Simulating the Structure and Dynamics of Heterogenous Nanoclusters

1. Simulating the Structure and Dynamics of Heterogenous Nanoclusters François G. Amar Department of Chemistry University of Maine Department of Chemistry & Physics, UNE January 23, 2009

2. Acknowledgements • Jinasena Hewage • (now at University of Ruhuna) • James Smaby • TJ Preston • Gérard Torchet & Marie-Françoise de Feraudy • Marcus Lundwall & Swedish group at Lund

3. Finite heterogeneous systems are also of intrinsic interest. • Motivation • Interested in how material properties vary as system size grows from atom to bulk. • Novel or special properties of ultra-small chunks of matter: catalysis, transport, fabrication. • Varying the stoichiometry as well as size of small particles adds another “tunable” parameter.

4. Ballistic deposition of Cu on Ag yields subsurface shells: ”onion”(MD with embedded atom potentials) At intermediate temperature fcc-A-core supports A-B-A growth while ico-A-core does not. F. Balleto, C. Mottet, and R. Ferrando, PRL 90(13) 5504 (2003)

5. Molecular Beam Source Ar P=1 bar T=300 K V=550 m/s

6. A Closer Look at the Beam In skimmed beam, T ~ 0.5 K V=550 m/s T T T T vs=13 m/s Mach # = V/ vs ~ 40

8. How do we know what clusters are predominant in the jet? • Sizes • Structure • Stoichiometry

9. ionizing e- beam hn UV-vis or IR spectrum mass spectrum Perform experiments! T T T T V=550 m/s electron diffraction 10 millisecond time window!

10. Notice maxima at rare gases

11. ? Hgn Why is mercury a metal? When does it become so? Recall, Hg: [Xe] (4f)14(5d)10(6s)2 Let’s look at that ionization energy again. 4.49 eV 10.3 eV Hg Hg (l)

12. Rademan, Kaiser, Even, Hensel, PRL 59, 2319 (1987)

13. Around n=20, change in slope suggests transition from van der Waals to metallic behavior 1/R ~ 1/n1/3

14. What about the theory of these small objects? • Structure • ab initio quantum mechanics or DFT • (for smaller clusters) • Semi-empirical quantum theory • Empirical force-fields or potential energy surfaces • van der Waals systems • larger clusters • PES from scattering experiments…

15. Dynamics • Quantum dynamics (9 degrees of freedom) • Quantum MD (classical MD with forces from DFT) • aka Car-Parrinello • Classical dynamics on potential energy surfaces • Large clusters • Long times: 10 nanoseconds! • Solve:

16. Thermodynamics • Path integral Monte Carlo; diffusion MC • Multiple histogram methods using classical dynamics on potential energy surfaces ; adiabatic switching • accurate classical densities of states (“heavy” atoms) • larger clusters

17. Two recent projects from our group • Ar/N2 cluster structure and dynamics • Simulating the photoelectron spectra of • Arn, Xen, ArnXem clusters

18. Two recent projects from our group • Ar/N2 cluster structure and dynamics • Simulating the photoelectron spectra of • Arn, Xen, ArnXem clusters

19. V(r) for Ar2

20. Ar/N2 Potential Models • Ar-Ar(Aziz-Chen4)Re=3.75 Å; De=99.4 cm-1 • N2-N2(exp-6 + 3-charge quadrupole2) • Canted parallel: • Re=3.98 Å; De=102.5 cm-1 • T-shape: • Re =4.15 Å; De=102.8 cm-1 • Ar-N2 (damped dispersion model fit to ab initio3) Re=3.64 Å; De=111.9 cm-1

22. Despite the stronger pair interaction, N2 appears to be less easily incorporated into the center of the cluster than Ar due to frustration effects. Ar7(N2)6 with Ar at center Ar7(N2)6 with N2 at center

23. Ar centered N2 centered The Caloric Curve: Heat both the Ar-centered and N2-centered isomers Inflection is a signature of “melting”

24. Caloric curve RMS bond fluctuation parameter Orientational order parameter

25. N --> ∞ small N E E Tm Tm Tm Tm What does melting mean away from the thermodynamic limit (large N)?

26. 0 10 20 30 40 50 60 T / K Ar-centered clusters

27. Ar-centered clusters N2-centered clusters

28. t = 0 ps t = 500 ps t = 5 ps t = 255 ps t = 450 ps (N2)13Ar42 Dynamics Initial structure: quenched cuboctahedron with N2 in center T = 41 K (liquid-like) N2 molecules mix throughout cluster and migrate to surface

29. Two recent projects from our group • Ar/N2 cluster structure and dynamics • Simulating the photoelectron spectra of • Arn, Xen, ArnXem clusters

30. “Phase” diagram of A55B55: a=eAB/eAAb=eBB/ eAA A.S. Clarke, R. Kapral, and G.N. Patey, JCP 101, 2432 (1994)

32. What does the photoelectron experiment measure? So… …calculate the final state polarization energy (the signal electrons--at 50 eV--leave in 10-16 seconds)

33. Potentials HFD type potentials with accurate well depths and equilibrium bond lengths. Cubic splines used for potential and force. a=0.72 b=0.54 aSlavicek et al, JCP 119, 2102 (2003) bAziz et al, JCP 78, 2402 (1982)

34. Making clusters Start with perfect ordered structures such as icosahedra and then warm and anneal within a bounding sphere. Xe300 ico 0 pdp 5 hcp 67 fcc 52 unknown 176

35. Polarization energy calculation Self-consistent polarization energy calculation in which each atom in a cluster takes the role of the ion The induced dipoles are iterated to self-consistency, taking about 6 to 8 iterations to achieve self-consistent energies to 1 part in 106. The polarization energies are binned to construct a histogram and we typically average over an ensemble of 10 to 20 clusters. [aXe=4.04Å3; aAr=1.64Å3]

36. Pure Xenon “4d5/2” Pure Argon “2p3/2” Xe150 Ar150 Xe250 Ar250 Xe500 Ar500 Xe1000 Ar1000

37. d R q r Signal Attenuation

38. What is the mean free path? Dependent on material and electron kinetic energy. Tchaplyguine et al, permit an estimate of: l=17 Å and 9 Å for Xe and Ar clusters, respectively for 50 eV signal electrons. Alternatively, the TPP-2M formula gives (IMFP) lXe=6.5 Å and lAr=10.9 Å at the same energy. We use lXe=6.5 Å and lAr=9 Å in the following.

39. Broadening Convolute screened histogram data with Voight profile of isolated atom signal provided by experimentalists

40. Xe309 “raw” Xe309 broadened Xe309 screened broadened Simulated Xe 4d5/2spectrum Structure in the raw histogram bulk peak reflects local environment but is no longer apparent after broadening. For Xe309, screening tends to “reduce” the bulk peak.

41. Ar250 Exp: <N>≈300 Ar500 Ar1000 Pure Ar cluster spectra at 50 eV (l=9Å)

42. l=17Å l=6.5Å Xe150 Xe250 Xe250 Xe500 Exp: <N>=900 Exp: <N>=900 Xe500 Xe1000 Pure Xe spectra

43. The polarization shift calculation appears to give semi-quantitative shifts Experimentalists report a Gaussian size distribution in their beam with a FWHM =<N>. 2) Point dipole model may be inadequate. 3) Thermal treatments may affect final spectrum

44. Mixed Clusters

45. Experimental data* *Thanks to to M. Lundwall for sharing these results prior to publication.

46. Xe spectrum Xe500Ar500 core/shell structure Ar spectrum

47. Modified clusters Start with Xe/Ar core-shell. SubstituteAr atoms with single Xe atoms (“pepper”) Substitute Ar atoms with small clusters of Xe (“plum”)

48. Xe396Ar527 “plum” Xe1000

49. Ar250 Xe396Ar527 “plum”

50. Conclusions • Polarization energy shift model captures the essential physics and is quantitative to within about 5%. • The bulk/surface shift model for pure clusters of Tchaplyguine et al is well supported by our atomistic calculations. • Our preliminary calculations of mixed clusters supports the layering model proposed by the Swedish group. As the Ar/Xe ratio in the beam increases it appears that the cluster will consist of a core/shell structure with trapped Xe atoms and/or small clusters in the outer Ar layer.