A modified steepest descent method with applications to maximizing likelihood functions

In maximizing a non-linear function G(), it is well known that the steepest descent method has a slow convergence rate. Here we propose a systematic procedure to obtain a 1–1 transformation on the variables , so that in the space of the transformed variables, the steepest descent method produces the solution faster. The final solution in the original space is obtained by taking the inverse transformation. We apply the procedure in maximizing the likelihood functions of some generalized distributions which are widely used in modeling count data. It was shown that for these distributions, the steepest descent method via transformations produced the solutions very fast. It is also observed that the proposed procedure can be used to expedite the convergence rate of the first derivative based algorithms, such as Polak-Ribiere, Fletcher and Reeves conjugate gradient methods as well.     

The dangers of using KBr,KI and CaI2 as mulling agents during the preparation of infrared discs of complexes

Tribochemical reactions of KBr, KI and CaI₂ with [Cu(L)Cl₂(EtOH)_3/2(H₂O)]1/2H₂O (L = formylhydrazine) give novel Cu^I and Cu^II complexes, which have been characterized by elemental analyses, spectral (i.r., u.v.–vis., ¹H-n.m.r.) and magnetic measurements. The i.r. spectra indicate that (L) behaves in a monodentate manner, coordinating via the azomethine nitrogen (C-N) group in the Cu^II complexes, but behaving as a bidentate ligand, via the carbonyl oxygen and NH₂ groups in the Cu^I complexes. KI and CaI₂ react with [Cu(L)Cl₂(EtOH)_3/2(H₂O)]-1/2H₂O in the solid state, accompanied by a colour change, substitution of the chloride by iodide ions, and reduction of Cu^II to Cu^I to give complexes with formulae [Cu(L)I(EtOH)_1/2] and [Cu_1.7(L)I_1.7(EtOH)_1/2]. On the other hand, the tribochemical reaction of KBr with [Cu(L)Cl₂(EtOH)_3/2(H₂O)]1/2H₂O is accompanied by a colour change; substitution of the chloride by bromide ions, but without reduction of Cu^II and yields a complex of formula [Cu(L)₂Br₂(EtOH)(H₂O)]1/2EtOH. The spectral and magnetic results suggest a distorted octahedral geometry for the Cu^II complexes while a tetrahedral geometry around the Cu^I ion. The non-stoichiometric structure of [Cu_1.7(L)I_1.7(EtOH)_1/2] is discussed.     

New stereoselective preparation of (Z)-3-perfluoroalkyl-3-magnesiated enoates by an iodine-magnesium exchange reaction

(Z)-Ethyl-3-perfluoroalkyl-3-magnesiated crotonates were prepared from (Z)-ethyl-3-perfluoroalkyl-3-iodo enoates by iodine-magnesium exchange reaction with isopropylmagnesium bromide in THF at -78 degrees C. These new reagents reacted with a range of electrophiles, leading to polyfunctional products bearing a perfluoroalkyl group.     

Enantioseparations by capillary electro-chromatography: differences exhibited by normal- and reversed-phase versions of polysaccharide stationary phases

The influence of using normal-phase and reversed-phase versions of four commercial polysaccharide stationary phases on chiral separations was investigated with capillary electrochromatography (CEC). Both versions of the stationary phases, Chiralcel OD, OJ, and Chiralpak AD, AS were tested for the separation of two basic, two acidic, a bifunctional, and a neutral compound. Different background electrolytes were used, two at low pH for the acid, bifunctional and neutral substances, and three at high pH for the basic, bifunctional and neutral ones. This setup allowed evaluating differences between both stationary-phase versions and between mobile-phase compositions on a chiral separation. Duplicate CEC columns of each stationary phase were in-house prepared and tested, giving information about the intercolumn reproducibility. In general, reversed-phase versions of the current commercial polysaccharide stationary phases are found to be best for reversed-phase CEC, even though at high pH no significant differences were seen between both versions. Most differences were observed at low pH. For acidic compounds, it was seen that an ammonium formate electrolyte performed best, which is also an excellent electrolyte if coupling with mass spectrometry is desired. For basic, bifunctional and neutral compounds, no significant differences between the three tested electrolytes were observed at high pH. Here, a phosphate buffer is preferred as electrolyte because of its buffering capacities. However, if coupling to mass spectrometry is wanted, the more volatile ammonium bicarbonate electrolyte can be used as an alternative.     

Absorption, fluorescence, and semiempirical ASED-MO studies on a typical Brooker''s merocyanine dye

Solvatochromism and Solvatofluorchromism of Brooker's merocyanine 1-methyl-4- (4′-hydroxystyryl) pyridinium betaine, M, were studied in twelve polar protic and aprotic solvents. Moderate hypsochromic fluorescence energy shifts are 4.57 kcal mole⁻¹ while strong hypsochromic absorption energy shifts are 16.63 kcal mole⁻¹. Decreasing of the dipole moment of M upon excitation is the factor, which is responsible for the difference between the two energy shifts. The change of both energies rectilinearly with solvent acidity scale shows the importance of oxygen atom of M as a strong basic center. The application of the atom superposition and electron delocalization molecular orbital (ASED-MO) theory reproduces geometrical and electronic structures for M, which agree well with the experimental observations. The calculations suggest strongly that the dye has a benzenoid valence structure in the ground state and shifts towards a quinonoid one upon excitation with an observed decreasing of the dipole moment. The changing of the dipole moment is explained clearly depending upon the calculated charge distribution over the whole skeleton of the molecule. The formation of a H-bond between the water molecule and the highly negative oxycyclic oxygen atom of M has slightly effect on its dipole moment in the ground state. This leads to suggest that this kind of interaction could be represented as attacking of water with acidic character on the basic site of M. Also, the calculations predict that the formation of monohydrated complex is an exothermic, down hill reaction, which is confirmed from the stabilization of the frontier molecular orbitals, oxygen lone-pair and the HOMO levels.     

Water Activities, Osmotic and Activity Coefficients and Some Correlation of Aqueous Mixtures of Alkaline-Earth and Ammonium Nitrates, NH4NO3-Y(NO3)2-H2O with Y ≡ Ba2+, Mg2+ and Ca2+ at T = 25 °C

The thermodynamic properties of the mixed aqueous electrolyte of ammonium and alkaline earth metal nitrates have been studied using the hygrometric method at 25?°C. The water activities of these {yNH₄NO₃+(1?y)Y(NO₃)₂}(aq) systems with Y ≡ Ba²⁺, Mg²⁺ and Ca²⁺ were measured at total molalities ranging from 0.10 mol?kg^?1 to saturation for different NH₄NO₃ ionic-strength fractions of y=0.20, 0.50 and 0.80. These data allow the calculation of osmotic coefficients. From these measurements, the ionic mixing parameters are determined and used to calculate the solute activity coefficients in the mixtures at different ionic-strength fractions. The results of these ternary solution measurements are compared with those for binary solutions of the alkaline earth nitrates of magnesium, calcium and barium with ammonium nitrates. The behavior of the aqueous electrolyte solutions containing mixtures of barium or calcium or magnesium with ammonium nitrates are correlated and show that ionic interactions are more important for the system containing Mg²⁺ than for Ca²⁺ or Ba²⁺. The trends are mainly due to the effects of the ionic size, polarizability and the hydration of the ions in these solutions.     

Conservation of [(C2H4NH3)3N]2·(ZrF7)2·H2O layers during the topotactic dehydration of [(C2H4NH3)3N]2·(ZrF7)2·9H2O

Tren amine cations [(C₂H₄NH₃)₃N]³⁺ and zirconate or tantalate anions adopt a ternary symmetry in two hydrates, [H₃tren]₂·(ZrF₇)₂·9H₂O and [H₃tren]₆·(ZrF₇)₂·(TaOF₆)₄·3H₂O, which crystallise in R32 space group with a_H = 8.871 (2) Å, c_H = 38.16 (1) Å and a_H = 8.758 (2) Å, c_H = 30.112 (9) Å, respectively. Similar [H₃tren]₂·(MX₇)₂·H₂O (M = Zr, Ta; X = F, O) sheets are found in both structures; they are separated by a water layer (O_w(2)-O_w(3)) in [H₃tren]₂·(ZrF₇)₂·9H₂O. Dehydration of [H₃tren]₂·(ZrF₇)₂·9H₂O starts at room temperature and ends at 90 °C to give [H₃tren]₂·(ZrF₇)₂·H₂O. [H₃tren]₂·(ZrF₇)₂·H₂O layers remain probably unchanged during this dehydration and the existence of one intermediate [H₃tren]₂·(ZrF₇)₂·3H₂O hydrate is assumed. O_w(1) molecules are tightly hydrogen bonded with -NH₃⁺ groups and decomposition of [H₃tren]₂·(ZrF₇)₂·H₂O occurs from 210 °C to 500 °C to give successively [H₃tren]₂·(ZrF₆)·(Zr₂F₁₂) (285 °C), an intermediate unknown phase (320 °C) and ZrF₄.     

Unveiling Carbon Dioxide and Ethanol Diffusion in Carbonated Water-Ethanol Mixtures by Molecular Dynamics Simulations

The diffusion of carbon dioxide (CO2) and ethanol (EtOH) is a fundamental transport process behind the formation and growth of CO2 bubbles in sparkling beverages and the release of organoleptic compounds at the liquid free surface. In the present study, CO2 and EtOH diffusion coefficients are computed from molecular dynamics (MD) simulations and compared with experimental values derived from the Stokes-Einstein (SE) relation on the basis of viscometry experiments and hydrodynamic radii deduced from former nuclear magnetic resonance (NMR) measurements. These diffusion coefficients steadily increase with temperature and decrease as the concentration of ethanol rises. The agreement between theory and experiment is suitable for CO2. Theoretical EtOH diffusion coefficients tend to overestimate slightly experimental values, although the agreement can be improved by changing the hydrodynamic radius used to evaluate experimental diffusion coefficients. This apparent disagreement should not rely on limitations of the MD simulations nor on the approximations made to evaluate theoretical diffusion coefficients. Improvement of the molecular models, as well as additional NMR measurements on sparkling beverages at several temperatures and ethanol concentrations, would help solve this issue.     

Efficient Oxidation of Cyclohexane over Bulk Nickel Oxide under Mild Conditions

Nickel oxide powder was prepared by simple calcination of nickel nitrate hexahydrate at 500 °C for 5 h and used as a catalyst for the oxidation of cyclohexane to produce the cyclohexanone and cyclohexanol—KA oil. Molecular oxygen (O₂), hydrogen peroxide (H₂O₂), t-butyl hydrogen peroxide (TBHP) and meta-chloroperoxybenzoic acid (m-CPBA) were evaluated as oxidizing agents under different conditions. m-CPBA exhibited higher catalytic activity compared to other oxidants. Using 1.5 equivalent of m-CPBA as an oxygen donor agent for 24 h at 70 °C, in acetonitrile as a solvent, NiO powder showed exceptional catalytic activity for the oxidation of cyclohexane to produce KA oil. Compared to different catalytic systems reported in the literature, for the first time, about 85% of cyclohexane was converted to products, with 99% KA oil selectivity, including around 87% and 13% selectivity toward cyclohexanone and cyclohexanol, respectively. The reusability of NiO catalyst was also investigated. During four successive cycles, the conversion of cyclohexane and the selectivity toward cyclohexanone were decreased progressively to 63% and 60%, respectively, while the selectivity toward cyclohexanol was increased gradually to 40%.