Quaternionic spherical wave functions

The scalar spherical wave functions (SWFs) are solutions to the scalar Helmholtz equation obtained by the method of separation of variables in spherical polar coordinates. These functions are complete and orthogonal over a sphere, and they can, therefore, be used as a set of basis functions in solving boundary value problems by spherical wave expansions. In this work, we show that there exists a theory of functions with quaternionic values and of three real variables, which is determined by the Moisil–Theodorescu‐type operator with quaternionic variable coefficients, and which is intimately related to the radial, angular and azimuthal wave equations. As a result, we explain the connections between the null solutions of these equations, on one hand, and the quaternionic hyperholomorphic and anti‐hyperholomorphic functions, on the other. We further introduce the quaternionic spherical wave functions (QSWFs), which refine and extend the SWFs. Each function is a linear combination of SWFs and products of ‐hyperholomorphic functions by regular spherical Bessel functions. We prove that the QSWFs are orthogonal in the unit ball with respect to a particular bilinear form. Also, we perform a detailed analysis of the related properties of QSWFs. We conclude the paper establishing analogues of the basic integral formulae of complex analysis such as Borel–Pompeiu's and Cauchy's, for this version of quaternionic function theory. As an application, we present some plot simulations that illustrate the results of this work. Copyright © 2016 John Wiley & Sons, Ltd.     

Intramolecular Cyclization of Butadiyne Functionalized Ligands coordinated to Triosmium‐Carbonyl Cluster

Reactions between diynes and [Os₃(CO)₁₁(CH₃CN)] in the presence of water give rise to the formation of intriguing hydride triosmium clusters [Os₃(μ‐H)(CO)₉{μ₃,η¹:η³:η¹‐RC₂COHC≡CR}] ( 1a – 1c ) under mild conditions in high yields. When these allylic alcohol compounds 1a – 1c are dissolved in dry polar and donor solvents, an intramolecular cyclization process takes place to give [Os₃(μ‐H)(CO)₉{μ₃,η¹:η³:η¹‐RC₂CH=COCR}] ( 2a – 2c ) in quantitative yield. The utilization of [Os₃(CO)₁₁(CH₃CN)] as starting material together with the addition of water can replace the inconvenient use of [Os₃(μ‐H)₂(CO)₁₀]. This method of synthesis provides a facile pathway for diyne cyclizations and has a clear advantage over those described to date in the literature. Additionally, the analogous cyclized mixed‐metal complex [Os₃(μ‐H)(CO)₉{μ₃,η¹:η³:η¹‐FcC₂CH=COCFc}] ( 2d ) (Fc = ferrocenyl), was synthesized in order to carry out a comparative electrochemical study with the related compounds [Os₃(CO)₁₁(μ₃‐FcC₄Fc)] ( I ) and [Os₃(CO)₁₀(μ₃‐FcC₄Fc)] ( II ), which were previously reported by R. D. Adams.     

Water exchange rates and mechanisms in tetrahedral [Be(H2O)4]2+ and [Li(H2O)4]+ complexes using DFT methods and cluster‐continuum models

The water exchange reactions in aquated Li⁺ and Be²⁺ ions were investigated with density functional theory calculations performed using the [Li(H₂O)₄]⁺·14H₂O and [Be(H₂O)₄]²⁺·8H₂O systems and a cluster‐continuum approach. A range of commonly used functionals predict water exchange rates several orders of magnitude lower than the experimental ones. This effect is attributed to the overstabilization of coordination number four by these functionals with respect to the five‐coordinated transition states responsible for the associative ( A ) or associative interchange ( I_a ) water exchange mechanisms. However, the M06 and M062X functionals provide results in good agreement with the experimental data: M062X/TZVP calculations yield a concerted I_a mechanism for the water exchange in [Be(H₂O)₄]²⁺·8H₂O that gives an average residence time of water molecules in the first coordination sphere of 260 μs. For [Li(H₂O)₄]⁺·14H₂O the water exchange reaction is predicted to follow an A mechanism with a residence time of inner‐sphere water molecules of 25 ps.     

Reinforcement of hydroxypropylcellulose films by cellulose nanocrystals in the presence of surfactants

Hydroxypropylcellulose (HPC) films were prepared by casting with cellulose nanocrystals in the presence of anionic surfactant sodium dodecylsulphate (SDS) and cationic surfactant hexadecyltrimethyl ammonium bromide (CTAB). The cellulose nanocrystals were isolated from maize straw, a biomass source produced in huge quantities as an agrowaste in Brazil. These bionanocomposite films had good transparency and their surface hydrophilic character was evidenced by static contact angle measurements. Thermogravimetry (TGA) measurement revealed that nanocrystals and surfactants changed the thermal stability of the HPC films. Dynamic mechanical analysis (DMA) showed that the tensile storage and loss moduli of the HPC films increased by increasing the contents of cellulose nanocrystals and surfactants, especially in the case of CTAB. This good reinforcing effect of HPC matrix can be explained as due to electrostatic attractive interactions brought about by the presence of CTAB and the nanocrystals.     

Synthesis and second-order nonlinear optical properties of new chromophores containing benzimidazole, thiophene, and pyrrole heterocycles

A new series of thermally stable benzimidazole-based nonlinear optical (NLO) chromophores 4 and 5 have been developed. These chromophores possess a thienylpyrrolyl π-conjugated system attached to functionalized benzimidazole heterocycles. This feature leads to robust chromophores with excellent solvatochromic properties, high thermal stabilities and good molecular optical nonlinearities.     

Taurocholate and taurodeoxycholate: gel formation and protonation constants

Taurocholate (TC) and taurodeoxycholate (TDC) in aqueous solutions, in the presence of sodium and hydrogen ions can give micellar products, even differently protonated. This phenomenon is investigated in this paper to explain whether the assumption of hydrogen ions is to attribute to the micellar aggregates, or to the protonation of taurocholate and taurodeoxycholate, respectively. In the course of this research, often the formation of gel occurred immediately after the mixture of the reagents (sodium, hydrogen ions and anions of bile acids) or after some time, depending on the concentrations of the reagents. No author mentions this evidence, but experiments carried out in the presence of gel are not reproducible because the investigated solutions cannot be considered in real equilibrium. The protonation study was performed by means of electromotive force measurements of a galvanic cell involving a glass electrode, at 25 degrees C and 1.00 mol dm(-3) NaCl, as ionic medium. The obtained protonation constants had the following values: log k1 = 0.07+/- 0.02 for TC and log k'1 = 1.60 +/- 0.03 for TDC.     

Solid-phase microextraction combined with gas chromatography and atomic emission detection for the determination of cyclopentadienylmanganese tricarbonyl and (methylcyclopentadienyl)manganese tricarbonyl in soils and seawaters

A method based on solid-phase microextraction with capillary gas chromatography and microwave-induced plasma atomic emission detection (SPME-GC-MIP-AED) for the determination of cyclopentadienylmanganese tricarbonyl (CMT) and its methyl derivative, (methylcyclopentadienyl)manganese tricarbonyl (MMT) in seawaters and soils was optimized and evaluated. The solvent-free preconcentration step was carried out in the headspace (HS) mode. Element-specific detection and quantification was carried out by monitoring the manganese (259 nm) emission line. A matrix effect was found for the soil samples investigated, so that standard additions were required for their quantification. On the other hand seawaters were analyzed by applying direct calibration against aqueous standards. Detection limits of 13 and 15 pg Mn L(-1) were obtained for CMT and MMT, respectively, in seawaters, and 0.62 and 0.65 pg Mn g(-1), respectively, for the soil samples. The method permitted recoveries of 76-113%, depending on the compound and the sample analyzed, confirming the reliability of the procedure and its suitability for routine monitoring purposes.