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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).
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Keywords:
- Pd-Pt clusters /
- Gupta potential /
- immune algorithm /
- dynamic lattice searching
[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 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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[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 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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