a doublet ground state for 1 with the remaining unpaired electron localized at the chromium center. For 2 no such direct metal-metal bond can be recognized. A very weak direct metal-metal interaction is induced by electron donation from the Cot2- ligand into a formally unoccupied metal-metal binding orbital combination. In the quartet ground state all three unpaired electrons are localized at the chromium center of the formally doubly positive charged CpCr unit, on which complex fragment [(CO)3Cr(eta5-Cot)]2- acts like a cyclopentadienyl ligand. The coordination sphere of the chromium center of the CpCr unit resembles that of a metallocene metal center and its metal 3d occupation scheme corresponds to that of vanadocene.     

Mixed-metal cluster chemistry Part 20. Syntheses, crystal structures and electrochemical studies of W2Ir2(μ-L)(CO)8(η-C5H4Me)2 (L=dppe, dppf)

The 60-electron tetrahedral clusters W₂Ir₂(μ-L)(CO)₈(η⁵-C₅H₄Me)₂ [L=dppe (2), dppf (3)] have been prepared from reaction between W₂Ir₂(CO)₁₀(η⁵-C₅H₄Me)₂ (1) and the corresponding diphosphine in 52 and 66% yields, respectively. A structural study of 2 reveals that three edges of a WIr₂ face are spanned by bridging carbonyls, that the iridium-ligated diphosphine coordinates diaxially and that the tungsten-bound methylcyclopentadienyls coordinate axially and apically with respect to the plane of bridging carbonyls. A structural study of 3 reveals that the dppf ligand bridges an Ir---Ir bond which is also spanned by a bridging carbonyl; tungsten-ligated methylcyclopentadienyl ligands and terminal carbonyls result in electronic asymmetry (17e and 19e iridium atoms) in the electron-precise cluster. Both clusters show two reversible one-electron oxidation processes and an irreversible two-electron reduction; the dppf-containing cluster 3 has a further, irreversible, one-electron oxidation process. UV–vis-NIR spectroelectrochemical studies of the 2→2⁺→2²⁺ progression reveal the appearance of a low-energy transition on oxidation to 2⁺ which persists on further oxidation to 2²⁺.     

Electrochemical oxidation of CoCp(CO)2: radical-substrate reaction of a 17 e-/18 e- pair and production of a unique dimer radical

Anodic oxidation of the important half-sandwich compound CoCp(CO)2, 1, has been studied under gentle electrolyte conditions, e.g., chlorinated hydrocarbons with weakly coordinating anion (WCA) supporting electrolyte anions. The 17-electron cation 1+ produced at E(1/2)(1) = 0.37 V vs FeCp2(0/+) undergoes a surprising reaction with neutral 1 to form the dimer radical cation [Co2Cp2(CO)4] +, 2+, which has a metal-metal bond unsupported by bridging ligands. The dimer radical is oxidized at a slightly more positive potential (E(1/2) = 0.47 V) to the corresponding dication 2(2+). Observation of the oxidation of 2+ is without precedent in confirming a radical-substrate (R-S) dimerization process by direct voltammetric detection of the R-S intermediate, K(eq) = 3 x 10(4) M(-1) for [2+]/[1][1+]. The R-S mechanism and the reaction products have been characterized by voltammetry, electrolysis, fiber-optic IR spectroscopy, and ESR measurements. DFT calculations indicate that removal of an electron from 1 results in rehybridization in 1+, thereby opening the metal center for interaction with the neutral compound 1, which has a relatively basic metal center. The LUMO of the dimer dication 2(2+) is metal-metal antibonding, and its half-occupancy in 2+ results in lengthening of the Co-Co bond from 2.64 A to 3.14 A. Inclusion of solvent in the (COSMO) calculations shows that solvation effects are necessary to account for the fact that E(1/2)(2) > E(1/2)(1). These results show the importance of medium effects in probing the fundamental redox chemistry of half-sandwich metal complexes.     

Binuclear manganese and rhenium carbonyls M2(CO)n (n = 10, 9, 8, 7): comparison of first row and third row transition metal carbonyl structures

The equilibrium geometries, thermochemistry, and vibrational frequencies of the homoleptic binuclear rhenium carbonyls Re2(CO)n (n = 10, 9, 8, 7) were determined using the MPW1PW91 and BP86 methods from density functional theory (DFT) with the effective core potential basis sets LANL2DZ and SDD. In all cases triplet structures for Re2(CO)n were found to be unfavorable energetically relative to singlet structures, in contrast to corresponding Mn2(CO)n derivatives, apparently owing to the larger ligand field splitting of rhenium. For M2(CO)10 (M = Mn, Re) the unbridged structures (OC)5M-M(CO)5 are preferred energetically over structures with bridging CO groups. For M2(CO)9 (M = Mn, Re) the two low energy structures are (OC)4M(micro-CO)M(CO)4 with an M-M single bond and a four-electron donor bridging CO group and (OC)4M[double bond, length as m-dash]M(CO)5 with no bridging CO groups and an M[double bond, length as m-dash]M distance suggesting a double bond. The lowest energy structures for Re2(CO)8 have Re[triple bond, length as m-dash]Re distances in the range 2.6-2.7 A suggesting the triple bonds required to give the Re atoms the favored 18-electron configuration. Low energy structures for Re2(CO)7 are either of the type (OC)(4)M[triple bond, length as m-dash]M(CO)3 with short metal-metal distances suggesting triple bonds or have a single four-electron donor bridging CO group and longer M-M distances consistent with single or double bonds. The 18-electron rule thus appears to be violated in these highly unsaturated Re2(CO)7 structures.     

Bond formation in diatomic transition metal hydrides: Insights from the analysis of domain‐averaged fermi holes

The analysis of domain‐averaged Fermi holes (DAFHs) is used to provide detailed insights into the electron reorganization that accompanies the splitting of the bonding electron pairs in simple diatomic transition metal hydrides MH (M = Sc–Cr). The dissociation process is followed by monitoring the geometry dependence of the dominant DAFH functions, as well as their populations and overlaps. In addition to providing a highly appealing visual picture of the geometry‐induced changes in the bonding interactions, the DAFH approach clearly confirms the close link between the progress of the dissociation and the extent of electron sharing. The results of the various DAFH analyses straightforwardly reveal the anticipated close parallel in the nature of the M? H bonds in the different systems studied, as well as the smooth character of the splitting of the associated shared electron pairs. In addition to a very basic resemblance between the different cases, subtle differences are revealed for individual systems. © 2012 Wiley Periodicals, Inc.     

Electron-deficient bonding in rhomboid rings

The bonding environment of boron is usually thought about in terms of localized 2c-2e/3c-2e bonding (as in diborane) or completely delocalized polyhedral bonding (as in B(12)H(12)(2)(-)). Recently, a number of boron compounds having a rhomboidal B(4) framework have been synthesized; these show an amazing variation in their skeletal electron count, one that cannot be interpreted in familiar ways. In this report, we systematically explore the origin of the range of electron counts in these compounds. We find that four skeletal MOs are primarily responsible for keeping the B(4) skeleton together. As a subunit in a macropolyhedral environment, termed rhombo-B(4), such an arrangement of B atoms deviates from Wade's rule by three electron pairs (if treated as a distorted arachno system derived from B(6)H(6)(2)(-)). Aided by this analysis, we examine the nature of bonding in Na(3)B(20), where the rhombo-B(4) unit forms linear chains fusing closo-B(7) units. Theory suggests that this structure requires one more electron per formula unit for optimal bonding. Finally, we study the nature of bonding in beta-SiB(3), where silicon atoms also adopt the rhomboid framework.     

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).     

Nature of the chemical bonding in D3h [MH3M]+ cations (M = Be,Mg)

Motivated by the particularly short metal-metal distance that has been predicted for the D_3h [BeH₃Be]⁺ cation, comparable to those anticipated for triple bonds, we investigate the nature of the bonding interactions in the D_3h [MH₃M]⁺ cations (M = Be, Mg). CCSD(T)/cc-pVQZ calculations are used to determine optimized geometries for all of the various species, including those “capped” by He or Ne atoms (as proxies for an inert gas matrix). The primary tools that are then used to investigate the nature of the chemical bonding are spin-coupled generalized valence bond calculations and the analysis of localized natural orbitals and of domain-averaged Fermi holes. The various results for all of the systems considered indicate the presence of highly polar three-center two-electron M─H─M bonding character instead of any significant direct metal-metal bonding.