A measure of the error in wave functions

The quantity ? = (Φ||(H ? E)Φ|) gives a measure of the error in the approximate solution, Φ (with corresponding energy expectation value E), to an eigenfunction of the Hamiltonian operator H of the system under consideration; this quantity vanishes for the exact function ψ. In a percentage scale (with 0% error for the exact function and 100% for a reference, approximate function), the error of Φ may be expressed as 100(?/?_r), where ?_r corresponds to the reference function (e.g., obtained with a minimal basis set). This approach eliminates the need of knowing beforehand the exact solution in order to have an estimate of the error of an approximate solution.     

Preparation and Crystal Structure of Potassium Iron Hydrogen Phosphate,KFe3(HPO4)2(H2PO4)6 · 4 H2O

Single crystals of potassium iron hydrogen phosphate, KFe₃(HPO₄)₂(H₂PO₄)₆ · 4 H₂O, were prepared hydrothermally by heating a mixture of Fe₂O₃, H₃PO₄ and K₂CO₃ with a small amount of water. It crystallizes monoclinic, space group C2/c (N° 15 Int. Tab.) with Z = 4 and a = 1701(2), b = 960.4(5), c = 1750(1) pm, β = 90.88(7)°. The crystal structure was solved by using 1716 unique reflections F₀ > 4σ(F₀) with a final wR2 value of 0.126 (SHELXL-93). The main feature of the crystal structure are layers formed by PO₄-tetrahedra around the FeO₆-octahedra parallel to (001). K⁺ and H₂O molecules connect these layers. Effective Coordination Numbers (ECoN), Mean Fictive Ionic Radii (MEFIR), Charge Distribution (CHARDI) and the Madelung Part of Lattice Energy (MAPLE) are calculated for the title compound. The existence of hydrogen bonds is confirmed by these calculations.     

Application of micellar electrokinetic chromatography to the quality control of a pharmaceutical preparation containing three bronchodilators

Theophylline(1,3-dimethylxanthine), dyphylline [7-(2,3-dihydroxypropyl)theophylline] and proxyphylline [7-(beta-hydroxypropyl)theophylline] are three bronchodilators administered jointly in a single pharmaceutical preparation used against asthma. A micellar electrokinetic chromatography (MEKC) method for their resolution using a background electrolyte consisting of 20 mM tetraborate at pH 8.5 and 100 mM sodium dodecyl sulfate is proposed. The method was used to determine the three active principles in a pharmaceutical preparation. The small amount of sample required and the expeditiousness of the procedure allow content uniformity to be determined in individual tablets. The values of the validation parameters for the method (viz. selectivity, linearity, accuracy, precision, limit of detection, limit of quantitation and robustness) are reported. A complete factor design (2(3)x2) including pH, the surfactant concentration and the ionic strength of the background electrolyte as factors was used to estimate robustness. Based on the results, the method is robust enough for quantitation purposes.     

Physical properties of many-electron atomic systems evaluated from analytical Hartree-Fock functions

The promotion energies, ionization potentials, electron affinities, and orbital electronegativities for the valence states of importance in atoms of the first two rows of the periodic system have been evaluated from analytical Hartree-Fock functions for the corresponding groundstates. The agreement with existing values, determined from experimental data, is very satisfactory.This work has been supported in part by the National Research Council of Canada.     

Stereoselective synthesis of substituted exo-glycals from 1-exo-methylene pyranoses

Halo-exo-glycals of the gluco-, manno- and galacto- series, readily prepared by reaction of 1-exo-methylene pyranoses with iodonium dicollidinium triflate (IDCT), undergo Suzuki or B-alkyl Suzuki cross-coupling reactions with boronic acids or alkyl boranes to yield, in a stereoselective manner, functionalized exo-glycals.     

Physical properties of many-electron atomic systems evaluated from analytical Hartree-Fock functions

Numerical values are presented for the electric field gradients (q) and nuclear quadrupole coupling constants (eqQ) for a series of neutral atoms and their positive and negative ions. The angular dependence of the field gradient integrals is tabulated for configurations involving equivalent p and d electrons, for LS-coupling and central-force-field functions (e.g., Hartree-Fock functions).

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Zusammenfassung Für eine Reihe neutraler Atome und ihre positiven und negativen Ionen werden Zahlenwerte für die elektrischen Feldgradienten (q) und die Kernquadrupolkopplungskonstanten (eqQ) berechnet. Für Konfigurationen, die gleichwertige p- und d-Elektronen enthalten, wird für LS-Kopplung und Zentralkraftfeldfunktionen (z. B. Hartree-Fock-Funktionen) die Winkelabhängigkeit der Feldgradientenintegrale in Tabellenform angegeben.

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Résumé On présente les valeurs numériques pour les gradients de champ (q) et les constantes de couplage quadrupolaire (eqQ) pour des atomes neutres et leurs ions positives et négatives. On a calculé les valeurs des intégrales qui donnent la dependence angulaire du gradient de champ pour des configurations avec des électrons p et d équivalents, pour le couplage LS et fonctions de champ central (par exemple, fonctions de Hartree-Fock).

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This work has been supported in part by the National Research Council of Canada.     

Convergent stereocontrolled synthesis of substituted exo-glycals by Stille cross-coupling of halo-exo-glycals and stannanes

(Z)-exo-Glycals can be conveniently prepared in a convergent manner by Stille cross-coupling of (Z)-halo(Br,I)-exo-glycals and aryl or alkenyl stannanes, the latter are readily obtained by addition of tributylstannyl radicals to terminal alkynes.