Role of Hartree-Fock and Kohn-Sham orbitals in the basis set superposition error for systems linked by hydrogen bonds

In this work the effect of the basis set superposition error (BSSE) is explored with the counterpoise method on the occupied and unoccupied Hartree-Fock (HF) and Kohn-Sham (KS) orbitals. Three different systems linked by hydrogen bonds, H(2)O...FH, H(2)O...H(2)O, and H(2)O...CFH(3), were studied by using the basis set families cc-pVXZ and aug-cc-pVXZ (X = D, T, Q). The basis sets were tested with the HF method and two approximations for the exchange-correlation functional of KS: a generalized gradient approximation and a hybrid approach. In addition to these methods, the second-order M?ller-Plesset perturbation theory, MP2, was considered. It was found that the presence of the "ghost" basis set affects the orbitals in two ways: (1) The occupied KS orbitals are more sensitive to the presence of this "ghost" basis set than the occupied HF orbitals. For this reason the BSSE observed in HF is less than that obtained with KS. (2) The unoccupied HF orbitals are more sensitive to the presence of the "ghost" basis set than their corresponding occupied orbitals. Because the MP2 method uses both, occupied and unoccupied HF orbitals, to compute the total energy, the contribution of the BSSE is bigger than that obtained with HF or KS methodologies.     

As, Bi, Sb and Sn determination in atmospheric particulate matter by direct solid sampling-hydride generation-electrothermal atomic absorption spectrometry

A novel, rapid and simple method by hydride generation-electrothermal atomic absorption spectrometry (HG-ETAAS) after direct As, Bi, Sb and Sn hydrides generation from untreated filters of atmospheric particulate matter (PM₁₀ and PM_2.5) was optimised. PM₁₀ and PM_2.5 were not subjected to any pre-treatment: circular portions between 0.28 and 6.28 cm² were directly placed into the reaction vessel of a batch mode generation system. A 2⁸ × 3/64 Plackett–Burman design was used as a multivariate strategy for the evaluation of the effects of several variables affecting the hydride generation, trapping and atomisation efficiencies. Trapping temperature was the most statistically significant variable for As, Bi and Sn. Atomisation temperature was also statistically significant for Sb determination. Optimum values of significant variables were selected by using univariate optimisation approaches. An aqueous calibration method was used throughout. The developed method has been found to be precise with relative standard deviations of 6.2, 5.3, 9.1 and 7.5% for 11 determinations in a filter sample containing 0.7, 1.0, 1.4 and 1.7 μg l⁻¹ for As, Bi, Sb and Sn, respectively. Results obtained by direct solid sampling-HG-ETAAS have been found statistically comparable with those obtained after conventional method based on an acid digestion followed to ICP-MS. Absolute detection limits were 37, 15, 30, and 41 ng l⁻¹ for As, Bi, Sb and Sn, respectively. Detection limits referred to the air volume sampled (in the range of 0.020–0.050 ng m⁻³) were low enough for the determination of several hydride-forming elements from PM₁₀ and PM_2.5 samples collected in a non-polluted suburban area of A Coruña (NW Spain).     

Symmetry numbers and chemical reaction rates

This article shows how to evaluate rotational symmetry numbers for different molecular configurations and how to apply them to transition state theory. In general, the symmetry number is given by the ratio of the reactant and transition state rotational symmetry numbers. However, special care is advised in the evaluation of symmetry numbers in the following situations: (i) if the reaction is symmetric, (ii) if reactants and/or transition states are chiral, (iii) if the reaction has multiple conformers for reactants and/or transition states and, (iv) if there is an internal rotation of part of the molecular system. All these four situations are treated systematically and analyzed in detail in the present article. We also include a large number of examples to clarify some complicated situations, and in the last section we discuss an example involving an achiral diasteroisomer.     

Reactions of Sulphate Radicals with Substituted Pyridines: A Structure–Reactivity Correlation Analysis

The kinetics of the oxidation of pyridine, 3‐chloropyridine, 3‐cyanopyridine, 3‐methoxypyridine and 3‐methylpyridine mediated by SO₄ ^{< M ‐>} radicals are studied by flash photolysis of peroxodisulphate, S₂O₈^2?, at pH 2.5 and 9. The absolute rate constants for the reactions of both, the basic and acid forms of the pyridines, are determined and discussed in terms of the Hammett correlation. The monosubstituted pyridines react about 10 times faster with sulphate radicals than their protonated forms, the pyridine ions. The organic intermediates are identified as the corresponding hydroxypyridine radical adducts and their absorption spectra compared with those estimated employing the time‐dependent density functional theory with explicit account for bulk solvent effects. A reaction mechanism which accounts for the observed intermediates and the pyridinols formed as products is proposed.     

Analysis of mono- and disaccharides in milk-based formulae by high-performance liquid chromatography with refractive index detection

A simple and reproducible method for the qualitative and quantitative analysis of free mono- and disaccharides (fructose, glucose, galactose, sucrose, lactulose and lactose) in milk-based formulae by high-performance liquid chromatography (HPLC) with refractive index (RI) detection was developed and validated. The method showed good linearity with determination coefficients exceeding 0.99. The limits of detection (DL) in these sugars were 0.17, 0.13, 0.06, 0.16, 0.05 and 0.25 mg/ml, respectively; and the limits of quantification (QL), 0.27, 0.24, 0.20, 0.26, 0.22 and 0.38 mg/ml. The relative standard deviations (R.S.D.s) for repeatability in fructose, sucrose, lactulose and lactose were 0.78, 0.99, 2.91 and 0.46 and the R.S.D.s for reproducibility were 4.8, 6.15, 7.04 and 2.49, respectively. Recoveries in all sugars were between 93 and 113%.     

Static headspace analysis of volatile organic compounds in soil and vegetation samples for site characterization

Traditional methodologies for the characterization of volatile organic compounds (VOCs) in subsurface soil are expensive, time-consuming processes that are often conducted on samples collected at random. The determination of VOCs in near-surface soils and vegetation is the foundation for a more efficient sampling strategy to characterize subsurface soil and improve understanding of environmental problems.In the absence of a standard methodology for the determination of VOCs in vegetation and in view of the high detection limits of the method for soils, we developed a methodology using headspace gas chromatography with an electron capture detector for the determination of low levels (parts-per-billion to parts-per-trillion) of VOCs in soils and vegetation. The technique demonstrates good sensitivity, good recoveries of internal standards and surrogate compounds, good performance, and minimal waste. A case study involving application of this technique as a first-step vadose-zone characterization methodology is presented.     

On the polynomial τ-functions for the KP hierarchy and the bispectral property

We show that the -functions obtained from Schur polynomials lead to wave functions w(x ₁, x ₂, ... ; k) that possess the following bispectral property: There exists a differential operator B{k,_k}, independent of x ₁ , such that B{k,_k}w = {x ₁}w, where {x ₁} is independent of k. This extends for the KP hierarchy some earlier results of J. J. Duistermaat and F. A. Grünbaum for the rational solutions of KdV and of P. Wright for certain rational solutions of the generalized KdV equations.     

Signatures andS-discrete lattice-ordered groups

The central theme of this article is the approximation of lattice-ordered groups (l-groups) first by Specker groups and, subsequently, by the so-calledS-discretel-groups. The sense of these approximations is made precise via the notion of a signature, defined below, and by that ofa ^*-subgroups. Sample result: ifG is a projectablel-group then it has anl-subgroupH which is Specker and for which the mapPPH defines a boolean isomorphism between the algebras of polars ofG andH.Presented by L. Fuchs.This article was written while this author was a Stouffer Visiting Professor at the University of Kansas. He wishes to thank the members of the Mathematics Department of that institution for their hospitality.     

Analysis of natural flavonoids by microchip-micellar electrokinetic chromatography with pulsed amperometric detection

Catechins (catechin and other derivatives) are naturally occurring flavonoids present in a number of plants and foods. They are also part of numerous nutraceutical formulations because they are believed to have antioxidant, cancer chemo-preventative, anti-inflammatory and antimicrobial properties. The determination of catechins has traditionally been performed by HPLC. However, this methodology is both time and sample intensive and generates large amounts of organic solvent waste. In the current report, an application of MEKC using a PDMS microchip is presented for the analysis of catechins. The system uses pulsed amperometric detection for direct analysis of important naturally occurring catechins. The effect of pH, surfactant concentration, detection potential and signal stability were analyzed. Linear relationships were found between the concentration and peak current, with good stability and limits of detection of 8 [micro sign]M for catechin, epigallocatechin gallate and epicatechin, and 14 [micro sign]M for epicatechin gallate. Optimum conditions were applied to the detection of selected catechins in a commercially available green tea extract nutraceutical and the results were compared to HPLC analysis. The analysis using microchip micellar electrokinetic chromatography and pulsed amperometric detection was completed in 4.5 min, 10 times faster than the HPLC analysis.