Mathematical Aspects of the Periodic Law

We review different studies of the Periodic Law and the set of chemical elements from a mathematical point of view. This discussion covers the first attempts made in the 19th century up to the present day. Mathematics employed to study the periodic system includes number theory, information theory, order theory, set theory and topology. Each theory used shows that it is possible to provide the Periodic Law with a mathematical structure. We also show that it is possible to study the chemical elements taking advantage of their phenomenological properties, and that it is not always necessary to reduce the concept of chemical elements to the quantum atomic concept to be able to find interpretations for the Periodic Law. Finally, a connection is noted between the lengths of the periods of the Periodic Law and the philosophical Pythagorean doctrine.     

What and How Physics Contributes to Understanding the Periodic Law

The current status of explanation worked out by Physics for the Periodic Law is considered from philosophical and methodological points of view. The principle gnosiological role of approximations and models in providing interpretation for complicated systems is emphasized. The achievements, deficiencies and perspectives of the existing quantum mechanical interpretation of the Periodic Table are discussed. The mainstream ab initio theory is based on analysis of selfconsistent one-electron effective potential. Alternative approaches employing symmetry considerations and applying group theory usually require some empirical information. The approximate dynamic symmetry of one-electron potential casts light on the secondary periodicity phenomenon. The periodicity patterns found in various multiparticle systems (atoms in special situations, atomic nuclei, clusters, particles in the traps, etc) comprise a field for comparative study of the Periodic Laws found in nature. This revised version was published online in July 2006 with corrections to the Cover Date.     

Topical use of liposomal copper palmitate formulation blocks porphyrin-induced photosensitivity in rats

Photodynamic therapy (PDT) is a new treatment modality that uses porphyrin derivatives and visible light, especially for the treatment of cancer. However, PDT with certain photosensitisers can cause prolonged skin photosensitization. This is particularly true for Photofrin II (Photofrin)-mediated PDT where patients are required to avoid direct exposure to sunlight for a period of 4-6 weeks. This is the only long-term adverse reaction to the drug. Recent studies have shown that topical copper treatment avoids this type of inflammatory reaction. In this study, we have tested the efficiency of the liposomal formulation of copper palmitate on porphyrin-photosensitized rats. Initially, adult male Sprague-Dawley rats were rendered photosensitive either by administration of Photofrin or aminolevulinic acid (ALA), a precursor of protoporphyrin IX (PpIX). Prior to this, their dorsal skin was shaved and treated topically with a cream consisting of either empty or copper palmitate-encapsulated liposomal formulation. After being kept in a dimmed light environment, the rats were exposed to visible light, and inflammatory responses were inspected. Histological studies revealed that no inflammatory cells were present at the skin sites treated with liposomal cream containing copper palmitate in the Photofrin-sensitized group while no reduction in the number of inflammatory cells was observed at the skin samples treated with the empty liposomes. In conclusion, the data demonstrate the significant protective effect of topically-applied liposome-encapsulated copper palmitate against both Photofrin and ALA-induced PpIX photosensitivity.     

Mendeleev's Discovery of the Periodic Law: The Origin and the Reception

This paper addresses the conceptual as well as social origins of Mendeleev’s discovery of the periodic law and its reception by the chemical community by taking account of three factors: Mendeleev’s early research and its relevance to the discovery; his concepts of chemistry, especially that of the chemical elements; and the social context of the discovery and the reception in the chemical community. Mendeleev's clear distinction between abstract elements and simple bodies was a departure from Lavoisier’s famous definition of elements as an endpoint of analysis and originated from his research in indefinite compounds. As a comparison, the paper also analyzes Lothar Meyer’s approach to the classification of the elements. Mendeleev’s new concept of chemical elements and the existence of an audience in the form of the newly established Russian Chemical Society, and his ``German connection', helped Mendeleev in his discovery and its reception. This revised version was published online in July 2006 with corrections to the Cover Date.     

现代元素周期律的化学微观视角探析*

由门捷列夫元素周期表到现代元素周期律的发展,将人们的关注点从元素化学性质相似性的宏观考量转移到原子电子组态周期性递变的微观探析上来。对原子核外电子排布“构造原理”的产生、发展及其作用展开讨论,尝试对元素周期律的微观本质进行探析。     

Exfoliated poly(methyl methacrylate) and polystyrene nanocomposites occur when the clay cation contains a vinyl monomer

The bulk polymerization of methyl methacrylate and styrene in the presence of an organically modified clay containing a vinyl group that can be involved in the polymerization produces exfoliated nanocomposites. These nanocomposites have been characterized by X‐ray diffraction, transmission electron microscopy, thermogravimetric analysis, mechanical properties, and cone calorimetry. The onset temperature of thermal degradation increases with the mechanical properties. The peak heat release rate is significantly reduced for nanocomposites containing 3 or 5% clay. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1124–1135, 2003     

Adequacy and Inadequacy in the Metrology of Chemical Analysis

The adequacy (inadequacy) of samples to each other and reference materials to test samples is an important notion in the metrology of chemical analysis. However, the literature gives no strict definition for this notion. In this paper, it was proposed to determine adequacy based on the measure of inadequacy. For the case of two samples, the measure of inadequacy is the absolute value of the difference between the systematic errors of the results of analyses of the samples; it depends on the difference in the composition and properties of the samples. The measure of inadequacy of a standard reference material to a series of test samples is the maximum distance between the systematic error of the reference material and one of the quantiles of the systematic error distribution of the test samples Q(0.025); Q(0.975); the errors in this case are due to the composition and the properties of the test samples. The samples are considered adequate if the measure of inadequacy can be neglected compared to the normalized error of the analysis. Using the determination of total cholesterol in the blood serum of humans as an example, it was shown that the standard reference material in the analysis of samples of complex composition is often inadequate to test samples.     

Hydrotalcite catalysis for the synthesis of new chiral building blocks

The use of hydrotalcites for the synthesis of two chiral building blocks in a simple way is described as a new and green methodology. The synthesis of these compounds implies a regioselective Baeyer–Villiger reaction in a very selective way with ulterior opening and lactonisation. This methodology should be considered green for the use of hydrogen peroxide as the only oxidant and hydrotalcites as the catalyst, and because no residues are produced apart from water. The procedure is very adequate for using in gram scale, in order to increase the value of the obtained compounds. The conditions are excellent and can be applied for nonstable compounds, as they are very mild. The synthesised compounds are magnific starting materials for the synthesis of biologically active or natural compounds. The use of a cheap, commercial and chiral compound as carvone disposable in both enantiomeric forms adds an extra value to this methodology.     

The 1/1 and 2/1 approximants in the Sc-Mg-Zn quasicrystal system: triacontahedral clusters as fundamental building blocks

Single-crystal structures are reported for Sc(3)Mg(0.18(1))Zn(17.73(3)), the 1/1 approximant crystal (AC), and Sc(11.18(9))Mg(2.5(1))Zn(73.6(2)), the 2/1 AC, in the corresponding icosahedral quasicrystal (i-QC) system. The 1/1 AC crystallizes in space group Im, a = 13.863(2) A, Z = 8, and the 2/1 AC, in Pa, a = 22.412 (2) A, Z = 8. The latter, which is valuable in pointing the way to the QC structure, is the best ordered and refined 2/1 example to date. The fundamental building blocks in both ACs are triacontahedral clusters centered by smaller multiply endohedral Tsai-type arrays; the former are condensed through body-centered-cubic packing in the 1/1 and primitive cubic packing in the 2/1 AC. Novel prolate rhombohedra centered by Sc-Sc dimers are also generated between triacontahedra in the 2/1 AC.     

Integrity of liposomes in presence of various formulation excipients, when dispersed in aqueous media and in hydrogels

The integrity of liposomes when dispersed in presence of various common formulation excipients is studied. Additionally, the effect of the excipients on the release of calcein from the same liposomes when dispersed in hydrogels is investigated and the results of the two sets of experiments are compared. Propyleneglycol (PG), transcutol CG (TR), cremophor EL (CR) and labrafac hydro WL 1219 (LB) are used at 10 or 25% (v/v) and the retention of liposome encapsulated calcein is followed for 24 or 48 h periods. Calcein entrapping multilamellar liposomes composed of phosphatidylcholine (PC) or 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC) with or without addition of different amounts of cholesterol (Chol) were prepared by the thin film hydration method.

Experimental results reveal that liposomes are affected more by the excipients in the order: LB > CR > PG  TR. Particularly LB and in some cases also CR result in rapid release of most or the entire vesicle encapsulated dye. Addition of Chol in both PC and DSPC liposomes results in substantial increase of vesicle integrity in all cases. Concerning the release of calcein form the liposomal gels, from DSPC/Chol (1:1) liposomal gels calcein release was not affected by addition of 25% of TR or PG in all gels studied, but LB caused a significant increase in calcein release. However, from PC-liposomal gels even TR and PG (at 25%), increases calcein release.

Conclusively, the results of this study suggest that liposomes are protected from excipients when dispersed in gels compared to aqueous media. This should be taken into account when liposomal drug formulations are designed.     

A new formulation of the PCM solvation method: PCM-QINTn

A new formulation of the PCM electrostatic solution problem is proposed. Through a new derivation of the PCM-CLSn expression we propose an interpolation formula that improved the convergence: PCM-QINTn. All the available formulations are applied to the evaluation of the electrostatic component of the free energy of solvation for some molecular systems. In addition, PCM-QINT derivatives of G _el with respect to atomic coordinates are evaluated. The computational costs are compared with those of PCM-direct formulation. Received: 21 October 1996 / Accepted: 7 January 1997     

A new operator formulation of the many-electron problem for molecules

An n-electron operatorX _n , called a wave operator, is associated with a 2n-electron molecular wave function. Electron densities and energy are written in terms ofX _n . An equation defining an exact wave operator is found. Thus, a 2n-electron vector problem (for the wave function) is rigorously reduced to an n-electron operator problem. Conditions are formulated which guarantee thatX _n corresponds to a state with a given spin. The configuration-interaction problem is considered and methods of approximate construction ofX _n are discussed. In particular, a matrix algorithm is proposed for calculations in the two-body approximation. A generalizaton of the approach to the case of systems with an odd number of electrons is given. The waveoperator model developed forms a general basis for construction of covariant electron models of molecules.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 25, No. 1, pp. 1–12, January–February, 1989.     

元素周期律复习教学中认识模型建构的有效策略

探查了元素周期律复习教学中认识模型构建的有效策略。从学生对于元素周期律的学后障碍点及相应的发展核心入手,在北京市选择了2所学生水平不同的学校分别进行了2课时的元素周期律复习教学。教学过程中基于学生认识发展的核心,选取了不同的模型构建组织策略,通过进阶式的教学任务对元素周期律的“位置-结构-性质”认识模型和物质性质的认识模型进行了构建。在问卷测查以及将本研究授课效果与常规授课进行对比后,证明并提炼了基于模型构建的元素周期律复习教学的有效策略。     

A new formulation of the phase change approach in the theory of conical intersections

We have reformulated the phase change approach to the theory of conical intersections suggested by Zilberg and Haas [S. Zilberg, Y. Haas, Adv. Chem. Phys. 124 (2002) 433]. We use the fact that the phase change loop variable in polar co-ordinates in the space of nuclear co-ordinates is related to the transformation of the diabatic VB states defined at the apex of the cone in a conical intersection. Thus one can use the basis transformation generated by θ to yield a sequence of orthogonal pairs of VB structures (anchors) at any value of in the loop in nuclear configuration space. In this way the branching plane concept becomes related to VB wavefunctions based on the correspondence between the two angles. The theory is developed in detail using a simple three orbital three electron example. Examples are presented for four and six orbitals. In the later case, our results differ from those of Zilberg and Haas.     

Adequacy in the metrology of chemical analysis and other complicated measurements

The adequacy of specimens to each other, and of reference material to routine specimens, is an important idea in the metrology of chemical analysis. However, the literature gives no strict definition for this notion. In this paper, a determination of adequacy based on the measure of adequacy is proposed. For the case of two specimens, the measure of adequacy is the absolute value of the difference between the systematic errors in the results from analysis of the specimens; it depends on the differences in the composition and properties of the specimens. The measure of adequacy of a certified reference material to a population of routine specimens is the maximum distance between the systematic error of the reference material and one of the quantiles of the systematic error distribution of the routine specimens Q(0.025); Q(0.975); the errors in this case are due to the composition and the properties of the routine specimens and other complicated measurements. When the measure of adequacy can be neglected compared to the permissible error of the analysis, the specimens are considered adequate. Using the determination of total cholesterol in the blood serum of human beings as an example, it was shown that the certified reference material used in the analysis of specimens of complex composition is often inadequate when compared to routine specimens.

教科书中的元素周期律:科学本质的视角

教科书是影响学生理解科学本质的诸多因素中最重要的因素之一.知识呈现的逻辑线索、科学史内容的呈现以及语言的运用明确地表述或潜隐地渗透了特定的科学本质观.通过对不同类型高中化学教材中元素周期律呈现的比较分析,发现新版教科书更为重视学生对科学本质的理解,但由于传统沿袭、相关研究薄弱等原因,仍然没有很大突破.     

A new outer boundary formulation and energy corrections for the nonlinear Poisson-Boltzmann equation

The nonlinear Poisson-Boltzmann equation (PBE) has been successfully used for the prediction of numerous electrostatic properties of highly charged biopolyelectrolytes immersed in aqueous salt solutions. While numerous numerical solvers for the 3D PBE have been developed, the formulation of the outer boundary treatments used in these methods has only been loosely addressed, especially in the nonlinear case. The de facto standard in current nonlinear PBE implementations is to either set the potential at the outer boundaries to zero or estimate it using the (linear) Debye-Hückel (DH) approximation. However, an assessment of how these outer boundary treatments affect the overall solution accuracy does not appear to have been previously made. As will be demonstrated here, both approximations can, under certain conditions, produce completely erroneous estimates of the potential and energy salt dependencies. A related concern for calculations carried out on grids of finite extent (e.g., all current finite difference and finite element implementations) is the contribution to the energy and salt dependence from the exterior region outside the computational grid. This too is shown to be significant, especially at low salt concentration where essentially all of the contributions to the excess osmotic pressure and ion stress energies originate from this exterior region. In this paper the authors introduce a new outer boundary treatment that is valid for both the linear and nonlinear PBE. The authors also formulate energy corrections to account for contributions from outside the computational domain. Finally, the authors also consider the effects of general ion exclusion layers upon biomolecular electrostatics. It is shown that while these layers tend to increase the surface electrostatic potential, under physiological salt conditions and high net charges their effect on the excess osmotic pressure term, which is a measure of the salt dependence of the total electrostatic free energy, is weak. To facilitate presentation and allow very fine resolutions and/or large computational domains to be considered, attention is restricted to the 1D spherically symmetric nonlinear PBE. Though geometrically limited, the modeling principles nevertheless extend to general PBE solvers as discussed in the Appendix. The 1D model can also be used to benchmark and validate the salt effect prediction capabilities of existing PBE solvers.     

基于提升学生科学论证能力的“元素周期律”进阶教学

以《化学2》中的"元素周期律"的教学设计为例,基于学习进阶理论建构高中元素周期律认识模型并设计学生进阶论证任务。通过学案上元素周期律的核心探究问题,驱动学生的"证据导向式"论证活动,在科学探究和数据分析的过程中,培养了学生基于证据和数据的实证研究意识,提升了学生逻辑推理和论证能力,以期为培养学生高阶思维的探究式教学提供案例参考。     

Synthesis of novel halo-oxybispyridines, new building blocks in cholinergic medicinal chemistry

This paper describes a method for the preparation of oxybispyridines bearing several halogens, which could be further transformed into other functional groups thus giving access to libraries with the bis-pyridyl ether moiety as the common structural feature of interest in cholinergic medicinal chemistry. Scope and limitation of the method are outlined.