基于内核构建的Cu-Au-Pd团簇稳定结构优化

吴夏; 魏征

doi:10.7498/aps.66.150202

摘要

具有特殊催化、磁性和化学活性的三元合金团簇已成为基础科学研究的热点问题.确定其稳定结构是研究团簇性质的重要前提.针对大尺寸Cu-Au-Pd团簇结构优化，提出了内核构建的方法改进了自适应免疫优化算法的效率（称为AIOA-IC算法）.采用基于紧束缚势二阶矩近似的多体Gupta势函数来描述三元合金团簇原子间相互作用.为测试算法效率优化了原子数为60的Ag-Pd-Pt团簇稳定结构.结果显示新得到的结构比文献报道的团簇结构势能量值更低，由此可知AIOA-IC算法具有更强的势能面搜索能力.运用该算法研究了38及55原子Cu-Au-Pd团簇的稳定结构.所研究的38原子Cu-Au-Pd团簇包含了五折叠、六折叠和截角八面体结构，并且原子成分比例影响了团簇的结构类型.而55原子Cu-Au-Pd团簇均为完整二十面体结构，序列参数显示Cu，Au和Pd原子分层现象明显.对于147原子Cu12Au93Pd42团簇完整二十面体结构，中心原子为Au，内层和次外层分别被12个Cu原子和42个Pd原子占据，最外层则被92个Au原子占满.通过原子半径及表面能分析了Cu，Pd和Au原子分别倾向于分布在内层、次外层和最外层的规律.

关键词:

Abstract

The trimetallic cluster has become a hot topic in the field of basic scientific research due to its special catalytic, magnetic and chemical activities. It is very important to determine the stable structures of clusters. In order to optimize the stable structure of large size Cu-Au-Pd cluster, a modification algorithm of adaptive immune optimization algorithm based on the construction of inner cores, called AIOA-IC algorithm, is proposed. The only difference between AIOA and AIOA-IC lies in their starting structures. Instead of generating the starting structure randomly in AIOA, an inner core in the AIOA-IC method is used for generating the starting structure. Several motifs, such as decahedron, icosahedron, face centered cubic, six-fold pancake structure, and Leary tetrahedron, are randomly selected as the inner cores. The size of the inner core is determined according to the cluster size. The Gupta potential based on the second moment approximation of tight binding potential is used to describe the interatomic interaction between Cu-Au-Pd clusters, and the corresponding potential parameters, such as the cohesive energy, lattice constants, and elastic constants are obtained by fitting the experimental values. To test the efficiency of the proposed algorithm, the stable structure of Ag-Pd-Pt cluster with 60 atoms is optimized. The results show that the new structure has lower energy than the cluster reported in the literature. It can be seen that the AIOA-IC algorithm has a stronger ability to search for the potential energy surface of the Gupta potential. Furthermore, the proposed algorithm is used to optimize the stable structures of 38-atom and 55-atom Cu-Au-Pd clusters. The structures of the investigated Cu6AunPd32-n, CunAu6Pd32-n and CunAu32-nPd6 (n=1-31) clusters can be categorized into three types:five-fold, six-fold, and truncated octahedron. Moreover, it is found that the compositions of Cu, Au and Pd atoms in the trimetallic clusters affect the structural type of the cluster. However, the Cu13AunPd42-n, CunAu13Pd42-n, and CunAu42-nPd13 (n=1-41) clusters each have a structure of complete Mackay icosahedron. Furthermore, the order parameter results show that Cu, Au and Pd atoms each have a significant segregation phenomenon. For the 147-atom Cu12Au93Pd42 cluster, the structure is also of an icosahedron. The central atom is Au, and the inner shell and sub-outer shell are occupied by 12 Cu and 42 Pd atoms, respectively. The outer shell is filled with 92 Au atoms. The results show that the Cu, Pd and Au atoms tend to be distributed in the inner shell, sub-outer shell, and outer shell, respectively. This can be further explained by the results of the atomic radius and the surface energy.

Keywords:

作者及机构信息

吴夏^1,2,
魏征^1,2

1.
安庆师范大学化学化工学院, 安庆 246011;

2.
安庆师范大学, 光电磁功能材料安徽省重点实验室, 安庆 246011

通信作者: 吴夏, xiawu@aqnu.edu.cn

基金项目: 安徽高校自然科学研究项目重点项目（批准号：KJ2017A349）资助的课题.

Authors and contacts

Wu Xia^1,2,
Wei Zheng^1,2

1.
School of Chemistry and Chemical Engineering, Anqing Normal University, Anqing 246011, China;

2.
Anhui Key Laboratory of Functional Coordination Compounds, Anqing Normal University, Anqing 246011, China

Corresponding author: Wu Xia, xiawu@aqnu.edu.cn

Funds: Project supported by the Key University Science Research Project of Anhui Province,China (Grant No.KJ2017A349).

参考文献

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[2]	Zhang M, Zhang J F, Gu T, Zhang H Y, Luo Y H, Cao W 2015 J. Phys. Chem. A 119 3458
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[4]	Ma Z N, Jiang M, Wang L 2015 Acta Phys. Sin. 64 187102 (in Chinese) [马振宁, 蒋敏, 王磊 2015 物理学报 64 187102]
[5]	Sattler K, Mhlbach J, Recknagel E 1980 Phys. Rev. Lett. 45 821
[6]	Ferrando R, Jellinek J, Johnston R L 2008 Chem. Rev. 108 845
[7]	Meitzner G, Via G H, Lytle F W, Sinfelt J H 1985 J. Chem. Phys. 83 4793
[8]	Mao H, Huang T, Yu A S 2014 J. Mater. Chem. A 2 16378
[9]	Zhang X, Zhang F, Chan K Y 2004 Catal. Commum. 5 749
[10]	Wu X, Liu Q M, Sun Y, Wu G H 2015 RSC Adv. 5 51142
[11]	Deaven D M, Tit N, Morris J R, Ho K M 1996 Chem. Phys. Lett. 256 195
[12]	Wales D J, Doye J P K 1997 J. Phys. Chem. A 101 5111
[13]	Cai W S, Shao X G 2002 J. Comput. Chem. 23 427
[14]	Shao X G, Cheng L J, Cai W S 2004 J. Chem. Phys. 120 11401
[15]	Johnston R L 2003 J. Chem. Soc. Dalton Trans. 22 4193
[16]	Doye J P K, Meyer L 2005 Phys. Rev. Lett. 95 063401
[17]	Wu X, Liu Q M, Duan R Y, Wei Z 2016 Acta Phys. Sin. 65 210202 (in Chinese) [吴夏, 刘启满, 段仁燕, 魏征 2016 物理学报 65 210202]
[18]	Northby J A 1987 J. Chem. Phys. 87 6166
[19]	Xiang Y H, Cheng L J, Cai W S, Shao X G 2004 J. Phys. Chem. A 108 9516
[20]	Yang X L, Cai W S, Shao X G 2007 J. Comput. Chem. 28 1427
[21]	Shao X G, Yang X L, Cai W S 2008 Chem. Phys. Lett. 460 315
[22]	Gupta R P 1981 Phys. Rev. B 23 6265
[23]	Cleveland C L, Landman U, Schaaff T G, Shafigullin M N, Stephens P W, Whetten R L 1997 Phys. Rev. Lett. 79 1873
[24]	Mantina M, Valero R, Truhlar D G 2009 J. Chem. Phys. 131 064706
[25]	Wu X, Wei Z, Liu Q M, Pang T, Wu G H 2016 J. Alloy Compd. 687 115
[26]	Darby S, Mortimer-Jones T V, Johnston R L, Roberts C 2002 J. Chem. Phys. 116 1536
[27]	Ismail R, Johnston R L 2010 Phys. Chem. Chem. Phys. 12 8607
[28]	Rossi G, Ferrano R, Rapallo A, Fortunelli A, Curley B C, Lloyd L D, Johnston R L 2005 J. Chem. Phys. 122 194309
[29]	Cheng L J, Cai W S, Shao X G 2004 Chem. Phys. Lett. 389 309
[30]	Wu X, Cai W S, Shao X G 2009 J. Comput. Chem. 30 1992
[31]	Wu X, Sun Y, Gao Y C, Wu G H 2013 J. Mol. Model. 19 3119
[32]	Wu X, Wu G H, Chen Y C, Qiao Y Y 2011 J. Phys. Chem. A 115 13316
[33]	Liu D C, Nocedal J 1989 Math. Program 45 503
[34]	Wu X, Sun Y, Wei Z, Chen T J 2017 J. Alloy Compd. 701 447

施引文献

[1]	Sharma S, Kurashiqe W, Nobusada K, Neqishi Y 2015 Nanoscale 7 10606
[2]	Zhang M, Zhang J F, Gu T, Zhang H Y, Luo Y H, Cao W 2015 J. Phys. Chem. A 119 3458
[3]	Li T J, Sun Y, Zheng J W, Shao G F, Liu T D 2015 Acta Phys. Sin. 64 153601 (in Chinese) [李铁军, 孙跃, 郑骥文, 邵桂芳, 刘暾东 2015 物理学报 64 153601]
[4]	Ma Z N, Jiang M, Wang L 2015 Acta Phys. Sin. 64 187102 (in Chinese) [马振宁, 蒋敏, 王磊 2015 物理学报 64 187102]
[5]	Sattler K, Mhlbach J, Recknagel E 1980 Phys. Rev. Lett. 45 821
[6]	Ferrando R, Jellinek J, Johnston R L 2008 Chem. Rev. 108 845
[7]	Meitzner G, Via G H, Lytle F W, Sinfelt J H 1985 J. Chem. Phys. 83 4793
[8]	Mao H, Huang T, Yu A S 2014 J. Mater. Chem. A 2 16378
[9]	Zhang X, Zhang F, Chan K Y 2004 Catal. Commum. 5 749
[10]	Wu X, Liu Q M, Sun Y, Wu G H 2015 RSC Adv. 5 51142
[11]	Deaven D M, Tit N, Morris J R, Ho K M 1996 Chem. Phys. Lett. 256 195
[12]	Wales D J, Doye J P K 1997 J. Phys. Chem. A 101 5111
[13]	Cai W S, Shao X G 2002 J. Comput. Chem. 23 427
[14]	Shao X G, Cheng L J, Cai W S 2004 J. Chem. Phys. 120 11401
[15]	Johnston R L 2003 J. Chem. Soc. Dalton Trans. 22 4193
[16]	Doye J P K, Meyer L 2005 Phys. Rev. Lett. 95 063401
[17]	Wu X, Liu Q M, Duan R Y, Wei Z 2016 Acta Phys. Sin. 65 210202 (in Chinese) [吴夏, 刘启满, 段仁燕, 魏征 2016 物理学报 65 210202]
[18]	Northby J A 1987 J. Chem. Phys. 87 6166
[19]	Xiang Y H, Cheng L J, Cai W S, Shao X G 2004 J. Phys. Chem. A 108 9516
[20]	Yang X L, Cai W S, Shao X G 2007 J. Comput. Chem. 28 1427
[21]	Shao X G, Yang X L, Cai W S 2008 Chem. Phys. Lett. 460 315
[22]	Gupta R P 1981 Phys. Rev. B 23 6265
[23]	Cleveland C L, Landman U, Schaaff T G, Shafigullin M N, Stephens P W, Whetten R L 1997 Phys. Rev. Lett. 79 1873
[24]	Mantina M, Valero R, Truhlar D G 2009 J. Chem. Phys. 131 064706
[25]	Wu X, Wei Z, Liu Q M, Pang T, Wu G H 2016 J. Alloy Compd. 687 115
[26]	Darby S, Mortimer-Jones T V, Johnston R L, Roberts C 2002 J. Chem. Phys. 116 1536
[27]	Ismail R, Johnston R L 2010 Phys. Chem. Chem. Phys. 12 8607
[28]	Rossi G, Ferrano R, Rapallo A, Fortunelli A, Curley B C, Lloyd L D, Johnston R L 2005 J. Chem. Phys. 122 194309
[29]	Cheng L J, Cai W S, Shao X G 2004 Chem. Phys. Lett. 389 309
[30]	Wu X, Cai W S, Shao X G 2009 J. Comput. Chem. 30 1992
[31]	Wu X, Sun Y, Gao Y C, Wu G H 2013 J. Mol. Model. 19 3119
[32]	Wu X, Wu G H, Chen Y C, Qiao Y Y 2011 J. Phys. Chem. A 115 13316
[33]	Liu D C, Nocedal J 1989 Math. Program 45 503
[34]	Wu X, Sun Y, Wei Z, Chen T J 2017 J. Alloy Compd. 701 447

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