Abstract
Computational modelling plays an important role in understanding the properties of nanoclusters, as it allows the prediction of structures for the lowest energy isomer (i.e. the global minimum, GM) [1], as well as providing information on preferential cluster geometries [2], or local minima, and further details such as metal segregation in bimetallic systems [3]. In this chapter the relative energetics will be discussed for different high-symmetry structures composed of Pd, Au, or a combination of the two. Clusters have been created using mathematical constructs, and then energetically minimised. Stability trends are identified for different compositions and geometries, in order to compare our results with experimental observations.
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References
R.L. Johnston, Atomic and Molecular Clusters (Taylor and Francis, London, 2002)
F. Baletto, R. Ferrando, A. Fortunelli, F. Montalenti, C. Mottet, Crossover among structural motifs in transition and noble-metal clusters. J. Chem. Phys. 116(9), 3856–3863 (2002)
R. Ferrando, J. Jellinek, R.L. Johnston, Nanoalloys: from theory to applications of alloy clusters and nanoparticles. Chem. Rev. 108(3), 845–910 (2008)
F. Baletto, R. Ferrando, Structural properties of nanoclusters: energetic, thermodynamic, and kinetic effects. Rev. Mod. Phys. 77, 371–423 (2005)
P. Nava, M. Sierka, R. Ahlrichs, Density functional study of palladium clusters. Phys. Chem. Chem. Phys. 5, 3372–3381 (2003)
G. Valerio, H. Toulhoat, Atomic sulfur and chlorine interaction with \({\rm {Pd}}_{n}\) clusters (n = 1–6): a density functional study. J. Phys. Chem. A 101(10), 1969–1974 (1997)
B. Kalita, R.C. Deka, Stability of small \({\rm {Pd}}_{n}\) (n = 1–7) clusters on the basis of structural and electronic properties: a density functional approach. J. Chem. Phys. 127(24), 244306–244316 (2007)
D.R. Jennison, P.A. Schultz, M.P. Sears, Ab initio calculations of Ru, Pd, and Ag cluster structure with 55, 135, and 140 atoms. J. Chem. Phys. 106(5), 1856–1862 (1997)
R. Guirado-López, M.C. Desjonquères, D. Spanjaard, Tight-binding study of relaxation in \({\rm {Rh}}_{N}\) and \({\rm {Pd}}_{N}\) clusters \((9 < N < 165)\). Phys. Rev. B 62(19), 13188–13195 (2000)
F. Aguilera-Granja, A. Vega, J. Rogan, G. Garcia, Metallic behavior of Pd atomic clusters. Nanotechnology 18(36), 365706–365711 (2007)
N. Watari, S. Ohnishi, Atomic and electronic structures of \({\rm {Pd}}_{13}\) and \({\rm {Pt}}_{13}\) clusters. Phys. Rev. B 58(3), 1665–1677 (1998)
F. Cleri, V. Rosato, Tight-binding potentials for transition metals and alloys. Phys. Rev. B 48(1), 22–33 (1993)
V. Rosato, M. Guillope, B. Legrand, Thermodynamical and structural properties of FCC transition metals using a simple tight-binding model. Philos. Mag. A 59(2), 321–336 (1989)
M. José-Yacamán, M. Marin-Almazo, J.A. Ascencio, High resolution TEM studies on palladium nanoparticles. J. Mol. Catal. A 173(1–2), 61–74 (2001)
M. José-Yacamán, J.A. Ascencio, H.B. Liu, J. Gardea-Torresdey, Structure shape and stability of nanometric sized particles. J. Vac. Sci. Technol. B 19(4), 1091–1103 (2001)
S.M. Morton, D.W. Silverstein, L. Jensen, Theoretical studies of plasmonics using electronic structure methods. Chem. Rev. 111, 3962–3994 (2011)
G. Bravo-Perez, I.L. Garzan, O. Novaro, Non-additive effects in small gold clusters. Chem. Phys. Lett. 313(3–4), 655–664 (1999)
J. Wang, G. Wang, J. Zhao, Density-functional study of \({\rm {Au}}_{n}\)(\(n\)=2–20) clusters: lowest-energy structures and electronic properties. Phys. Rev. B 66(3), 35418–35424 (2002)
V. Bonačić-Koutecký, J. Burda, R. Mitrić, M. Ge, G. Zampella, P. Fantucci, Density functional study of structural and electronic properties of bimetallic silver-gold clusters: comparison with pure gold and silver clusters. J. Chem. Phys. 117(7), 3120–3131 (2002)
J. Li, X. Li, H.J. Zhai, L.S. Wang, \({\rm {Au}}_{20}\): a tetrahedral cluster. Science 299(5608), 864–867 (2003)
J. Wang, G. Wang, J. Zhao, Structures and electronic properties of \({\rm {Cu}}_{20}\), \({\rm {Ag}}_{20}\), and \({\rm {Au}}_{20}\) clusters with density functional method. Chem. Phys. Lett. 380, 716–720 (2003)
K. Michaelian, N. Rendón, I.L. Garzón, Structure and energetics of Ni, Ag, and Au nanoclusters. Phys. Rev. B 60, 2000–2010 (1999)
C.L. Cleveland, U. Landman, M.N. Shafigullin, P.W. Stephens, R.L. Whetten, Structural evolution of larger gold clusters. Z. Phys. D 40, 503–508 (1997)
N.T. Wilson, R.L. Johnston, Modelling gold clusters with an empirical many-body potential. Eur. Phys. J. D. 12(1), 161–169 (2000)
M.M. Alvarez, J.T. Khoury, T.G. Schaaff, M.N. Shafigullin, I. Vezmar, R.L. Whetten, Optical absorption spectra of nanocrystal gold molecules. J. Phys. Chem. B 101(19), 3706–3712 (1997)
H. Häkkinen, R.N. Barnett, U. Landman, Electronic structure of passivated \({\rm {Au}}_{38}({\rm {SCH3}})_{24}\) nanocrystal. Phys. Rev. Lett. 82(16), 3264–3267 (1999)
H. Häkkinen, M. Walter, H. Grönbeck, Divide and protect: capping gold nanoclusters with molecular gold-thiolate rings. J. Phys. Chem. B 110(20), 9927–9931 (2006)
J. Akola, M. Walter, R.L. Whetten, H. Häkkinen, H. Grönbeck, On the structure of thiolate-protected \({\rm {Au}}_{25}\). J. Am. Chem. Soc. 130(12), 3756–3757 (1999)
M. Walter, J. Akola, O. Lopez-Acevedo, P.D. Jadzinsky, G. Calero, C.J. Ackerson, R.L. Whetten, H. Grönbeck, H. Häkkinen, A unified view of ligand-protected gold clusters as superatom complexes. Proc. Natl. Acad. Sci. 105, 9157–9162 (2008)
O. Lopez-Acevedo, J. Akola, R.L. Whetten, H. Grönbeck, H. Häkkinen, Structure and bonding in the ubiquitous icosahedral metallic gold cluster \({\rm {Au}}_{144}({\rm {SR}})_{60}\). J. Phys. Chem. C 113, 5035–5038 (2009)
O. Lopez-Acevedo, H. Tsunoyama, T. Tsukuda, H. Häkkinen, C.M. Aikens, Chirality and electronic structure of the thiolate-protected \({\rm {Au}}_{38}\) nanocluster. J. Am. Chem. Soc. 132(23), 8210–8218 (2010)
Z. Wang, O. Toikkanen, B.M. Quinn, R.E. Palmer, Real-space observation of prolate monolayer-protected \({\rm {Au}}_{38}\) clusters using aberration-corrected scanning transmission electron microscopy. Small 7(11), 1542–1545 (2011)
Z.Y. Li, N.P. Young, M. Di Vece, S. Palomba, R.E. Palmer, A.L. Bleloch, B.C. Curley, R.L. Johnston, J. Jiang, J. Yuan, Three-dimensional atomic-scale structure of size-selected gold nanoclusters. Nature 451(7174), 46–48 (2008)
B.C. Curley, R.L. Johnston, N.P. Young, Z.Y. Li, M. Di Vece, R.E. Palmer, A.L. Bleloch, Combining theory and experiment to characterize the atomic structures of surface-deposited \({\rm {Au}}_{309}\) clusters. J. Phys. Chem. C 111(48), 17846–17851 (2007)
N.J. Cookson, Preparation and Characterisation of Bimetallic Core-Shell Nanoparticles, School of Chemistry, University of Birmingham, Edgbaston, Birmingham, Master’s thesis, 2009
M.J. Cabrera-Trujillo, J.M. Montejano-Carrizales, J.L. Rodriguez-Lopez, W. Zhang, J.J. Velazquez-Salazar, M. José-Yacamán, Nucleation and growth of stellated gold clusters: experimental synthesis and theoretical study. J. Phys. Chem. C 114(49), 21051–21060 (2010)
R.L. Johnston, Evolving better nanoparticles: genetic algorithms for optimising cluster geometries. Dalton Trans. 22, 4193 (2003)
F. Pittaway, L.O. Paz-Borbón, R.L. Johnston, H. Arslan, R. Ferrando, C. Mottet, G. Barcaro, A. Fortunelli, Theoretical studies of palladium-gold nanoclusters: Pd-Au clusters with up to 50 atoms. J. Phys. Chem. C 113, 9141–9152 (2009)
R. Ismail, R.L. Johnston, Investigation of the structures and chemical ordering of small pd-au clusters as a function of composition and potential parameterisation. Phys. Chem. Chem. Phys. 12(30), 8607–8619 (2010)
B. Shan, L. Wang, S. Yang, J. Hyun, N. Kapur, Y. Zhao, J.B. Nicholas, K. Cho, First-principles-based embedded atom method for PdAu nanoparticles. Phys. Rev. B 80, 035404 (2009)
H.B. Liu, U. Pal, A. Medina, C. Maldonado, J.A. Ascencio, Structural incoherency and structure reversal in bimetallic Au–Pd nanoclusters. Phys. Rev. B 71, 075403 (2005)
A.R. Miedema, Surface energy of solid metals. Z. Metal. 69(5), 287–292 (1978)
D. Ferrer, A. Torres-Castro, X. Gao, S. Sepúlveda-Guzmán, U. Ortiz-Méndez, M. José-Yacamán, Three-layer core/shell structure in Au-Pd bimetallic nanoparticles. Nano Lett. 7, 1701–1705 (2007)
T.P. Martin, Shells of atoms. Phys. Rep. 273, 199–241 (1996)
X. Xing, B. Yoon, U. Landman, J.H. Parks, Structural evolution of Au nanoclusters: From planar to cage to tubular motifs. Phys. Rev. B 74(16), 165423 (2006)
A.J. Logsdail, R.L. Johnston, Interdependence of structure and chemical order in high symmetry \(({\rm {pdau}})_{N}\) nanoclusters. RSC Adv. 2, 5863–5869 (2012)
J.N. Murrell, R.E. Mottram, Potential energy functions for atomic solids. Mol. Phys. 69, 571–585 (1990)
A.P. Sutton, J. Chen, Long-range Finnis-Sinclair potentials. Philos. Mag. Lett. 61(3), 139–146 (1990)
M.S. Daw, M.I. Baskes, Embedded-atom method: derivation and application to impurities, surfaces, and other defects in metals. Phys. Rev. B 29(12), 6443–6453 (1984)
R.P. Gupta, Lattice relaxation at a metal surface. Phys. Rev. B 23(12), 6265–6270 (1981)
R. Ferrando. Personal communication, 2009.
C. Kittel, Introduction To Solid State Physics, 6th edn. (Wiley, New York, 1986)
C.L. Cleveland, U. Landman, The energetics and structure of nickel clusters: size dependence. J. Chem. Phys. 94(11), 7376–7396 (1991)
J. Uppenbrink, D.J. Wales, Structure and energetics of model metal clusters. J. Chem. Phys. 96(11), 8520–8534 (1992)
A.J. Logsdail, Z.Y. Li, R.L. Johnston, Faceting preferences for \({\rm {au}}_{N}\) and \({\rm {pd}}_{N}\) nanoclusters with high-symmetry motifs. Phys. Chem. Chem. Phys. 15, 3473 (2013)
J. Uppenbrink, R.L. Johnston, J.N. Murrell, Modelling transition metal surfaces with empirical potentials. Surf. Sci. 304(1–2), 223–236 (1994)
Nanoalloys: From theory to applications. Faraday Discussions No.138, vol. 138, 2008.
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Logsdail, A.J. (2013). Calculating the Structural Preference of High Symmetry Clusters for \({\text {Pd}}_{N}\), \({\text {Au}}_{N}\), and \(({\text {PdAu}})_{N}\) . In: Computational Characterisation of Gold Nanocluster Structures. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-01493-7_2
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