Central Limit Theorems for Multiple Skorokhod Integrals

In this paper, we prove a central limit theorem for a sequence of multiple Skorokhod integrals using the techniques of Malliavin calculus. The convergence is stable, and the limit is a conditionally Gaussian random variable. Some applications to sequences of multiple stochastic integrals, and renormalized weighted Hermite variations of the fractional Brownian motion are discussed.     

Low-Dimensional Compounds Containing Cyanido Groups. XX. Synthesis,Crystal Structure and Spectroscopic Properties of Polymeric 1,10-Phenanthroline-<Emphasis Type=Italic>N</Emphasis>,<Emphasis Type=Italic>N</Emphasis>′-Copper(II) Tetracyanidoplatinate(II)

Abstract  

Polymeric {[Cu(phen)][Pt(CN)₄]} _n compound (phen = 1,10-phenanthroline) has been prepared under hydrothermal conditions using CuSO₄ · 5H₂O, phen and K₂[Pt(CN)₄] · 3H₂O, and characterized by chemical analysis and IR spectroscopy. The X-ray structure analysis [C2/c, a = 6.6057(7), b = 19.747(2), c = 11.5891(13) ?, β = 91.723(10)°] has revealed that the coordination geometry of the Cu(II) atom, situated on a two-fold rotation axis, is tetragonally distorted octahedral. Two nitrogen donor atoms originate from one blocking phen ligand, chelate coordinated in the equatorial plane at the distance of 2.026(4) ? (2×). The remaining four coordination sites are occupied by the nitrogen atoms [Cu–N = 1.975(5) (2×) and 2.574(5) ? (2×)] of two pairs symmetrically related bridging cyanido groups. These link Cu(II) with Pt(II) atoms, which lie on symmetry centers and are coordinated by four C-bonded cyanido ligands in the square planar form. Thus infinite 2D wave-like net is formed in the ac plane stabilized by π–π interactions between the phen molecules.     

Positive Systems of Kostant Roots

Let \(\mathfrak {g}\) be a simple complex Lie algebra and let \(\mathfrak {t} \subset \mathfrak {g}\) be a toral subalgebra of \(\mathfrak {g}\). As a \(\mathfrak {t}\)-module \(\mathfrak {g}\) decomposes as

$$\mathfrak{g} = \mathfrak{s} \oplus \left( \oplus_{\nu \in \mathcal{R}}~ \mathfrak{g}^{\nu}\right)$$

where \(\mathfrak {s} \subset \mathfrak {g}\) is the reductive part of a parabolic subalgebra of \(\mathfrak {g}\) and \(\mathcal {R}\) is the Kostant root system associated to \(\mathfrak {t}\). When \(\mathfrak {t}\) is a Cartan subalgebra of \(\mathfrak {g}\) the decomposition above is nothing but the root decomposition of \(\mathfrak {g}\) with respect to \(\mathfrak {t}\); in general the properties of \(\mathcal {R}\) resemble the properties of usual root systems. In this note we study the following problem: “Given a subset \(\mathcal {S} \subset \mathcal {R}\), is there a parabolic subalgebra \(\mathfrak {p}\) of \(\mathfrak {g}\) containing \(\mathcal {M} = \oplus _{\nu \in \mathcal {S}} \mathfrak {g}^{\nu }\) and whose reductive part equals \(\mathfrak {s}\)?”. Our main results is that, for a classical simple Lie algebra \(\mathfrak {g}\) and a saturated \(\mathcal {S} \subset \mathcal {R}\), the condition \((\text {Sym}^{\cdot }(\mathcal {M}))^{\mathfrak {s}} = \mathbb {C}\) is necessary and sufficient for the existence of such a \(\mathfrak {p}\). In contrast, we show that this statement is no longer true for the exceptional Lie algebras F₄,E₆,E₇, and E₈. Finally, we discuss the problem in the case when \(\mathcal {S}\) is not saturated.

     

Activation by oxidation and ligand exchange in a molecular manganese vanadium oxide water oxidation catalyst

Despite their technological importance for water splitting, the reaction mechanisms of most water oxidation catalysts (WOCs) are poorly understood. This paper combines theoretical and experimental methods to reveal mechanistic insights into the reactivity of the highly active molecular manganese vanadium oxide WOC [Mn₄V₄O₁₇(OAc)₃]³⁻ in aqueous acetonitrile solutions. Using density functional theory together with electrochemistry and IR-spectroscopy, we propose a sequential three-step activation mechanism including a one-electron oxidation of the catalyst from [Mn₂³⁺Mn₂⁴⁺] to [Mn³⁺Mn₃⁴⁺], acetate-to-water ligand exchange, and a second one-electron oxidation from [Mn³⁺Mn₃⁴⁺] to [Mn₄⁴⁺]. Analysis of several plausible ligand exchange pathways shows that nucleophilic attack of water molecules along the Jahn–Teller axis of the Mn³⁺ centers leads to significantly lower activation barriers compared with attack at Mn⁴⁺ centers. Deprotonation of one water ligand by the leaving acetate group leads to the formation of the activated species [Mn₄V₄O₁₇(OAc)₂(H₂O)(OH)]⁻ featuring one H₂O and one OH ligand. Redox potentials based on the computed intermediates are in excellent agreement with electrochemical measurements at various solvent compositions. This intricate interplay between redox chemistry and ligand exchange controls the formation of the catalytically active species. These results provide key reactivity information essential to further study bio-inspired molecular WOCs and solid-state manganese oxide catalysts.

Combined theoretical and experimental studies shed light on the initial steps of redox-activation of a molecular manganese vanadium oxide water oxidation catalyst.     

[3+2] Annulation of 2-substituted 3-nitro-2H-chromenes with mercaptoacetaldehyde: stereoselective synthesis of tetrahydro-4H-thieno[3,2-c]chromen-3-ols

Chemistry of Heterocyclic Compounds - A diastereoselective method was developed for the synthesis of 4-trifluoromethyl- and 4-phenyl-substituted...     

Benzothiadiazole vs. iso-Benzothiadiazole: Synthesis,Electrochemical and Optical Properties of D–A–D Conjugated Molecules Based on Them

This paper presents an improved synthesis of 4,7-dibromobenzo[d][1,2,3]thiadiazole from commercially available reagents. According to quantum-mechanical calculations, benzo[d][1,2,3]thiadiazole (isoBTD) has higher values of E_LUMO and energy band gap (E_g), which indicates high electron conductivity, occurring due to the high stability of the molecule in the excited state. We studied the cross-coupling reactions of this dibromide and found that the highest yields of π-spacer–acceptor–π-spacer type compounds were obtained by means of the Stille reaction. Therefore, 6 new structures of this type have been synthesized. A detailed study of the optical and electrochemical properties of the obtained π-spacer–acceptor–π-spacer type compounds in comparison with isomeric structures based on benzo[c][1,2,5]thiadiazole (BTD) showed a red shift of absorption maxima with lower absorptive and luminescent capacity. However, the addition of the 2,2′-bithiophene fragment as a π-spacer resulted in an unexpected increase of the extinction coefficient in the UV/vis spectra along with a blue shift of both absorption maxima for the isoBTD-based compound as compared to the BTD-based compound. Thus, a thorough selection of components in the designing of appropriate compounds with benzo[d][1,2,3]thiadiazole as an internal acceptor can lead to promising photovoltaic materials.     

Spectral Signatures of Oxidation States in a Manganese-Oxo Cubane Water Oxidation Catalyst

We report IR and UV/Vis spectroscopic signatures that allow discriminating between the oxidation states of the manganese-based water oxidation catalyst [(Mn₄O₄)(V₄O₁₃)(OAc)₃]³⁻. Simulated IR spectra show that V=O stretching vibrations in the 900–1000 cm⁻¹ region shift consistently by about 20 cm⁻¹ per oxidation equivalent. Multiple bands in the 1450–1550 cm⁻¹ region also change systematically upon oxidation/reduction. The computed UV/Vis spectra predict that the spectral range above 350 nm is characteristic of the managanese-oxo cubane oxidation state, whereas transitions at higher energy are due to the vanadate ligand. The presence of absorption signals above 680 nm is indicative of the presence of Mn^III atoms. Spectroelectrochemical measurements of the oxidation from [Mn Mn ] to [Mn ] showed that the change in oxidation state can indeed be tracked by both IR and UV/Vis spectroscopy.     

Polymerization Isomerism in Co-M (M = Cu,Ag, Au) Carbonyl Clusters: Synthesis,Structures and Computational Investigation

The reaction of [Co(CO)₄]⁻ (1) with M(I) compounds (M = Cu, Ag, Au) was reinvestigated unraveling an unprecedented case of polymerization isomerism. Thus, as previously reported, the trinuclear clusters [M{Co(CO)₄}₂]⁻ (M = Cu, 2; Ag, 3; Au, 4) were obtained by reacting 1 with M(I) in a 2:1 molar ratio. Their molecular structures were corroborated by single-crystal X-ray diffraction (SC-XRD) on isomorphous [NEt₄][M{Co(CO)₄}₂] salts. [NEt₄](3)represented the first structural characterization of 3. More interestingly, changing the crystallization conditions of solutions of 3, the hexanuclear cluster [Ag₂{Co(CO)₄}₄]²⁻ (5) was obtained in the solid state instead of 3. Its molecular structure was determined by SC-XRD as Na₂(5)·C₄H₆O₂, [PPN]₂(5)·C₅H₁₂ (PPN = N(PPh₃)₂]⁺), [NBu₄]₂(5) and [NMe₄]₂(5) salts. 5 may be viewed as a dimer of 3 and, thus, it represents a rare case of polymerization isomerism (that is, two compounds having the same elemental composition but different molecular weights) in cluster chemistry. The phenomenon was further studied in solution by IR and ESI-MS measurements and theoretically investigated by computational methods. Both experimental evidence and density functional theory (DFT) calculations clearly pointed out that the dimerization process occurs in the solid state only in the case of Ag, whereas Cu and Au related species exist only as monomers.     

Determination of Antiviral Drugs and Their Metabolites Using Micro-Solid Phase Extraction and UHPLC-MS/MS in Reversed-Phase and Hydrophilic Interaction Chromatography Modes

Two new ultra-high performance liquid chromatography (UHPLC) methods for analyzing 21 selected antivirals and their metabolites were optimized, including sample preparation step, LC separation conditions, and tandem mass spectrometry detection. Micro-solid phase extraction in pipette tips was used to extract antivirals from the biological material of Hanks balanced salt medium of pH 7.4 and 6.5. These media were used in experiments to evaluate the membrane transport of antiviral drugs. Challenging diversity of physicochemical properties was overcome using combined sorbent composed of C₁₈ and ion exchange moiety, which finally allowed to cover the whole range of tested antivirals. For separation, reversed-phase (RP) chromatography and hydrophilic interaction liquid chromatography (HILIC), were optimized using extensive screening of stationary and mobile phase combinations. Optimized RP-UHPLC separation was carried out using BEH Shield RP18 stationary phase and gradient elution with 25 mmol/L formic acid in acetonitrile and in water. HILIC separation was accomplished with a Cortecs HILIC column and gradient elution with 25 mmol/L ammonium formate pH 3 and acetonitrile. Tandem mass spectrometry (MS/MS) conditions were optimized in both chromatographic modes, but obtained results revealed only a little difference in parameters of capillary voltage and cone voltage. While RP-UHPLC-MS/MS exhibited superior separation selectivity, HILIC-UHPLC-MS/MS has shown substantially higher sensitivity of two orders of magnitude for many compounds. Method validation results indicated that HILIC mode was more suitable for multianalyte methods. Despite better separation selectivity achieved in RP-UHPLC-MS/MS, the matrix effects were noticed while using both chromatographic modes leading to signal enhancement in RP and signal suppression in HILIC.     

From Extended Nanofluidics to an Autonomous Solar-Light-Driven Micro Fuel-Cell Device

Autonomous micro/nano mechanical, chemical, and biomedical sensors require persistent power sources scaled to their size. Realization of autonomous micro-power sources is a challenging task, as it requires combination of wireless energy supply, conversion, storage, and delivery to the sensor. Herein, we realized a solar-light-driven power source that consists of a micro fuel cell (μFC) and a photocatalytic micro fuel generator (μFG) integrated on a single microfluidic chip. The μFG produces hydrogen by photocatalytic water splitting under solar light. The hydrogen fuel is then consumed by the μFC to generate electricity. Importantly, the by-product water returns back to the photocatalytic μFG via recirculation loop without losses. Both devices rely on novel phenomena in extended-nano-fluidic channels that ensure ultra-fast proton transport. As a proof of concept, we demonstrate that μFG/μFC source achieves remarkable energy density of ca. 17.2 mWh cm⁻² at room temperature.