Application of cholesky-like matrix decomposition methods to the evaluation of atomic orbital integrals and integral derivatives

When viewed as a square two-indexed matrix, the array of atomic orbital-based, two-electron integrals (ij|kl) is a positive semidefinite array. Beebe and Linderberg showed, in 1977, that actual or near linear dependencies often exist within the types of atomic orbital basis sets employed in conventional quantum chemical calculations. In fact, large (i.e., higher quality) bases were shown to be substantially more redundant than smaller or more spatially separated bases. In situations where there exists significant basis near redundancy, the rank (r) of the (ij|kl) ≡ V_l,J matrix of integrals will be significantly smaller than the matrix dimension M. When this occurs, it proves computationally tractable to decompose the M-dimensional matrix V into components L ( V = LL ^T) which contain all of the information needed to form the full V matrix. The Cholesky algorithm allow such a decomposition to be carried out and forms the basis of the work described here. The method is found to be highly successful in reducing the number of integrals and integral derivatives that must actually be calculated. In particular, results on the C₂ molecule indicate that the algorithm can be superior to traditional methods of integral derivative generation if the orbital basis is large enough to contain appreciable near redundancy. In contrast, results on benzene with a more spatially delocalized basis show that conventional methods are preferred whenever substantial basis (near) redundancy is not present.     

Quantitative surface analysis of Fe?Ni alloy films by XPS,AES and SIMS

A comparison of quantitative surface analyses of Fe? Ni alloy thin films by various methods has been proposed as a pilot study by the Surface Analysis Working Group of the Consultative Committee for Amount of Substance (CCQM). To test the suitability of Fe? Ni for this purpose, alloy films with different compositions were grown on Si(100) wafers by ion‐beam sputter deposition and the compositions were certified by an isotope dilution method using inductively coupled plasma‐mass spectrometry. The alloy compositions measured with X‐ray photoelectron spectroscopy (XPS) and Auger electron spectroscopy (AES) using sensitivity factors determined from pure Fe and Ni metal films agreed with the certified mean values to better than 2%. The alloy compositions quantified by secondary ion mass spectrometry (SIMS) with a C₆₀ ion source agreed to better than 4% with the certified compositions if one of the alloys was used to establish the relative sensitivity factors (RSFs). These results indicate that the quantification of the Fe? Ni alloy is a good method for a CCQM pilot study because matrix effects and ion‐sputtering effects are small for these analytical methods. Copyright © 2007 John Wiley & Sons, Ltd.     

Spectral simplification in proton magnetic resonance spectrometry for 3-(4-aminophenyl)-3-ethyl-2,6-piperidinedione (aminoglutethimide) with achiral and chiral lanthanide shift reagents

The 60-MHz ¹H-NMR spectra of racemic aminoglutethimide (A; 3-(4-aminophenyl)-3- ethyl-2,6-piperidinedione) are studied with the achiral shift reagent, tris(6,6,7,7,8,8,8- heptafluoro-2,2-dimethyl-3,5-octanedionato)europiura(III) (B) and the chiral reagents, tris[3-(trifluororaethylhydroxyraethylene)-D-caraphorato]europium(III) (C) and tris[3- heptafluoropropylhydroxyraethylene-D-caraphorato]europiura(III) (D). Appreciable values of the enantioraeric shift difference, ΔΔδ, were observed for both sets of aryl protons and the methyl protons in CDCl₃ solutions ar 28°C with added C or D. Optical purity determinations were done with good reliability by using the methyl resonance and a D:A molar ratio near 0.5. Results are discussed in terms of possible coordination of the europiura at the amine or amide carbonyl groups. Some significant differences in results with B, C and D were noted.     

Development and validation of a sensitive UHPLC‐MS/MS method for the simultaneous analysis of tramadol,dextromethorphan chlorpheniramine and their major metabolites in human plasma in forensic context: application to pharmacokinetics

The prerequisites for forensic confirmatory analysis by LC/MS/MS with respect to European Union guidelines are chromatographic separation, a minimum number of two MS/MS transitions to obtain the required identification points and predefined thresholds for the variability of the relative intensities of the MS/MS transitions (MRM transitions) in samples and reference standards. In the present study, a fast, sensitive and robust method to quantify tramadol, chlorpheniramine, dextromethorphan and their major metabolites, O‐desmethyltramadol, dsmethyl‐chlorpheniramine and dextrophan, respectively, in human plasma using ibuprofen as internal standard (IS) is described. The analytes and the IS were extracted from plasma by a liquid–liquid extraction method using ethyl acetate–diethyl‐ether (1:1). Extracted samples were analyzed by ultra‐high‐performance liquid chromatography coupled to electrospray ionization tandem mass spectrometry (UHPLC‐ESI‐MS/MS). Chromatographic separation was performed by pumping the mobile phase containing acetonitrile, water and formic acid (89.2:11.7:0.1) for 2.0 min at a flow rate of 0.25 μL/min into a Hypersil‐Gold C₁₈ column, 20 × 2.0 mm (1.9 µm) from Thermoscientific, New York, USA. The calibration curve was linear for the six analytes. The intraday precision (RSD) and accuracy (RE) of the method were 3–9.8 and ?1.7–4.5%, respectively. The analytical procedure herein described was used to assess the pharmacokinetics of the analytes in 24 healthy volunteers after a single oral dose containing 50 mg of tramadol hydrochloride, 3 mg chlorpheniramine maleate and 15 mg of dextromethorphan hydrobromide. Copyright © 2014 John Wiley & Sons, Ltd.     

Absolute X-ray yields of light muonic atoms

The intensities of X-rays from muonic atoms formed in low pressure Ne, O₂, N₂, He, and H₂ gas was measured. For the pressure chosen external electron refilling can be neglected. Absolute yields were extracted and compared to results of cascade calculations. Knowledge of the yields of the circular X-ray transitions allows an in situ efficiency calibration of X-ray detectors down to energies of 1.5 keV. This revised version was published online in August 2006 with corrections to the Cover Date.     

Approaching the Alethic Modal Hexagon of Opposition

Modal logic like many others sustains a hexagon of opposition, with the two ??additional?? vertices expressing contingency and non-contingency. We first illustrate hexagons of opposition generally by treating them as cut-down entailment lattices with order distinctions among multiple arguments suppressed. We then approach the modal case by treating it heuristically as a particular case of the hexagon for quantified propositions. Historically, possibility and contingency were sometimes confused: we show using the notion of duality that contingency, as negation-symmetric, is logically less interesting than possibility.     

An (m+1)-step iterative method of convergence order (m+2) for linear complementarity problems

In this paper, we present an (m+1)-step iterative method of convergence order (m+2) for solving linear complementarity problems. The proposed iterative method is simple and easy to construct, and requiring only third Fréchet differentiation. Computational efficiency in its general form is discussed and a comparison between the efficiency of the proposed method and existing ones is made. The performance is tested through numerical experiments on some test problems.     

In vacuo isotope coded alkylation technique (IVICAT); an N-terminal stable isotopic label for quantitative liquid chromatography/mass spectrometry proteomics

We present a new isotopic labeling strategy to modify the N-terminal amino group of peptides in a quantifiable reaction without the use of expensive reagents or solvents. The In Vacuo Isotope Coded Alkylation Technique (IVICAT) is a methylation reaction, carried out at low pressure (<100 mTorr), that results in a stable quaternary trimethylammonium group, thus adding a permanent positive charge at the N-terminus of peptides without modifying the epsilon-amino groups of lysine. The methylation reaction increases the signal intensity of modified peptides in matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS) and liquid chromatography (LC)/MS and the isotopic peak pair differs by 9 mass units which can be easily resolved by either instrument. N-terminally trimethylated peptides exhibit collision-induced dissociation (CID) mass spectra that differ from their unmodified analogues by an enhanced b-ion series in MS2 spectra due to the fixed positive charge. Using LC/MS/MS with an LTQ mass analyzer for quantification, the experimentally determined ratios of H9- to D9-trimethyl-labeled peptides of beta-casein provided accurate estimates of the actual ratios with low % error. IVICAT labeling also accurately quantified proteins in rat kidney inner medullary collecting duct cell types, as judged by comparison with relative quantification by subsequent immunoblotting experiments. IVICAT labeling, when used in conjunction with the new proteomics software QUIL, can accurately report relative protein abundances and increase the sequence coverage of proteins of tissue proteomes.