Activation and Cleavage of the N-O Bond in Dinuclear Mixed-Metal Nitrosyl Systems and Comparative Analysis of Carbon Monoxide, Dinitrogen, and Nitric Oxide Activation

The activation and scission of the N–O bond in nitric oxide using dinuclear mixed-metal species, comprising transition elements with d3 and d2 configurations and trisamide ligand systems, have been investigated by means of density functional calculations. The [Cr(III)–V(III)] system is analyzed in detail and, for comparative purposes, the [Mo(III)–Nb(III)], [W(III)–Ta(III)], and (mixed-row) [Mo(III)–V(III)] systems are also considered. The overall reaction and individual intermediate steps are favourable for all systems, including the case where first row (Cr and V) metals are exclusively involved, a result that has not been observed for the related dinitrogen and carbon monoxide systems. In contrast to the cleavage of dinitrogen by three-coordinate Mo amide complexes where the dinuclear intermediate possesses a linear [Mo–NN–Mo] core, the [M–NO–M′] core must undergo significant bending in order to stabilize the dinuclear species sufficiently for the reaction to proceed beyond the formation of the nitrosyl encounter complex. A comparative bonding analysis of nitric oxide, dinitrogen and carbon monoxide activation is also presented. The overall results indicate that the π interactions are the dominant factor in the bonding across the [M–L1L2–M′] (L1L2 = N–O, N–N, C–O) moiety and, consequently, the activation of the L1–L2 bond. These trends arise from the fact that the energy gaps between the π orbitals on the metal and small molecule fragments are much more favourable than for the corresponding σ orbitals. The π energy gaps decrease in the order [NO \u3c N2 \u3c CO] and consequently, for each individual π orbital interaction, the back donation between the metal and small molecule increases in the order [CO \u3c N2 \u3c NO]. These results are in accord with previous findings suggesting that optimization of the π interactions plays a central role in increasing the ability of these transition metal systems to activate and cleave small molecule bonds

Application of density functional theory to the calculation of molecular core-electron binding energies

The procedure for calculating core-electron binding energies (CEBEs), based on the unrestricted generalized transition state (uGTS) model combined with density functional theory (DFT) employing Becke's 1988 exchange (B88) and Perdew's 1986 correlation (P86) functionals, which has proven to yield highly accurate results for C, N, O, and F cases, was extended to boroncontaining molecules and to Si, P, S, CI, and Ar cases. Both unsealed and scaled basis sets were used in the studies of boroncontaining molecules. The scaled-pVTZ basis set was as highly efficient for boron as it had been found to be for C, N, O, and F cases; the average absolute deviation (AAD) of the calculated CEBEs from experiment was 0.24 eV, compared to 0.23 eV for the much larger cc-pV5Z basis set. A generalization of the exponent-scaling methodology was proposed and tested on boron-containing molecules, and was found not to improve the original results to a significant extent. The preliminary calculations of Si, P, S, CI, and Ar CEBEs indicated that, in order to achieve the accuracy obtained for second-period elements, refinement of the basis sets and inclusion of relativistic effects are necessary. As an additional application of the DFT/uGTS/scaled-pVTZ approach, the CEBEs of four isomers of C₃H₅NO were calculated. The distinctive nature of the core-ionization spectra of the isomers was depicted by the results, thus illustrating the potential utilization of accurate theoretical predictions as a complement to electron spectroscopy for chemical analysis. The model error in uGTS calculations and the errors in the functionals employed were calculated. It was observed that the high accuracy of the B88/P86 combination was due to a fortuitous cancellation of the functional and model errors. In view of this finding, a Kohn-Sham total-energy difference approach, which eliminates the model error, was investigated. Ten functional combinations and several basis sets (including unsealed, scaled, and core-valence correlated functions) were tested using a database of reliable observed CEBEs. The functionals designed by Perdew and Wang (1986 exchange and 1991 correlation) were found to give the best performance with an A A D from experiment of 0.15 eV. The scaled basis sets did not perform as well as they did in the uGTS calculations, but it was found that the core-valence correlated cc-pCVTZ basis functions were an excellent alternative to the cc-pV5Z set as they provided equally accurate results and could be applied to larger molecules.Science, Faculty ofChemistry, Department ofGraduat

Metal-Metal Interactions in Mixed-Valance [M 2 Cl 9 ] 2- Species: Electronic Structure of d 1 d 2 (V, Nb, Ta) and d 4 d 5 (Fe, Ru, Os) Face-Shared Systems

The molecular and electronic structures of mixed-valence d 1d2 (V, Nb, Ta) and d4d5 (Fe, Ru, Os) face-shared [M2Cl9]2- dimers have been calculated by density functional methods in order to investigate metal-metal bonding in this series. General similarities are observed between d 1d2 and d4d5 systems and can be considered to reflect the electron-hole equivalence of the individual d 1-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 d 1d2 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 [V 2Cl9]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) [Ru2Cl 9]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

Metal-metal bonding in molecular actinide compounds: electronic structure of [M 2 X 8 ] 2- (M = U, Np, Pu; X = Cl, Br, I) complexes and comparison with d-block analogues

Density functional and multiconfigurational (ab initio) calculations have been performed on [M2X8]2- (X = Cl, Br, I) complexes of 4d (Mo, Tc, Ru), 5d (W, Re, Os), and 5f (U, Np, Pu) metals in order to investigate general trends, similarities and differences in the electronic structure and metal-metal bonding between f-block and d-block elements. Multiple metal-metal bonds consisting of a combination of σ and π interactions have been found in all species investigated, with δ-like interactions also occurring in the complexes of Tc, Re, Np, Ru, Os, and Pu. The molecular orbital analysis indicates that these metal-metal interactions possess predominantly dz2 (σ), dxz and dyz (π), or d xy and dx2-y2 (δ) character in the d-block species, and fz3 (σ), fz2x and fz2y (π), or fxyz and fz (δ) character in the actinide systems. In the latter, all three (σ, π, δ) types of interaction exhibit bonding character, irrespective of whether the molecular symmetry is D 4h or D4d. By contrast, although the nature and properties of the σ and π bonds are largely similar for the D4h and D4d forms of the d-block complexes, the two most relevant metal-metal δ-like orbitals occur as a bonding and antibonding combination in D 4h symmetry but as a nonbonding level in D4d symmetry. Multiconfigurational calculations have been performed on a subset of the actinide complexes, and show that a single electronic configuration plays a dominant role and corresponds to the lowest-energy configuration obtained using density functional theory

Computational Analysis of Mo and W Oxoanions through Bond Order and Bonding Energy Approaches

A detailed bonding analysis of Mo and W [MO4]2-, [M2O7]2-, and [M6O19]2- anions has been carried out. The nature of the metal-oxygen interactions and the bonding properties of oxygen sites have been explored by combining population analysis, including bond and valency indexes, with information based on the composition of molecular orbitals and the calculation of bonding energetics. Particular attention has been focused on the effects of basis sets and functional on the correlations between the various approaches. The results obtained from population analysis have been found to be qualitatively consistent with those provided by bonding-energy approaches for basis sets of triple-ζ quality and all functionals tested. Use of smaller basis sets has had only a relatively minor effect on the bonding-energy results but has led to some significant discrepancies in the population analysis

Electronic Structure and Metal-Metal Interactions in Trinuclear Face-Shared [M 3 X 12 ] 3- (M ) Mo, W; X ) F, Cl, Br, I) Systems

The molecular and electronic structures of trinuclear face-shared [M 3X12]3- species of Mo (X = F, Cl, Br, I) and W (X = Cl), containing linear chains of metal atoms, have been investigated using density functional theory. The possibility of variations in structure and bonding has been explored by considering both symmetric (D3d) and unsymmetric (C3v) forms, the latter having one long and one short metal-metal distance. Analysis of the bonding in the structurally characterized [Mo3I12]3- trimer reveals that the metal-metal interaction qualitatively corresponds to a two-electron three-center σ bond between the Mo atoms and, consequently, a formal Mo-Mo bond order of 0.5. However, the calculated spin densities suggest that the electrons in the metal-metal σ bond are not fully decoupled and therefore participate in the antiferromagnetic interactions of the metal cluster. Although the same observation applies to [Mo3X12]3- (X = Br, Cl, F) and [W3Cl12]3-, both the spin densities and shorter distances between the metal atoms indicate that the metal-metal interaction is stronger in these systems. The broken-symmetry approach combined with spin projection has been used to determine the energy of the low-lying spin multiplets arising from the magnetic coupling between the metal centers. Either the symmetric and unsymmetric S = 3/2 state is predicted to be the ground state for all five systems. For [Mo3X12]3- (X = Cl, Br, I), the symmetric form is more stable but the unsymmetric structure, where two metal centers are involved in a metal-metal triple bond while the third center is decoupled, lies close in energy and is thermally accessible. Consequently, at room temperature, interconversion between the two energetically equivalent configurations of the unsymmetric form should result in an averaged structure that is symmetric. This prediction is consistent with the reported structure of [Mo3I12]3-, which, although symmetric, indicates significant movement of the central Mo atom toward the terminal Mo atoms on either side. In contrast, unsymmetric structures with a triple bond between two metal centers are predicted for [Mo3F 2]3- and [W3C12]3-, as the symmetric structure lies too high in energy to be thermally accessible

On the Paucity of Molecular Actinide Complexes with Unsupported Metal-Metal Bonds: A Comparative Investigation of the Electronic Structure and Metal-Metal Bonding in U 2 X 6 (X = Cl, F, OH, NH 2 , CH 3 ) Complexes and d-Block Analogues

Density functional calculations have been performed on M2X 6 complexes (where M = U, W, and Mo and X = Cl, F, OH, NH 2, and CH3) to investigate general aspects of their electronic structures and explore the similarities and differences in metal-metal bonding between f-block and d-block elements. A detailed analysis of the metal-metal interactions has been conducted using molecular orbital theory and energy decomposition methods. Multiple (σ and π) bonding is predicted for all species investigated, with predominant f-f and d-d metal orbital character, respectively, for U and W or Mo complexes. The energy decomposition analysis involves contributions from orbital interactions (mixing of occupied and unoccupied orbitals), electrostatic effects (Coulombic attraction and repulsion), and Pauli repulsion (associated with four-electron two-orbital interactions). The general results suggest that the overall metal-metal interaction is stronger in the Mo and W species, relative to the U analogues, as a consequence of a significantly less destabilizing contribution from the combined Pauli and electrostatic ("pre-relaxation") effects. Although the orbital-mixing ("post-relaxation") contribution to the total bonding energy is predicted to have a larger magnitude in the U complexes, this is not sufficiently strong to compensate for the comparatively greater destabilization that originates from the Pauli-plus-electrostatic effects. Of the pre-relaxation terms, the Pauli repulsion is comparable in analogous U and d-block compounds, contrary to the electrostatic term, which is (much) less favorable in the U systems than in the W and Mo systems. This generally weak electrostatic stabilization accounts for the large pre-relaxation destabilization in the U complexes and, ultimately, for the relative weakness of the U-U bonds. The origin of the small electrostatic term in the U compounds is traced primarily to MX3 fragment overlap effects

A comparative Investigation of Structure and Bonding in Mo and W [TeM 6 O 24 ] 6- and [PM 12 O 40 ] 3- Heteropolyanions

The structure and bonding in [TeM6O24]6- (Anderson) and [PM12O40]3- (α-Keggin) heteropolyanions have been investigated by density-functional methods. Various molecular-orbital and population approaches have been employed in the analysis of the structura

Influence of the Ligand on the Coupling between the Metal-Based Electrons in Face-Shared [M 2 X 9 ] 3- (M = Mo, W; X = F, Cl, Br, I Systems

Orbital overlap and spin polarization effects in Mo and W [M 2X9]3- halide and in [M 2X′3X″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 speci