Generation of random bivariate normal deviates and computation of related integrals

A method which transforms two random variables having rectangular distributions into a pair of bivariate normal deviates with prescribed covariance matrix is described. The same transformation is used for integrating the bivariate normal distribution over areas which are the intersection of the domain outside an equiprobability ellipse and a sector determined by two lines through the point of gravity of the normal distribution.     

A soluble molecular variant of the semiconducting silicondiselenide

Silicondiselenide is a semiconductor and exists as an insoluble polymer (SiSe₂)_n which is prepared by reacting elemental silicon with selenium powder in the temperature range of 400–850 °C. Herein, we report on the synthesis, isolation, and characterization of carbene stabilized molecular silicondiselenide in the form of (cAAC)₂Si₂Se₄ (3) [cAAC = cyclic alkyl(amino)carbene]. 3 is synthesized via reaction of diatomic silicon(0) compound (cAAC)₂Si₂ (2) with black selenium powder at –78 °C to room temperature. The intensely orange colored compound 3 is soluble in polar organic solvents and stable at room temperature for a month under an inert atmosphere. 3 decomposes above 245 °C. The molecular structure of 3 has been confirmed by X-ray single crystal diffraction. It is also characterized by UV-vis, IR, Raman spectroscopy and mass spectrometry. The stability, bonding, and electron density distributions of 3 have been studied by theoretical calculations.     

Approaching an experimental electron density model of the biologically active trans‐epoxysuccinyl amide group—Substituent effects vs. crystal packing

The trans‐epoxysuccinyl amide group as a biologically active moiety in cysteine protease inhibitors such as loxistatin acid E64c has been used as a benchmark system for theoretical studies of environmental effects on the electron density of small active ingredients in relation to their biological activity. Here, the synthesis and the electronic properties of the smallest possible active site model compound are reported to close the gap between the unknown experimental electron density of trans‐epoxysuccinyl amides and the well‐known function of related drugs. Intramolecular substituent effects are separated from intermolecular crystal packing effects on the electron density, which allows us to predict the conditions under which an experimental electron density investigation on trans‐epoxysuccinyl amides will be possible. In this context, the special importance of the carboxylic acid function in the model compound for both crystal packing and biological activity is revealed through the novel tool of model energy analysis.     

On the stability of a variety of organic photovoltaic devices by IPCE and in situ IPCE analyses - the ISOS-3 inter-laboratory collaboration

This work is part of the inter-laboratory collaboration to study the stability of seven distinct sets of state-of-the-art organic photovoltaic (OPV) devices prepared by leading research laboratories. All devices have been shipped to and degraded at RIS?-DTU up to 1830 hours in accordance with established ISOS-3 protocols under defined illumination conditions. In this work, we apply the Incident Photon-to-Electron Conversion Efficiency (IPCE) and the in situ IPCE techniques to determine the relation between solar cell performance and solar cell stability. Different ageing conditions were considered: accelerated full sun simulation, low level indoor fluorescent lighting and dark storage. The devices were also monitored under conditions of ambient and inert (N(2)) atmospheres, which allows for the identification of the solar cell materials more susceptible to degradation by ambient air (oxygen and moisture). The different OPVs configurations permitted the study of the intrinsic stability of the devices depending on: two different ITO-replacement alternatives, two different hole extraction layers (PEDOT:PSS and MoO(3)), and two different P3HT-based polymers. The response of un-encapsulated devices to ambient atmosphere offered insight into the importance of moisture in solar cell performance. Our results demonstrate that the IPCE and the in situ IPCE techniques are valuable analytical methods to understand device degradation and solar cell lifetime.     

Prompt HO2 formation following the reaction of OH with aromatic compounds under atmospheric conditions

The secondary formation of HO(2) radicals following OH + aromatic hydrocarbon reactions in synthetic air under normal pressure and temperature was investigated in the absence of NO after pulsed production of OH radicals. OH and HO(x) (=OH + HO(2)) decay curves were recorded using laser-induced fluorescence after gas-expansion. The prompt HO(2) yields (HO(2) formed without preceding NO reactions) were determined by comparison to results obtained with CO as a reference compound. This approach was recently introduced and applied to the OH + benzene reaction and was extended here for a number of monocyclic aromatic hydrocarbons. The measured HO(2) formation yields are as follows: toluene, 0.42 ± 0.11; ethylbenzene, 0.53 ± 0.10; o-xylene, 0.41 ± 0.08; m-xylene, 0.27 ± 0.06; p-xylene, 0.40 ± 0.09; 1,2,3-trimethylbenzene, 0.31 ± 0.06; 1,2,4-trimethylbenzene, 0.37 ± 0.09; 1,3,5-trimethylbenzene, 0.29 ± 0.08; hexamethylbenzene, 0.32 ± 0.08; phenol, 0.89 ± 0.29; o-cresol, 0.87 ± 0.29; 2,5-dimethylphenol, 0.72 ± 0.12; 2,4,6-trimethylphenol, 0.45 ± 0.13. For the alkylbenzenes HO(2) is the proposed coproduct of phenols, epoxides, and possibly oxepins formed in secondary reactions with O(2). In most product studies the only quantified coproducts were phenols whereas only a few studies reported yields of epoxides. Oxepins have not been observed so far. Together with the yields of phenols from other studies, the HO(2) yields determined in this work set an upper limit to the combined yields of epoxides and oxepins that was found to be significant (≤0.3) for all investigated alkylbenzenes except m-xylene. For the hydroxybenzenes the currently proposed HO(2) coproducts are dihydroxybenzenes. For phenol and o-cresol the determined HO(2) yields are matching the previously reported dihydroxybenzene yields, indicating that these are the only HO(2) forming reaction channels. For 2,5-dimethylphenol and 2,4,6-trimethylphenol no complementary product studies are available.     

Verification of uncertainty budgets

The quality of analytical results is expressed by their uncertainty, as it is estimated on the basis of an uncertainty budget; little effort is, however, often spent on ascertaining the quality of the uncertainty budget. The uncertainty budget is based on circumstantial or historical data, and therefore it is essential that the applicability of the overall uncertainty budget to actual measurement results be verified on the basis of current experimental data. This should be carried out by replicate analysis of samples taken in accordance with the definition of the measurand, but representing the full range of matrices and concentrations for which the budget is assumed to be valid. In this way the assumptions made in the uncertainty budget can be experimentally verified, both as regards sources of variability that are assumed negligible, and dominant uncertainty components. Agreement between observed and expected variability is tested by means of the T-test, which follows a chi-square distribution with a number of degrees of freedom determined by the number of replicates. Significant deviations between predicted and observed variability may be caused by a variety of effects, and examples will be presented; both underestimation and overestimation may occur, each leading to correcting the influence of uncertainty components according to their influence on the variability of experimental results. Some uncertainty components can be verified only with a very small number of degrees of freedom, because their influence requires samples taken at long intervals, e.g., the acquisition of a new calibrant. It is therefore recommended to include verification of the uncertainty budget in the continuous QA/QC monitoring; this will eventually lead to a test also for such rarely occurring effects.     

Donor-acceptor-stabilized silicon analogue of an acid anhydride

A stable silicon analogue of an acid anhydride {PhC(Bu(t)N)(2)}Si{═O·B(C(6)F(5))(3)}O-Si(H){═O·B(C(6)F(5))(3)}{(NBu(t))(HNBu(t))CPh} (4) with a O═Si-O-Si═O core has been prepared by treating monochlorosilylene PhC(Bu(t)N)(2)SiCl (1) with H(2)O·B(C(6)F(5))(3) in the presence of NHC (NHC = 1,3-bis(2,6-diisopropylphenyl)imidazol-2-ylidene). Compound 4 has been characterized by elemental analysis and multinuclear NMR spectroscopic investigations. The molecular structure of 4 has been established by single-crystal X-ray diffraction studies, and DFT calculations support the experimental results.     

On Partial Classes Containig All Monotone and Zero-Preserving Total Boolean Functions

We describe sets of partial Boolean functions being closed under the operations of superposition. For any class A of total functions we define the set ??(A) consisting of all partial classes which contain precisely the functions of A as total functions. The cardinalities of such sets ??(A) can be finite or infinite. We state some general results on ??(A). In particular, we describe all 30 closed sets of partial Boolean functions which contain all monotone and zero-preserving total Boolean functions.     

Stabilization of a Two‐Coordinate Mononuclear Cobalt(0) Compound

Compound (Me₂‐cAAC:)₂Co⁰ ( 2 ; Me₂‐cAAC:=cyclic (alkyl) amino carbene; :C(CH₂)(CMe₂)₂N‐2,6‐iPr₂C₆H₃) was synthesized by the reduction of the precursor (Me₂‐cAAC:)₂Co^ICl ( 1 ) with KC₈ in THF. The cyclic voltammogram of 1 exhibited one‐electron reduction, which suggests that synthesis of a bent 2‐metallaallene ( 2 ) from 1 should be possible. Compound 2 contains one cobalt atom in the formal oxidation state zero, which is stabilized by two Me₂‐cAAC: ligands. Bond lengths from X‐ray diffraction are 1.871(2) and 1.877(2) Å with a C‐Co‐C bond angle of 170.12(8)°. The EPR spectrum of 2 exhibited a broad resonance attributed to the unique quasi‐linear structure, which favors near degeneracy and gives rise to very rapid relaxation conditions. The cAAC?Co bond in 2 can be considered as a typical Dewar–Chatt–Duncanson type of bonding, which in turn retains 2.5 electron pairs on the Co atom as nonbonding electrons.