中文摘要：

应用密度泛函理论（DFT）,在B3LYP/6-31＋G（d）水平上对含有5～24个碳原子的部分液相链烷烃进行结构优化和量化计算其分子中各个原子间空间拓扑距离,并构建拓扑距离矩阵。结合分子中各原子的支化度,应用原子的平衡电负性对分子图进行着色,得到新型结构拓扑指数PXm（m=1,2,3）。采用多元线性回归技术建立液相链烷烃热导率λ与PXm（m=1,2,3）的定量关系拓扑模型,并用该模型对热导率λ进行预测与估算,结果表明实验值与预测值、估算值均很吻合。同时,采用留一法（leave-one-out）和外检验方法测试模型的内部稳定性和外部预测能力。与文献结果比较,本文所用参数少,计算简便,为液相链烷烃导热的研究提供了一种新方法。

英文摘要：

Some liquid alkanes bearing 5—24 carbon atoms were optimized in structure and the topological distance matrix was built with the space topological distance among atoms calculated by using density functional theory（DFT）at the B3LYP/6-31＋G（d）level.A new group of topological index PXm（m=1,2,3）was introduced based on the topological distance matrix,and branch vertex of atoms in a molecule was put forward by coloring atoms in the molecular graph with equilibrium electro-negativity.The topological model of quantitative relationship between thermal conductivity λ and PXm of liquid alkanes was proposed by the multivariate linear regression（MLR）.The results from the formula indicated that the deviation between calculated values and experimental data and that between predicted values and experimental data were small and within the experimental errors.To validate the estimation stability for internal samples and the predictive ability for external samples of the models,the method of leave-one-out （LOO）cross validation（CV）and external validation were performed.Compared with other results reported,the number of parameters in this model is much fewer and the calculation is much easier.It provides a new method for predicting the thermal conductivity of liquid alkanes.