Structure and properties of organic molecules. 2. Graph-theoretical study of alkenes and alcohols

Topological indices for describing organic compounds with multiple bonds and heteroatoms are treated. The Schultz indices (including modified ones) and the connectivity indices of various types are calculated for saturated alkenes and alcohols. The discriminating ability of the indices and their applicability for structure-property correlations are examined. Various functions approximating the property-index correlations are tested using regression analysis. The Schultz and connectivity indices possess nearly the same correlation ability, as shown by reference to formation enthalpy, molar volume, evaporation heat, and boiling temperature. They may be effectively used for calculating and predicting the physicochemical properties of the title compounds. Tver State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 3, pp. 493–499, May–June, 1998. This work was supported by RFFR grant No. 96-03-32384.     

Molecular modeling of wine polyphenols

Due to wide range of health effects of wine polyphenols, it is important to investigate the relationship between their structure and physical properties (quantitative structure–property relationship, QSPR). We have investigated linear, nonlinear (polynomial), and multiple linear relationships between given topological indices and molecular properties of main pharmacological active components of wine, such as molecular weight (MW), van der Waals volume (Vw), molar refractivity (MR), polar molecular surface area (PSA) and lipophilicity (log P). Partition coefficient (log P) was calculated using three different computer program (CLOGP, ALOGPS and MLOGP). The best models were achieved using the MLOGP program. Topological indices used for correlation analysis include: the Wiener index, W(G); connectivity indices, χ(G); the Balaban index, J(G); information-theoretic index, I(G); and the Schultz index, MTI(G). QSPR was performed on the set of 19 polyphenols and, particularly, on the group of phenolic acids, and on the group of flavonoids with resveratrol. The connectivity index has been successfully used for describing almost all parameters. Significant correlations were achieved between the Wiener index and van der Waals volume, as well as molecular weight.     

Further Insights into the Porous Structure of TEOS Derived Silica Gels

The porous structure of TEOS derived silica gels was studied using nitrogen adsorption at 77 K. Silica gels were prepared using TEOS, H₂O and ethanol for different molar ratios. No catalyst was used in this study. Silica gels were also heat treated up to 1000°C. The nitrogen sorption isotherms were analyzed by two models: Fractal and Percolation Theories. Using the fractal analysis approach, the surface roughness of the porous structure of silica gels was determined. The surface fractal dimension depends on the hydrolysis conditions and heat treatment. The surface fractal dimension decreases with increasing H₂O/TEOS molar ratio or heating temperature. For the silica gels studied, the surface fractal dimension changed from 2.6 to 2.5 after heating the gels, and from 2.4 to 2.6 with decreasing H₂O/TEOS ratio.Using the Percolation theory, we have determined the connectivity of the porous structure of silica gels. The extent of sorption hysteresis of the nitrogen isotherms reflects the connectivity of the pore network. The mean coordination number (connectivity) Z, and the linear dimension of the network, L, have been calculated from the hysteresis of the isotherms. For the as-prepared silica gels, Z was about 8 and L close to 2. On heating the gels, Z decreases to 4 and L increases to 7, results which are in accordance with the collapse of the porous network.     

Structure and properties of organic molecules. 1. Three-dimensional topological indices of alkanes

The Winer and Schultz three-dimensional topological indices of alkanes are considered and compared with ordinary two-dimensional indices. Methods of index design and details of calculations are discussed. Unlike two-dimensional indices, three-dimensional ones adequately reflect differences between both structural and rotational isomers. Regression analysis of property-index correlations for formation enthalpy, molar volume, evaporation heat, and boiling temperature is performed using various two- and three-parameter (linear, quadratic, exponential, logarithmic, and power) functions. The ability of three-dimensional indices to correlate with these properties is found to be as good as that of two-dimensional ones. Tver State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 3, pp. 484–492, May–June, 1998. This work was supported by RFFR grant No. 96-03-32384.     

Overall connectivities/topological complexities: a new powerful tool for QSPR/QSAR

Earlier attempts to assess the complexity of molecules are analyzed and summarized in a number of definitions of general and topological complexity. A concept which specifies topological complexity as overall connectivity, and generalizes the idea of molecular connectivities of Randic, Kier, and Hall, is presented. Two overall connectivity indices, TC and TC1, are defined as the connectivity (the sum of the vertex degrees) of all connected subgraphs in the molecular graph. The contributions to TC and TC1, which originate from all subgraphs having the same number of edges e, form two sets of eth-order overall connectivities, eTC and eTC1. The total number of subgraphs K is also analyzed as a complexity measure, and the vector of its eth-order components, eK, is examined as well. The TC, TC1, and K indices match very well the increase in molecular complexity with the increase in the number of atoms and, at a constant number of atoms, with the increased degree of branching and cyclicity of the molecular skeleton, as well as with the multiplicity of bonds and the presence of heteroatoms. The potential of the three sets of eth-order complexities for applications to QSPR was tested by the modeling of 10 alkane properties (boiling point, critical temperature, critical pressure, critical volume, molar volume, molecular refraction, heat of formation, heat of vaporization, heat of atomization, and surface tension), in parallel with Kier and Hall's molecular connectivity indices (k)chi. The topological complexity indices were shown to outperform molecular connectivity indices in 44 out of the 50 pairs of models compared, including all models with four and five parameters.     

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     

A new approach for devising local graph invariants: Derived topological indices with low degeneracy and good correlation ability

A new approach is presented for obtaining graph invariants which have very high discriminating ability for different vertices within a graph. These invariants are obtained as the solution set (local invariant set, LOIS) of a system of linear equationsQ · X = R, whereQ is a topological matrix derived from the adjacency matrix of the graph, andR is a column vector which encodes either a topological property (vertex degree, number of vertices in the graph, distance sum) or a chemical property (atomic number). Twenty examples of LOOIs are given and their degeneracy and ordering ability of vertices is discussed. Interestingly, in some cases the ordering of vertices obtained by means of these invariants parallels closely the ordering from an entirely different procedure based on Hierarchically Ordered Extended Connectivities which was recently reported. New topological indices are easily constructed from LOISs. Excellent correlations are obtained for the boiling points and vaporization enthalpies of alkanesversus the topological index representing the sum of local vertex invariants. Les spectacular correlations with NMR chemical shifts, liquid phase density, partial molal volumes, motor octane numbers of alkanes or cavity surface areas of alcohols emphasize, however, the potential of this approach, which remains to be developed in the near future.     

Local relaxation of polymers in dense media: Cooperative kinematics theory and applications

Cooperative kinematics (CK) theory and its recent applications are presented. CK theory has been developed as an efficient approach for predicting the mechanism of segmental relaxation processes in bulk polymers. The theory aims at determining the most probable changes in atomic coordinates, occurring collectively in response to a given, external or localized, structural perturbation. The basic postulate is the minimization of the energy change involved in the overall conformational motion, which naturally yields the optimal pathway of cooperative relaxation. Attention has been confined here to the collective motions accompanying the rotational transitions of backbone bonds in polyethylene (PE) and polybutadiene (PB). The strong dependence of the mechanism of motions on the geometry of the repeat unit and on chain connectivity is emphasized. The differences in the types of correlated transitions operating in different structures, the effective conformational energy changes triggered by bond rotational jumps, and the correlation lengths for particular bond isomerizations are analyzed. The reorientations of C H bond vectors in cis- and trans-PB are also examined to explain the shorter correlation time of cis units, compared to trans, detected by NMR. A good agreement between various CK predictions and results from molecular dynamics (MD) simulations is obtained. The fact that CK calculations are at least two orders of magnitude faster than MD simulations invites attention to the utility of the CK method as an efficient tool for elucidating the pathway of motion in complex systems.     

摩尔响应值与拓扑指数的关系

考察了链烷烃、链烷醇、酮和苯系列化合物的摩尔响应值与拓扑指数的关系,结果表明两者之间存在良好的线性关系。     

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.     

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.     

Thermodynamic Properties of Peptide Solutions. Part 17. Partial Molar Volumes and Heat Capacities of the Tripeptides GlyAspGly and GlyGluGly,and Their Salts K[GlyAspGly] and Na[GlyGluGly] in Aqueous Solution at 25 °C

The partial molar volumes, V^o₂, and partial molar heat capacities, C_p,2^o, at infinite dilution have been determined for the two tripeptides glycylaspartylglycine (glyaspgly) and glycylglutamylglycine (glyglugly), and also for their salts K[glyaspgly] and Na[glyglugly], in aqueous solution at 25 °C. The ionization constants at 25 °C for the aspartyl and glutamyl side-chains have also been determined. These new thermodynamic results have been combined with literature data for electrolytes to obtain the volume and heat capacity changes upon ionization of the acidic side-chains of the peptides. The results are compared with those for other carboxylic acid systems. The partial molar heat capacities and volumes have also been used to calculate the contributions of the acidic amino acid side-chains to the thermodynamic properties.     

A modified variation–perturbation approach to zero-point vibrational motion

We present a detailed investigation of the perturbation approach for calculating zero-point vibrational contributions to molecular properties. It is demonstrated that if the sum of the potential energy and the zero-point vibrational energy is regarded as an effective potential energy, the leading contribution to the first-order wave function vanishes in the perturbation approach. Two different perturbation approaches have been investigated numerically by calculations of some magnetic properties for a few diatomic molecules and the results obtained have been compared to the exact numerical results. It is shown that only a few terms need to be included in a perturbation expansion to obtain an accuracy in the calculated rovibrational contribution better than the quality normally obtained for the potential and property surfaces in electronic structure calculations. Received: 16 April 1999 / Accepted: 1 July 1999 / Published online: 4 October 1999