A kinetic and thermodynamic study of the unexpected comproportionation reaction between cis-[Os(VIII)O4(OH)2](2-) and trans-[Os(VI)O2(OH)4](2-) to form a postulated [Os(VII)O3(OH)3](2-) complex anion

C(sp3)-H bond activation by the carboxylate-adduct of osmium tetroxide (OsO4)

The reaction of osmium tetroxide (OsO₄) and carboxylate anions (acetate: X^- = AcO^- and benzoate: X^- = BzO^-) gave 1 : 1 adducts, [OsO₄(X)]^- (1X), the structures of which were determined by X-ray crystallographic analysis. In both cases, the carboxylate anion X coordinates to the osmium centre to generate a distorted trigonal bipyramidal osmium(VIII) complex. The carboxylate adducts show a negative shift of the redox potentials (E_1/2) and a red shift of the ν_OsO stretches as compared to those of tetrahedral OsO₄ itself. Despite the negative shift of E_1/2, the reactivity of these adduct complexes 1X was enhanced compared to that of OsO₄ in benzylic C(sp³)-H bond oxidation. The reaction obeyed the first-order kinetics on both 1X and the substrates, giving the second-order rate constant (k₂), which exhibits a linear correlation with the C-H bond dissociation energy (BDE_C-H) of the substrates (xanthene, 9,10-dihydroanthracene, fluorene and 1,2,3,4-tetrahydronaphthalene) and a kinetic deuterium isotope effect (KIE) of 9.7 (k₂(xanthene-h₂)/k₂(xanthene-d₂)). On the basis of these kinetic data together with the DFT calculation results, we propose a stepwise reaction mechanism involving rate-limiting benzylic hydrogen atom abstraction and subsequent rebound of the generated organic radical intermediate to a remaining oxido group on the osmium centre.

Kinetic UV-Vis Spectroscopic and DFT Mechanistic Study of the Redox Reaction of [OsVIIIO4(OH)n]n- (n = 1, 2) and Methanol in a Basic Aqueous Matrix

This combined experimental and computational study builds on our previous studies to elucidate the reaction mechanism of methanol oxidation by Os^VIII oxido/hydroxido species (in basic aqueous media) while accounting for the simultaneous formation of Os^VII species via a comproportionation reaction between Os^VIII and Os^VI. UV-Vis spectroscopy kinetic analyses with either CH₃OH or the deuterated analogue CD₃OH as a reducing agent revealed that transfer of α-carbon-hydrogen of methanol is the partial rate-limiting step. The resulting relatively large KIE value of approximately 11.82 is a combination of primary and secondary isotope effects. The Eyring plots for the oxidation of these isotopologues of methanol under the same reaction conditions are parallel to each other and hence have the same activation enthalpy [Δ^⧧H° = 14.4 ± 1.2 kcal mol^-1 (CH₃OH) and 14.5 ± 1.3 kcal mol^-1 (CD₃OH)] but lowered activation entropy (Δ^⧧S°) from -12.5 ± 4.1 cal mol^-1 K^-1 (CH₃OH) to -17.1 ± 4.4 cal mol^-1 K^-1 (CD₃OH). DFT computational studies at the PBE-D3 level with QZ4P (Os) and pVQZ (O and H) basis sets provide clear evidence to support the data and interpretations derived from the experimental kinetic work. Comparative DFT mechanistic investigations in a simulated aqueous phase (COSMO) indicate that methanol and Os^VIII first associate to form a noncovalent adduct bound together by intermolecular H-bonding interactions. This is followed by spin-forbidden α-carbon-hydrogen transfer (not O-H transfer) from methanol to Os^VIII by means of HAT, which is found to be the partial rate-limiting step. Without the organic and inorganic fragments dissociating from each other during the entire stepwise redox reaction (in order to avoid formation of highly energetically unfavorable monomer species), the HAT step is followed by PT and then ET before the final product monomers formaldehyde and Os^VI dissociate from each other. DFT-calculated Δ^⧧H° is within 5 kcal mol^-1 of the experimentally obtained value, while the DFT Δ^⧧S° is three times larger than that found from the experiment.

A DFT study to unravel the ligand exchange kinetics and thermodynamics of Os(VIII) oxo/hydroxido/aqua complexes in aqueous matrices

The Os(VIII) oxo/hydroxido complexes that are abundant in mild to relatively concentrated basic aqueous solutions are Os(VIII)O4, [Os(VIII)O4(OH)](-) and two cis-[Os(VIII)O4(OH)2](2-) species. Os(VIII) complexes that contain water ligands are thermodynamically unfavoured w.r.t. the abovementioned species. Os(VIII)O4 reacts with hydroxide in two, consecutive, elementary coordination sphere expansion steps to form the [Os(VIII)O4(OH)](-) complex and then the cis-[Os(VIII)O4(OH)2](2-) species. The Gibbs energy of activation for both reactions, in the forward and reverse direction, are in the range of 6-12 kcal mol(-1) and are relatively close to diffusion-controlled. The thermodynamic driving force of the first reaction is the bonding energy of the Os(VIII)-OH metal-hydroxido ligand, while of the second reaction it is the relatively large hydration energy of the doubly-charged cis-[Os(VIII)O4(OH)2](2-) product compared to the singly-charged reactants. The DFT-calculated (PBE-D3 functional) in the simulated aqueous phase (COSMO) is -2.4 kcal mol(-1) for the first reaction and -0.6 kcal mol(-1) for the second reaction and agree to within 1 kcal mol(-1) with reported experimental values, at -2.7 and 0.3 kcal mol(-1) respectively. From QTAIM and EDA analyses it is deduced that the Os(VIII)[double bond, length as m-dash]O bonding interactions are ionic (closed-shell) and that Os(VIII)-OH bonding interactions are polar covalent (dative). In contrast to QTAIM, NCI analysis allowed for the identification of relatively weak intramolecular hydrogen bonding interactions between neighbouring oxo and hydroxido ligands in both [Os(VIII)O4(OH)](-) and cis-[Os(VIII)O4(OH)2](2-) complexes.

Method of continuous variations: applications of job plots to the study of molecular associations in organometallic chemistry

Applications of the method of continuous variations (MCV or the Method of Job) to problems of interest to organometallic chemists are described. MCV provides qualitative and quantitative insights into the stoichiometries underlying association of m molecules of A and n molecules of B to form A(m)B(n) . Applications to complex ensembles probe associations that form metal clusters and aggregates. Job plots in which reaction rates are monitored provide relative stoichiometries in rate-limiting transition structures. In a specialized variant, ligand- or solvent-dependent reaction rates are dissected into contributions in both the ground states and transition states, which affords insights into the full reaction coordinate from a single Job plot. Gaps in the literature are identified and critiqued.