分子树拓扑指数与羧酸化合物pK_a值的定量构效关系

The Quantitative Structure-Property Relationships Between the Topological Indices of Molecular Tree and pK_a Values of Carboxylic Acids

基于Randic的碳原子支化度 (δi)提出非氢原子的酸性点价 (δai) ,由δai 建构分子树拓扑指数 (mF)及其分支指数 :树干指数 (mFc)、树叶指数 (mFx) ,用0 Fx、0 Fc、1Fc 及新提出的xp、L、x′、I等 12种结构参数与 38种羧酸化合物的酸性强度 (pKa)关联 ;用最佳变量子集算法拟合的最佳七元回归方程为 :pKa=11 4 0 933- 1 2 4 32 70 Fx- 0 6 172 30 Fc+0 0 970 0 1Fc- 0 982 0 0xp+1 2 8371L - 0 2 0 0 4 7x′ - 0 86 2 10I ,R =0 9871,S =0 16 8。模型经Jackknife法检验 ,结果表明 ,相关系数呈正态分布 ,具有总体稳健性。建立pKa 的十二元回归模型 ,其R=0 9886 ,平均误差为 0 116 ,优于文献的分子力学方法 (CoMFA)的分析结果 (其R =0 988,平均误差为0 12 1)。

A new acidity point valence(δ a_i) of non-hydrogen atom based on Randic′s branching degree(δ_i) is derived. A novel topological index(~mF) of molecular tree and its trunk index(~mF_c), leaf index(~mF_x) are set up from δ a_i. The ~0F_ x, ~0F_c, ~1F_c and other structural parameters(x_p,L,x′,I) exhibit an excellent correlation to the acidity pK_a of 38 carboxylic acids. The best linear equation of heptvariant regression is proposed:pK_a= 11.409 33-1.243 27~0F_x-0.617 23~0F_c+0.097 00~1F_c-0.982 00x_p+1.283 71L-0.200 47x′-0.862 10I, R=0.987 1, S=0.168. The model could be used effectively to predict the pK_a values of carboxylic acids. Furthermore, a modified Jackknife test is used to validate the model robustness. On the basis of 12 structural parameters, a satisfactory equation of the pK_a has been obtained, whose correlation coefficient(R) and mean error(S) were 0.988 6 and 0.116, respectively. The correlativity is better than the results obtained from comparative molecular field analysis(CoMFA) reported in the literature, where R and S were 0.988 and 0.121, respectively.