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改进的自适应免疫优化算法用于Pd-Pt合金团簇结构快速优化

吴夏 刘启满 段仁燕 魏征

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改进的自适应免疫优化算法用于Pd-Pt合金团簇结构快速优化

吴夏, 刘启满, 段仁燕, 魏征

A modified adaptive immune optimization algorithm for geometrical optimization of Pd-Pt clusters

Wu Xia, Liu Qi-Man, Duan Ren-Yan, Wei Zheng
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  • Pd-Pt合金团簇在催化、光学和磁学等基础科学及应用领域吸引了广泛的研究兴趣,优化不同元素序列组成的最稳定结构是探究其特殊性质的首要任务.本文结合了启发式优化算法的优点及动态建模的思想,提出了一种自适应免疫优化算法(AIOA)的改进算法,称之为AIOA-BDLS-ILS算法,用于合金团簇结构快速优化.运用该算法优化标准的二元Lennard-Jones模型团簇结构以测试算法效率,结果表明与BDLS-ILS算法相比该算法更为高效.优化34原子Pd-Pt团簇时发现了12个能量更低的结构.此外,50及79原子Pd-Pt团簇中,十面体及外层密堆积的十面体构型为主要构型,还存在双面心立方结构及少量的不完整二十面体结构.序列参数显示Pd-Pt团簇中Pd和Pt分层现象明显.
    Bimetallic Pd-Pt clusters have attracted wide interest because of their special catalytic, optical, electronic, and magnetic properties. However, the geometrical optimization of Pd-Pt cluster has been a difficult task due to the homotopic problem, i.e., in some binary clusters, these clusters are identical in configuration, but different in relative arrangement of two types of atoms. For a fixed geometrical configuration the iterated local search(ILS) method is adopted to search the optimal homotop. By the combination of the merit of heuristic optimization algorithm and the idea of dynamic lattice searching(DLS), an adaptive immune optimization algorithm(AIOA) is modified, and the modified AIOA is called AIOA-BDLS-ILS method. To evaluate the efficiency of the improved method, the optimization of binary Lennard-Jones clusters up to 100 atoms is performed. The Results show that the CPU time for one hit of the global minima is less than 5000 s for all clusters and it is less than 1000 s for most clusters. Compared with previously reported BDLS-ILS method, the proposed method is very efficient. The method is thus proved to be efficient. It can be deduced that the method should be a universal algorithm for the fast optimization of binary or bimetallic clusters. Furthermore, the Gupta potential is used to describe the interatomic interactions in Pd-Pt clusters, which is based on the second moment approximation to tight binding theory, and the corresponding potential parameters are fitted to the experimental values of cohesive energy, lattice constant, and elastic constants for the face centered cubic crystal structure at 0 K. The structural optimizations of Pd-Pt clusters with 34, 50 and 79 atoms are performed by the AIOA-BDLS-ILS method. Results show that for optimizing the 34-atom Pd-Pt clusters, 12 new structures with lower energies are found. In 34-atom bimetallic Pd-Pt clusters, the motifs can be categorized into five classes, i.e., 12 decahedral structures, 3 decahedral structures with close packing anti-layers, 7 incomplete Mackay icosahedral structures, 6 poly-icosahedral structures, and 5 structures composed of two 19-atom double icosahedra. In 50- and 79-atom Pd-Pt clusters, the structural characteristics and the atomic distributions are analyzed. The results indicate that the decahedral and decahedral structures with close-packed configurations are dominant, and twin face centered cubic and partial icosahedral structures are also found. Moreover, the order parameter is adopted to analyze the distributions of different types of atoms in Pd-Pt clusters, which are calculated by the average distance of Pd or Pt atoms from the center of a cluster. The results show that there exists the segregation phenomenon of Pd and Pt atoms in Pd-Pt clusters, i.e., Pd atoms tend to occupy the surface sites, and Pt atoms prefer to occupy the inner core sites. This is explained by the lower surface energy of Pd(125-131 meV-2) than that of Pt(155-159 meV-2).
      通信作者: 吴夏, xiawu@aqnu.edu.cn
    • 基金项目: 国家自然科学基金(批准号:21203002,31570417)资助的课题.
      Corresponding author: Wu Xia, xiawu@aqnu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China(Grant Nos. 21203002, 31570417).
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    Doye J P K, Meyer L 2005 Phys. Rev. Lett. 95 063401

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    Marques J M C, Pereira F B 2010 Chem. Phys. Lett. 485 211

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    Ye T, Xu R C, Huang W Q 2011 J. Chem. Inf. Model. 51 572

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    Rondina G G, Da Silva J L F 2013 J. Chem. Inf. Model. 53 2282

    [25]

    Lai X J, Xu R C, Huang W Q 2011 J. Chem. Phys. 135 164109

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    Wu X, Cheng W 2014 J. Chem. Phys. 141 124110

    [27]

    Shao X G, Yang X L, Cai W S 2008 Chem. Phys. Lett. 460 315

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    Shao X G, Wu X, Cai W S 2010 J. Phys. Chem. A 114 12813

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    Liu D C, Nocedal J 1989 Math. Program. 45 503

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    Lim B, Wang J G, Camargo P H C, Cobley C M, Kim M J, Xia Y N 2009 Angew. Chem. Int. Ed. 48 6304

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    Liu H B, Pal U, Medina A, Maldonado C, Ascencio J A 2005 Phys. Rev. B 71 075403

    [32]

    Pittaway F, Paz-Borbon L O, Johnston R L, Arslan H, Ferrando R, Mottet C, Barcaro G, Fortunelli A 2009 J. Phys. Chem. C 113 9141

  • [1]

    Ferrando R, Jellinek J, Johnston R L 2008 Chem. Rev. 108 845

    [2]

    Baletto F, Mottet C, Ferrando R 2003 Phys. Rev. Lett. 90 135504

    [3]

    Brown J A, Mishin A 2003 Phys. Rev. B 67 195414

    [4]

    Bazin D, Guillaume D, Pichon C, Uzio D, Lopez S 2005 Oil Gas Sci. Technol. 60 801

    [5]

    Stanislaus A, Cooper B H 1994 Catal. Rev.-Sci. Eng. 36 75

    [6]

    Barcaro G, Fortunelli A, Polak M, Rubinovich L 2011 Nano Lett. 11 1766

    [7]

    Paz-Borbón L O, Johnston R L, Barcaro G, Fortunelli A 2007 J. Phys. Chem. C 111 2936

    [8]

    Paz-Borbón L O, Mortimer-Jones T V, Johnston R L, Posada-Amarillas A, Barcaro G, Fortunelli A 2007 Phys. Chem. Chem. Phys. 9 5202

    [9]

    Cheng D J, Huang S P, Wang W C 2006 Chem. Phys. 330 423

    [10]

    Cheng D J, Cao D P 2008 Chem. Phys. Lett. 461 71

    [11]

    Liu T D, Chen J R, Hong W P, Shao G F, Wang T N, Zheng J W, Wen Y H 2013 Acta Phys. Sin. 62 193601(in Chinese)[刘暾东, 陈俊仁, 洪武鹏, 邵桂芳, 王婷娜, 郑骥文, 文玉华2013物理学报62 193601]

    [12]

    Liu T D, Zheng J W, Shao G F, Fan T E, Wen Y H 2015 Chin. Phys. B 24 033601

    [13]

    Deaven D M, Tit N, Morris J R, Ho K M 1996 Chem. Phys. Lett. 256 195

    [14]

    Wales D J, Doye J P K 1997 J. Phys. Chem. A 101 5111

    [15]

    Cai W S, Shao X G 2002 J. Comput. Chem. 23 427

    [16]

    Shao X G, Cheng L J, Cai W S 2004 J. Chem. Phys. 120 11401

    [17]

    Shao X G, Cheng L J, Cai W S 2004 J. Comput. Chem. 25 1693

    [18]

    Johnston R L 2003 J. Chem. Soc. Dalton Trans. 22 4193

    [19]

    Cassioli A, Locatelli M, Schoen F 2009 Optim. Methods Softw. 24 819

    [20]

    Wu X, Cai W S, Shao X G 2009 J. Comput. Chem. 30 1992

    [21]

    Doye J P K, Meyer L 2005 Phys. Rev. Lett. 95 063401

    [22]

    Marques J M C, Pereira F B 2010 Chem. Phys. Lett. 485 211

    [23]

    Ye T, Xu R C, Huang W Q 2011 J. Chem. Inf. Model. 51 572

    [24]

    Rondina G G, Da Silva J L F 2013 J. Chem. Inf. Model. 53 2282

    [25]

    Lai X J, Xu R C, Huang W Q 2011 J. Chem. Phys. 135 164109

    [26]

    Wu X, Cheng W 2014 J. Chem. Phys. 141 124110

    [27]

    Shao X G, Yang X L, Cai W S 2008 Chem. Phys. Lett. 460 315

    [28]

    Shao X G, Wu X, Cai W S 2010 J. Phys. Chem. A 114 12813

    [29]

    Liu D C, Nocedal J 1989 Math. Program. 45 503

    [30]

    Lim B, Wang J G, Camargo P H C, Cobley C M, Kim M J, Xia Y N 2009 Angew. Chem. Int. Ed. 48 6304

    [31]

    Liu H B, Pal U, Medina A, Maldonado C, Ascencio J A 2005 Phys. Rev. B 71 075403

    [32]

    Pittaway F, Paz-Borbon L O, Johnston R L, Arslan H, Ferrando R, Mottet C, Barcaro G, Fortunelli A 2009 J. Phys. Chem. C 113 9141

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出版历程
  • 收稿日期:  2016-06-21
  • 修回日期:  2016-07-28
  • 刊出日期:  2016-11-05

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