氟化氢团簇(HF)n(n=2~8)拓扑性区别氢键构型的图论列举法和量子化学计算法研究

doi:10.7503/cjcu20160275

摘要/Abstract

摘要：

利用提出的图论程序列举出氟化氢团簇(HF)_n(n=2~8)所有可能存在的拓扑性区别氢键构型, 通过精密调查获得有可能存在的拓扑性区别构型, 发现了满足HF团簇稳定性的若干条件, 在这些条件的基础上编写FORTRAN程序和Python语言执行程序, 再用画图软件包GraphViz2.37自动画出对应的有向图或条件性有向图. 以对应的有向图作理论框架, 分别利用从头算法Moller-Plesset(MP2)二级微扰方法和密度泛函理论(DFT)方法B3LYP计算水平的 6-31G^**(d,p)基组对氟化氢团簇(HF)_n(n=3~7)所有拓扑性区别条件性有向图对应的初始结构进行结构优化并作振动频率分析, 获得氟化氢团簇(HF)_n(n=2~7)的最稳定构型, 发现了氟化氢团簇的五聚体(HF)₅、六聚体(HF)₆和七聚体(HF)₇等一些新的稳定结构.

关键词: 氟化氢团簇, 图论列举法, 氢键矩阵, 有向图, 拓扑性区别, 量子化学计算

Abstract:

A graph theoretical procedure to generate all the possible topology-distinct structures for hydrogen fluoride(HF) clusters was presented and all the possible topology-distinct structures for hydrogen fluoride (HF)_n(n=2—8) clusters were enumerated in this work. On the basis of the restrictions found, FORTRAN program was designed and executed by Python program, and the corresponding diagraphs or restrictive digraphs were drawn by means of free graph visualization software, GraphViz 2.38 for HF cluster (HF)_n(n=2—8) . Within the theoretical framework of the corresponding digraphs or restrictive digraphs, all the topology-distinct local minima for (HF)_n(n=3—7) were optimized and analyzed by means of ab initio method and density functional theory(DFT) method at the level of MP2/6-31G^**(d,p) and B3LYP/6-31G^**(d,p), respectively. The local minimum structures for (HF)_n(n=3—7) are the same as those in the previous works. For HF pentamer, hexamer and heptamer, some new local minimum structures were obtained.

Key words: Hydrogen fluoride cluster, Graph theoretical enumeration, Hydrogen bond matrix, Digraph, Topology-distinct, Quantum chemical calculation

中图分类号:

O641

TrendMD:

买合木提江·杰力, 阿布来提·麦麦提, 阿里木江·艾拜都拉, 买买提·吐尔逊. 氟化氢团簇(HF)_n(n=2~8)拓扑性区别氢键构型的图论列举法和量子化学计算法研究. 高等学校化学学报, 2016, 37(12): 2275.

MAHMUTJAN Jelil, ABLAT Mamat, ALIMJAN Abaydulla, MAMAT Tursun. Investigation of Topology-distinct Stable Structures for Hydrogen Fluoride Clusters (HF)_n(n=2—8) by the Methods of Graph Theoretical Enumerations and Quantum Chemical Calculations^†. Chem. J. Chinese Universities, 2016, 37(12): 2275.

图/表 9

Fig.1 Structure of a hydrogen-bonded HF cluster trimer(A) with the equivalent graph(B) and the corresponding adjacency matrix(C)

Fig.2 Structure of a hydrogen-bonded HF cluster trimer with the equivalent digraph and the corresponding hydrogen-bond matrix

Table 1 Numbers of graphs, digraphs, and restrictive digraphs of HF clusters(HF)n(n=2—8) and the number of stable structures of HF clusters(HF)n(n=2—7) under the calculation method of MP2/6-31G**(d,p)

Project	No. of vertice
Project	2	3	4	5	6	7	8
Graph	1	2	7	21	112	697	6386
Digraph	1	5	27	247	3272	55005	1104449
Restrictive digraph		2	2	9	51	320	2443
Local minima	1	2	2	4	8	14

Fig.3 All the enumerated possible topology-distinct graphs and digraphs with n vertices for(HF)n(n=2—4) The designated patterns(2A, 3A, 3B, 4A and 4B) correspond to the stable structures.

Fig.4 Enumerated restrictive digraphs generated from H-B matrices by Python program andGraphViz 2.37 program package corresponding to HF pentamer and hexamerThe designated patterns(f, g, h and i) correspond to the stable structures.

Fig.5 Digraphs and the optimized geometries of HF clusters(HF)n(n=2—7)

Table 2 14 local minima and corresponding total energy and relative total energy of the (HF)7 clusters[MP2/6-31G**(d,p)]

Local minima	E/eV	ΔE/eV	ΔE/kJ
7A	-19083.58598	0	0
7G	-19083.07658	0.50864	49.16
7F	-19083.04035	0.54672	52.68
7N	-19082.62860	0.95744	92.42
7H	-19082.71929	0.86768	83.64
7J	-19082.98659	0.59840	57.86
7D	-19083.34520	0.24208	23.22
7K	-19082.98847	0.59840	57.66
7L	-19082.93640	0.65008	20.89
7B	-19083.36094	0.22576	21.71
7E	-19083.09200	0.49504	47.70
7C	-19083.38822	0.19856	19.08
7M	-19082.85767	0.72896	70.29
7I	-19082.92199	0.66368	64.10

Fig.6 Relative energy of the local minima of (HF)7 with the calculation method of MP2/6-31G**(d,p)

Fig.7 Relative energy and the numbers of hydrogen bond of the local minima of (HF)7 with the calculation method of B3LYP/6-31G**(d,p)

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