The gold-ammonia bonding patterns of neutral and charged complexes Au m 0+/-1-(NH3)n. I. Bonding and charge alternation.

Kryachko, Eugène; Remacle, Françoise

doi:10.1063/1.2786996

Article (Scientific journals)

The gold-ammonia bonding patterns of neutral and charged complexes Au m 0+/-1-(NH3)n. I. Bonding and charge alternation.

Kryachko, Eugène; Remacle, Françoise

2007 • In Journal of Chemical Physics, 127 (19), p. 194305

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DOI
10.1063/1.2786996

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18035881

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Abstract :

[en] The gold-ammonia bonding patterns of the complexes which are formed between the ammonia clusters (NH/sub 3/)/sub 1<or=n<or=3/ and gold clusters of different sizes that range from one gold atom to the tri-, tetra-, and 20-nanogold clusters are governed by two basic and fundamentally different ingredients: the anchoring Au-N bond and the nonconventional N-H ... Au hydrogen bond. The latter resembles, by all features, a conventional hydrogen bond and is formed between a typical conventional proton donor N-H group and the gold cluster that behaves as a nonconventional proton acceptor. We provide strong computational evidence that the gold-ammonia bonding patterns exhibit distinct characteristics as the Z charge state of the gold cluster varies within Z=0,+/-1. The analysis of these bonding patterns and their effects on the N-H ... N H-bonded ammonia clusters are the subject of this paper.

Disciplines :

Chemistry

Author, co-author :

Kryachko, Eugène ; Université de Liège - ULiège > Département de chimie (sciences) > Laboratoire de chimie physique théorique

Remacle, Françoise ; Université de Liège - ULiège > Département de chimie (sciences) > Laboratoire de chimie physique théorique

Language :

English

Title :

The gold-ammonia bonding patterns of neutral and charged complexes Au m 0+/-1-(NH3)n. I. Bonding and charge alternation.

Publication date :

2007

Journal title :

Journal of Chemical Physics

ISSN :

0021-9606

eISSN :

1089-7690

Publisher :

American Institute of Physics, New York, United States - New York

Volume :

127

Issue :

Pages :

194305

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 05 January 2010

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(a) E. S. Kryachko and F. Remacle, in Recent Advances in the Theory of Chemical and Physical Systems, edited by, J.-P. Julien, J. Maruani, D. Mayou, S. Wilson, and, G. Delgado-Barrio, (Springer, Dordrecht, 2006), Vol. 15, pp. 433-450; (b) E. S. Kryachko and F. Remacle, Chem. Phys. Lett. 0009-2614 404, 142 (2005); (c) E. S. Kryachko, A. Karpfen, and F. Remacle, J. Phys. Chem. A 109, 7309 (2005); (d) E. S. Kryachko and F. Remacle, in Theoretical Aspects of Chemical Reactivity, edited by, A. Torro-Labbe, Vol. 16 of Theoretical and Computational Chemistry, edited by, P. Politzer, (Elsevier, Amsterdam, 2006), pp. 219-250.
(a) E. S. Kryachko and F. Remacle, in Recent Advances in the Theory of Chemical and Physical Systems, edited by, J.-P. Julien, J. Maruani, D. Mayou, S. Wilson, and, G. Delgado-Barrio, (Springer, Dordrecht, 2006), Vol. 15, pp. 433-450; (b) E. S. Kryachko and F. Remacle, Chem. Phys. Lett. 0009-2614 404, 142 (2005); (c) E. S. Kryachko, A. Karpfen, and F. Remacle, J. Phys. Chem. A 109, 7309 (2005); (d) E. S. Kryachko and F. Remacle, in Theoretical Aspects of Chemical Reactivity, edited by, A. Torro-Labbe, Vol. 16 of Theoretical and Computational Chemistry, edited by, P. Politzer, (Elsevier, Amsterdam, 2006), pp. 219-250.
(a) E. S. Kryachko and F. Remacle, in Recent Advances in the Theory of Chemical and Physical Systems, edited by, J.-P. Julien, J. Maruani, D. Mayou, S. Wilson, and, G. Delgado-Barrio, (Springer, Dordrecht, 2006), Vol. 15, pp. 433-450; (b) E. S. Kryachko and F. Remacle, Chem. Phys. Lett. 0009-2614 404, 142 (2005); (c) E. S. Kryachko, A. Karpfen, and F. Remacle, J. Phys. Chem. A 109, 7309 (2005); (d) E. S. Kryachko and F. Remacle, in Theoretical Aspects of Chemical Reactivity, edited by, A. Torro-Labbe, Vol. 16 of Theoretical and Computational Chemistry, edited by, P. Politzer, (Elsevier, Amsterdam, 2006), pp. 219-250.
(a) H. Schneider, A. D. Boese, and J. M. Weber, J. Chem. Phys. 0021-9606 10.1063/1.2006092 123, 084307 (2005); (b) H. Nuss and M. Jansen, Angew. Chem., Int. Ed. 1433-7851 45, 4369 (2006); (c) H. Nuss and M. Jansen, Z. Naturforsch. Sect. B, J. Chem. Sci. 61, 1205 (2006); (d) G. S. Shafai, S. Shetty, S. Krishnamurty, and D. G. Kanhere, J. Chem. Phys. 126, 014704 (2007).
(a) H. Schneider, A. D. Boese, and J. M. Weber, J. Chem. Phys. 0021-9606 10.1063/1.2006092 123, 084307 (2005); (b) H. Nuss and M. Jansen, Angew. Chem., Int. Ed. 1433-7851 45, 4369 (2006); (c) H. Nuss and M. Jansen, Z. Naturforsch. Sect. B, J. Chem. Sci. 61, 1205 (2006); (d) G. S. Shafai, S. Shetty, S. Krishnamurty, and D. G. Kanhere, J. Chem. Phys. 126, 014704 (2007).
(a) H. Schneider, A. D. Boese, and J. M. Weber, J. Chem. Phys. 0021-9606 10.1063/1.2006092 123, 084307 (2005); (b) H. Nuss and M. Jansen, Angew. Chem., Int. Ed. 1433-7851 45, 4369 (2006); (c) H. Nuss and M. Jansen, Z. Naturforsch. Sect. B, J. Chem. Sci. 61, 1205 (2006); (d) G. S. Shafai, S. Shetty, S. Krishnamurty, and D. G. Kanhere, J. Chem. Phys. 126, 014704 (2007).
(a) H. Schneider, A. D. Boese, and J. M. Weber, J. Chem. Phys. 0021-9606 10.1063/1.2006092 123, 084307 (2005); (b) H. Nuss and M. Jansen, Angew. Chem., Int. Ed. 1433-7851 45, 4369 (2006); (c) H. Nuss and M. Jansen, Z. Naturforsch. Sect. B, J. Chem. Sci. 61, 1205 (2006); (d) G. S. Shafai, S. Shetty, S. Krishnamurty, and D. G. Kanhere, J. Chem. Phys. 126, 014704 (2007).
This has been particularly shown in the recent works of the present authors on the neutral and charged clusters of gold: (a) F. Remacle and E. S. Kryachko, Adv. Quantum Chem. 0065-3276 47, 423 (2004); (b) F. Remacle and E. S. Kryachko, J. Chem. Phys. 122, 044304 (2005); and in the recent reviews in Refs..
This has been particularly shown in the recent works of the present authors on the neutral and charged clusters of gold: (a) F. Remacle and E. S. Kryachko, Adv. Quantum Chem. 0065-3276 47, 423 (2004); (b) F. Remacle and E. S. Kryachko, J. Chem. Phys. 122, 044304 (2005); and in the recent reviews in Refs..
T. M. Bernhardt, Int. J. Mass. Spectrom. 243, 1 (2005), and references therein.
M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery, Jr., T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, C. Gonzalez, and J. A. Pople, GAUSSIAN 03, Revision A.1, Gaussian, Inc., Pittsburgh, PA, 2003.
(a) R. B. Ross, J. M. Powers, T. Atashroo, W. C. Ermler, L. A. LaJohn, and P. A. Christiansen, J. Chem. Phys. 0021-9606 10.1063/1.458934 93, 6654 (1990); (b) P. J. Hay and W. R. Wadt, J. Chem. Phys. 0021-9606 10.1063/1.448799 82, 270 (1985); P. J. Hay and W. R. Wadt, J. Chem. Phys. 82, 299 (1985).
(a) R. B. Ross, J. M. Powers, T. Atashroo, W. C. Ermler, L. A. LaJohn, and P. A. Christiansen, J. Chem. Phys. 0021-9606 10.1063/1.458934 93, 6654 (1990); (b) P. J. Hay and W. R. Wadt, J. Chem. Phys. 0021-9606 10.1063/1.448799 82, 270 (1985); P. J. Hay and W. R. Wadt, J. Chem. Phys. 82, 299 (1985).
(a) R. B. Ross, J. M. Powers, T. Atashroo, W. C. Ermler, L. A. LaJohn, and P. A. Christiansen, J. Chem. Phys. 0021-9606 10.1063/1.458934 93, 6654 (1990); (b) P. J. Hay and W. R. Wadt, J. Chem. Phys. 0021-9606 10.1063/1.448799 82, 270 (1985); P. J. Hay and W. R. Wadt, J. Chem. Phys. 82, 299 (1985).
F. M. Abu-Awwad, J. Mol. Struct.: THEOCHEM 683, 57 (2004), and references therein.
C. G. Pimentel and A. L. McClellan, The Hydrogen Bond (Freeman, San Francisco, 1960); The Hydrogen Bond. Recent Developments in Theory and Experiments, edited by, P. Schuster, G. Zundel, and, C. Sandorfy, (North-Holland, Amsterdam, 1976).
C. G. Pimentel and A. L. McClellan, The Hydrogen Bond (Freeman, San Francisco, 1960); The Hydrogen Bond. Recent Developments in Theory and Experiments, edited by, P. Schuster, G. Zundel, and, C. Sandorfy, (North-Holland, Amsterdam, 1976).
(a) D. Feller, E. D. Glendening, and W. A. de Jong, J. Chem. Phys. 0021-9606 10.1063/1.477814 110, 1475 (1999); (b) H. M. Lee, S. K. Min, E. C. Lee, J.-H. Min, S. Odde, and K. S. Kim, J. Chem. Phys. 0021-9606 10.1063/1.1849134 122, 064314 (2005); (c) H. M. Lee, M. Diefenbach, S. B. Suh, P. Tarakeshwar, and K. S. Kim, J. Chem. Phys. 123, 074328 (2005).
(a) D. Feller, E. D. Glendening, and W. A. de Jong, J. Chem. Phys. 0021-9606 10.1063/1.477814 110, 1475 (1999); (b) H. M. Lee, S. K. Min, E. C. Lee, J.-H. Min, S. Odde, and K. S. Kim, J. Chem. Phys. 0021-9606 10.1063/1.1849134 122, 064314 (2005); (c) H. M. Lee, M. Diefenbach, S. B. Suh, P. Tarakeshwar, and K. S. Kim, J. Chem. Phys. 123, 074328 (2005).
(a) D. Feller, E. D. Glendening, and W. A. de Jong, J. Chem. Phys. 0021-9606 10.1063/1.477814 110, 1475 (1999); (b) H. M. Lee, S. K. Min, E. C. Lee, J.-H. Min, S. Odde, and K. S. Kim, J. Chem. Phys. 0021-9606 10.1063/1.1849134 122, 064314 (2005); (c) H. M. Lee, M. Diefenbach, S. B. Suh, P. Tarakeshwar, and K. S. Kim, J. Chem. Phys. 123, 074328 (2005).
(a) J. Hrusák, D. Scröder, and H. Schwarz, Chem. Phys. Lett. 0009-2614 10.1016/0009-2614(94)87104-3 225, 416 (1994); (b) H. M. Lee, S. K. Min, E. C. Lee, J.-H. Min, S. Odde, and K. S. Kim, J. Chem. Phys. 122, 064314 (2005).
(a) J. Hrusák, D. Scröder, and H. Schwarz, Chem. Phys. Lett. 0009-2614 10.1016/0009-2614(94)87104-3 225, 416 (1994); (b) H. M. Lee, S. K. Min, E. C. Lee, J.-H. Min, S. Odde, and K. S. Kim, J. Chem. Phys. 122, 064314 (2005).
The experimental value of IEexpt (Au) =9.225 67 eV: (a) C. E. Moore, Atomic Energy Levels, Natl. Bur. of Stand. (U.S.) Circ. No. 467 (U.S. GPO, Washington, DC, 1958), Vol. III; (b) For comparison with other methods see, e.g., W. Liu and C. van Wüllen, J. Chem. Phys. 0021-9606 10.1063/1.478237 110, 3730 (1999); (c) K. A. Barakat, T. R. Cundari, H. Rabaâ, and M. A. Omary, J. Phys. Chem. B 1089-5647 110, 14645 (2006), and references therein; (d) the experimental value of EAexpt (Au) =2.927±0.050 eV: K. J. Taylor, C. L. Pettiette-Hall, O. Cheshnovsky, and R. E. Smalley, J. Chem. Phys. 0021-9606 10.1063/1.461927 96, 3319 (1992); (e) EAtheor (Au) =2.33 eV: S. Buckart, G. Ganteför, Y. D. Kim, and P. Jena, J. Am. Chem. Soc. 0002-7863 125, 14205 (2003) and EAtheor (Au) =2.166 eV: (f) A. M. Joshi, W. N. Delgass, and K. T. Thomson, J. Phys. Chem. B 109, 22392 (2005).
The experimental value of IEexpt (Au) =9.225 67 eV: (a) C. E. Moore, Atomic Energy Levels, Natl. Bur. of Stand. (U.S.) Circ. No. 467 (U.S. GPO, Washington, DC, 1958), Vol. III; (b) For comparison with other methods see, e.g., W. Liu and C. van Wüllen, J. Chem. Phys. 0021-9606 10.1063/1.478237 110, 3730 (1999); (c) K. A. Barakat, T. R. Cundari, H. Rabaâ, and M. A. Omary, J. Phys. Chem. B 1089-5647 110, 14645 (2006), and references therein; (d) the experimental value of EAexpt (Au) =2.927±0.050 eV: K. J. Taylor, C. L. Pettiette-Hall, O. Cheshnovsky, and R. E. Smalley, J. Chem. Phys. 0021-9606 10.1063/1.461927 96, 3319 (1992); (e) EAtheor (Au) =2.33 eV: S. Buckart, G. Ganteför, Y. D. Kim, and P. Jena, J. Am. Chem. Soc. 0002-7863 125, 14205 (2003) and EAtheor (Au) =2.166 eV: (f) A. M. Joshi, W. N. Delgass, and K. T. Thomson, J. Phys. Chem. B 109, 22392 (2005).
The experimental value of IEexpt (Au) =9.225 67 eV: (a) C. E. Moore, Atomic Energy Levels, Natl. Bur. of Stand. (U.S.) Circ. No. 467 (U.S. GPO, Washington, DC, 1958), Vol. III; (b) For comparison with other methods see, e.g., W. Liu and C. van Wüllen, J. Chem. Phys. 0021-9606 10.1063/1.478237 110, 3730 (1999); (c) K. A. Barakat, T. R. Cundari, H. Rabaâ, and M. A. Omary, J. Phys. Chem. B 1089-5647 110, 14645 (2006), and references therein; (d) the experimental value of EAexpt (Au) =2.927±0.050 eV: K. J. Taylor, C. L. Pettiette-Hall, O. Cheshnovsky, and R. E. Smalley, J. Chem. Phys. 0021-9606 10.1063/1.461927 96, 3319 (1992); (e) EAtheor (Au) =2.33 eV: S. Buckart, G. Ganteför, Y. D. Kim, and P. Jena, J. Am. Chem. Soc. 0002-7863 125, 14205 (2003) and EAtheor (Au) =2.166 eV: (f) A. M. Joshi, W. N. Delgass, and K. T. Thomson, J. Phys. Chem. B 109, 22392 (2005).
The experimental value of IEexpt (Au) =9.225 67 eV: (a) C. E. Moore, Atomic Energy Levels, Natl. Bur. of Stand. (U.S.) Circ. No. 467 (U.S. GPO, Washington, DC, 1958), Vol. III; (b) For comparison with other methods see, e.g., W. Liu and C. van Wüllen, J. Chem. Phys. 0021-9606 10.1063/1.478237 110, 3730 (1999); (c) K. A. Barakat, T. R. Cundari, H. Rabaâ, and M. A. Omary, J. Phys. Chem. B 1089-5647 110, 14645 (2006), and references therein; (d) the experimental value of EAexpt (Au) =2.927±0.050 eV: K. J. Taylor, C. L. Pettiette-Hall, O. Cheshnovsky, and R. E. Smalley, J. Chem. Phys. 0021-9606 10.1063/1.461927 96, 3319 (1992); (e) EAtheor (Au) =2.33 eV: S. Buckart, G. Ganteför, Y. D. Kim, and P. Jena, J. Am. Chem. Soc. 0002-7863 125, 14205 (2003) and EAtheor (Au) =2.166 eV: (f) A. M. Joshi, W. N. Delgass, and K. T. Thomson, J. Phys. Chem. B 109, 22392 (2005).
The experimental value of IEexpt (Au) =9.225 67 eV: (a) C. E. Moore, Atomic Energy Levels, Natl. Bur. of Stand. (U.S.) Circ. No. 467 (U.S. GPO, Washington, DC, 1958), Vol. III; (b) For comparison with other methods see, e.g., W. Liu and C. van Wüllen, J. Chem. Phys. 0021-9606 10.1063/1.478237 110, 3730 (1999); (c) K. A. Barakat, T. R. Cundari, H. Rabaâ, and M. A. Omary, J. Phys. Chem. B 1089-5647 110, 14645 (2006), and references therein; (d) the experimental value of EAexpt (Au) =2.927±0.050 eV: K. J. Taylor, C. L. Pettiette-Hall, O. Cheshnovsky, and R. E. Smalley, J. Chem. Phys. 0021-9606 10.1063/1.461927 96, 3319 (1992); (e) EAtheor (Au) =2.33 eV: S. Buckart, G. Ganteför, Y. D. Kim, and P. Jena, J. Am. Chem. Soc. 0002-7863 125, 14205 (2003) and EAtheor (Au) =2.166 eV: (f) A. M. Joshi, W. N. Delgass, and K. T. Thomson, J. Phys. Chem. B 109, 22392 (2005).
The experimental value of IEexpt (Au) =9.225 67 eV: (a) C. E. Moore, Atomic Energy Levels, Natl. Bur. of Stand. (U.S.) Circ. No. 467 (U.S. GPO, Washington, DC, 1958), Vol. III; (b) For comparison with other methods see, e.g., W. Liu and C. van Wüllen, J. Chem. Phys. 0021-9606 10.1063/1.478237 110, 3730 (1999); (c) K. A. Barakat, T. R. Cundari, H. Rabaâ, and M. A. Omary, J. Phys. Chem. B 1089-5647 110, 14645 (2006), and references therein; (d) the experimental value of EAexpt (Au) =2.927±0.050 eV: K. J. Taylor, C. L. Pettiette-Hall, O. Cheshnovsky, and R. E. Smalley, J. Chem. Phys. 0021-9606 10.1063/1.461927 96, 3319 (1992); (e) EAtheor (Au) =2.33 eV: S. Buckart, G. Ganteför, Y. D. Kim, and P. Jena, J. Am. Chem. Soc. 0002-7863 125, 14205 (2003) and EAtheor (Au) =2.166 eV: (f) A. M. Joshi, W. N. Delgass, and K. T. Thomson, J. Phys. Chem. B 109, 22392 (2005).
(a) The chain structure is the most stable conformer of Au3 lying below the triangular one by 2.4 kcal mol-1, after ZPVE. However, within a so-called DFT error (see Ref. and references therein), both these clusters are considered as almost isoenergetic; (b) the experimental value of IEexpt (Au3) =7.15 eV
(a) The chain structure is the most stable conformer of Au3 lying below the triangular one by 2.4 kcal mol-1, after ZPVE. However, within a so-called DFT error (see Ref. and references therein), both these clusters are considered as almost isoenergetic; (b) the experimental value of IEexpt (Au3) =7.15 eV
(a) The chain structure is the most stable conformer of Au3 lying below the triangular one by 2.4 kcal mol-1, after ZPVE. However, within a so-called DFT error (see Ref. and references therein), both these clusters are considered as almost isoenergetic; (b) the experimental value of IEexpt (Au3) =7.15 eV
(a) The chain structure is the most stable conformer of Au3 lying below the triangular one by 2.4 kcal mol-1, after ZPVE. However, within a so-called DFT error (see Ref. and references therein), both these clusters are considered as almost isoenergetic; (b) the experimental value of IEexpt (Au3) =7.15 eV
(a) The chain structure is the most stable conformer of Au3 lying below the triangular one by 2.4 kcal mol-1, after ZPVE. However, within a so-called DFT error (see Ref. and references therein), both these clusters are considered as almost isoenergetic; (b) the experimental value of IEexpt (Au3) =7.15 eV
(a) The chain structure is the most stable conformer of Au3 lying below the triangular one by 2.4 kcal mol-1, after ZPVE. However, within a so-called DFT error (see Ref. and references therein), both these clusters are considered as almost isoenergetic; (b) the experimental value of IEexpt (Au3) =7.15 eV
(a) The chain structure is the most stable conformer of Au3 lying below the triangular one by 2.4 kcal mol-1, after ZPVE. However, within a so-called DFT error (see Ref. and references therein), both these clusters are considered as almost isoenergetic; (b) the experimental value of IEexpt (Au3) =7.15 eV
(a) J. Li, X. Li, H.-J. Zhai, and L.-S. Wang, Science 0036-8075 10.1126/science.1079879 299, 864 (2003); (b) R. B. King, Z. Chen, and P. v. R. Schleyer, Inorg. Chem. 0020-1669 10.1021/ic049628r 43, 4564 (2004); (c) see also E. S. Kryachko and F. Remacle, Int. J. Quantum Chem. 108, 000 (2008) for a review on the 20-nanogold cluster.
(a) J. Li, X. Li, H.-J. Zhai, and L.-S. Wang, Science 0036-8075 10.1126/science.1079879 299, 864 (2003); (b) R. B. King, Z. Chen, and P. v. R. Schleyer, Inorg. Chem. 0020-1669 10.1021/ic049628r 43, 4564 (2004); (c) see also E. S. Kryachko and F. Remacle, Int. J. Quantum Chem. 108, 000 (2008) for a review on the 20-nanogold cluster.
(a) J. Li, X. Li, H.-J. Zhai, and L.-S. Wang, Science 0036-8075 10.1126/science.1079879 299, 864 (2003); (b) R. B. King, Z. Chen, and P. v. R. Schleyer, Inorg. Chem. 0020-1669 10.1021/ic049628r 43, 4564 (2004); (c) see also E. S. Kryachko and F. Remacle, Int. J. Quantum Chem. 108, 000 (2008) for a review on the 20-nanogold cluster.
L. H. Skibsted and J. Bjerrum, Acta Chem. Scand., Ser. A 28, 740 (1974).
(a) L. M. Molina and B. Hammer, J. Catal. 0021-9517 10.1016/j.jcat.2005. 04.037 233, 399 (2005);
(b) H.-F. Zhang, M. Stender, R. Zhang, C. Wang, J. Li, and L.-S. Wang, J. Phys. Chem. B 108, 12259 (2004).