扩展的距离矩阵指数W~*及其应用研究

重新定义了距离矩阵及距离矩阵拓扑指数W~*，该定义考虑分子中每一原子的 性质和成键情况以及分子中每一原子与所有其它原子的结合情况。拓扑指数W~*对 于饱和碳氢体系可还原为Wiener的距离矩阵指数W，同时，W~*还可一般地应用于含 多重键及杂质原子的有机体系和无机体系。本研究用W~*相关的卤代甲烷标准生成 焓、SiX_n（X = F，Cl，Br，I，n = 1～4）体系的标准生成焓，相关系数均在0. 99以上，置信度大于99.9%。并用W~*研究了含苯环的碳氢体系气相色谱保留指数， 含氧原子的醛酮体系的标准生成焓以及卤代苯体系的辛醇/水分配系数。对饱和碳 氢体，W为W~*的特殊形式。

Study on the Enlarged topological Index of Distance Matrix and Its Application

The distance matrix S and the topological index of distance matrix W~* were redefined in this paper. W~* = MSI, M = (m_1, m_2, …, m_n), S = (S_(ij)_(n * n)), I = (I_1, I_2, …, I_n)~T, m_i is the number of bonded electrons. I_i is electronegativity, S_(ij), R_(ij) is the sum of bond length from i to j. To AB_n molecules, W~* = n(1 + ΔI)·[I_1 + 0.5(3n-1)I_2]/R. W~* is equal to the distance matrix topological index W of Wiener's to the systems of saturated hydrocarbons, but W~* can generally be applied to the systems of unsaturated hydrocarbons, organic compounds which include some heteroatoms and inorganic compounds. In this paper several systems were studied by W~*, the standard formative enthalpies of halide methyl, the standard formative enthalpies of SiX_n (X = F, Cl, Br, I, n = 1 ～ 4), the standard formative enthalpies of saturated hydrocarbons, the retention indices of gas chromatography RI of unsaturated hydrocarbon. All the correlation coefficients are larger than 0.99. W is the special form of W~* to saturated hydrocarbons.