Randic支化度指数与环烷烃沸点的相关性

Relativity between Randic’ branch degree index and boiling points of cycloalkanes

按Randic的碳原子支化度(δi),在分子拓扑图的邻接矩阵基础上构建环烷烃的支化度指数(mXt)。用mXt及碳原子数(N)等参数,与258种环烷烃沸点(Tb)关联,经逐步回归建立最佳四元回归方程的相关系数(R)为0.9964。其平均计算误差为4.11K,符合Mihalic等人的R>0.99及小于5K的建模要求。经Jackknife法检验该模型具有总体稳健性,并能较准确估算与预测环烷烃的沸点。进入最佳数学模型的4个结构参数:一是0Xp与N反映环烷烃分子的大小,二是4Xp与3Xc反映分子的空间形状,它们共同揭示了影响环烷烃沸点的本质因素。

On the basis of molecular topological diagram＇s adjacency matric, Randic＇ carbon atom branch degree index （mXt） of cycloalkane has been developed. Correlation between mXt, the number of Carbon atoms（N）, and the boiling points（Tb） of 258 cycloalkanes was examined and the best regression formula was obtained by stepwise regression, whose correlation coefficient（R） is 0.996 4. The average relative error is 4.11K, agreeing with the Mihalic＇ standard about constructing model ： R 〉 0.99 and the average error less than 5K, which could provide estimation and prediction for the boiling points（Tb） of cycloalkanes. Furthermore, the model is examined to validate overall robustness with Jackknife tests. Form the four parameters of the best model, it is known that the dominant influence factors of the boiling points（Tb） for cycloalkanes are the molecular size（based on the 0Xp and N） and the space factors（based on the 4Xp and 3Xc）. The four structural parameters in the best model reflect the essential factors which influence the boiling points（Tb） of cycloalkanes.