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采用4种自相关拓扑指数和多元线性回归方法对29种烷烃的分子拓扑结构和辛烷值的关系进行了详细研究.其中用F(t)=∑n0i.5n0j.5方程计算得到的本征函数值优于其他3种方法,方程中的n表示与节点碳原子连接的碳原子数目或氢原子数目.忽略拓扑指数的高阶项即F(5)和F(6)项时,拟合方程的相关系数变化不大,自相关拓扑指数能够恰当地反映这些烷烃的分支程度和分子大小.在C节点—C连接和C节点—H连接两种方式中,相关系数对于马达法辛烷值(MON)和研究法辛烷值(RON)分别是0.980 2、0.983 1和0.992 0、0.989 3.当同时结合C节点—C连接和C节点—H连接的自相关拓扑指数时,拟合结果进一步改进,相关系数和平均误差分别为0.991 2、2.4(MON)和0.994 4、2.3(RON).
The relationship between the molecular topological structure and octane number of 29 paraffins has been studied in detail by using four kinds of autocorrelation topological indices and multiple linear regression methods, in which the eigenvalues calculated by F (t) = Σn0i.5n0j.5 equation The function value is superior to the other three methods, where n represents the number of carbon atoms or hydrogen atoms connected to the node carbon atom, and ignoring the higher-order terms F (5) and F (6) of the topological index, the fitting The correlation coefficient of the equation does not change much, and the autocorrelation topological index can properly reflect the degree of branching and the molecular size of these alkanes.In the two methods of C node-C connection and C node-H connection, the correlation coefficient for motor octane number (MON) and research octane number (RON) were 0.980, 2.0.983 1 and 0.992 0, respectively, 0.8989 3. When the autocorrelation topological index of the C-node-C junction and the C-node-H junction were combined, For further improvement, the correlation coefficient and the average error were 0.991, 2.24 (MON) and 0.994 4, 2.3 (RON), respectively.