New indices for analysing partial ranking diagrams

Interest is growing in decision making strategies and several techniques are now available. The assessment of priorities is a typical premise before final decisions are taken. Total and partial order ranking (POR) strategies, which from a mathematical point of view are based on elementary methods of discrete mathematics, appear as an attractive and simple tool to asses priorities. Despite the well-known total ranking strategies, which are scalar methods combining the different criteria values into a global index which always ranks elements in an ordered sequence, the partial order ranking is a vectorial approach which recognises that not all the elements can be directly compared with all the others. In fact when many criteria are considered, contradictions in the ranking are bound to exist and the higher the number of criteria, the higher the probability that contradictions in the ranking occur. The Hasse diagram technique (HDT) is a very useful tool to perform partial order ranking. The results of the partial order ranking are visualised in a diagram, called Hasse diagram. Incomparable elements are located at the same geometrical height and as high as possible in the diagram, thus incomparable elements are arranged in levels. The quality of a ranking procedure has to be evaluated by a deep analysis and by several indices, i.e. scalar functions that describe features of an ordered set and allow comparison among different rankings. For this purpose, new indices for ranking analysis are proposed here, compared with the ones found in literature and tested on theoretical examples and on real data.     

On the role of localized molecular orbitals in the formation of bond dipoles

The hypothesis of the classical chemistry about bond dipoles resulting from shifts of separate pairs of electrons is proved using the non-canonical method of molecular orbitals (MOs). To this end, a relation is sought between the total charge distribution inside an individual chemical bond of a polyatomic molecule and the square of the respective single localized MO (LMO). General expressions for these MOs are obtained directly on the basis of the Brillouin theorem without invoking additional localization criteria. The two characteristics under comparison are presented in an explicit algebraic form in terms of meaningful components. Reshaping of square of the ‘own’ LMO of the given bond is shown to play the decisive role in the formation of secondary dipoles of initially homopolar bonds (e.g. of C–C and C–H bonds in substituted alkanes), as well as of bonds of relatively low initial polarity. Thus, representability of these dipoles by shifts of the ‘own’ pairs of electrons of respective bonds is supported. For bonds of a high initial polarity, the secondary dipoles are shown to originate mainly from contributions of LMOs of other bonds extending over the antibonding basis orbital of the given bond. Moreover, the actual secondary bond dipole takes an opposite direction vs. that predicted by the shift of the respective ‘own’ pair of electrons in this case. The latter result serves to account for the known low nucleofugality of highly electronegative heteroatoms in the S_N2 reactions.     

Closer asymptotic approximations for the distributions of the power divergence goodness-of-fit statistics

Summary The members of the power divergence family of statistics order="0"> all have an asymptotically equivalent χ² distribution (Cressie and Read [1]). An asymptotic expansion for the distribution function is derived which shows that the speed of convergence to this asymptotic limit is dependent on λ. Known results for Pearson'sX ² statistic and the log-likelihood ratio statistic then appear as special cases in a continuum rather than as separate (unrelated) expansions.     

Elution order in gas chromatography

The retention behavior of a heterogeneous group of solutes has been examined on seven different stationary phases under isothermal and temperature-programmed conditions. Both ΔH_v (enthalpy of solute vaporization from the stationary phase) and ΔS_v (entropy of solute vaporization from the stationary phase) values were determined for each solute – stationary phase combination under isothermal conditions. Both program rate and carrier gas velocity were shown to affect solute elution order. Unless these and other experimental factors discussed are controlled, column equivalency studies based on solute elution order have dubious value.     

Magnetism and structural chemistry of the n=2 Ruddlesden-Popper phase La3LiMnO7

Polycrystalline samples of the n=2 Ruddlesden-Popper phase La₃LiMnO₇ have been prepared and characterized. X-ray and neutron diffraction suggest that the structure is tetragonal with a disordered distribution of Li and Mn cations over the octahedral sites, but ⁶Li MAS NMR shows that the Li and Mn are 1:1 ordered locally. Electron microscopy shows that the stacking of the cation-ordered, perovskite-like bilayers along the crystallographic z-axis is disordered on the distance scale sampled by X-ray and neutron diffraction. Magnetometry data and neutron diffraction data collected at 2 K together suggest that the Mn cations within each structural domain order antiferromagnetically at 14 K, but that the disorder along z prevents the establishment of long-range magnetic order.     

Computer-assisted choice of discrete spacers for anionic isotachophoresis separations

In isotachophoresis (ITP), the sample constituents migrate, depending on their concentrations in the loaded sample, either in fully developed zones or in the boundary layers between the zones of constituents of the corresponding effective mobilities. The latter (spike) migration mode is analytically beneficial in selective detections of trace analytes, especially, when appropriately chosen discrete spacers minimize detection interferences due to matrix constituents. To facilitate a search for suitable mixtures of discrete spacers, a two-step calculation procedure was developed in this work. Using a pool of discrete spacers consisting of 42 anionic and zwitterionic constituents, this procedure was shown effective in the anionic ITP separations performed at pH = 6.5-10.0. Besides the predictions of the migration orders, it was helpful in identifying the spacing constituents that could cause resolution problems due to an uncertainty with which pH of the leading electrolyte solution is known. The ionic mobility and pKa data, taken for the spacing constituents from the literature and the ones obtained from the ITP experiments carried out in this work, were used in the calculations performed in a context with the choice of spacers. Although the data obtained from the ITP experiments provided better results, small uncertainties with which they were acquired (attributable to fluctuations in the experimental conditions) set practical limits in the calculation based choice of multi-component mixtures of the spacing constituents.     

Modular design of icosahedral metal clusters

The concept of crystalline module, that is, an unambiguously isolated, repeated quasi-molecular element, is introduced. This concept is more general than the concept of crystal lattice. The generalized modular approach allows extension of the methods and principles of crystallography to quasi-crystals, clusters, amorphous solids, and periodic biological structures. Principles of construction of aperiodic, nonequilibrium regular modular structures are formulated. Limitations on the size of icosahedral clusters are due to the presence of spherical shells with non-Euclidean tetrahedral tiling in their structure. A parametric relationship between the structures of icosahedral fullerenes and metal clusters of the Chini series was found.     

Enantioseparations of polyhalogenated 4,4’-bipyridines on polysaccharide-based chiral stationary phases and molecular dynamics simulations of selector–selectand interactions

2’-(4-Pyridyl)- and 2’-(4-hydroxyphenyl)-TCIBPs (TCIBP = 3,3’,5,5’-tetrachloro-2-iodo-4,4’-bipyridyl) are chiral compounds that showed interesting inhibition activity against transthyretin fibrillation in vitro. We became interested in their enantioseparation since we noticed that the M-stereoisomer is more effective than the P-enantiomer. Based thereon, we recently reported the enantioseparation of 2’-substituted TCIBP derivatives with amylose-based chiral columns. Following this study, herein we describe the comparative enantioseparation of both 2’-(4-pyridyl)- and 2’-(4-hydroxyphenyl)-TCIBPs on four cellulose phenylcarbamate-based chiral columns aiming to explore the effect of the polymer backbone, as well as the nature and position of substituents on the side groups on the enantioseparability of these compounds. In the frame of this project, the impact of subtle variations of analyte and polysaccharide structures, and mobile phase (MP) polarity on retention and selectivity was evaluated. The effect of temperature on retention and selectivity was also considered, and overall thermodynamic parameters associated with the analyte adsorption onto the CSP surface were derived from van ’t Hoff plots. Interesting cases of enantiomer elution order (EEO) reversal were observed. In particular, the EEO was shown to be dependent on polysaccharide backbone, the elution sequence of the two analytes being P-M and M-P on cellulose and amylose tris(3,5-dimethylphenylcarbamate), respectively. In this regard, a theoretical investigation based on molecular dynamics (MD) simulations was performed by using amylose and cellulose tris(3,5-dimethylphenylcarbamate) nonamers as virtual models of the polysaccharide-based selectors. This exploration at the molecular level shed light on the origin of the enantiodiscrimination processes.     

Cycloadditions of 8,8-dicyanoheptafulvene to styrenes: manifestation of dual reactivity modes

A facile cycloaddition reaction of 8,8-dicyanoheptafulvene with styrenes leading to the corresponding [8+2] and [4+2] adducts in excellent yields is described.     

锂在共轭双键高分子中的电化学嵌入反应III. 锂嵌入聚噻吩的量子化学计算†

采用Gaussian软件和HF方法, 通过从头计算(ab initio)法选取4-31G基组计算锂离子嵌入聚噻吩过程中结构与结合能的变化关系. 发现噻吩聚合时主要生成三或四聚合物. 聚合物在Li原子(或Li^＋离子)嵌入后, 聚噻吩间距离明显变小, 同时发生电荷转移, 形成稳定嵌合物; 并使噻吩环的C-α—C-β键级变小. 同时, 研究了锂离子(或原子)嵌入后体系的HOMO, LUMO能级. 聚噻吩在嵌入锂离子时LUMO轨道能级变为负值, 成为电池反应得电子的正极. 而金属Li₂ 释放Li^＋后的Li^－的HOMO能级为＋0.7427 eV, 则成为给电子的负极. 由此, 可以完成由锂/聚噻吩在高氯酸锂电解质中组成的放电过程, 并提出嵌合键级概念用来表征锂在聚噻吩间的结合程度.