Free energy surface of two- and three-dimensional transitions of Au 12 nanoclusters obtained by ab initio metadynamics

Physical Review B - Condensed Matter and Materials Physics

Volumn 81, Issue 17, 2010, Pages

  Santarossa, Gianluca ^a   Vargas, Angelo ^a   Iannuzzi, Marcella ^b   Baiker, Alfons ^a  

^a ETH ZURICH   (Switzerland)

^b UNIVERSITY OF ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77955446862     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.81.174205     Document Type: Article

References (118)

1. J. P. Wilcoxon and B. L. Abrams, Chem. Soc. Rev. 35, 1162 (2006). 10.1039/b517312b (Pubitemid 44611728)
2. F. Baletto and R. Ferrando, Rev. Mod. Phys. 77, 371 (2005). 10.1103/RevModPhys.77.371 (Pubitemid 41490661)
3. C. Burda, X. Chen, R. Narayanan, and M. El-Sayed, Chem. Rev. (Washington, D.C.) 105, 1025 (2005). 10.1021/cr030063a (Pubitemid 40600877)
4. D. L. Feldheim and C. A. Foss, Jr., Metal Nanoparticles: Synthesis, Characterization and Applications (CRC Press, Boca Raton, FL/ Taylor & Francis Group, London, 2002).
5. T. Schalkhammer, Monatsch. Chem. 129, 1067 (1998).
6. F. Viñes, F. Illas, and K. M. Neyman, J. Phys. Chem. A 112, 8911 (2008). 10.1021/jp8014854
7. Q. Ge, C. Song, and L. Wang, Comput. Mater. Sci. 35, 247 (2006). 10.1016/j.commatsci.2005.05.003 (Pubitemid 41742137)
8. C. Song, Q. Ge, and L. Wang, J. Phys. Chem. B 109, 22341 (2005). 10.1021/jp0546709
9. T. Pawluk, Y. Hirata, and L. Wang, J. Phys. Chem. B 109, 20817 (2005). 10.1021/jp053563b (Pubitemid 41698340)
10. L. Xiao and L. Wang, Chem. Phys. Lett. 392, 452 (2004). 10.1016/j.cplett.2004.05.095
11. L. Xiao and L. Wang, J. Phys. Chem. A 108, 8605 (2004). 10.1021/jp0485035
12. N. E. Schultz, A. W. Jasper, D. Bhatt, J. I. Siepmann, and D. G. Truhlar, Multiscale Simulation Methods for Nanomaterials (Wiley, New York, 2008).
13. S. Alkis, J. L. Krause, J. N. Fry, and H. P. Cheng, Phys. Rev. B 79, 121402 (R) (2009). 10.1103/PhysRevB.79.121402
14. D. H. Seo, H. Y. Kim, J. H. Ryu, and H. M. Lee, J. Phys. Chem. C 113, 10416 (2009). 10.1021/jp900862t
15. I. F. Golovnev, E. I. Golovneva, and V. M. Fomin, Phys. Mesomech. 11, 19 (2008). 10.1016/j.physme.2008.03.002
16. A. Moitra, S. Kim, J. Houze, B. Jelinek, S.-G. Kim, S.-J. Park, R. M. German, and M. F. Horstemeyer, J. Phys. D 41, 185406 (2008). 10.1088/0022-3727/41/18/185406
17. I. Baranov, Nucl. Instrum. Methods Phys. Res. B 266, 1993 (2008). 10.1016/j.nimb.2008.03.094
18. S. K. R. S. Sankaranarayanan, V. R. Bhethanabotla, and B. Joseph, J. Phys. Chem. C 111, 2430 (2007). 10.1021/jp066132h (Pubitemid 46778285)
19. M. Iannuzzi, Computational Methods in Catalysis and Materials Science (Wiley-VCH Verlag GmbH & Co, KGaA, Weinheim, 2009).
20. D. Marx and J. Hutter, Modern Methods and Algorithms of Quantum Chemistry (John von Neumann Institute for Computing, Forschungszentrum Jülich, 2000), pp. 301-449.
21. C. Yannouleas, U. Landman, and R. Barnett, Metal Clusters (Wiley, New York, 1999), pp. 145-180.
22. L. Wille, Comput. Mater. Sci. 17, 551 (2000). 10.1016/S0927-0256(00) 00086-0
23. C. H. Hu, C. Chizallet, H. Toulhoat, and P. Raybaud, Phys. Rev. B 79, 195416 (2009). 10.1103/PhysRevB.79.195416
24. N. Metropolis and S. Ulam, J. Am. Stat. Assoc. 44, 335 (1949). 10.2307/2280232
25. D. Wales and H. Scheraga, Science 285, 1368 (1999). 10.1126/science.285. 5432.1368 (Pubitemid 29411661)
26. D. Wales and J. Doye, J. Phys. Chem. A 101, 5111 (1997). 10.1021/jp970984n
27. R. L. Johnston, Dalton Trans. 2003, 4193. 10.1039/b305686d
28. I. Garzon, M. Beltran, G. Gonzalez, I. Gutierrez-Gonzalez, K. Michaelian, J. Reyes-Nava, and J. Rodriguez-Hernandez, Eur. Phys. J. D 24, 105 (2003). 10.1140/epjd/e2003-00187-4 (Pubitemid 36977514)
29. M. Wolf and U. Landman, J. Phys. Chem. A 102, 6129 (1998). 10.1021/jp9814597
30. M. Mitchell, An Introduction to Genetic Algorithms (MIT Press, Cambridge, MA, 1996).
31. X. Shao, X. Yang, and W. Cai, J. Comput. Chem. 29, 1772 (2008). 10.1002/jcc.20938
32. T. J. Toai, G. Rossi, and R. Ferrando, Faraday Discuss. 138, 49 (2008). 10.1039/b707813g
33. G. Bond and D. Thompson, Gold Bull. 33, 41 (2000).
34. M. Haruta, N. Yamada, T. Kobayashi, and S. Iijima, J. Catal. 115, 301 (1989). 10.1016/0021-9517(89)90034-1
35. M. Haruta, T. Kobayashi, H. Sano, and N. Yamada, Chem. Lett. 16, 405 (1987). 10.1246/cl.1987.405
36. B. Hammer and J. K. Nørskov, Nature (London) 376, 238 (1995). 10.1038/376238a0
37. C. R. Martin and P. Kohli, Nat. Rev. Drug Discovery 2, 29 (2003). 10.1038/nrd988 (Pubitemid 37361622)
38. A. Tkachenko, H. Xie, D. Coleman, W. Glomm, J. Ryan, M. Anderson, S. Franzen, and D. Feldheim, J. Am. Chem. Soc. 125, 4700 (2003). 10.1021/ja0296935 (Pubitemid 36505350)
39. Q. Wang, T. Lin, L. Tang, J. Johnson, and M. Finn, Angew. Chem., Int. Ed. 41, 459 (2002). 10.1002/1521-3773(20020201)41:3<459::AID-ANIE459>3.0. CO;2-O (Pubitemid 34146072)
40. M. Tsoli, H. Kuhn, W. Brandau, H. Esche, and G. Schmid, Small 1, 841 (2005). 10.1002/smll.200500104 (Pubitemid 43951714)
41. M.-C. Daniel and D. Astruc, Chem. Rev. (Washington, D.C.) 104, 293 (2004). 10.1021/cr030698+
42. H. Zhang, G. Schmid, and U. Hartmann, Nano Lett. 3, 305 (2003). 10.1021/nl0258980 (Pubitemid 37130500)
43. H. Häkkinen, Chem. Soc. Rev. 37, 1847 (2008). 10.1039/b717686b
44. X. Zhou, W. Xu, G. Liu, D. Panda, and P. Chen, J. Am. Chem. Soc. 132, 138 (2010). 10.1021/ja904307n
45. G. Shafai, S. Hong, M. Bertino, and T. S. Rahman, J. Phys. Chem. C 113, 12072 (2009). 10.1021/jp811200e
46. A. Prestianni, A. Martorana, F. Labat, I. Ciofini, and C. Adamo, J. Mol. Struct.: THEOCHEM 903, 34 (2009). 10.1016/j.theochem.2009.01.016
47. S. M. Lang, T. M. Bernhardt, R. N. Barnett, B. Yoon, and U. Landman, J. Am. Chem. Soc. 131, 8939 (2009). 10.1021/ja9022368
48. C. Harding, V. Habibpour, S. Kunz, A. N.-S. Farnbacher, U. Heiz, B. Yoon, and U. Landman, J. Am. Chem. Soc. 131, 538 (2009). 10.1021/ja804893b
49. G. M. Veith, A. R. Lupini, S. Rashkeev, S. J. Pennycook, D. R. Mullins, V. Schwartz, C. A. Bridges, and N. J. Dudney, J. Catal. 262, 92 (2009). 10.1016/j.jcat.2008.12.005
50. M. B. Torres, E. M. Fernandez, and L. C. Balbas, J. Phys. Chem. A 112, 6678 (2008). 10.1021/jp800247n
51. K. P. McKenna, P. V. Sushko, and A. L. Shluger, J. Chem. Phys. 126, 154704 (2007). 10.1063/1.2722751 (Pubitemid 46644951)
52. K. P. McKenna, P. V. Sushko, and A. L. Shluger, J. Phys. Chem. C 111, 2823 (2007). 10.1021/jp067801u (Pubitemid 46384287)
53. K. P. McKenna and A. Shluger, J. Phys. Chem. C 111, 18848 (2007). 10.1021/jp710043s (Pubitemid 351147678)
54. J. A. van Bokhoven and J. T. Miller, J. Phys. Chem. C 111, 9245 (2007). 10.1021/jp070755t (Pubitemid 47166865)
55. U. Landman, B. Yoon, C. Zhang, U. Heiz, and M. Arenz, Top. Catal. 44, 145 (2007). 10.1007/s11244-007-0288-6
56. C. Zhang, B. Yoon, and U. Landman, J. Am. Chem. Soc. 129, 2228 (2007). 10.1021/ja0684545 (Pubitemid 46362526)
57. B. Yoon, P. Koskinen, B. Huber, O. Kostko, B. von Issendorff, H. Häkkinen, M. Moseler, and U. Landman, ChemPhysChem 8, 157 (2007). 10.1002/cphc.200600524
58. M. Arenz, U. Landman, and U. Heiz, ChemPhysChem 7, 1871 (2006). 10.1002/cphc.200600029
59. M. Walter and H. Häkkinen, Phys. Chem. Chem. Phys. 8, 5407 (2006). 10.1039/b612221c
60. B. Yoon, H. Häkkinen, U. Landman, A. Worz, J. Antonietti, S. Abbet, K. Judai, and U. Heiz, Science 307, 403 (2005). 10.1126/science.1104168 (Pubitemid 40139980)
61. I. N. Remediakis, N. Lopez, and J. K. Nørskov, Appl. Catal., A 291, 13 (2005). 10.1016/j.apcata.2005.01.052
62. L. M. Molina and B. Hammer, Appl. Catal., A 291, 21 (2005). 10.1016/j.apcata.2005.01.050
63. C. T. Campbell, Science 306, 234 (2004). 10.1126/science.1104246 (Pubitemid 39336857)
64. H. Häkkinen, S. Abbet, A. Sanchez, U. Heiz, and U. Landman, Angew. Chem., Int. Ed. 42, 1297 (2003). 10.1002/anie.200390334 (Pubitemid 36406617)
65. B. Yoon, H. Häkkinen, and U. Landman, J. Phys. Chem. A 107, 4066 (2003). 10.1021/jp027596s
66. G. Mills, M. Gordon, and H. Metiu, J. Chem. Phys. 118, 4198 (2003). 10.1063/1.1542879
67. A. Sanchez, S. Abbet, U. Heiz, W. Schneider, H. Häkkinen, R. Barnett, and U. Landman, J. Phys. Chem. A 103, 9573 (1999). 10.1021/jp9935992
68. Z. Y. Li, N. P. Young, M. D. Vece, S. Palomba, R. E. Palmer, A. L. Bleloch, B. C. Curley, R. L. Johnston, J. Jiang, and J. Yuan, Nature (London) 451, 46 (2008). 10.1038/nature06470
69. D. Tian and J. Zhao, J. Phys. Chem. A 112, 3141 (2008). 10.1021/jp7116938
70. J. Wang, H. Ning, Q.-M. Ma, Y. Liu, and Y.-C. Li, J. Chem. Phys. 129, 134705 (2008). 10.1063/1.2987715
71. W. Huang, M. Ji, C.-D. Dong, X. Gu, L.-M. Wang, X. G. Gong, and L.-S. Wang, ACS Nano 2, 897 (2008). 10.1021/nn800074b
72. A. J. Karttunen, M. Linnolahti, T. A. Pakkanen, and P. Pyykkö, Chem. Commun. (Cambridge) 2008, 465. 10.1039/b715478j
73. D. Tian, J. Zhao, B. Wang, and R. B. King, J. Phys. Chem. A 111, 411 (2007). 10.1021/jp066272r
74. A. Lechtken, D. Schooss, J. R. Stairs, M. N. Blom, F. Furche, N. Morgner, O. Kostko, B. von Issendorff, and M. M. Kappes, Angew. Chem., Int. Ed. 46, 2944 (2007). 10.1002/anie.200604760 (Pubitemid 46981304)
75. X. Gu, S. Bulusu, X. Li, X. C. Zeng, J. Li, X. G. Gong, and L.-S. Wang, J. Phys. Chem. C 111, 8228 (2007). 10.1021/jp071960b (Pubitemid 47012675)
76. L. Xiao, B. Tollberg, X. Hu, and L. Wang, J. Chem. Phys. 124, 114309 (2006). 10.1063/1.2179419
77. M. P. Johansson, D. Sundholm, and J. Vaara, Angew. Chem., Int. Ed. 43, 2678 (2004). 10.1002/anie.200453986 (Pubitemid 39257694)
78. X. Gu, M. Ji, S. H. Wei, and X. G. Gong, Phys. Rev. B 70, 205401 (2004). 10.1103/PhysRevB.70.205401 (Pubitemid 40153564)
79. E. M. Fernandez, J. M. Soler, and L. C. Balbas, Phys. Rev. B 73, 235433 (2006). 10.1103/PhysRevB.73.235433 (Pubitemid 43967810)
80. H. Häkkinen, M. Moseler, O. Kostko, N. Morgner, M. A. Hoffmann, and B. v. Issendorff, Phys. Rev. Lett. 93, 093401 (2004). 10.1103/PhysRevLett.93. 093401
81. H. Häkkinen, M. Moseler, and U. Landman, Phys. Rev. Lett. 89, 033401 (2002). 10.1103/PhysRevLett.89.033401
82. F. Furche, R. Ahlrichs, P. Weis, C. Jacob, S. Gilb, T. Bierweiler, and M. Kappes, J. Chem. Phys. 117, 6982 (2002). 10.1063/1.1507582 (Pubitemid 35354144)
83. P. Pyykko, Inorg. Chim. Acta 358, 4113 (2005). 10.1016/j.ica.2005.06.028 (Pubitemid 41656054)
84. P. Pyykko, Angew. Chem., Int. Ed. 43, 4412 (2004). 10.1002/anie.200300624 (Pubitemid 39257379)
85. P. Pyykko, Chem. Rev. (Washington, D.C.) 88, 563 (1988). 10.1021/cr00085a006
86. P. Gruene, D. M. Rayner, B. Redlich, A. F. G. van der Meer, J. T. Lyon, G. Meijer, and A. Fielicke, Science 321, 674 (2008). 10.1126/science.1161166
87. S. Bulusu, X. Li, L.-S. Wang, and X. C. Zeng, Proc. Natl. Acad. Sci. U.S.A. 103, 8326 (2006). 10.1073/pnas.0600637103 (Pubitemid 43838454)
88. E. Apra, R. Ferrando, and A. Fortunelli, Phys. Rev. B 73, 205414 (2006). 10.1103/PhysRevB.73.205414 (Pubitemid 43752531)
89. J. Li, X. Li, H. Zhai, and L. Wang, Science 299, 864 (2003). 10.1126/science.1079879 (Pubitemid 36182439)
90. A. Lechtken, C. Neiss, M. M. Kappes, and D. Schooss, Phys. Chem. Chem. Phys. 11, 4344 (2009). 10.1039/b821036e
91. A. Vargas, G. Santarossa, M. Iannuzzi, and A. Baiker, Phys. Rev. B 80, 195421 (2009). 10.1103/PhysRevB.80.195421
92. P. Koskinen, H. Häkkinen, B. Huber, B. von Issendorff, and M. Moseler, Phys. Rev. Lett. 98, 015701 (2007). 10.1103/PhysRevLett.98.015701 (Pubitemid 46135125)
93. M. P. Johansson, A. Lechtken, D. Schooss, M. M. Kappes, and F. Furche, Phys. Rev. A 77, 053202 (2008). 10.1103/PhysRevA.77.053202 (Pubitemid 351706818)
94. X. Xing, B. Yoon, U. Landman, and J. H. Parks, Phys. Rev. B 74, 165423 (2006). 10.1103/PhysRevB.74.165423 (Pubitemid 44656291)
95. A. S. Barnard, N. P. Young, A. I. Kirkland, M. A. van Huis, and H. Xu, ACS Nano 3, 1431 (2009). 10.1021/nn900220k
96. W. Huang, S. Bulusu, R. Pal, X. C. Zeng, and L.-S. Wang, ACS Nano 3, 1225 (2009). 10.1021/nn900232d
97. E. van Lenthe, E. J. Baerends, and J. Snijders, J. Chem. Phys. 99, 4597 (1993). 10.1063/1.466059
98. J. Tao, J. P. Perdew, V. N. Staroverov, and G. E. Scuseria, Phys. Rev. Lett. 91, 146401 (2003). 10.1103/PhysRevLett.91.146401
99. A. Laio and F. L. Gervasio, Rep. Prog. Phys. 71, 126601 (2008). 10.1088/0034-4885/71/12/126601
100. A. Laio and M. Parrinello, Lect. Notes Phys. 703, 315 (2006). 10.1007/3-540-35273-2-9
101. M. Iannuzzi, A. Laio, and M. Parrinello, Phys. Rev. Lett. 90, 238302 (2003). 10.1103/PhysRevLett.90.238302
102. A. Laio and M. Parrinello, Proc. Natl. Acad. Sci. U.S.A. 99, 12562 (2002). 10.1073/pnas.202427399
103. C. Micheletti, A. Laio, and M. Parrinello, Phys. Rev. Lett. 92, 170601 (2004). 10.1103/PhysRevLett.92.170601
104. J. VandeVondele, M. Krack, F. Mohamed, M. Parrinello, T. Chassaing, and J. Hutter, Comput. Phys. Commun. 167, 103 (2005). 10.1016/j.cpc.2004.12.014 (Pubitemid 40391124)
105. G. Lippert, J. Hutter, and M. Parrinello, Theor. Chem. Acc. 103, 124 (1999). 10.1007/s002140050523
106. G. Lippert, J. Hutter, and M. Parrinello, Mol. Phys. 92, 477 (1997). 10.1080/00268979709482119
107. S. Goedecker, M. Teter, and J. Hutter, Phys. Rev. B 54, 1703 (1996). 10.1103/PhysRevB.54.1703
108. J. VandeVondele and J. Hutter, J. Chem. Phys. 127, 114105 (2007). 10.1063/1.2770708 (Pubitemid 47461992)
109. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996). 10.1103/PhysRevLett.77.3865
110. S. Grimme, J. Comput. Chem. 27, 1787 (2006). 10.1002/jcc.20495 (Pubitemid 44672561)
111. S. Grimme, J. Comput. Chem. 25, 1463 (2004). 10.1002/jcc.20078
112. S. Nose, J. Chem. Phys. 81, 511 (1984). 10.1063/1.447334
113. C. Broyden, Math. Comput. 24, 365 (1970). 10.2307/2004483
114. J. Nocedal, Math. Comput. 35, 773 (1980). 10.2307/2006193
115. D. Liu and J. Nocedal, SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 10, 1 (1989). 10.1137/0910001
116. D. Shanno and P. Kettler, Math. Comput. 24, 657 (1970). 10.2307/2004841
117. D. Goldfarb, Math. Comput. 24, 23 (1970). 10.2307/2004873
118. See supplementary material at http://link.aps.org/supplemental/10.1103/ PhysRevB.81.174205 for Figures S1 and S2 showing the conformations of the minima isolated on the PES, for the complete set of coordinates of the conformations isolated on the FES, and for their projections on the PES.