Successive heterolytic cleavages of H2 achieve N2 splitting on silica-supported tantalum hydrides: a DFT proposed mechanism

DFT(B3PW91) calculations have been carried out to propose a pathway for the N(2) cleavage by H(2) in the presence of silica-supported tantalum hydride complexes [(≡SiO)(2)TaH(x)] that forms [(≡SiO)(2)Ta(NH)(NH(2))] (Science 2007, 317, 1056). The calculations, performed on the cluster models {μ-O[(HO)(2)SiO](2)}TaH(1) and {μ-O[(HO)(2)SiO](2)}TaH(3), labelled as (≡SiO)(2)TaH(x) (x = 1, 3), show that the direct hydride transfers to coordinated N-based ligands in (≡SiO)(2)TaH(η(2)-N(2)) and (≡SiO)(2)TaH(η(2)-HNNH) have high energy barrier barriers. These high energy barriers are due in part to a lack of energetically accessible empty orbitals in the negatively charged N-based ligands. It is shown that a succession of proton transfers and reduction steps (hydride transfer or 2 electron reduction by way of dihydride reductive coupling) to the nitrogen-based ligands leads to more energetically accessible pathways. These proton transfers, which occur by way of heterolytic activation of H(2), increase the electrophilicity of the resulting ligand (diazenido, N(2)H(-), and hydrazido, NHNH(2)(-), respectively) that can thus accept a hydride with a moderate energy barrier. In the case of (≡SiO)(2)TaH(η(2)-HNNH), the H(2) molecule that is adding across the Ta-N bond is released after the hydride transfer step by heterolytic elimination from (≡SiO)(2)TaH(NH(2))(2), suggesting that dihydrogen has a key role in assisting the final steps of the reaction without itself being consumed in the process. This partly accounts for the experimental observation that the addition of H(2) is needed to convert an intermediate, identified as a diazenido complex [(≡SiO)(2)TaH(η(2)-HNNH)] from its ν(N-H) stretching frequency of 3400 cm(-1), to the final product. Throughout the proposed mechanism, the tantalum remains in its preferred high oxidation state and avoids redox-type reactions, which are more energetically demanding.     

Equilibria between alpha- and beta-agostic stabilized rotamers of secondary alkyl niobium complexes.

The isopropyl chloro complex Tp(Me2)NbCl(i-Pr)(PhC&tbd1;CMe) (2) [Tp(Me2) = hydrotris(3,5-dimethylpyrazolyl)borate] exhibits a beta-agostic structure in the crystal. The conformation of the alkyl group is such that the agostic methyl group lies in the Calpha-Nb-Cl plane and the nonagostic one, in a wedge formed by two pyrazole rings. As observed by solution NMR spectroscopy, restricted rotation about the Nb-C bond allows the observation of an equilibrium between this species, 2beta, and a minor alpha-agostic rotamer 2alpha. A putative third rotamer which would have the secondary hydrogen in the wedge is not observed. Similar behavior is observed for related Tp'NbCl(i-Pr)(R(2)C=CMe) [Tp' = Tp(Me2), R(2) = Me (3); Tp' = Tp(Me2,4Cl), R(2) = Ph (4)]. The two diastereomers of the sec-butyl complex Tp(Me2)NbCl(sec-Bu)(MeC=CMe) (5) have been separated. In the crystal, 5CR-AS has a beta-agostic methyl group with the ethyl group located in the wedge formed by two pyrazole rings. The same single beta-agostic species is observed in solution. The other diastereomer, 5AR-CS has a beta-agostic methylene group in the solid state, and the methyl group sits in the wedge. In solution, an equilibrium between this beta-agostic methylene complex 5AR-CSbeta and a minor alpha-agostic species 5AR-CSalpha, where the ethyl substituent of the sec-Bu group is located in the wedge between two pyrazole rings, is observed. NMR techniques have provided thermodynamic parameters for these equilibria (K = 2beta/2alpha = 4.0 +/- 0.1 at 193 K, DeltaG(o)(193) = -2.2 +/- 0.1, DeltaH(o) = -7.4 +/- 0.1 kJ mol(-)(1), and DeltaS(o) = -27 +/- 1 J K(-)(1) mol(-)(1)), as well as kinetic parameters for the rotation about the Nb-C bond (at 193 K, DeltaG(2)= 47.5 +/- 2.5, DeltaH= 58.8 +/- 2.5 kJ mol(-)(1), and DeltaS = 59.0 +/- 10 J K(-)(1) mol(-)(1)). Upon selective deuteration of the beta-methyl protons in Tp(Me2)NbCl[CH(CD(3))(2)](PhC=CMe) (2-d(6)), an expected isotope effect that displaces the equilibrium toward the alpha-agostic rotamer is observed (K = 2-d(6)beta/2-d(6)alpha = 3.1 +/- 0.1 at 193 K, DeltaG(o)(193) = -1.8 +/- 0.1, DeltaH(o) = -8.3 +/- 0.4 kJ mol(-)(1) and DeltaS(o)= -34 +/- 2 J K(-)(1) mol(-)(1)). The anomalous values for DeltaH(o) and DeltaS(o) are discussed. Hybrid quantum mechanics/molecular mechanics calculations (IMOMM (B3LYP:MM3)) on the realistic model Tp(Me2)NbCl(i-Pr)(HC=CMe) have reproduced the energy differences between the alpha- and beta-agostic species with remarkable accuracy. Similar calculations show that Tp(Me2)NbCl(CH(2)Me)(HC=CMe) is alpha-agostic only and that Tp(5)(-)(Me)NbCl(CH(2)Me)(HC=CMe), which has no methyl groups at the 3-positions of the pyrazole rings, is beta-agostic only. Analysis and discussion of the computational and experimental data indicate that the unique behavior observed for the secondary alkyl complexes stems from competition between electronic effects favoring a beta-agostic structure and steric effects directing a bulky substituent in the wedge between two pyrazole rings of Tp(Me2). All of the secondary alkyl complexes thermally rearrange to the corresponding linear alkyl complexes via a first-order reaction.     

Quantitative Acoustic Microscopy for Determination of Properties of Hard Coatings

 For quantitative assessment of the properties of hard coatings there is an increasing demand for testing methods with high reliability of the test results, especially concerning the independence of the method and the comparability between different laboratories. This includes the knowledge about all the factors which influence the test procedure itself, determination of best testing conditions, testing of these conditions in round-robins to get a view of the comparability of results, and formulation of guidelines for standardization. In a European project several test methods for hard coatings on steel were investigated for this purpose and the elastic moduli of the coating and coating thickness were determined non-destructively by means of quantitative acoustic microscopy. This method and the instruments available had not yet been certified in the fields of coatings simply owing to the absence of standardised signal processing, followed by the determination of sound velocities and materials parameter extraction. For this purpose four laboratories carried out investigations and measurements on reference samples and on two types of hard coatings (titanium nitride and C-doped chromium) on M2 tool steel.     

Stability,domination and irredundance in a graph

In a graph G, a set X is called a stable set if any two vertices of X are nonadjacent. A set X is called a dominating set if every vertex of V – X is joined to at least one vertex of X. A set X is called an irredundant set if every vertex of X, not isolated in X, has at least one proper neighbor, that is a vertex of V – X joined to it but to no other vertex of X. Let α′ and α, γ, and Γ, ir and IR, denote respectively the minimum and maximum cardinalities of a maximal stable set, a minimal dominating set, and a maximal irredundant set. It is known that ir ? γ ? α′ ? α ? Γ ? IR and that if G does not contain any induced subgraph isomorphic to K_1,3, then γ = α′. Here we prove that if G contains no induced subgraph isomorphic to K_1,3 or to the graph H of figure 1, then ir = γ = α′. We prove also that if G contains no induced subgraph isomorphic to K_1,3, to H, or to the graph h of figure 3, then Γ = IR. Finally, we improve a result of Bollobas and Cockayne about sufficient conditions for γ = ir in terms of forbidden subgraphs.     

A Hundred‐Year‐Old Experiment Re‐evaluated: Accurate Ab Initio Monte Carlo Simulations of the Melting of Radon

State‐of‐the‐art relativistic coupled‐cluster theory is used to construct many‐body potentials for the noble‐gas element radon to determine its bulk properties including the solid‐to‐liquid phase transition from parallel tempering Monte Carlo simulations through either direct sampling of the bulk or from a finite cluster approach. The calculated melting temperature are 200(3) K and 200(6) K from bulk simulations and from extrapolation of finite cluster values, respectively. This is in excellent agreement with the often debated (but widely cited) and only available value of 202 K, dating back to measurements by Gray and Ramsay in 1909.