基于拓扑指数的链烷烃临界温度预测及外延

Prediction of critical temperatures of acyclic alkanes using topological indexes and its extrapolation

采用衍生于结构特征和非氢原子连接关系的23维拓扑指数代表链烷烃,并将该指数递交到多元线性回归用于建立临界温度预测模型。为了得到稳定的模型,采用两种方法(M5法与贪心算法)进行变量选择,并采用所得变量子集建立数学模型。所得结果显示:对于最好模型的测试集,相关系数的平方是R^2=0.9924;平均绝对误差是MAE=2.2532K。若将沸点实验值加入链烷烃描述符,则测试集的MAE值显著地降低。基于这些令人满意的结果,我们开展了外延预测研究。将碳原子数n≤9的链烷烃分入训练集,而C_(10)H_(22)(n=10)的同分异构体分入测试集,则所得测试集的MAE=3.6867K。若将八分之一的C_(10)H_(22)的同分异构体加到训练集用于建立模型,并预测余下的C_(10)H_(22)同分异构体,结果显示测试集的MAE值明显下降,即所得到的外推结果令人满意。

Acyclic alkanes were represented by 23-dimensional topological indices derived from structure characteristics and the con- nectivity of non-hydrogen atoms, and then the indices of acyclic alkanes were fed to multiple linear regressions （MLR） to build predic- tion models of critical temperatures. In order to obtain stable models, two methods of variables selections （M5 method and greedy method） were performed, and the subset of selected variables were used to construct mathematics models. The obtained results showed that the squared correlation coefficient is R2 = 0.9924 and mean absolute error is MAE = 2.2532K for the test set of the best model. If experimental boiling points were added to the descriptors of acyclic alkanes, the MAE of the test set were obviously decreased. Based on these satisfactory results, the researches of extrapolation were explored. Acyclic alkanes with carbon number of n ≤9 were classified as training set and the isomers of C10H22 （n = 10） as test set, and then the MAE = 3.6867K was obtained for the test set. If one eighth isomers of C10H22 were added to training set and the constructed models were used to predict the remaining isomers of C10H22, the re- suits showed that the MAE were obviously decreased for the test set. That means the results of extrapolation are satisfactory.