Novel topological index F based on incidence matrix

Based on incidence matrix W, the novel topological index F is defined by the matrices L, W, X as F = LWX. The properties, the chemical environments, and the interaction of the vertexes in a molecule are taken into account in this definition. Several good QSPR models in the hetero-atom-containing organic compounds and inorganic compounds are obtained. Moreover, based on the definition of F and the values C(i) of the vertexes or the values (m)F(ij) of the chemical bonds, we have obtained serial indices, (m)F(v), (m)F(b), and F(w). They are successfully applied to QSPR models and good correlation results have been obtained as well.     

Modification of the Wiener Index. 2

A novel topological index based on the Wiener Index is proposed as W = 1/2, summation(n/ij)=S*(ij) the element S*(ij) of the distance matrix is defined either as S*(ij)= square root (E(i)E(j)/R(ij) (atoms i and j are adjacent) or as S*(ij)=(j-i+1)square root (E(i)...xE /R(ij) (atoms i and j are not adjacent), where E(i) and E(j) represent the total energy of the valence electrons of vertexes i and j, respectively, R(ij) is the sum of the distance between the vertexes i and j in a molecular graph. The distance and the energy of the vertexes in a molecule are taken into account in this definition. Hence the application of the index W to multiple bond and heteroatom-containing organic systems and inorganic systems is possible. Good correlation coefficients are achieved not only in the standard formation enthalpy of methyl halides, halogen-silicon, but also in the retention index of gas chromatography of the hydrocarbons.     

利用分子路径指数矢量对烷烃摩尔响应值的估计与预测

 利用分子路径指数矢量表示烷烃分子结构方法 ,结合多元线性回归算法及反传神经网络算法 ,对烷烃摩尔响应值进行处理 ,获得了比文献更佳的预测效果 ,交互校验的相关系数达 0 96 8以上。     

Modification of Wiener Index and its application

A novel topological index based on the Wiener Index is proposed as W* = 1/2 sigma (n)(i,j=1) S(*)(ij), the element S(*)(ij) of the distance matrix is defined either as S(*)(ij) = alpha x square root of I(i)I(j)/R(ij) (atoms i and j are adjacent) or as S(*)(ij) = = alpha x (j-i+1)square root of I(i) x x x x x I(j)/R(ij) (atoms i and j are not adjacent), where I(i) and I(j) represent the electronegativity of vertices i or j, respectively, R(ij)() is the sum of the bond length between the vertices i and j in a molecular graph, and alpha = (Z(i)/Z(j))(0.5), where Z(i) and Z(j) are the atomic numbers of the positive valence atom i and the negative valence atom j, respectively. The properties and the interaction of the vertices in a molecule are taken into account in this definition. That is why the application of the index W to heteroatom-containing and multiple bond organic systems and inorganic systems is possible. Correlation coefficients above 0.97 are achieved in the prediction of the retention index of gas chromatography of the hydrocarbons, the standard formation enthalpy of methyl halides, halogen-silicon, and inorganic compounds containing transition metals.     

计算机自动结构解析专家系统研究──一个新的拓扑等价性识别算法

介绍了一个正确识别化合物结构或结构片断中各原子的拓扑等价性问题的新算法。算法中引入了节点矩阵Ｎ和键矩阵Ｂ，并由这两个新矩阵来计算化合物结构图中的各节点的特征值，以此来表征节点的环境特征，从而识别节点的拓扑等价性，以保证结构解析专家系统结构产生器的穷举和非冗余性。     

A generalized graph-theoretical matrix of heterosystems and its application to the VMV procedure

The extensions of generalized (molecular) graph-theoretical matrix and vector-matrix-vector procedure are considered. The elements of the generalized matrix are redefined in order to describe molecules containing heteroatoms and multiple bonds. The adjacency, distance, detour and reciprocal distance matrices of heterosystems, and corresponding vectors are derived from newly defined generalized graph matrix. The topological indices, which are most widely used in predicting physicochemical and biological properties/activities of various compounds, can be calculated from the new generalized vector-matrix-vector invariant.     

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.     

Degeneracy of some matrix graph invariants

New matrices associated with graphs and induced global and local topological indices of molecular graphs were proposed recently by Diudea, Minailiuc and Balaban. These matrices in canonical form are matrix graph invariants. A combined degeneracy of such invariants is considered. For every case of degeneracy corresponding graphs are presented.     

The multiplicative version of the Wiener index

The classical Wiener index, W(G), is equal to the sum of the distances between all pairs of vertexes of a (molecular) graph, G. We now consider a related topological index, pi(G), equal to the product of distances between all pairs of vertexes of G. The basic properties of the pi index are established and its possible physicochemical applications examined. In the case of alkanes, pi and W are highly correlated; a slightly curvilinear correlation exists between In pi and W.     

Novel atomic-level-based AI topological descriptors: application to QSPR/QSAR modeling

Novel atomic level AI topological indexes based on the adjacency matrix and distance matrix of a graph is used to code the structural environment of each atomic type in a molecule. These AI indexes, along with Xu index, are successfully extended to compounds with heteroatoms in terms of novel vertex degree v(m), which is derived from the valence connectivity delta(v) of Kier-Hall to resolve the differentiation of heteroatoms in molecular graphs. The multiple linear regression (MLR) is used to develop the structure-property/activity models based on the modified Xu and AI indices. The efficiency of these indices is verified by high quality QSPR/QSAR models obtained for several representative physical properties and biological activities of several data sets of alcohols with a wide range of non-hydrogen atoms. The results indicate that the physical properties studied are dominated by molecular size, but other atomic types or groups have small influences dependent on the studied properties. Among all atomic types, -OH groups seem to be most important due to hydrogen-bonding interactions. On the contrary, -OH groups play a dominant role in biological activities studied, although molecular size is also an important factor. These results indicate that both Xu and AI indices are useful model parameters for QSPR/QSAR analysis of complex compounds.     

价电子轨道能量拓扑指数mZ及其应用

受Randic分子连接性拓扑指数^mZ的启发,本文构建了价电子轨道能量拓扑指数^mZ。用^mZ的0、1阶指数分别与无机氢化物的pKa1值、20种碱金属卤化物的晶格能U、生成焓△rHm、水化能△rG^0m和气态碱金属卤化物核间距R0关联,拟合的回归方程的相关系(指)数,满足优级或良级标准。预测取得较好的结果。     

一种新的分子拓扑指数及其在QSPR/QSAR研究中的应用

通过引入量子数、键参数,认为分子的性质与其中各原子的电负性、价电子数、成键电子数、价层主量子数及各化学键的键长有关,提出了一种新的分子拓扑指数mAY.采用该拓扑指数对饱和烷烃、烷基苯、烷氧氯硅烷、卤代苯、含氮杂环化合物、碱金属卤化物及卤化锡的性质/活性进行了相关关系的研究.结果表明,mAY与有机物和无机物的性质/活性间具有良好的相关性.