三梯级和四梯级圆筒和Mbius分子的拓扑特性研究

Walba等以其卓越的工作,合成了三-THYME(C_(42)H_(72)O_(18))和四-THYME(C_(56)H_(96)O_(24))圆筒及其Mbius扭曲环带分子,被誉为拓扑学进入有机化学领域的奇迹,成为迄今为止拓扑立体化学研究的重要内容,但从拓扑学的观点探索分子图拓扑结构特性尚缺乏深入研究,本文作者考虑到一般性,曾将扭曲数T为偶数(0,2,4)的定义为Hckel型,扭曲数     

Molecular graphs as topological objects in space

Stereochemistry deals primarily with distinctions based on rigid geometry, e.g., bond angles and lengths. But some chemical species have molecular graphs (such as knots, catenanes, and nonplanar graphs K₅ and K_3.3) that reside in space in a topologically nontrivial way. For such molecules there is hope of using topological methods to gain chemical information. Viewing a molecular graph as a topological object in space makes it unrealistically flexible; but if one proves that a certain graph is “topologically chiral” or that two graphs are “topological diastereomers,” then one has ruled out interconversion under any physical conditions for which the molecular graph still makes sense. In this paper, we consider several kinds of topological questions one might ask about graphs in space, methology and results available, and specific topological properties of various molecules.     

Topological effects for nonsymmetrical configurations: the C2H+2 as a case study

During the last decade the study of topological effects formed by molecular systems became a routine but it was always carried out for configurations that were limited by symmetry conditions. To be more specific this applied to the Jahn-Teller (JT) effect formed by molecular configurations of planar symmetry [see, e.g., Baer et al., Faraday Discuss. 127, 337 (2004)] and the Renner-Teller effect formed by configurations of axial symmetry [see, e.g., Halasz et al., J. Chem. Phys. 126, 154309 (2007)]. In this article we consider for the first time molecular configurations that avoid any symmetry conditions or, in other words, are characterized by the C(1) point group. We report on a detailed study of topological effects formed by such a molecular system. The study concentrates on both, the two-state (Abelian) case and the multistate (non-Abelian) case. It is shown that the theory that was originally developed to treat topological effects due the JT intersection and also applies for the study of topological effects in the most general case. The study is accompanied with numerical results.     

拓扑指数法用于稀土显色剂和镱的显色反应灵敏度的相关性研究

计算了２０种不对称变色酸双偶膦酸型显色的Ａｍ拓扑指数和分子联接性指数，并将其与镱显色反应灵敏度进行相关性研究，讨论了显色剂结构对拓扑指数及灵敏度的影响     

Molecular connectivity methods for the characterization of surface energetics of liquids and polymers

In the topological approach to structure-property relationships, the molecular structure is described in terms of appropriate weighted graphs to which suitable topological parameters, usually known as molecular connectivity indices, can be associated. Molecular connectivity indices are here applied to the prediction of surface free energy and Good-van Oss-Chaudhury acid-base components of organic compounds. To this aim, some quantitative structure-property relationships (QSPRs) are determined, involving both topological indices and group indicator variables of the customary functional group theory. The semiempirical models obtained to appear satisfactory and show significant advantages with respect to the models based on the purely functional group approach.     

Novel Indices for the Topological Complexity of Molecules

Abstract

The development of molecular complexity measures is reviewed. Two novel sets of indices termed topological complexities are introduced proceeding from the idea that topological complexity increases with the overall connectivity of the molecular graph. The latter is assessed as the connectivity of all connected subgraphs in the molecular graph, including the graph itself. First-order, second-order, third-order, etc., topological complexities ⁱ TC are defined as the sum of the vertex degrees in the connected subgraphs with one, two, three, etc., edges, respectively. Zero-order complexity is also specified for the simplest subgraphs–the graph vertices. The overall topological complexity TC is then defined as the sum of the complexities of all orders. These new indices mirror the increase in complexity with the increase in the number of atoms and, at a constant number of atoms, with the increase in molecular branching and cyclicity. Topological complexities compare favorably to molecular connectivities of Kier and Hall, as demonstrated in detail for the classical QSPR test-the boiling points of alkanes. Related to the wide application of molecular connectivities to QSAR studies, a similar importance of the new indices is anticipated.     

Study of Gamma-Irradiated Polyamide Using Thermomechanical Spectrometry and Radiothermoluminescence

The molecular–topological structure of polyamide before and after γ-irradiation has been first studied by thermomechanical spectrometry. The γ-irradiation with a dose up to 300 kGy does not change the topological structure of the polymer, the four-block pseudo-network structure of which contains crystalline segments of macromolecules and polyassociative entities of the cluster type in addition to low-and high-temperature amorphous blocks. During irradiation, only interblock mass transfer of the chain segments occurs, resulting in different dose-dependent values for the molecular weight of the chains, their weight fraction in each topological block, and the glass transition and molecular flow temperatures of the polymer. Radiothermoluminescence curves exhibit three maxima at 152, 200, and 330 K, of which the last one is detected in a temperature region close to the glass transition temperature of the high-temperature amorphous block on the thermomechanical analysis curve of the polymer.     

Multidimensional persistence in biomolecular data

Persistent homology has emerged as a popular technique for the topological simplification of big data, including biomolecular data. Multidimensional persistence bears considerable promise to bridge the gap between geometry and topology. However, its practical and robust construction has been a challenge. We introduce two families of multidimensional persistence, namely pseudomultidimensional persistence and multiscale multidimensional persistence. The former is generated via the repeated applications of persistent homology filtration to high‐dimensional data, such as results from molecular dynamics or partial differential equations. The latter is constructed via isotropic and anisotropic scales that create new simiplicial complexes and associated topological spaces. The utility, robustness, and efficiency of the proposed topological methods are demonstrated via protein folding, protein flexibility analysis, the topological denoising of cryoelectron microscopy data, and the scale dependence of nanoparticles. Topological transition between partial folded and unfolded proteins has been observed in multidimensional persistence. The separation between noise topological signatures and molecular topological fingerprints is achieved by the Laplace–Beltrami flow. The multiscale multidimensional persistent homology reveals relative local features in Betti‐0 invariants and the relatively global characteristics of Betti‐1 and Betti‐2 invariants. © 2015 Wiley Periodicals, Inc.     

Characterization of Molecular Structures Using Topological Indices

Abstract

The characterization of molecular structure using structural invariants has increased greatly over the last ten years. Specifically, topological indices have become more widely used in the quantification of molecular structure for use in quantitative structure-activity relationship studies, chemical documentation, and molecular similarity studies. The basis, calculation, and utility of topological indices has been examined, with an eye to the specific advantages and problems in their use. In addition, variable clustering and principal component analysis are examinee as two potential solutions to the problem of index intercorrelation.     

Structural interpretation of the topological index. 2. The molecular connectivity index, the Kappa index, and the atom-type E-State index

The structural interpretation is extended to the topological indices describing cyclic structures. Three representatives of the topological index, such as the molecular connectivity index, the Kappa index, and the atom-type E-State index, are interpreted by mining out, through projection pursuit combining with a number theory method generating uniformly distributed directions on unit sphere, the structural features hidden in the spaces spanned by the three series of indices individually. Some interesting results, which can hardly be found by individual index, are obtained from the multidimensional spaces by several topological indices. The results support quantitatively the former studies on the topological indices, and some new insights are obtained during the analysis. The combinations of several molecular connectivity indices describe mainly three general categories of molecular structure information, which include degree of branching, size, and degree of cyclicity. The cyclicity can also be coded by the combination of chi cluster and path/cluster indices. The Kappa shape indices encode, in combination, significant information on size, the degree of cyclicity, and the degree of centralization/separation in branching. The size, branch number, and cyclicity information has also been mined out to interpret atom-type E-State indices. The structural feature such as the number of quaternary atoms is searched out to be an important factor. The results indicate that the collinearity might be a serious problem in the applications of the topological indices.