Rational approximations,software and test methods for sine and cosine integrals

Rational approximations to the sine integralSi(x) and cosine-integralCi(x) are developed which give an accuracy of 20sf. The robust construction of software for these functions is discussed, together with a test procedure for assessing the performance of such codes. Use of the tests discovers a major error in the netlib library FN codes forSi. Fortran versions of the codes and tests are available by electronic mail.     

Finite‐size corrections at the hard edge for the Laguerre β ensemble

A fundamental question in random matrix theory is to quantify the optimal rate of convergence to universal laws. We take up this problem for the Laguerre β ensemble, characterized by the Dyson parameter β, and the Laguerre weight , in the hard edge limit. The latter relates to the eigenvalues in the vicinity of the origin in the scaled variable . Previous work has established the corresponding functional form of various statistical quantities—for example, the distribution of the smallest eigenvalue, provided that . We show, using the theory of multidimensional hypergeometric functions based on Jack polynomials, that with the modified hard edge scaling , the rate of convergence to the limiting distribution is , which is optimal. In the case , general the explicit functional form of the distribution of the smallest eigenvalue at this order can be computed, as it can for and general . An iterative scheme is presented to numerically approximate the functional form for general .     

The calculation of pH

A model for the pH of a mixture of a monoprotic acid and its associated salt leads to a cubic equation. This equation is shown to have real roots — one positive and two negative. The exact theory for cubic equations provides a simple expression for the positive root. Due to rounding errors the use of this formula can give poor results, so the use of Newton‐Raphson is considered.     

A Computational and Experimental Approach Linking Disorder,High‐Pressure Behavior,and Mechanical Properties in UiO Frameworks

Whilst many metal–organic frameworks possess the chemical stability needed to be used as functional materials, they often lack the physical strength required for industrial applications. Herein, we have investigated the mechanical properties of two UiO‐topology Zr‐MOFs, the planar UiO‐67 ([Zr₆O₄(OH)₄(bpdc)₆], bpdc: 4,4′‐biphenyl dicarboxylate) and UiO‐abdc ([Zr₆O₄(OH)₄(abdc)₆], abdc: 4,4′‐azobenzene dicarboxylate) by single‐crystal nanoindentation, high‐pressure X‐ray diffraction, density functional theory calculations, and first‐principles molecular dynamics. On increasing pressure, both UiO‐67 and UiO‐abdc were found to be incompressible when filled with methanol molecules within a diamond anvil cell. Stabilization in both cases is attributed to dynamical linker disorder. The diazo‐linker of UiO‐abdc possesses local site disorder, which, in conjunction with its longer nature, also decreases the capacity of the framework to compress and stabilizes it against direct compression, compared to UiO‐67, characterized by a large elastic modulus. The use of non‐linear linkers in the synthesis of UiO‐MOFs therefore creates MOFs that have more rigid mechanical properties over a larger pressure range.     

Addition of HCl to a Cluster-Bound Vinylidene Ligand: Preparation and Structure of Ru5(μ3-SMe)(μ3-CMe)(μ-Cl)(μ-SMe)(μ-PPh2)2(CO)9·PhMe

Addition of aqueous HCl to Ru₅( ₃-C=CH₂)(-SMe)₂(-PPh₂)₂(CO)₁₀ afforded the structurally characterized carbyne complex Ru₅( ₃-SMe)( ₃-CMe)(-Cl)(-SMe)(-PPh₂)₂(CO)₉, formed by addition of H to the vinylidene ligand; a Cl atom bridges an Ru–Ru bond.     

Carbonyl substitution chemistry of some trimetallic transition metal cluster complexes with polyfunctional ligands

The trimetallic clusters [Ru₃(CO)₁₀(dppm)], [Ru₃(CO)₁₂] and [RuCo₂(CO)₁₁] react with a number of multifunctional secondary phosphine and tertiary arsine ligands to give products consequent on carbonyl substitution and, in the case of the secondary phosphines, PH activation. The reaction with the unresolved mixed P/S donor, 1-phenylphosphino-2-thio(ethane), HSCH₂CH₂PHPh ( LH₂), gave two products under various conditions which have been characterised by spectroscopic and crystallographic means. These two complexes [Ru₃(μ-dppm)(H)(CO)₇(LH)] and [Ru₃(μ-dppm)(H)(CO)₈(LH)Ru₃(μ-dppm)(CO)₉], show the versatility of the ligand, with it chelating in the former and bridging two Ru₃ units in the latter. The stereogenic centres in the molecules gave rise to complicated spectroscopic data which are consistent with the presence of diastereoisomers. In the case of [Ru₃(CO)₁₂] the reaction with LH₂ gave a poor yield of a tetranuclear butterfly cluster, [Ru₄(CO)₁₀(L)₂], in which two of the ligands bridge opposite hinge wingtip bonds of the cluster. A related ligand, HSCH₂CH₂AsMe(C₆H₄CH₂OMe), reacted with [RuCo₂(CO)₁₁] to give a low yield of the heterobimetallic Ru-Co adduct, [RuCo(CO)₆(SCH₂CH₂AsMe(C₆H₄CH₂OMe))], which appears to be the only one of its type so far structurally characterised.The secondary phosphine, HPMe(C₆H₄(CH₂OMe)) and its oxide HP(O)Me(C₆H₄(CH₂OMe)) also react with the cluster [Ru₃(CO)₁₀(dppm)] to give carbonyl substitution products, [Ru₃(CO)₅(dppm)(μ₂-PMe(C₆H₄CH₂OMe))₄], and [Ru₃H(CO)₇(dppm)(μ₂,η¹-P(O)Me(C₆H₄CH₂OMe))]. The former consists of an open Ru₃ triangle with four phosphide ligands bridging the metal-metal bonds; the latter has the O atom symmetrically bridging one Ru-Ru bond, the P atom being attached to a non-bridged Ru atom.     

Photosensitizers derived from 132-oxo-methyl pyropheophorbide-a: enhanced effect of indium(III) as a central metal in in vitro and in vivo photosensitizing efficacy

The effects of an additional keto group on absorption wavelength and the corresponding metal complexes Zn(II), Cu(II) In(III) on singlet oxygen production and photodynamic efficacy were examined among the alkyl ether analogs of pyropheophorbide-a. For the preparation of the desired photosensitizers, the methyl 13(2)-oxo-pyropheophorbide-a obtained by reacting methyl pyropheophorbide-a with aqueous LiOH-THF was converted into a series of alkyl ether analogs. These compounds were evaluated for photophysical properties and in vitro (by means of the MTT assay and intracellular localization in RIF cells) and in vivo (in C3H mice implanted with RIF tumors) photosensitizing efficacy. Among the alkyl ether derivatives, the methyl 3-decyloxyethyl-3-devinyl-13(2)-oxo-pyropheophorbide-a was found to be most effective and the insertion of In(III) into this analog further enhanced its in vitro and in vivo photosensitizing efficacy. Fluorescence microscopy showed that, in contrast to the hexyl and dodecyl ether derivatives of HPPH (which localize in mitochondria and lysosomes, respectively), the diketo-analogs and their In(III) complexes localized in Golgi bodies. The preliminary in vitro and in vivo results suggest that, in both free-base and metalated analogs, the introduction of an additional keto group at the five-member exocyclic ring in pyropheophorbide-a diminishes its photosensitizing efficacy. This may be due to a shift in subcellular localization from mitochondria to the Golgi bodies. The further introduction of In(III) enhances photoactivity, but not by shifting the localization of the photosensitizer.     

An experimental and theoretical study of the reactions OIO+NO and OIO+OH

The kinetics of the reaction OIO+NO were studied by pulsed laser photolysis/time-resolved cavity ring-down spectroscopy, yielding k(235-320 K)=7.6(+4.0)(-3.1) x 10(-13) exp[(607+/-128)/T] cm3 molecule-1 s-1. Quantum calculations on the OIO+NO potential-energy surface show that the reactants form a weakly bound OIONO intermediate, which then dissociates to the products IO+NO2. Rice-Ramsberger-Kassel-Markus (RRKM) calculations on this surface are in good accord with the experimental result. The most stable potential product, IONO2, cannot form because of the significant rearrangement of OIONO that would be required. The reaction OIO+OH was then investigated by quantum calculations of the relevant stationary points on its potential-energy surface. The very stable HOIO2 molecule can form by direct recombination, but the bimolecular reaction channels to HO2+IO and HOI+O2 are closed because of significant energy barriers. RRKM calculations of the HOIO2 recombination rate coefficient yield krec,0=1.5x10(-27) (T/300 K)(-3.93) cm6 molecule-2 s-1, krec,infinity=5.5x10(-10) exp(46/T) cm3 molecule-1 s-1, and Fc=0.30. The rate coefficients of both reactions are fast enough around 290 K and 1 atm pressure for these reactions to play a potentially important role in the gas phase and aerosol chemistry in the marine boundary layer of the atmosphere.     

Reactive uptake of NO3, N2O5, NO2, HNO3, and O3 on three types of polycyclic aromatic hydrocarbon surfaces

We investigated the reactive uptake of NO3, N2O5, NO2, HNO3, and O3 on three types of solid polycyclic aromatic hydrocarbons (PAHs) using a coated wall flow tube reactor coupled to a chemical ionization mass spectrometer. The PAH surfaces studied were the 4-ring systems pyrene, benz[a]anthracene, and fluoranthene. Reaction of NO3 radicals with all three PAHs was observed to be very fast with the reactive uptake coefficient, gamma, ranging from 0.059 (+0.11/-0.049) for benz[a]anthracene at 273 K to 0.79 (+0.21/-0.67) for pyrene at room temperature. In contrast to the NO3 reactions, reactions of the different PAHs with the other gas-phase species (N2O5, NO2, HNO3, and O3) were at or below the detection limit (gamma 相似文献