芳烃分子描述符的修正和沸点预测建模

doi:10.11949/0438-1157.20190425

摘要/Abstract

摘要：

根据芳烃分子中碳原子所处化学环境的差异，修正分子描述符Randi?连接性指数中碳原子支化度参数δ_i ，提出新的分子描述符Modran；通过对比分析表明描述符Modran对芳烃分子的化学结构具有更好的选择性。分析芳烃沸点的影响因素，采用最优子集选择法，发现Modran一阶和二阶支化度指数、分子极化率和芳环碳原子占比四个分子描述符参数的组合对芳烃沸点具有良好的预测能力，进而建立包含Modran等四分子描述符的线性组合模型和神经网络模型。与Marrero-Pardillo基团贡献法比较，四分子描述符的神经网络模型将芳烃沸点预测的平均绝对误差由12.26 K降低到4.56 K。

关键词: 分子描述符, 芳烃, 沸点预测, 构效关系, 神经网络

Abstract:

According to the differences of chemical environment of carbon atoms in aromatic hydrocarbons, the carbon atom branching degree index δ_i in the Randi? connectivity index is modified, and a new molecular descriptor Modran is presented. Comparative analysis shows that the descriptor Modran has better selectivity for the chemical structure of aromatic molecules. Through analyzing the factors influencing the boiling points of aromatic hydrocarbons and using the best subset selection method, it is found that the combination of four molecular descriptors, such as Modran first-order and second-order branching index, molecular polarizability and aromatic ring carbon atom ratio, has good predictive ability for aromatics boiling point, and then linear combination model and neural network model including the four descriptors are established. Compared with the Marrero-Pardillo group contribution method, the neural network model of the four-molecule descriptor reduces the average absolute error of the boiling point prediction of aromatics from 12.26 K to 4.56 K.

Key words: molecular descriptor, aromatic hydrocarbons, boiling point prediction, quantitative structure-property relationship, neural network

中图分类号:

TQ 028.8

马香成, 秦蔚, 陈清林, 张冰剑. 芳烃分子描述符的修正和沸点预测建模[J]. 化工学报, 2019, 70(11): 4306-4314.

Xiangcheng MA, Wei QIN, Qinglin CHEN, Bingjian ZHANG. Modification of molecular descriptor and modeling for boiling point prediction of aromatic hydrocarbons[J]. CIESC Journal, 2019, 70(11): 4306-4314.

图/表 12

表1 部分芳烃化合物的沸点及其Wiener、Randi?、Modran分子描述符值

Table 1 Boiling point of some aromatic compounds and their Wiener, Randi? and Modran molecular descriptor values

No.	Name	lnW	$X 1 0.5$	$X M 1 0.5$	TB/K^①	Uncertainty/K^①
1	1-methyl-2-n-propylbenzene	4.796	2.201	1.242	457.82	0.7830
2	4-ethyl-m-xylene	4.754	2.176	1.205	461.51	0.5370
3	p-xylene	4.127	1.946	1.084	411.46	0.0593
4	m-xylene	4.111	1.946	1.086	412.22	0.0261
5	1-isopropyl-4-methylbenzene	4.787	2.167	1.197	450.27	0.0771
6	2-ethyl-1,4-dimethylbenzene	4.745	2.176	1.205	459.72	0.7230
7	1-ethyl-3,5-dimethylbenzene	4.754	2.173	1.209	457.07	1.1400
9	1-isopropyl-2-methylbenzene	4.736	2.171	1.201	451.45	0.0946
10	1-isopropyl-3-methylbenzene	4.762	2.167	1.200	448.20	1.3500
12	1-methyl-4-propylbenzene	4.844	2.197	1.239	456.50	0.7670
13	1,3-diethylbenzene	4.796	2.205	1.240	454.27	0.1890
14	sec-butylbenzene	4.796	2.201	1.235	446.44	0.0313
15	1,2,3,5-tetramethylbenzene	4.700	2.147	1.168	471.07	0.8890
16	1,2,4,5-tetramethylbenzene	4.710	2.147	1.166	469.88	1.6300
17	1-tert-butyl-3-methylbenzene	4.997	2.236	1.240	462.38	2.5900
18	1-tert-butyl-4-ethylbenzene	5.303	2.353	1.287	485.26	2.7000

表1 部分芳烃化合物的沸点及其Wiener、Randi?、Modran分子描述符值

Table 1 Boiling point of some aromatic compounds and their Wiener, Randi? and Modran molecular descriptor values

No.	Name	lnW	$X 1 0.5$	$X M 1 0.5$	TB/K^①	Uncertainty/K^①
1	1-methyl-2-n-propylbenzene	4.796	2.201	1.242	457.82	0.7830
2	4-ethyl-m-xylene	4.754	2.176	1.205	461.51	0.5370
3	p-xylene	4.127	1.946	1.084	411.46	0.0593
4	m-xylene	4.111	1.946	1.086	412.22	0.0261
5	1-isopropyl-4-methylbenzene	4.787	2.167	1.197	450.27	0.0771
6	2-ethyl-1,4-dimethylbenzene	4.745	2.176	1.205	459.72	0.7230
7	1-ethyl-3,5-dimethylbenzene	4.754	2.173	1.209	457.07	1.1400
9	1-isopropyl-2-methylbenzene	4.736	2.171	1.201	451.45	0.0946
10	1-isopropyl-3-methylbenzene	4.762	2.167	1.200	448.20	1.3500
12	1-methyl-4-propylbenzene	4.844	2.197	1.239	456.50	0.7670
13	1,3-diethylbenzene	4.796	2.205	1.240	454.27	0.1890
14	sec-butylbenzene	4.796	2.201	1.235	446.44	0.0313
15	1,2,3,5-tetramethylbenzene	4.700	2.147	1.168	471.07	0.8890
16	1,2,4,5-tetramethylbenzene	4.710	2.147	1.166	469.88	1.6300
17	1-tert-butyl-3-methylbenzene	4.997	2.236	1.240	462.38	2.5900
18	1-tert-butyl-4-ethylbenzene	5.303	2.353	1.287	485.26	2.7000

图1 芳烃分子沸点与Wiener拓扑指数（lnW）的线性拟合关系

Fig.1 Linear fitting between boiling point of aromatic hydrocarbons and Wiener topological index (lnW)

图3 芳烃分子沸点与新的Modran连接指数（ X M 1 0.5 ）的线性拟合关系

Fig.3 Linear fitting between boiling point of aromatic hydrocarbons and Modran index ( X M 1 0.5 )

图2 芳烃分子沸点与Randi?连接指数（ X 1 0.5 ）的线性拟合关系

Fig.2 Linear fitting between boiling point of aromatic hydrocarbons and Randi? index ( X 1 0.5 )

表2 最优子集选择法分子描述符筛选

Table 2 Selection of molecular descriptors by optimal subset method

No.	XM ₀	XM ₁	HOMA	lnSp	ACD	CIC2	R ²	F	RSE
1	*						0.9728	2280	11.70
2		*		*			0.9896	3010	7.29
3	*	*		*			0.9905	2160	7.03
4	*	*		*	*		0.9910	1680	6.90
5	*	*	*	*	*		0.9913	1360	6.85
6	*	*	*	*	*	*	0.9913	1130	6.89

图4 采用RSS、调整R 2、Cp和BIC参数对不同规模的模型进行最优子集选择的结果

Fig.4 Result of optimal subset selection for different scale models by RSS, adjustment R 2, Cp and BIC

图5 模型中四个分子描述符对芳烃沸点的贡献程度

Fig. 5 Contribution of four molecular descriptors to boiling point of aromatics in model

图6 用于芳烃沸点预测的单隐层神经网络

Fig.6 Single hidden layer neural network for boiling point prediction of aromatic hydrocarbons

表3 神经网络训练模型权重及阈值

Table 3 Weight and threshold of neural network training model

w	i ₁	i ₂	i ₃	i ₄	No.	θ(j)	γ(k)
j ₁	0.961	3.964	-0.678	2.084	1	4.496	5.985
j ₂	1.345	0.629	3.33	-2.316	2	-0.761
j ₃	-0.783	1.732	2.183	1.618	3	2.332

图7 芳烃沸点预测模型

Fig.7 Boiling point prediction model of aromatic hydrocarbons

图8 芳烃沸点QSPR-ML模型交叉验证

Fig.8 Cross-validation of aromatics boiling point QSPR-ML model

表4 基团贡献法、QSPR与QSPR-ML模型对于芳烃沸点预测效果对比

Table 4 Comparison of group contribution method, QSPR and QSPR-ML models for predicting boiling point of aromatics

模型	数据	R ²	MSE	RSE	AAE	APE/%	分子类型
M-P基团贡献法	66	0.9602	334.71	16.03	12.26	2.434	单环芳烃
QSPR 训练集	66	0.9910	43.96	6.90	5.11	1.038	单环芳烃
QSPR 测试集	66	0.9897	50.69	7.20	5.56	1.134	单环芳烃
QSPR-ML 训练集	66	0.9936	33.37	5.77	4.56	0.933	单环芳烃
QSPR-ML 测试集	66	0.9942	38.03	5.75	5.06	1.057	单环芳烃
HMC-WL-ANN	20	—	—	—	26.85	3.814	多环芳烃
QSPR（Dai）	50	0.9910	—	6.46	—	—	不饱和烃

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