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†

doi:10.7503/cjcu20160275

Abstract

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

CLC Number:

O641

TrendMD:

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^†[J]. Chem. J. Chinese Universities, 2016, 37(12): 2275.

Figures/Tables 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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