Kinetics and Equilibria for Complex Formation between Palladium(II) and Chloroacetate

Kinetics and equilibria for the formation of a 1:1 complex between palladium(II) and chloroacetate were studied by spectrophotometric measurements in 1.00 mol HClO₄ at 298.2 K. The equilibrium constant, K, of the reaction

Vibrational isotope effect by the low rank perturbation method

Mathematical formalism of the Low Rank Perturbation method (LRP) is applied to the vibrational isotope effect in the harmonic approximation with a standard assumption that force field does not change under isotopic substitutions. A pair of two n-atom isotopic molecules A and B which are identical except for isotopic substitutions at ρ atomic sites is considered. In the LRP approach vibrational frequencies ω _k and normal modes of the isotopomer B are expressed in terms of the vibrational frequencies ν _i and normal modes of the parent molecule A. In those relations complete specification of the normal modes is not required. Only amplitudes at sites τ affected by the isotopic substitutions and in the coordinate direction s (s = x, y, z) are needed. Out-of-plane vibrations of the (H,D)-benzene isotopomers are considered. Standard error of the LRP frequencies with respect to the DFT frequencies is on average . This error is due to the uncertainty of the input data (± 0.5 cm⁻¹) and in the absence of those uncertainties and in the harmonic approximation it should disappear. In comparing with experiment, one finds that LRP frequencies reproduces experimental frequencies of (H,D)-benzene isotopomers better () than scaled DFT frequencies () which are designed to minimize (by frequency scaling technique) this error. In addition, LRP is conceptually and numerically simple and it also provides a new insight in the vibrational isotope effect in the harmonic approximation.     

The First Structurally Characterized Mn(III) Substituted Sandwich-type Polyoxotungstates

The new polyoxotungstates H₂O (1), · 28H₂O (2) and H₂O (3) were synthesized in aqueous solution and characterized by IR and Raman spectroscopy, energy dispersive X-ray fluorescence and single-crystal X-ray analysis. The anions in 1 and 2 are the first structurally characterized sandwich-type polyoxoanions which contain trivalent manganese atoms. The manganese atoms are coordinated by four oxygen atoms of two Keggin fragments and one water molecule, forming a square pyramid. The manganese(II) containing anions in 3 are linked via Mn–O–W-bonds, forming a two-dimensional network.Dedicated to Prof. M.T. Pope on the occasion of his retirement.     

Electrocatalytic Reduction of O2 by a Cu(II)-Substituted Electron-Rich Wheel-Type Oxomolybdate Nanocluster

Catalysis of electron transfer by a Cu-substituted wheel-type oxomolybdate cluster–anion, , (1), is demonstrated. Data provided include aqueous-solution chemistry (stability) studies of 1 and , (2), derivatives of the “plenary” {Mo₁₅₄} anion, , (3). Combined use of cyclic voltammetry and UV–vis spectroscopy shows that, while both 1 and 2 appear to be stable in solution at pH 0.33 (0.5 M H₂SO₄), 1 is more stable than 2 at pH 3 (in 0.2 M Na₂SO₄). Cyclic voltammetric analysis in the presence of O₂ shows that 1 is an electrocatalyst for electron transfer to O₂. Bulk electrolysis of 1 in the presence of O₂ (ca. 1 mM) is used to assess catalyst stability under turnover conditions, and to demonstrate that the final product of electrocatalytic reduction is water, rather than H₂O₂. Finally, control experiments using 1, 2, and CuSO₄ (no oxomolybdate-cluster present), show that catalytic activity is due to specific interaction(s) between Cu ions and the Mo₁₄₂ type oxomolybdate structure of 1.     

Densities and Volumetric Properties of Binary Mixtures of Formamide with 1-Butanol, 2-Butanol, 1,3-Butanediol and 1,4-Butanediol at Temperatures between 293.15 and 318.15 K

The densities of binary mixtures of formamide (FA) with 1-butanol, 2-butanol, 1,3-butanediol, and 1,4-butanediol, including those of the pure liquids, over the entire composition range were measured at temperatures (293.15, 298.15, 303.15, 308.15, 313.15 and 318.15) K and atmospheric pressure. From the experimental data, the excess molar volume, V _m ^E, partial molar volumes, and , at infinite dilution, and excess partial molar volumes, and , at infinite dilution were calculated. The variation of these parameters with composition and temperature of the mixtures are discussed in terms of molecular interactions in these mixtures. The partial molar expansivities, and , at infinite dilution and excess partial molar expansivities, and , at infinite dilution were also calculated. The V _m ^E values were found to be positive for all the mixtures at each temperature studied, except for FA + 1-butanol which exhibits a sigmoid trend wherein V _m ^E values change sign from positive to negative as the concentration of FA in the mixture is increased. The V _m ^E values for these mixtures follow the order: 1-butanol < 2-butanol < 1,3-butanediol < 1,4-butanediol. It is observed that the V _m ^E values depend upon the number and position of hydroxyl groups in these alkanol molecules.     

Cluster Oxalate Complexes [W3(μ3-Q)(μ2-Q)3 (C2O4)3(H2O)3]2? (Q=S, Se): Mechanochemical Synthesis and Crystal Structure

Mechanochemical reaction of cluster coordination polymers (Q=S, Se) with solid leads to the cluster core excision with the formation of anionic complexes . Extraction of the reaction mixture with water followed by crystallization gives crystalline (main product) and (1) (minor product). In the case of the Se cluster, the complex could not be isolated, and the treatment of the aqueous extract with PPh₃ gave (2) in a low yield. Alternatively, it was obtained from and in high yield. Both 1 and 2 were characterized by X-ray structure analysis. Dedicated to Academician I. I. Moiseev on the occasion of his 75th birthday and in recognition of his outstanding contribution to cluster chemistry.     

Interaction of a finite quantum system with an infinite quantum system that contains a single one-parameter eigenvalue band

Interaction of a finite quantum system that contains ρ eigenvalues and eigenstates with an infinite quantum system that contains a single one-parameter eigenvalue band is considered. A new approach for the treatment of the combined system is developed. This system contains embedded eigenstates with continuous eigenvalues , and, in addition, it may contain isolated eigenstates with discrete eigenvalues . Two ρ × ρ eigenvalue equations, a generic eigenvalue equation and a fractional shift eigenvalue equation are derived. It is shown that all properties of the system that interacts with the system can be expressed in terms of the solutions to those two equations. The suggested method produces correct results, however strong the interaction between quantum systems and . In the case of the weak interaction this method reproduces results that are usually obtained within the formalism of the perturbation expansion approach. However, if the interaction is strong one may encounter new phenomena with much more complex behavior. This is also the region where standard perturbation expansion fails. The method is illustrated with an example of a two-dimensional system that interacts with the infinite system that contains a single one-parameter eigenvalue band. It is shown that all relevant completeness relations are satisfied, however strong the interaction between those two systems. This provides a strong verification of the suggested method.     

On the largest eigenvalues of trees with perfect matchings

Let λ₁ (G) and Δ (G), respectively, denote the largest eigenvalue and the maximum degree of a graph G. Let be the set of trees with perfect matchings on 2m vertices, and . Among the trees in , we characterize the tree which alone minimizes the largest eigenvalue, as well as the tree which alone maximizes the largest eigenvalue when . Furthermore, it is proved that, for two trees T ₁ and T ₂ in (m≥ 4), if and Δ (T ₁) > Δ (T ₂), then λ₁ (T ₁) > λ₁ (T ₂).     

Germyl mesolytic dissociations in the allylgermane and penta- 2,4-dienylgermane radical anions. A theoretical study

In two stable structures have a trigonal bipyramidal arrangement around Ge, with the extra electron in equatorial (tbp eq) or axial (tbp ax) position. In only tbp ax is found, while a second structure with a tetrahedral germyl group has the extra electron on the conjugated π system. C−Ge bond cleavage yields allyl/ pentadienyl radicals plus germide. Both dissociation reactions require 4–6 kcal mol⁻¹, less than the analogous C and Si systems (ca. 30 and 14 kcal mol⁻¹, respectively). Fragmentation is dramatically activated with respect to homolysis in the corresponding neutrals. The wavefunction is dominated by one single configuration at all distances, in contrast to homolytic cleavage, in which two configurations are important. C−Ge bond dissociation is at variance also with heterolysis, due to spin recoupling of one of the C−Ge bond electrons with the originally unpaired electron. Contribution to the Fernando Bernardi Memorial Issue.     

Two Group 8 Carbonyl Clusters Containing a Naked {\varvec{\mu}}_5-Sb Atom

The synthesis and structural characterisation of two novel clusters, 2, and 3, are presented. They are the first examples of osmium and ruthenium clusters containing a naked atom.     

Apparent Michaelis constant of the enzyme modified porous electrode

Plate-gap model of enzyme doped porous electrode was utilized in order to calculate apparent Michaelis constants () and apparent maximal currents () of modeled amperometric biosensor for the wide range of given reaction/diffusion parameters. It was found that of plate-gap biosensor linearly depends on when rates of enzymatic reaction are lower than critical. Theoretically predicted linear correlation between apparent parameters was observed experimentally for the case of carbon paste electrodes, which were modified by PQQ-dependent alcohol dehydrogenases. At overcritical rates (or apparent maximal currents), is practically independent on Michaelis constant of soluble enzyme. Therefore, apparent Michaelis constant can be regarded as biosensor’s topology representing parameter which, in fact, is not related to the specificity of enzyme kinetics. High and rate-independent values of indicate that reaction proceeds at substrate-exposed top layer of the gap. In this case, reaction–diffusion system formally is stratified into separate reaction (top) and diffusion (bottom) zones. Topology of such reaction–diffusion system reminds “inverted” planar electrode, which contains diffusion layer below reaction layer. The net effect of plate-gap topology of working electrode on apparent Michaelis constant is similar to the effect of diffusion layer covering enzymatic planar electrode.     

Gas phase ion chemistry of methyl acetate,methyl propanoate and their enolic tautomers. An experimental approach

From a combination of isotopic substitution, time-resolved measurements and sequential collision experiments, it was proposed that whereas ionized methyl acetate prior to fragmentation rearranges largely into \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_3 \mathop {\rm C}\limits^ + ({\rm OH}){\rm O}\mathop {\rm C}\limits^{\rm .} {\rm H}_2 $\end{document}, in contrast, methyl propanoate molecular ions isomerize into \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm C}\limits^. {\rm H}_2 {\rm CH}_2 \mathop {\rm C}\limits^ + ({\rm OH}){\rm OCH}_3 $\end{document}. Metastably fragmenting methyl acetate molecular ions are known predominantly to form H₂?OH together with \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_3 - \mathop {\rm C}\limits^ + = {\rm O} $\end{document}, whereas ionized methyl propanoate largely yields H₃CO˙ together with \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_3 {\rm CH}_2 - \mathop {\rm C}\limits^ + = {\rm O} $\end{document}. The observations were explained in terms of the participation of different distonic molecular ions. The enol form of ionized methyl acetate generates substantially more H₃CO˙ in admixture with H₂?OH than the keto tautomer. This is ascribed to the rearrangement of the enol ion to the keto form being partially rate determining, which results in a wider range of internal energies among metastably fragmenting enol ions. Extensive ab initio calculations at a high level of theory would be required to establish detailed reaction mechanisms.     

Understanding the chemical reactivity of phenylhalocarbene systems: an analysis based on the spin-polarized density functional theory

Global and local indices based on the spin-polarized density functional theory (SP-DFT) have been used to rationalize the philicity power and spin polarization pattern of a family of singlet substituted phenylhalocarbenes, (pYPhXC, Y = –NO₂ , –CN, –CHO, –F, –H, –CH₃ , –OH, –OCH₃ , –NH₂ ; X = –F, –Cl, –Br). The local reactivity may be traced out by the simple condensed-to-atoms model for the SP-DFT Fukui functions, namely and . For the addition of some singlet phenylhalocarbenes on tetramethylethylene a linear correlation among the global and local electrophilicity index , and the observed rate constants were found. This result supports a mechanistic model where the carbene adds to the olefin in a single step that is controlled by the carbene electrophilicity. These results emphasize the usefulness of general SP-DFT philicities in the rationalization of chemical reactivity at initial stages of reactions that could involve both charge transfer and spin polarization processes.     

Improvement of the electrochemical properties of “as-grown” boron-doped polycrystalline diamond electrodes deposited on tungsten wires using ethanol

The electrochemical properties of boron-doped diamond (BDD) polycrystalline films grown on tungsten wire substrates using ethanol as a precursor are described. The results obtained show that the use of ethanol improves the electrochemistry properties of “as-grown” BDD, as it minimizes the graphitic phase upon the surface of BDD, during the growth process. The BDD electrodes were characterized by Raman spectroscopy, scanning electronic microscopy, cyclic voltammetry (CV), and electrochemical impedance spectroscopy (EIS). The boron-doping levels of the films were estimated to be ∼10²⁰ B/cm³. The electrochemical behavior was evaluated using the and redox couples and dopamine. Apparent heterogeneous electro-transfer rate constants were determined for these redox systems using the CV and EIS techniques. values in the range of 0.01–0.1 cm s⁻¹ were observed for the and redox couples, while in the special case of dopamine, a lower value of 10⁻⁵ cm s⁻¹ was found. The obtained results showed that the use of CH₃CH₂OH (ethanol) as a carbon source constitutes a promising alternative for manufacturing BDD electrodes for electroanalytical applications.     

On the inner and outer radial density functions

Starting from the two-electron radial density D ₂(r ₁,r ₂), a generalized partitioning of the one-electron radial density function D(r) into two component densities D _a (r) and D _b (r) is discussed for many-electron systems. The literature partitioning (Koga and Matsuyama Theor Chem Acc 115:59, 2006) of D(r) into the inner D _<(r) and outer D _>(r) radial densities is shown to minimize the average variance of the two component density functions D _a (r) and D _b (r). It is also found that the average radial separation halved, , constitutes a lower bound to the standard deviation σ of D(r).     

Stable [C2H7O2]+ isomers: Experimental and theoretical evidence for the existence of protonated peroxides and proton-bound dimers in the gas phase

Evidence is presented for the gas phase generation of at least eight stable isomeric [C₂H₇O₂]⁺ ions. These include energy-rich protonated peroxides (ions \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} {\rm CH}_2 {\rm O}\mathop {\rm O}\limits^{\rm + } {\rm H}_{\rm 2} $\end{document} (e), \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} {\rm CH}_{\rm 2} \mathop {\rm O}\limits^{\rm + } {\rm (H)OH} $\end{document} (f) and \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} {\rm O}\mathop {\rm O}\limits^{\rm + } {\rm (H)CH}_{\rm 3} {\rm (g)),} $\end{document} (g)), proton-bound dimers (ions \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} {\rm CH = O} \cdot \cdot \cdot \mathop {\rm H}\limits^{\rm 3} \cdot \cdot \cdot {\rm OH}_{\rm 2} $\end{document} (h) and \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH2 = O} \cdot \cdot \cdot \mathop {\rm H}\limits^{\rm + } \cdot \cdot \cdot {\rm HOCH}_{\rm 3} $\end{document} (i)) and hydroxy-protonated species (ions \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 2} {\rm (OH)CH}_{\rm 2} \mathop {\rm O}\limits^{\rm + } {\rm H}_{\rm 2} (a), $\end{document} \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} {\rm CH(OH)}\mathop {\rm O}\limits^{\rm + } {\rm H}_{\rm 2} $\end{document} (b) and \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} {\rm OCH}_{\rm 2} \mathop {\rm O}\limits^{\rm + } {\rm H}_{\rm 2} $\end{document} (c)). The important points of the present study are (i) that these ions are prevented by high barriers from facile interconversion and (ii) that both electron-impact- and proton-induced gas phase decompositions seem to proceed via multistep reactions, some of which eventually result in the formation of proton-bound dimers.     

On the charge storage mechanism at RuO<Subscript>2</Subscript>/0.5 M H<Subscript>2</Subscript>SO<Subscript>4</Subscript> interface

Comparative study of capacitative properties of RuO₂/0.5 M H₂SO₄ and Ru/0.5 M H₂SO₄ interfaces has been performed with a view to find out the nature of electrochemical processes involved in the charge storage mechanism of ruthenium (IV) oxide. The methods of cyclic voltammetry and scanning electron microscopy (SEM) were employed for the investigation of electrochemical behavior and surface morphology of RuO₂ electrodes. It has been suggested that supercapacitor behavior of RuO₂ phase in the potential E range between 0.4 and 1.4 V vs reference hydrogen electrode (RHE) should be attributed to double-layer-type capacitance, related to non-faradaic highly reversible process of ionic pair formation and annihilation at RuO₂/electrolyte interface as described by following summary equation:

Recurrence and Differential Relations for Spherical Spinors

We present a comprehensive table of recurrence and differential relations obeyed by spin one-half spherical spinors (spinor spherical harmonics) Ω_{κ μ}(n) used in relativistic atomic, molecular, and solid state physics, as well as in relativistic quantum chemistry. First, we list finite expansions in the spherical spinor basis of the expressions A·B Ω_κμ(n) and A·(B×C) Ω_κμ(n), where A, B, and C are either of the following vectors or vector operators: n=r/r (the radial unit vector), e ₀, e _±1 (the spherical, or cyclic, versors), (the 2×2 Pauli matrix vector), (the dimensionless orbital angular momentum operator; I is the 2×2 unit matrix), (the dimensionless total angular momentum operator). Then, we list finite expansions in the spherical spinor basis of the expressions A·B F(r)Ω_κμ(n) and A·(B×C) F(r)Ω_κμ(n), where at least one of the objects A, B, C is the nabla operator , while the remaining ones are chosen from the set .     

Electrochemical study of the thermodynamics and kinetics of hydrophilic ion transfers across water | <Emphasis Type="Italic">n</Emphasis>-octanol interface

Thermodynamics and kinetics of hydrophilic ion transfers across water|n-octanol (W|OCT) interface have been electrochemically studied by means of novel three-phase and thin-film electrodes. Three-phase electrodes used for thermodynamics measurements comprise edge plane pyrolytic graphite, the surface of which was partly modified with an ultrathin film of OCT, containing hydrophobic lutetium bis(tetra-tert-butylphthalocyaninato) (Lu[tBu₄Pc]₂) as a redox probe. The transfers of anions and cations from W to OCT were electrochemically driven by reversible redox transformations of Lu[tBu₄Pc]₂ to chemically stable lipophilic monovalent cation and anion , respectively. Upon reduction of Lu[tBu₄Pc]₂, the transfers of alkali metal cations from W to OCT have been studied for the first time, enabling estimation of their Gibbs transfer energies. For kinetic measurements, a thin-film electrode configuration has been used, consisting of the same electrode covered completely with a thin layer of OCT that contained the redox probe and a suitable electrolyte. Combining the fast and sensitive square-wave voltammetry with thin-film electrodes, the kinetics of , , and Cl⁻ transfers have been estimated. Dedicated to Professor Dr. Yakov I. Tur’yan on the occasion of his 85th birthday.     

Structures and relative energies of gas-phase [C2H7N]+˙ radical cations

Ab initio molecular orbital calculations with split-valence plus polarization basis sets and incorporating electron correlation and zero-point energy corrections have been used to examine possible equilibrium structures on the [C₂H₇N]⁺˙ surface. In addition to the radical cations of ethylamine and dimethylamine, three other isomers were found which have comparable energy, but which have no stable neutral counterparts. These are \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm C}\limits^{\rm .} {\rm H}_{\rm 2} {\rm CH}_{\rm 2} \mathop {\rm N}\limits^{\rm + } {\rm H}_{\rm 3} $\end{document}, \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} \mathop {\rm C}\limits^{\rm .} {\rm H}\mathop {\rm N}\limits^{\rm + } {\rm H}_{\rm 3} $\end{document}and\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} \mathop {\rm N}\limits^{\rm + } {\rm H}_{\rm 2} \mathop {\rm C}\limits^. {\rm H}_{\rm 2} {\rm }, $\end{document} with calculated energies relative to the ethylamine radical cation of ?33, ?28 and 4 kJ mol^?1, respectively. Substantial barriers for rearrangement among the various isomers and significant binding energies with respect to possible fragmentation products are found. The predictions for \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm C}\limits^. {\rm H}_{\rm 2} {\rm CH}_{\rm 2} \mathop {\rm N}\limits^ + {\rm H}_{\rm 3} $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} \mathop {\rm C}\limits^{\rm .} {\rm H}\mathop {\rm N}\limits^{\rm + } {\rm H}_{\rm 3}$\end{document} are consistent with their recent observation in the gas phase. The remaining isomer, \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} \mathop {\rm N}\limits^{\rm + } {\rm H}_{\rm 2} \mathop {\rm C}\limits^{\rm .} {\rm H}_{\rm 2} {\rm },$\end{document}is also predicted to be experimentally observable.