Variable connectivity index as a tool for modeling structure-property relationships

We report on the calculation of normal boiling points for a series of n = 58 aliphatic alcohols using the variable connectivity index in which variables x and y are used to modify the weights on carbon (x) and oxygen atoms (y) in molecular graphs, respectively. The optimal regressions are found for x = 0.80 and y = -0.90. Comparison is made with available regressions on the same data reported previously in the literature. A refinement of the model was considered by introducing different weights for primary, secondary, tertiary, and quaternary carbon atoms. The standard error in the case of the normal boiling points of alcohols was slightly reduced with optimal weights for different carbon atoms from s = 4.1 degrees C (when all carbon atoms were treated as alike) to s = 3.9 degrees C.     

一种修正分子连接性指数杂原子点价的新方法

提出了一种对分子连接性指数中杂原子点价进行修正的新方法,新点价统一了碳原子与其它杂原子点价的定义公式,使杂原子的价点价与非价点价的定义具有了唯一性。对原点价的一些不足,尤其是在处理高氧化态原子时得到显著改进,且保持了碳原子与原定义的非价和价点价具有相同的数值,并继承了分子连接性指数原有的好的性质。新点价物理意义明确,具有与原子电负性相近的定义,其价与非价之差与原子的Mulliken电负性有很好的相关性,且在保持了与体积具有良好相关性的基础上,在处理原子的电性性能上明显改进,进一步明确了价与非价指数的概念,并提出了杂原子取代效应的概念。实际计算应用表明,新点价在处理杂原子,尤其是具有高氧化态和不同氧化态的原子上有明显的改进。     

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.     

Chain numbering and encoding of cyclic hydrocarbons

The numbering of carbon atoms in organic molecules is called chain numbering. It is suggested that bonds be classified as chain bonds (between atoms with consecutive indices) and nonchain bonds. Among atoms we distinguish the first atom (No. 1) and the last atom (having the largest index) as well as initial and final atoms (starting and finishing unbranched sections of atomic chains). Also, internal numbering of elements within these classes is proposed. For condensed cyclic hydrocarbons, formulas for deriving the number of cycles are given, and a linear-chain encoding system is worked out; in this system, nonchain bonds are assigned the indices of their atoms. Rules for unique numbering (canonical chain numbering) are developed; they involve maximization of the indices of the initial atoms and nonchain bonds. The linear-chain encoding of cyclic hydrocarbon structures ensures unification and systematization of their names. Tambov State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 4, pp. 731–736, July–August, 1995. Translated by L. Smolina     

Novel shape descriptors for molecular graphs.

We report on novel graph theoretical indices which are sensitive to the shapes of molecular graphs. In contrast to the Kier's kappa shape indices which were based on a comparison of a molecular graph with graphs representing the extreme shapes, the linear graph and the "star" graph, the new shape indices are obtained by considering for all atoms the number of paths and the number of walks within a graph and then making the quotients of the number of paths and the number of walks the same length. The new shape indices show much higher discrimination among isomers when compared to the kappa shape indices. We report the new shape indices for smaller alkanes and several cyclic structures and illustrate their use in structure-property correlations. The new indices offer regressions of high quality for diverse physicochemical properties of octanes. They also have lead to a novel classification of physicochemical properties of alkanes.     

The overall Wiener index--a new tool for characterization of molecular topology.

Recently, the concept of overall connectivity of a graph G, TC(G), was introduced as the sum of vertex degrees of all subgraphs of G. The approach of more detailed characterization of molecular topology by accounting for all substructures is extended here to the concept of overall distance OW(G) of a graph G, defined as the sum of distances in all subgraphs of G, as well as the sum of eth-order terms, (e)OW(G), with e being the number of edges in the subgraph. Analytical expressions are presented for OW(G) of several basic classes of graphs. The overall distance is analyzed as a measure of topological complexity in acyclic and cyclic structures. The potential usefulness of the components of this generalized Wiener index in QSPR/QSAR is evaluated by its correlation with a number of properties of C3-C8 alkanes and by a favorable comparison with models based on molecular connectivity indices.     

Efficient enumeration of stereoisomers of outerplanar chemical graphs using dynamic programming

Exhaustive and nonredundant generation of stereoisomers of a chemical compound with a specified constitution is an important tool for molecular structure elucidation and molecular design. It is known that many chemical compounds have outerplanar graph structures. In this paper we deal with chemical compounds composed of carbon, hydrogen, oxygen, and nitrogen atoms whose graphical structures are outerplanar and consider stereoisomers caused only by asymmetry around carbon atoms. Based on dynamic programming, we propose an algorithm of generating all stereoisomers without duplication. We treat a given outerplanar graph as a graph rooted at its structural center. Our algorithm first recursively computes the number of stereoisomers of the subgraph induced by the descendants of each vertex and then constructs each stereoisomer by backtracking the process of computing the numbers of stereoisomers. Our algorithm correctly counts the number of stereoisomers in O(n) time and space and correctly enumerates all of the stereoisomers in O(n3) time per stereoisomer on average and in O(n) space, where n is the number of atoms in a given structure.     

取代脂环烃物理化学性质的拓扑化学研究

为了探讨有机化合物的分子结构与理化性质的关系,作者在以前的工作基础上,基于一阶分子连通性拓扑指数构建了一个信息拓扑指数.将拓扑指数与取代脂环烃系列分子的气态标准生成热、气态标准熵、气态标准生成自由能、沸点、临界温度、临界压力、临界体积、汽化热、密度、热容及表面张力等十一种热力学性质及物理化学性质相关联,用一个通用公式对各类性质进行概括,然后用已有的实验数据与拓扑指数进行回归分析,得到一系列计算各性质的经验公式.回归结果发现,分子的理化性质与拓扑指数有较好的相关性,有5类性质的复相关系数大于0.99.用经验公式对各类性质进行重新计算,其结果与实验值比较符合,用实验值对计算值作图,发现各数据点紧靠对角线,说明误差较小.残差分布呈正态分布.     

External factor variable connectivity index

A new variable index, external factor variable connectivity index (EFVCI), is proposed, in which the atomic attribute is divided into two parts. The innate part is denoted as outer-shell electrons and external part or perturbation by other atoms is represented as summation, multiplied by a variable x, of squared reciprocal matrix of i row (corresponds to atom A(i)). The division of atomic attribute in EFVCI is interpreted by using topological structure. In the correlation of boiling point of 149 acyclic alkanes, the optimal values will approach to a constant at -0.29 by using the zero to higher order indices of the same series. The new index, with high regression quality (R = 0.9986, s = 2.26, and F = 7088.4), is compared favorably with variable connectivity index and molecular connectivity index.     

聚炔、累积多烯与全碳环分子的模糊对称性

近年来我们关于分子模糊对称性的工作多属于模糊点对称性的研究, 关于模糊空间对称性探讨较少. 聚炔作为线状一维模糊周期分子, 我们曾对其进行了初步分析. 虽然对于聚炔分子骨架的分析比较全面, 但由于繁冗的计算使我们对分子轨道(MO)模糊对称性的分析只限于少数典型分子. 本文将对不同的聚炔分子MO模糊对称性特征进行较为系统的分析. 结果表明包含不同碳原子数目的分子轨道模糊对称性参数值之间有一定相关性. 此外我们还对一些相关体系分子的MO进行分析, 累积多烯分子虽然并非线型分子, 但其π-MO相关的碳原子处于线性位置, 可依模糊一维周期的G11体系处理. 按Born-Karman近似, 即n个单元的一维周期对称群与Cn点群同构, 本文还分析了相关的全碳环分子的MO的对称性和模糊对称性. 努力寻求与一维周期性相关的模糊对称性规律性特征.     

Statistical properties of carbon nanostructures

We look at modeling carbon nanostructures from a theoretical graph network view, where a graph has atoms at a vertex and links represent bonds. In this way, we can calculate standard statistical mechanics functions (entropy, enthalpy, and free energy) and matrix indices (Wiener index) of finite structures, such as fullerenes and carbon nanotubes. The Euclidean Wiener index (topographical index) is compared with its topological (standard) counterpart. For many of these parameters, the data have power law behavior, especially when plotted versus the number of bonds or the number of atoms. The number of bonds in a carbon nanotube is linear with the length of the nanotube, thus enabling us to calculate the heat of formation of capped (5,5) and (10,10) nanotubes. These properties are determined from atomic coordinates using MATLAB routines.     

Accurate mass measurement of low molecular weight compounds by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry

We report the application of matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS) for the accurate measurement of mass of low molecular weight compounds (smaller than 1500 Da), a linear peptide, two types of cyclic depsipeptides, a polyhydroxy-macrocyclic lactone, and two prenylated flavonoids, with delayed extraction in the reflector mode. The performance of the MALDI-TOF instrument was less than those of fast atom bombardment and Fourier-transform ion cyclotron resonance mass spectrometry instruments and insufficient to give acceptable accuracy for literature reporting. Nevertheless, when combined with NMR spectrometry and/or amino acid analysis to give information on the numbers of carbon atoms and index of hydrogen deficiency, MALDI was useful for determination of the elemental composition of the low molecular weight compounds available in small quantities.     

TGSA-Flex: Extending the capabilities of the Topo-Geometrical Superposition Algorithm to handle flexible molecules

In this work, an extension of the already studied Topo-Geometrical Superposition Approach (TGSA) is presented. TGSA, a general-purpose, fast, automatic, and user-intuitive three-dimensional molecular alignment procedure, was originally designed to superpose rigid molecules simply based on atomic numbers, molecular coordinates, and connectivity. The algorithm is further developed to enable handling rotations around single bonds; in this way, common structural features, which were not properly aligned due to conformational causes, can be brought together, thus improving the molecular similarity picture of the final alignment. The present procedure, implemented in Fortran 90 and named TGSA-Flex, is deeply detailed and tested over four molecular sets: amino acids, nordihydroguaiaretic acid (NDGA) derivatives, HIV-1 protease inhibitors, and 1-[2-hydroxyethoxy)methyl]-6-(phenylthio)thymine (HEPT) derivatives. TGSA-Flex performance is evaluated by means of computational time, number of superposed atoms (also comparing it with respect to the rigid approach), and index of fit between the compared structures.     

Topology, connectivity, and electronic structure of C and B cages and the corresponding nanotubes

After a brief discussion of the structural trends which appear with an increasing number of atoms in B cages, a one-to one correspondence between the connectivity of B cages and C cage structures will be proposed. The electronic level spectra of both systems from Hartree-Fock calculations is given and discussed. The relation of curvature introduced into an originally planar graphitic fragment to pentagonal "defects" such as are present in buckminsterfullerene is also briefly treated. A study of the structure and electronic properties of B nanotubes will then be introduced. We start by presenting a solution of the free-electron network approach for a "model boron" planar lattice with local coordination number 6. In particular the dispersion relation E(k) for the pi-electron bands, together with the corresponding electronic Density Of States (DOS), will be exhibited. This is then used within the zone-folding scheme to obtain information about the electronic DOS of different nanotubes obtained by folding this model boron sheet. To obtain the self-consistent potential in which the valence electrons move in a nanotube, "the March model" in its original form was invoked, and the results are reported for a carbon nanotube. Finally, heterostructures, such as BN cages and fluorinated buckminsterfullerene, will be briefly treated, the new feature here being electronegativity difference.     

对无环分子编码的一个新方法：CMP法

By the use of ordering-tree and connectivity matrix, a new algorithm to code non-circle molecules, called connectivity matrix polynomial (CMP) algorithm, is developed. The algorithm can not only differentiate asymmetrical atoms. but also make the two-direction mapping between codes and non-circle molecular structures. That is, from the molecular structure, a unique code can be obtained, and from the unique code, the specific molecular structure can be derived     

Analysis of electron delocalization in aromatic systems: individual molecular orbital contributions to para-delocalization indexes (PDI)

Our research group has recently defined two new aromaticity indexes based on the analysis of electron delocalization in aromatic species using the quantum theory of atoms-in-molecules. One of these indexes is the para-delocalization index (PDI) that measures the electronic delocalization between para-related carbon atoms in six-membered rings. In this paper, we show that this index can be partitioned into individual molecular orbital contributions. We have applied this PDI decomposition to several polycyclic aromatic hydrocarbons showing that this partitioning provides new insight into the origin of aromaticity.     

Gaseous alkyne ions

Using the relative abundance of metastable ions, collisional activation spectra, field ionization kinetic measurements, isotopic labelling, appearance energy and kinetic energy release data, it is shown that linear alkyne radical cations with more than six carbon atoms do not isomerize to equilibrating structures prior to decomposition. At the shortest ion lifetimes the molecular ions of linear alkynes decompose mainly by simple β-bond fission which allows an unequivocal localization of the triple bond. At medium ion lifetimes fragmentation occurs predominantly via a McLafferty rearrangement, while at long ion lifetimes competing alkyl losses prevail. These alkyl losses occur via cyclic intermediates leading to thermochemically stable cycloalkenyl ions. All these reactions occur with a high specificity with respect to the carbon and hydrogen atoms involved and are preceded by little or no hydrogen exchange reactions.