两个修正的分子连接性指数用于有机物反磁磁化率的改进QSPR研究

为了预测有机物的摩尔反磁磁化率，基于分子图的连接矩阵和可变的原子价连接性指数δi’提出了一种可变的分子连接性指数mχ’ 及其逆指数mχ”。包含在δi’、 mχ’ 和mχ”定义式中的三个可变参数x、 a和y的最佳值可通过优化方法得到。当x=2.9、a=1.10、y=0.36时, 通过最佳子变量集合法可以构建一个良好的5参数模型。对721个有机物（训练集），该模型的相关系数r、标准偏差s和平均绝对偏差分别是0.9930、4.96 cgs和3.74cgs。交叉验证说明，从统计学角度该模型具有良好的稳定性。另外该模型对另外360个有机物（测试集）摩尔反磁磁化率预测结果的平均绝对偏差为4.37cgs。结果表明本文的方法在预测有机物摩尔反磁磁化率方面比文献方法更有效。多元线性方法能得到比较理想的预测有机物摩尔反磁磁化率的模型。

Improved QSPR Study of Diamagnetic Susceptibilities for Organic Compounds Using Two Novel Molecular Connectivity Indexes

For predicting the molar diamagnetic susceptibilities of organic compounds, a variable molecular connectivity index ^mχ' and its converse index ^mχ'' based on adjacency matrix of molecular graphs and the variable atomic valence connectivity index δ_i' were proposed. The optimal values of parameters x, a, and y included in definition of δ_i', ^mχ' and ^mχ'' can be found by an optimization method. When x2.9, a1.10, and y0.36, a good five‐parameter model for the molar diamagnetic susceptibilities can be constructed from ⁰χ', ¹χ', ²χ', ¹χ'' and ²χ'' by using the best subset regression analysis method. The correlation coefficient r, standard error s, and average absolute deviation of the multilinear regression (MLR) model are 0.9930, 4.96 cgs, and 3.74 cgs, respectively, for the 721 organic compounds (training set). The cross‐validation by using the leave‐one‐out method demonstrates that the MLR model is highly reliable from the point of view of statistics. The average absolute deviation of predicted values of the molar diamagnetic susceptibility of another 360 organic compounds (test set) is 4.37 cgs for the MLR model. The results show that the current method is more effective than literature methods for estimating the molar diamagnetic susceptibility of an organic compound. The MLR method can provide an acceptable model for the prediction of the molar diamagnetic susceptibilities of organic compounds.