The exact expression of the Voigt profile function

We solve in exact and closed-form a classical problem of mathematical physics of great interest in spectroscopy: the convolution of a Gaussian and a Lorentzian distribution that define the Voigt profile function, V(x). The solution is based in three steps: a power series development following the integral expression for V(x), the ordinary differential equation (ODE) satisfied by that expansion, and the corresponding solution of the ODE. This work converts in obsolete all graphical, numerical and semi-analytical approximations published previously. All results are clearly expressed in terms of the complementary error function Φ_c(a)=1-erf(a), where is, basically, the relation between Lorentzian and Gaussian widths.     

A heuristic screening approach for atoms includingl-splitting

Summary  TheZ-expansion theory of Atomic Structure is supplemented with the inclusion of the external screening concept, calculated from a simplified version of the works of M. Kregar, where the two-body potential energy operators are split into the sum of effective one-body operators. The use ofZ- andN-dependent screening parameters instead of screening constants, gives a simplified Screened Hydrogenic Model which compares favourably with more sophisticated methods, specially for ionized atoms. The author of this paper has agreed to not receive the proofs for correction. Member of the Consejo Nacional de Investigaciones Cientificas y Tecnicas, Argentina, and Associate Member ICTP (Trieste, Italy).     

Enlarging the size of calix[4]arene-crowns-6 to improve Cs/K selectivity: a theoretical and experimental study

Ab initio calculations in the gas-phase indicate that the substitution of an ethylene with a propylene moiety in the polyether bridge of 1,3-di-iso-propoxycalix[4]arene-crowns-6 could result in an enhanced Cs⁺/K⁺ selectivity which is of particular interest in nuclear waste treatment. We therefore synthesised two novel calix[4]arene-crown-6 compounds (1 and 2) having a propylene moiety in their structure and for this named calix[4]arene-propylene-crown-6. The structures of compounds 1 and 2 were elucidated by NMR in solution and for 1 also by X-ray diffraction studies in the solid state. Association constants (K_a) in CHCl₃ of the two novel calix-crowns were measured and pointed out a plateau selectivity towards alkali metal ions which was not predicted by molecular modelling calculations. These results indicate the important role played by the solvent molecules and counter-anions in binding for this class of ionophores.     

Palladium-Catalyzed Low Pressure Carbonylation of Allylic Alcohols by Catalytic Anhydride Activation

A direct carbonylation of allylic alcohols has been realized for the first time with high catalyst activity at low pressure of CO (10 bar). The procedure is described in detail for the carbonylation of E-nerolidol, an important step in a new BASF-route to (−)-ambrox. Key to high activities in the allylic alcohol carbonylation is the finding that catalytic amounts of carboxylic anhydride activate the substrate and are constantly regenerated with carbon monoxide under the reaction conditions. The identified reaction conditions are transferrable to other substrates as well.     

Evidence for cation-π interactions in calixcrown·KPic complexes from X-ray crystal structure analysis and energy calculations

Abstract

The crystal and molecular structures of the 1,3-diisopropoxy-p-tertbutyl calix[4]arene crown-5 fixed in the partial cone conformation and that of its potassium picrate salt have been determined by single crystal X-ray diffraction studies. Energy calculations have been performed to gain more insight on the stabilizing cation…ligand interactions. The calculation of the total potential energy indicates that the contribution which comes from the electrostatic polarization induced by the electric field of the cation on the rotated nucleus gives a net stabilizing contribution of almost 6 kcal/mol. A comparison between the molecular geometry of some partial cone 1,3-disubstituted-p-tertbutylcalix[4]arene derivatives is reported and discussed in view of the preorganization principle.     

New Calix[4]arene-monobenzo- and -dibenzo-crown-6 as Cesium Selective Ionophores in the Radioactive Waste Treatment: Synthesis, Complexation and Extraction Properties

Cesium possesses two long lived isotopes ¹³⁵Cs and ¹³⁷Cs and the first one has a very long (2.3 × 10⁶ y) half life and is one of the most mobile nuclides in a repository.Calix[4]arene-crowns-6 in the 1,3-alternate conformation areemerging as a new class of ionophores exhibiting a very high efficiency and selectivity in the complexation of cesium ion and itsremoval from highly acidic ([HNO₃] = 3–4 M) radioactive waste having also high sodium nitrate concentration ([NaNO₃] = 2–4 M). In order to improve both efficiency and cesium selectivity we have synthesised the novel calix[4]arene dibenzo-crowns-6 1 and 2 and thecalix[4]arene-monobenzocrown-6 3 in 1,3-alternate conformationand evaluated their complexation properties towards alkali metal cations in homogeneous solution and in two phase systems, togetherwith their performance in radioactive waste treatment. All data confirm the higher Cs/Na selectivity of the 1,3-alternate calix[4]crown-6 1–3 containing aromatic rings in the polyether loop, in comparison to previously synthesised compounds of the same series.     

Water soluble calix[4]arenes. A thermodynamic investigation of proton complex formation

Abstract

Thermodynamic parameters of protonation of calix[4]arene-p-tetra sulphonate were potentiometrically and calorimetrically determined in aqueous solution at 25 °C and I = 0.1 mol dm^?3 (NaNO₃). These values were compared with literature findings. ΔH° and ΔS° values reveal that the penta-anion protonation is energetically costly. In this connection the role played by hydrogen bonding and the cone conformation stabilization are critically discussed. Proton formation constants of the calix[4]arene-p-tetrasulphonate-tetra-carboxylate derivative in the cone conformation were also potentiometrically determined under the same experimental conditions.     

An advanced multivariate approach for processing X-ray fluorescence spectral and hyperspectral data from non-invasive in situ analyses on painted surfaces

In the last decades, in situ non-invasive analytical techniques have been widely used for the analysis of paintings. These techniques are useful to extensively map the surface in a non-invasive way, in order to identify the most representative areas to be sampled. When spectroscopic investigations, such as X ray fluorescence (XRF), are conducted, they usually imply the acquisition of a huge amount of measurements. Subsequently, all these data should be processed in situ, in order to immediately support the sampling strategies. To this aim, an appropriate and fast strategy for multivariate treatment of XRF spectral and hyperspectral data sets is presented, able to account for inter-correlation among variables, which is an issue of high importance for elemental analyses. The main advantage of the approach is that XRF spectral profiles are analysed directly, without computation of derived parameters, by means of principal component analysis (PCA). This procedure allows a fast interpretation of results that can be accomplished in situ. Particular attention was paid to the selection of proper spectral pre-treatments to be applied on data together with the use of several chemometric tools (peak alignment, spectra normalisation and exploratory analysis) aimed at improving the interpretation of XRF results. In addition, the application of multivariate exploratory analysis on XRF hyperspectral maps was studied by using an interactive brushing procedure. The multivariate approach was validated on data obtained from the analysis of the famous Renaissance panel painting “The Ideal City”, exhibited in Palazzo Ducale of Urbino, Italy.     

Optical isomer separation of flavanones and flavanone glycosides by nano-liquid chromatography using a phenyl-carbamate-propyl-β-cyclodextrin chiral stationary phase

In this paper a phenyl-carbamate-propyl-β-cyclodextrin stationary phase was employed for the enantioseparation of several flavonoids, including flavanones and methoxyflavanones by using nano-liquid chromatography (nano-LC). The same stationary phase was also used for the diastereoisomeric separation of two flavanone glycosides. The compounds: flavanone, 2′-hydroxyflavanone, 4′-hydroxyflavanone, 6-hydroxyflavanone, 7-hydroxyflavanone, 4′-methoxyflavanone, 6-methoxyflavanone, 7-methoxyflavanone, hesperetin, hesperidin, naringenin and naringin were studied using reversed, polar organic and normal elution modes. The effect of the nature and composition of the mobile phase (organic modifier type, buffer and water content in the reversed phase mode) on the enantioresolution (R_s), retention factor (k) and enantioselectivity (α) were investigated. Baseline resolution of all studied flavonoids, with the exception of 2′-hydroxyflavanone and naringin, was achieved in reversed phase mode using a mixture of MeOH/H₂O at different ratios as mobile phase. Good results, in terms of peak efficiency and short analysis time, were obtained adding 1% triethylammonium acetate pH 4.5 buffer to MeOH/H₂O mixture. The separation of the studied compounds was also performed in polar organic mode. By using 100% of MeOH as mobile phase, the resolution was achieved for the studied analytes, except for 7-hydroxyflavanone, 2′-hydroxyflavanone, naringenin, hesperidin and naringin. Normal mode was tested employing a mixture of EtOH/hexane/TFA as mobile phase achieving the enantiomeric and diastereomeric separation of only hesperetin and hesperidin, respectively. The use of nano-LC technique for the resolution of flavanones optical isomers allowed to achieve good resolutions in shorter analysis time compared to the results reported in literature with conventional HPLC.