Testing for Hermite Rank in Gaussian Subordination Processes

Statistical inference for time series with long-range dependence is often based on the assumption of Gaussian subordination X_t = G(Z_t). Although the Hermite rank m of G plays an essential role for statistical inference in these situations, the question of estimating m or of testing hypotheses about the Hermite rank has not been addressed in the literature. In this article, a method is introduced for testing H₀: m = 1 against H₁: m > 1. This allows for deciding whether inference based on the usual assumption of m = 1 is appropriate. Simulations and data examples illustrate the method.     

Experimental and Computational Mechanistic Studies of the β-Diketiminatoiron(II)-Catalysed Hydroamination of Primary Aminoalkenes

A comprehensive mechanistic study by means of complementary experimental and computational approaches of the exo-cyclohydroamination of primary aminoalkenes mediated by the recently reported β-diketiminatoiron(II) complex B is presented. Kinetic analysis of the cyclisation of 2,2-diphenylpent-4-en-1-amine ( 1 a ) catalysed by B revealed a first-order dependence of the rate on both aminoalkene and catalyst concentrations and a primary kinetic isotope effect (KIE) (k_H/k_D) of 2.7 (90 °C). Eyring analysis afforded ΔH^≠=22.2 kcal mol⁻¹, ΔS^≠=−13.4 cal mol⁻¹ K⁻¹. Plausible mechanistic pathways for competitive avenues of direct intramolecular hydroamination and oxidative amination have been scrutinised computationally. A kinetically challenging proton-assisted concerted N−C/C−H bond-forming non-insertive pathway is seen not to be accessible in the presence of a distinctly faster σ-insertive pathway. This operative pathway involves 1) rapid and reversible syn-migratory 1,2-insertion of the alkene into the Fe−N_amido σ bond at the monomer {N^N}Fe^II amido compound; 2) turnover-limiting Fe−C σ bond aminolysis at the thus generated transient {N^N}Fe^II alkyl intermediate and 3) regeneration of the catalytically competent {N^N}Fe^II amido complex, which favours its dimer, likely representing the catalyst resting state, through rapid cycloamine displacement by substrate. The collectively derived mechanistic picture is consonant with all empirical data obtained from stoichiometric, catalytic and kinetics experiments.     

Mechanistic Exploration of Intramolecular Aminodiene Hydroamination/Cyclisation Mediated by Constrained Geometry Organoactinide Complexes: A DFT Study

The present computational mechanistic study explores comprehensively the organoactinide‐mediated intramolecular hydroamination/cyclisation (IHC) of aminodienes by employing a reliable DFT method. All the steps of a plausible catalytic reaction course have been scrutinised for the IHC of (4E,6)‐heptadienylamine 1 t by [(CGC)Th(NMe₂)₂] precatalyst 2 (CGC=[Me₂Si(η⁵‐Me₄C₅)(tBuN)]^2?). For each of the relevant elementary steps the most accessible pathway has been identified from a multitude of mechanistic possibilities. The operative mechanism involves rapid substrate association/dissociation equilibria for the 3 t ‐S resting state and also for azacyclic intermediates 4 a , 4 s , easily accessible and reversible exocyclic ring closure, supposedly facile isomerisation of the azacycle’s butenyl tether prior to turnover‐limiting protonolysis. The following aspects are in support of this scenario: 1) the derived rate law is consistent with the experimentally obtained empirical rate law; 2) the accessed barrier for turnover‐limiting protonolysis does agree remarkably well with observed performance data; 3) the ring‐tether double‐bond selectivity is consistently elucidated, which led to predict the product distribution correctly. This study provides a computationally substantiated rationale for observed activity and selectivity data. Steric demands at the CGC framework appear to be an efficient means for modulating both performance and ring‐tether double‐bond selectivity. The careful comparison of (CGC)4f‐element and (CGC)5f‐element catalysts revealed that aminodiene IHC mediated by organoactinides and organolanthanides proceeds through a similar mechanistic scenario. However, cyclisation and protonolysis steps, in particular, feature a markedly different reactivity pattern for the two catalyst classes, owing to enhanced bond covalency of early actinides when compared to lanthanides.     

Effect of dopants on the analysis of pesticides by means of differential mobility spectrometry with atmospheric pressure photoionization

The chances to improve the detection of pesticides using differential mobility spectrometry (DMS) with an atmospheric pressure photoionization (APPI) ion source by means of dopants was investigated. The effect of employing benzene, anisole and chlorobenzene as dopants is described regarding sensitivity, limits of detection and peak displacements in the spectra. For typical pesticides an improvement of detection limits up to two orders of magnitude could be determined, while for the peak shift of individual substances no uniform behaviour was observed. Possible mechanisms of action in respect to atmospheric pressure photoionization (APPI) processes are discussed.     

Influence of N‐Alkyl Substituents and Counterions on the Structural and Mesomorphic Properties of Guanidinium Salts: Experiment and Quantum Chemical Calculations

A series of N‐4‐(4′‐alkoxybiphenyl)‐N′,N′,N”,N“‐tetramethylguanidinium salts was synthesized with varying alkoxy chain lengths and additional N‐alkyl substituents, each with a number of different counterions. X‐ray crystal‐structure analyses of 1b I , 1b PF₆ , 2a I , and 4a I reveal bilayer structures in the solid state and, for the 1b and 1b PF₆ salts, a hydrogen‐bond‐type connectivity between the guanidinium N‐H group and the anion is found. For the N‐alkyl homologues 2a I and 4a I the anion is still oriented close to the head group, although at a larger distance. Ion pairs are present also in solution, as demonstrated by ¹H NMR: the N‐H chemical shift shows a good linear correlation with the radius, and hence the hardness, of the anion. The intramolecular conformational flexibility of 1b I , 2b I , 3b I, and 4b I was studied by temperature‐dependent ¹H NMR spectroscopy and discrete activation barriers were determined for rotations about each of the three C? N partial double bonds of the guanidinium core. The relative heights of the individual barriers change between the N‐H and the N‐alkylguanidinium salts. A fourth barrier is observed for the rotation about the N? biphenyl bond. DFT calculations of charge densities show that the positive charge resides primarily on the central carbon atom. Rotational barriers were calculated for N′‐substituted 2‐amino‐1,3‐dimethylimidazolidinium cations as models, and are in qualitatively good agreement with the NMR data. Mesomorphic properties were studied by differential‐scanning calorimetry, polarizing optical microscopy, and X‐ray diffraction (WAXS/SAXS). All liquid‐crystalline guanidinium salts exhibit smectic A mesophases. Clearing temperatures show a linear correlation with the anionic radius. Substitution of the N‐H group with methyl, ethyl, or propyl results in decreasing mesophase widths and a concomitant shrinkage of the layer spacings.     

Validation and evaluation of an HPLC methodology for the quantification of the potent antimitotic compound (+)‐discodermolide in the Caribbean marine sponge Discodermia dissoluta

The sponge Discodermia dissoluta is the source of the potent antimitotic compound (+)‐discodermolide. The relatively abundant and shallow populations of this sponge in Santa Marta, Colombia, allow for studies to evaluate the natural and biotechnological supply options of (+)‐discodermolide. In this work, an RP‐HPLC‐UV methodology for the quantification of (+)‐discodermolide from sponge samples was tested and validated. Our protocol for extracting this compound from the sponge included lyophilization, exhaustive methanol extraction, partitioning using water and dichloromethane, purification of the organic fraction in RP‐18 cartridges and then finally retrieving the (+)‐discodermolide in the methanol–water (80:20 v/v) fraction. This fraction was injected into an HPLC system with an Xterra RP‐18 column and a detection wavelength of 235 nm. The calibration curve was linear, making it possible to calculate the LODs and quantification in these experiments. The intra‐day and inter‐day precision showed relative standard deviations lower than 5%. The accuracy, determined as the percentage recovery, was 99.4%. Nine samples of the sponge from the Bahamas, Bonaire, Curaçao and Santa Marta had concentrations of (+)‐discodermolide ranging from 5.3 to 29.3 μg/g^?1 of wet sponge. This methodology is quick and simple, allowing for the quantification in sponges from natural environments, in situ cultures or dissociated cells.     

A concept to tailor electron delocalization: applying QTAIM analysis to phenyl-terpyridine compounds

To gain a deeper understanding of how structural modifications may influence photochemical properties of 4'-phenyl-2,2':6',2'-terpyridines, the investigations presented here focus on electron delocalization in 4'-phenyl-2,2':6',2'-terpyridine derivatives and their Ru(II) and Zn(II) complexes. In those systems of neighboring aromatic rings the considerable torsion between the rings is commonly regarded to be the limiting factor for a well pronounced π-conjugation between the rings. A common approach to improve the π-conjugation is to lower the steric hindrance, thus achieving a more planar geometry. Here, we present a fundamentally different approach towards enhanced π-conjugation by manipulation of the electronic properties of the pyridine-phenyl (py-ph) bond. This is accomplished by introducing various substituents at the phenylene moiety or coordinating the terpyridine moiety to transition metal ions. The electron delocalization was quantified via the DFT-calculated ellipticity in the bond-critical point (BCP) of the py-ph bond. This ellipticity can be modified due to substituents in the para position of phenylene and via the transition metals coordinated to the terpyridine moiety. Changes in electron density distribution induced by the substituents and the metal ions are further studied by means of intermolecular electron density difference plots. It was shown that a NH(2) group in the para position of the phenyl ring as well as the coordination to Ru(II) or Zn(II) ions significantly enhances the π-character of the py-ph bond. Surprisingly, an even higher π-character of the py-ph bond is achieved by introducing additional NH(2) groups in ortho position to the py-ph bond, despite the increased torsion between pyridine and phenylene. The introduction of other substituents (-NO(2), -Br, -CN, -vinyl, -ethynyl) studied within the presented work enables an actuation of the electron delocalization between terpyridine and phenylene. In doing so, the ellipticity is a concise quantity to characterize electron delocalization in the studied systems. Furthermore, the ellipticity in the BCP of the py-ph bond is related to the corresponding geometrical properties (e.g., bond length and dihedral angle) and to the DFT-calculated HOMO and LUMO energies.     

XPS investigations of thick,oxygen-containing cubic boron nitride coatings

Cubic boron nitride (c-BN) coatings produced by PVD and PECVD techniques usually exhibit very high compressive stresses and poor adhesion due to intense ion bombardments of the growing surface that are mandatory during the formation of the cubic phase. Our previous investigations indicate, however, that a controlled addition of oxygen during film deposition can lead to a drastic reduction of the detrimental stress, yet having minor effect on the cubic phase content in the resulting low-stress, oxygen-containing c-BN:O coatings (as already confirmed by various analytical methods like X-ray diffraction (XRD), high-resolution transmission electron microscopy (HRTEM) and electron diffraction, and Fourier transform infra-red spectroscopy (FTIR)). This stress-reduction technique makes possible the deposition of well-adhered, superhard c-BN:O layer about 2 μm thick through magnetron sputtering on top of an adhesion-promoting base layer and via a compositional-graded nucleation process. In the present paper, we report on the atomic bonding structure relating in particular to the incorporated oxygen within such a thick c-BN:O coating using X-ray photoelectron spectroscopy (XPS). The c-BN:O top layer was found to consist of about 49.8 at% boron, 42.2 at% nitrogen, 5.5 at% oxygen, as well as small amounts of carbon (1.4 at%) and argon (1.1 at%). Because of the low oxygen concentration, it was difficult to categorize the bonding state of oxygen according to the XPS spectra of B 1s and N 1s elemental lines. However, the detailed results in terms of the O 1s spectrum strongly indicated that the lattice nitrogen of c-BN was partially replaced by the added oxygen.