Analysis of supramolecular interactions in alendroniate alkali metal salts: synthesis,structure, and properties of novel sodium alendronate polymorph

A new polymorph of anhydrous sodium alendronate, C₄H₁₂NO₇P₂Na, has been synthesized and characterized by single crystal X-ray diffraction as well as infrared spectroscopy and thermal analysis. The title compound crystallizes in the monoclinic P2₁/c space group. Asymmetric unit consists of one alendronic anion and one sodium cation. An interplay of classical strong O-H^…O, N-H^…O and non-classical weak C-H^…O hydrogen bonds creates 3D framework in the crystal. Contrary to previously reported sodium alendronate salts, in which Na⁺ cation is surrounded by six-coordinated sphere, in compound (1), the Na⁺ cation is five-coordinated in a distorted trigonal-bipyramidal geometry. In order to provide a detailed investigation of the molecular arrangement in view of intermolecular interactions, the title compound was compared with alendronic acid and other known alkali metal alendronate salts, retrieved from the Cambridge Crystal Structure Database. The intercontacts were qualitatively and quantitatively compared using Hirshfeld surface analysis. It highlights that strong O^…H/H^…O and subtle H^…H contacts play an influential role in the total surface area. The Me^+…H/H^…Me⁺ and Me^+…O/O^…Me⁺ contacts are meaningful as well. These evidently simple systems show a diverse complexity. Moreover, the powder X-ray diffraction, DSC, thermogravimetry/derivative thermogravimetry, and FT-IR results are also reported.

     

Estimating a density and its derivatives via the minimum distance method

Summary This paper deals with minimum distance (MD) estimators and minimum penalized distance (MPD) estimators which are based on the L _p distance. Rates of strong consistency of MPD density estimators are established within the family of density functions which have a bounded m-th derivative. For the case p=2, it is also proved that the MPD density estimator achieves the optimum rate of decrease of the mean integrated square error and the L ₁ error. Estimation of derivatives of the density is considered as well.In a class parametrized by entire functions, it is proved that the rate of convergence of the MD density estimator (and its derivatives) to the unknown density (its derivatives) is of order in expected L ₁ and L ₂ distances. In the same class of distributions, MD estimators of unknown density and its derivatives are proved to achieve an extraordinary rate (log log n/n)^1/2 of strong consistency.     

A specialised cyclic reduction algorithm for linear algebraic equation systems with quasi-tridiagonal matrices

Extensions have been developed, of several variants of the stride of two cyclic reduction method. The extensions refer to quasi-tridiagonal linear equation systems involving two additional nonzero elements in the first and last rows of the equation matrix, adjacent to the main three diagonals. Equations of this kind arise, for example, in the simulations of biosensors or other electrochemical systems by solving relevant ordinary or partial differential equations by finite difference methods, when boundary derivatives are approximated by one-sided, multipoint finite differences. The correctness of the algorithms developed has been verified using example matrices with pseudo-random coefficients, under conditions of both sequential and parallel execution.     

On Center Cycles in Grid Graphs

Finding good cycles in graphs is a problem of great interest in graph theory as well as in locational analysis. We show that the center and median problems are NP-hard in general graphs. This result holds both for the variable cardinality case (i.e., all cycles of the graph are considered) and the fixed cardinality case (i.e., only cycles with a given cardinality p are feasible). Hence it is of interest to investigate special cases where the problem is solvable in polynomial time. In grid graphs, the variable cardinality case is, for instance, trivially solvable if the shape of the cycle can be chosen freely. If the shape is fixed to be a rectangle one can analyze rectangles in grid graphs with, in sequence, fixed dimension, fixed cardinality, and variable cardinality. In all cases a complete characterization of the optimal cycles and closed form expressions of the optimal objective values are given, yielding polynomial time algorithms for all cases of center rectangle problems. Finally, it is shown that center cycles can be chosen as rectangles for bounded cardinalities such that the center cycle problem in grid graphs is in these cases completely solved.     

Comparison of linear and non-linear equations for univariate calibration

Univariate data accumulated for the purpose of calibration of chromatographic and spectroscopic methods often exhibit slight but definite curvature. In this paper the performance of a non-linear calibration equation with the capacity to account empirically for the curvature, y = a + bx(m), (m not equal to 1) is compared with the commonly used linear equation, y = a + bx, as well as the quadratic equation, y = a + bx + cx2. All equations were applied to high quality HPLC calibration data using unweighted least squares. Parameter estimates and their standard errors were calculated for each equation. Standard errors and 95% prediction intervals in analyte concentrations were estimated with the aid of the fitted equations and their respective covariance matrices. Results indicate that the non-linear and quadratic equations each provide a better fit than the linear equation to the data considered here, as judged by the Akaikes information criterion (AIC), the adjusted coefficient of multiple determination, the magnitude and scatter of residuals, standard errors in estimated analyte concentrations and lack of fit analysis of variance (ANOVA). While the difference between the equations y = a + bx + cx2 and y = a + bx(m) as judged by the same criteria is more marginal, this work suggests that the non-linear calibration equation should be considered when a curve is required to be fitted to low noise calibration data which exhibit slight curvature.     

Enantioselective [4 + 2]-annulation of chiral crotylsilanes: application to the synthesis of a C1-C22 fragment of leucascandrolide A

[reaction: see text] The asymmetric synthesis of a C1-C22 fragment (2) of leucascandrolide A is described. Synthetic highlights include the construction of the C9-C22 pyran fragment using a formal [4 + 2]-annulation of a chiral organosilane. A diastereoselctive Mukaiyama aldol was used to introduce the C9 stereocenter and complete the assembly of the macrocycle's carbon skeleton.     

Synthesis, crystal structures and the preliminary evaluation of the new dibenzotetraaza[14]annulene-based DNA/RNA binding agents

A series of water-soluble dicationic dibenzotetraaza[14]annulenes have been prepared in order to examine their interactions with nucleic acids. Pendant water-solubilizing N-pyridinium, 4,4′-bipyridinium and N-methyl pyridinium moieties have been attached to the central core via linkers generated by direct N-alkylations and ester creating couplings, respectively. The crystal structures of derivatives equipped with 3-(N-pyridinium-1-yl)propyl and 3-(4,4′-bipyridinium-1-yl)propyl substituents have been determined. Interactions with ct-DNA have been studied and evidenced by means of spectrophotometric titrations with Scatchard analysis and thermal denaturation experiments.     

The small‐scale preparation and NMR characterization of isotopically enriched organotin compounds

Synthetic methods for the small‐scale laboratory preparation of isotopically enriched dibutyltin dichloride, dibutyltin di‐iodide, tributyltin chloride, tributyltin iodide, diphenyltin dichloride, triphenyltin chloride and triphenyltin iodide have been successfully established. Organotin iodides were prepared from redistribution reactions between tin(IV) iodide and the corresponding tetraorganotin, with the exception of dibutyltin di‐iodide, which was prepared directly from the reaction between tin metal and iodobutane. The development of novel procedures for the dealkylation/dearylation of tetraorganotins by acid hydrolysis produced superior yields of tributyltin chloride and diphenyltin dichloride in comparison with redistribution reactions. Organotin iodide redistribution reaction products were converted to their chloride analogues via the fluoride salts using an aqueous ethanolic solution of potassium fluoride. The insolubility of organotin fluoride salts was exploited to isolate and purify the isotopically enriched compounds, and to prevent losses during the purification procedure. The nuclear magnetic resonance (NMR) spectroscopic study of ‘natural abundance’ and isotopically enriched organotin compounds gave proton (¹H) and carbon‐13 (¹³C) spectra for butyltins, Bu_4−nSnX_n, and phenyltins, Ph_4−nSnX_n (X = I, Cl), allowing the assignment of ­¹H and ¹³C chemical shifts, and ¹¹⁹Sn–¹³C and ¹¹⁷Sn–¹³C coupling constants. The ¹³C NMR spectroscopic analysis of ¹¹⁷Sn‐enriched organotin compounds has allowed the assignment of certain resonances and tin–carbon coupling constants which were previously unobservable. The spectral patterns show that Δ(¹H) and Δ(¹³C) values are sensitive to structural changes, and that ¹³C shielding decreases with an increase in the electronegativity of the substituent. The tin–carbon coupling constants are also sensitive to structural changes, and for alkyl and aryl compounds the couplings decrease in the order ¹J > ³J > ²J > ⁴J. The ¹³C chemical shift values and the magnitude of tin–carbon coupling constants are shown to be solvent‐dependent. The ¹³C spectra of the isotopically enriched compounds show that the degree of isotopic enrichment and the nature of the isotope used (magnetic or non‐magnetic) are reflected in the spectral pattern obtained. Copyright © 2000 John Wiley & Sons, Ltd.