Basics of Nanoscience 2008 Nanoclusters and nanoparticles II Hannu Häkkinen 22.1.2008 University of Jyväskylä Nanoscience Center Departments of Physics and Chemistry Hannu Häkkinen, Nanoscience Center, University of Jyväskylä Thermodynamic properties 1
Thermodynamic properties - general � Thermodynamics of small systems complicated and not always well defined ! � Experimental concerns: formation of clusters depends on source conditions, sometimes driven by thermodynamics, sometimes kinetics � Nanoclusters exhibit a rich palette of thermodynamic phenomena: size- dependent melting, surface pre-melting, solid-solid structural transitions, freezing transitions, coalescence phenomena… � Sometimes surprises in store: ”non-melting clusters” (melting point appears to be higher that in bulk, e.g. Sn � bonding different in clusters) � Bi-stability of ”phases” Experimentally the best studied cluster melting problem: Na clusters, � work by Haberland group (original exp: Nature 393 , 238 (1998) + many later papers) � Computational challenge: sampling of the phase-space � Good review: Baletto, Ferrando, Rev. Mod. Phys. 77, 371 (2005) Global optimisation and potential energy surfaces • Generally: finding the global optimal geometry for a given cluster size is a highly non-trivial problem • A well-known example: 38-atom Lennard-Jones cluster has a narrow funnel for the global TO ground-state, but a wide funnel for icosahedral local minima • A useful website for global minima: Cambridge Cluster Database www-wales.ch.cam.ac.uk./CCD.html Rev Mod Phys. 77 , 371 (2005) 2
Dynamics of gold clusters from DFT-TB Supercooling to ”wrong” dimensionality (experimental time scale of cooling: MD of Au11- at 750 K: 0.1 to 10 microseconds) co-existence of 2D/3D liquid Koskinen et al, PRL 98, 015701 (2007) Video in EPAPS Electronic, chemical and catalytic properties of gold clusters 3
Chemical and catalytic properties of gold clusters � Bulk gold inert � Finely dispersed gold (as nanoparticles) catalytically active, for review see eg. Haruta, Catal. Today 36 , 153 (1997) � Oxide-supported size-selected clusters catalyze CO oxidation (Yoon, Häkkinen, Landman, Wörz, Antonietti, Abbet, Judai, Heiz, Science 307 , 403 (2005)) � Active site / charge state under debate � Known for long: gold atom chemically active in many oxidation states (rich complex chemistry) � Gas-phase reactivity with O2: anionic gold needed, highly size- dependent reactivity � Reactivity associated with electron transfer to O2 π * orbital Gold: Electron affinity & reactivity with O2 16 Taylor et al JCP 96, 3319 (1992) Anomalously inert Au16- Gantefor group CPL 377, 170 (2003) 4
Electronic structure of free Au clusters: Comparison to bulk band structure I Opahle, PhD Thesis, Dresden ”Band picture” of gold clusters: The Au(5d) derived band ”embedded” in the Au(6s6p) derived conduction electron shells, which Yoon, Koskinen, Huber, Kostko, can be found at E ≈ Emin and E ≈ Ef von Issendorff, Häkkinen, Moseler, Landman, ChemPhysChem 8, 157 (2007) These shells display symmetries expected from the delocalized electron shell model of simple metal clusters (1S-1P-2S/1D-1F…)!! Au16 : electronic structure and reactivity Si@Au16 Si@Au16- Au16 double-anion is a closed-electron-shell + O2 cluster with ”18e” shell closing (jellium-type 1S, 1P, 1D shells in a cage) � high EA � no electron transfer to O2 � no reactivity Dope with Si � ”20e” shell closing (2S now in) � anion now reactive with O2 5
Catalytic oxidation of CO by gas-phase Au 2 - • Low-T activity (low barriers) - (C) • Key intermediates: AuCOO 2 or AuCO 3 - (D) • 2 scenarios I, II • Eley-Rideal mechanism I II J. Am. Chem. Soc. 125, 10437 (2003) Theory: Häkkinen, Landman Experiment: Wöste group (Berlin) � Clusters on a supporting surface 6
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Only indirect observation via IR spectroscopy Yoon et al, Science 307 (2005) 403 Direct observation via STM Au/MgO(100) Sterrer et al, PRL 98 (2007) 96107 Au/NaCl(100) Repp et al, Science 305 (2004) 493 Direct experimental observations of Au clusters with STM Scale: 30 nm minima Sterrer et al, Angew.Chem.In.Ed . 45 (2006) 2630 8
Assumptions Clusters bind to oxygen vacancy (FC) Au atom on plain MgO: 0.8 eV, on FC: 2.8 eV Assume barrier 2 >> barrier 1 Positive bias = negative tip -> STM probes unocc. States Negative bias = positive tip -> STM probes occ. states Tersoff-Hamann approximation: STM probes local DOS Au 8 periodic versus cluster approach I = 0.25 nA 9
Delocalised electrons in gold clusters Janssens et al, NJP 5 (2003) 46 Walter et al, PCCP 8 (2006) 5407 Yoon et al, ChemPhysChem 8 (2007) 157 Flat Au 20 structure motive Same motive like supported Au 8 0eV 0.3eV 0.6eV 10
Flat structure: 2D Harmonic Oscillator model Free electrons of monovalent Gold LDOS of flat Au 20 @MgO 11
STM pictures I = 10 pA HOMO-1 HOMO average LUMO LUMO+1 average Au 13 : open shell cluster positive bias negative bias => STM sees the same picture independent of the bias 12
Conclusions ● Au clusters for 8-20 atoms appear as 1-2 nm particles in STM ● STM shows Gold wfs in the band-gap of MgO ● STM figures show nodes of delocalized wfs and not atoms ● Symmetries of the delocalized states can be understood in a simple monovalent Gold jellium model Ligand-protected gold clusters 13
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Review of optical properties: Wyrwas et al EPJD 2007 15
Science Oct 19, 2007 The first experimental total-structure-determination of a thiolate-protected gold cluster 16
Anatomy of the Stanford cluster I: Au102(p-MBA)44, Two visualizations ( p-MBA = para-mercapto benzoic acid ) Initial coordinates: Jadzinsky et al Science Oct 19, 2007 - necessary H added & CH bonds and COOH groups relaxed Full complex: 762 atoms and 3366 valence electrons (Walter et al, 2008 to be published) Anatomy of the Stanford cluster II: core – shell ! Au102(p-MBA)44 = Au79 + Au23(p-MBA)44 Two views of the (D5h, within 0.4 A) Au79 core 40-atom surface of the core + 21 RSAu-(RSAu)x-SR units (x=0 for 19 units and x=1 for 2 units) 2 Au(core) atoms with 2 SAu bonds each long unit, x=1 17
Anatomy of the Stanford cluster III: The two types of ligands RSAu-(RSAu)x-SR with x=0,1 R=(C6H4)(COOH) Anatomy of the Stanford cluster IV : A metallic, electronically inert Au79 core Radial analysis of charge re-distribution upon ionizing: virtually no changes inside 5Å radius, 10 % of the charge at the surface of Au79, 90% charging inside the Au23(p-MBA)44 protective layer Q(R) Note: 23 Au atoms in the protective layer (cf. ”Divide and Protect” model for Surface layer (40 atoms) of the Au79 core Au38(SR)24 = Au14(Au4SR4)6 Häkkinen, Walter, Grönbeck, JPCB 110, 9927 2006)) 18
(Global) angular momentum analysis of Au(6s6p)-derived ”conduction electron” states in the gold core Evaluate the coefficients c(R0) for each Kohn-Sham state n (done up to ������� I-symmetry) The EDOS of the Stanford cluster region of interest 19
Electronic structure: Angular momentum projected DOS around Fermi level (at E=0) • Au79 core supports the (expected) shell structure (58, 92 e gaps , proper symmetries) • Upon dressing the core with 21 (RSAu-(RSAu)x-SR) units, 21 conduction electrons depleted from the 3S+2D+1H manifold ( � surface- covalent S-Au(core) bonds), thereby revealing the 58 e gap, which becomes the HOMO-LUMO gap of the LPAuNC !! 2P+1G 2P+1G 3S+2D+1H Au79 KS levels and effective radial potential 6s-only calculation (M. Walter) 20
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