Bonding Analysis of the Trimethylenemethane (TMM) Complexes [(η⁶‑C₆H₆)M-TMM] (M = Fe, Ru, Os), [(η⁵‑C₅H₅)M-TMM] (M = Co, Rh, Ir), and [(η⁴‑C₄H₄)M-TMM] (M = Ni, Pd, Pt)

Quantum chemical calculations using gradient corrected density functional theory at the BP86/def2-TZVPP level have been carried out for the sandwichlike trimethylenemethane complexes of group 8 (η⁶-C₆H₆)­M-TMM (BzM-TMM), where M = Fe, Ru, Os, group 9 (η⁵-C₅H₅)­M-TMM (CpM-TMM), where M = Co, Rh, Ir, and group 10, (η⁴-C₄H₄)­M-TMM (CbM-TMM), where M = Ni, Pd, Pt. The nature of the metal–TMM bonding has been investigated with charge and energy decomposition analyses. The geometry optimization of the complexes gives sandwichlike structures where the terminal carbon atoms of the TMM ligands have significantly longer distances to the metal than to the central carbon. The calculated bond dissociations energies <i>D</i>_e of the TMM ligand are between 89.9 and 153.0 kcal/mol. The intrinsic interaction energies Δ<i>E</i>_int and the <i>D</i>_e values for the heavier group 8 and group 9 elements become larger for the heavier atoms in the order BzFe-TMM < BzRu-TMM < BzOs-TMM and CpCoTMM < CpRh-TMM < CpIr-TMM, respectively. The group 10 elements exhibit a V-shaped trend for Δ<i>E</i>_int and the <i>D</i>_e values with the sequence CbPd-TMM < CbNi-TMM < CbPt-TMM. The analysis of the bonding situation shows that the dominant orbital interactions come from the degenerate π interactions between the singly occupied degenerate π orbitals of the metal fragment and the TMM ligand. The degenerate π orbital of TMM has coefficients only at the terminal atom. In agreement with the shape of the orbitals, the EDA-NOCV method suggests that the metal–TMM bonding takes place mainly between the terminal carbon atoms and the metal while the σ bonding between the central carbon atom and the metal is rather weak. In contrast, the AIM analysis gives a bond path only between the metal atom and the closer central carbon atom but not to the more distant carbon atoms. This clearly shows that the AIM analysis does not faithfully represent the strongest pairwise interactions between the atoms in a molecule. The EDA-NOCV and the NBO methods agree that the TMM ligand in the complex carries only a small partial charge, which may be negative or positive

1,3-Metal–Carbon Bonding Predicts Rich Chemistry at the Edges of Aromatic Hydrocarbons

The existence of a hitherto unrecognized 1,3-metal–carbon bond (1,3-MC bond) in particular types of transition-metal complexes is proposed using evidence from CCD X-ray structure analysis and DFT calculations. The name “edge complex” is suggested for the molecules, because the metal is coordinated at the V-shaped edges of olefinic and aromatic hydrocarbon moieties. Several edge complexes of group 4 metals have been identified from inspection of CCD data. The 1,3-MC bond is due to a d_π–p_π interaction between the metal and a β-carbon in the four-membered metallacycle region. The 1,3-MC-bonded metallacycle exhibits significant planar tetracoordinate character of the C_β atom. Moreover, the metallacycle possesses a catastrophic ring critical point (rcp) in AIM analysis, where the highest eigenvalue of the rcp exhibits a linear correlation with the M–C_β distance. The formation of hitherto unknown 1,3-MC-bonded multinuclear edge complexes of polycyclic aromatic hydrocarbons is predicted. Their electronic properties are attractive for the design of optoelectronic materials

1,3-Metal–Carbon Bonding and Alkyne Metathesis: DFT Investigations on Model Complexes of Group 4, 5, and 6 Transition Metals

The formation of metallacyclobutadienes (MCBs) from chloro-ligated alkylidyne complexes of group 4, 5, and 6 transition metals (MCl_<i>n</i>(C₃H₃)) has been studied at the BP86/def2-TZVPP level. All the MCBs showed M–C_β distances (∼2.1 Å) very close to M–C_α distances (1.8–2.0 Å), suggesting a bonding interaction between the metal and the β-carbon (1,3-MC bond). Energy decomposition analysis using <i>C</i>_2<i>v</i> symmetric structures revealed that a b₂ orbital composed of mainly metal d_π and C_β p_π overlap and an agostic a₁ orbital contributed to the orbital interaction of the 1,3-MC bond. The bond order of the 1,3-MC bond is a minimum of 0.26 for M = Cr and a maximum of 0.43 for M = Ta. Further, all the MCBs showed a characteristic δ orbital interaction through an a₂ orbital, which contributed to the double-bond character of M–C_α bonds (bond order 1.27–1.44). Although the formation of b₂ and a₂ orbitals increased the M–C interactions, they significantly reduced the π interactions within the C₃H₃ fragment (C–C bond order 1.09–1.18). 1,3-MC bonding suggested a planar tetracoordinate configuration for C_β, as the C_α–C_β bonds possessed largely formal C_sp2–C_sp2 single-bond character. Electron density analysis showed a “catastrophic” character of the 1,3-MC bond. In groups 4 and 5, MCBs were more stable than the isomeric η³-structures (metallatetrahedranes). A mechanistic study on the reaction between acetylene and alkylidyne complex MCl_<i>n</i>CH showed that a nearly barrierless and exothermic pathway exists for MCB formation (exothermic value 75–102 kcal/mol for groups 4 and 5; 6–27 kcal/mol for group 6). The rich metathesis chemistry associated with Mo and W is attributed mainly to the moderate activation energy required for the alkyne disproportionation step of metathesis. A mechanistic possibility other than Katz's is also proposed for alkyne metathesis that showed that the 1,3-MC bonded MCB complex can act as a metathesis catalyst by reacting with alkyne to form a bicyclic intermediate and subsequently disproportionating to yield the alkyne and the MCB. For this mechanism to be effective, rearrangement of the bicyclic intermediate to a more stable cyclopentadienyl complex has to be prevented

Design of Neutral Lewis Superacids of Group 13 Elements

A general approach toward superstrong neutral Lewis acids, featuring both the pyramidalization of acceptor molecules and the introduction of electron-withdrawing substituents, is proposed and examined theoretically. Complexes of group 13 element derivatives with ammonia at the B3LYP and MP2 levels of theory with def2-TZVPP basis set are considered as examples. Pyramidalization of the acceptor molecule significantly increases its Lewis acidity (by 50–60 kJ mol^–1 for aluminum and gallium compounds and by 120–130 kJ mol^–1 for boron compounds). An additional increase of the complex stability of 55–75 kJ mol^–1 may be achieved by fluorination. The combined increase of the bond dissociation energy amounts to 110–190 kJ mol^–1, which is equivalent to 19–33 orders of magnitude in Lewis acidity

A Spatial Approach to Mereology

When do several objects compose a further object? The last twenty years have seen a great deal of discussion of this question. According to the most popular view on the market, there is a physical object composed of your brain and Jeremy Bentham’s body. According to the second-most popular view on the market, there are no such objects as human brains or human bodies, and there are also no atoms, rocks, tables, or stars. And according to the third-ranked view, there are human bodies, but still no brains, atoms, rocks, tables, or stars. Although it’s pleasant to have so many crazy-sounding views around, I think it would also be nice to have a commonsense option available. The aim of this paper is to offer such an option. The approach I offer begins by considering a mereological question other than the standard one that has been the focus of most discussions in the literature. I try to show that the road to mereological sanity begins with giving the most straightforward and commonsensical answer to this other question, and then extending that answer to further questions about the mereology of physical objects. On the approach I am recommending, it turns out that all of the mereological properties and relations of physical objects are determined by their spatial properties and relations

Comparison between Alkalimetal and Group 11 Transition Metal Halide and Hydride Tetramers: Molecular Structure and Bonding

A comparison between alkalimetal (M = Li, Na, K, and Rb) and group 11 transition metal (M = Cu, Ag, and Au) (MX)₄ tetramers with X = H, F, Cl, Br, and I has been carried out by means of the Amsterdam Density Functional software using density functional theory at the BP86/QZ4P level of theory and including relativistic effects through the ZORA approximation. We have obtained that, in the case of alkalimetals, the cubic isomer of <i>T</i>_<i>d</i> geometry is more stable than the ring structure with <i>D</i>_4<i>h</i> symmetry, whereas in the case of group 11 transition metal tetramers, the isomer with <i>D</i>_4<i>h</i> symmetry (or <i>D</i>_2<i>d</i> symmetry) is more stable than the <i>T</i>_<i>d</i> form. To better understand the results obtained we have made energy decomposition analyses of the tetramerization energies. The results show that in alkalimetal halide and hydride tetramers, the cubic geometry is the most stable because the larger Pauli repulsion energies are compensated by the attractive electrostatic and orbital interaction terms. In the case of group 11 transition metal tetramers, the <i>D</i>_4<i>h</i>/<i>D</i>_2<i>d</i> geometry is more stable than the <i>T</i>_<i>d</i> one due to the reduction of electrostatic stabilization and the dominant effect of the Pauli repulsion

Isolation of Bridging and Terminal Coinage Metal–Nitrene Complexes

Transition metal complexes featuring a metal–nitrogen multiple bond have been widely studied due to their implication in dinitrogen fixation and catalytic nitrogen–carbon bond formation. Terminal copper– and silver–nitrene complexes have long been proposed to be the key intermediates in aziridination and amination reactions using azides as the nitrogen source. However, due to their high reactivity, these species have eluded isolation and spectroscopic characterization even at low temperatures. In this paper we report that a stable phosphinonitrene reacts with coinage metal trifluoro­methane­sulfonates, affording bridging and terminal copper– and silver–nitrene complexes, which are characterized by NMR spectroscopy and single crystal X-ray diffraction analysis

Reaction Pathways for Addition of H₂ to Amido-Ditetrylynes R₂N–EE–NR₂ (E = Si, Ge, Sn). A Theoretical Study

Quantum chemical calculations of the reaction profiles for addition of one and two H₂ molecules to amido-substituted ditetrylynes have been carried using density functional theory at the BP86/def2-TZVPP//BP86/def2-TZVPP level of theory for the model systems L′EEL′ and BP86/def2-TZVPP//BP86/def-SVP for the real compounds. The hydrogenation of the digermyne LGeGeL (L = N­(SiMe₃)­Ar*; Ar* = C₆H₂Me­{C­(H)­Ph₂}₂-4,2,6) follows a stepwise reaction course. The addition of the first H₂ gives the singly bridged species LGe­(μ-H)­GeHL, which rearranges with very low activation barriers to the symmetrically hydrogenated compound LHGeGeHL and to the most stable isomer LGeGe­(H)₂L, which is experimentally observed. The addition of the second H₂ proceeds with a higher activation energy under rupture of the Ge–Ge bond, yielding LGeH and LGeH₃ as reaction products. Energy calculations which consider dispersion interactions using Grimme’s D3 term suggest that the latter reaction is thermodynamically unfavorable. The second hydrogenation reaction LGeGe­(H)₂L → L­(H)₂GeGe­(H)₂L possesses an even higher activation barrier than the bond-breaking hydrogenation step. Further calculations which consider solvent effects change the theoretically predicted reaction profile very little. The calculations of the model system L′GeGeL′ (L′ = NMe₂) give a very similar reaction profile. Calculations of the model disilyne and distannyne homologues L′SiSiL′ and L′SnSnL′ suggest that the reactivity of the amido-substituted ditetrylynes always has the order Si > Ge > Sn. The most stable product of the addition of one H₂ to the distannyne L′SnSnL′ is the doubly bridged species L′Sn­(μ-H)₂SnL′, which has been experimentally observed when bulky groups are employed. Analysis of the H₂–L′EEL′ interactions in the transition state for the addition of the first H₂ with the EDA-NOCV method reveals that the HOMO–LUMO and LUMO–HOMO interactions have similar magnitudes

Bonding in Binuclear Carbonyl Complexes M₂(CO)₉ (M = Fe, Ru, Os)

Quantum-chemical density functional theory calculations using the BP86 functional in conjunction with a triple-ζ basis set and dispersion correction by Grimme with Becke-Johnson damping D3­(BJ) were performed for the title molecules. The nature of the bonding was examined with the quantum theory of atoms in molecules (QTAIM) and natural bond order (NBO) methods and with the energy decomposition analysis in conjunction with the natural orbital for chemical valence (EDA-NOCV) analysis. The energetically lowest-lying form of Fe₂(CO)₉ is the triply bridged <i>D</i>_3<i>h</i> structure, whereas the most stable structures of Ru₂(CO)₉ and Os₂(CO)₉ are singly bridged <i>C</i>₂ species. The calculated reaction energies for the formation of the cyclic trinuclear carbonyls M₃(CO)₁₂ from the dinuclear carbonyls M₂(CO)₉ are in agreement with experiment, as the iron complex Fe₂(CO)₉ is thermodynamically stable in these reactions, but the heavier homologues Ru₂(CO)₉ and Os₂(CO)₉ are not. The metal–CO bond to the bridging CO ligands is stronger than the bonds to the terminal CO ligands. This holds for the triply bridged <i>D</i>_3<i>h</i> structures as well as for the singly bridged <i>C</i>₂ or <i>C</i>_2<i>v</i> species. The analysis of the orbital interactions with the help of the EDA-NOCV method suggests that the overall M→CO π backdonation is always stronger than the M←CO σ donation. The bridging carbonyls are more strongly bonded than the terminal CO ligands, and they are engaged in stronger σ donation and π backdonation, but the formation of bridging carbonyls requires reorganization energy, which may or may not be compensated by the stronger metal–ligand interactions. The lower-lying <i>D</i>_3<i>h</i> form of Fe₂(CO)₉ and <i>C</i>₂ structures of Ru₂(CO)₉ and Os₂(CO)₉ are due to a delicate balance of several forces

Coinage Metals Binding as Main Group Elements: Structure and Bonding of the Carbene Complexes [TM(cAAC)₂] and [TM(cAAC)₂]⁺ (TM = Cu, Ag, Au)

Quantum chemical calculations using density functional theory have been carried out for the cyclic (alkyl)­(amino)­carbene (cAAC) complexes of the group 11 atoms [TM­(cAAC)₂] (TM = Cu, Ag, Au) and their cations [TM­(cAAC)₂]⁺. The nature of the metal–ligand bonding was investigated with the charge and energy decomposition analysis EDA-NOCV. The calculations show that the TM–C bonds in the charged adducts [TM­(cAAC)₂]⁺ are significantly longer than in the neutral complexes [TM­(cAAC)₂], but the cations have much higher bond dissociation energies than the neutral molecules. The intrinsic interaction energies Δ<i>E</i>_int in [TM­(cAAC)₂]⁺ take place between TM⁺ in the ¹S electronic ground state and (cAAC)₂. In contrast, the metal–ligand interactions in [TM­(cAAC)₂] involve the TM atoms in the excited ¹P state yielding strong TM p­(π) → (cAAC)₂ π backdonation, which is absent in the cations. The calculations suggest that the cAAC ligands in [TM­(cAAC)₂] are stronger π acceptors than σ donors. The trends of the intrinsic interaction energies and the bond dissociation energies of the metal–ligand bonds in [TM­(cAAC)₂] and [TM­(cAAC)₂]⁺ give the order Au > Cu > Ag. Calculations at the nonrelativistic level give weaker TM–C bonds, particularly for the gold complexes. The trend for the bond strength in the neutral and charged adducts without relativistic effects becomes Cu > Ag > Au. The EDA-NOCV calculations suggest that the weaker bonds at the nonrelativistic level are mainly due to stronger Pauli repulsion and weaker orbital interactions. The NBO picture of the C–TM–C bonding situation does not correctly represent the nature of the metal–ligand interactions in [TM­(cAAC)₂]