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TDDFT computational study of optical photoabsorption in Au n and Au n Ag m nanoclusters

This study aims to design a computational scheme using DFT/TDDFT to describe the photoabsorption of alloyed nanoclusters, validate it with experimental data, identify trends in alloys, and rationalize these trends in terms of electronic structure.

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TDDFT computational study of optical photoabsorption in Au n and Au n Ag m nanoclusters

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  1. TDDFT computational study of optical photoabsorption in Aun and AunAgm nanoclusters Mauro Stener1,2, Nicola Durante3 and Alessandro Fortunelli3 1Università degli Studi di Trieste, Dipartimento di Scienze Chimiche 2INSTM, Consorzio Interuniversitario per la Scienza e la Tecnologia dei materiali 3CNR-IPCF, Istituto per i Processi Chimico-Fisici (IPCF) of the Italian Consiglio Nazionale delle Ricerche (CNR), via. G. Moruzzi 1, 56124, Pisa, Italy European Cost Action MP0903 Nanoalloys as advanced materials: from structure to properties and applications Joint Working Group Meetings, Faculty of Chemistry, Universitat de Barcelona April 14-16, 2011

  2. Objectives • Design of a DFT/TDDFT computational scheme to describe photoabsorption of alloyed nanoclusters • Validation with respect to experimental data • Identification of trends in alloys (composition, chemical ordering, cluster shape) • Rationalization of trends in terms of electronic structure

  3. Computational scheme: geometry • Cluster geometry: DFT geometry optimization or experimental bulk interatomic distances (2.88 Å for Au) • Standard DFT-KS method: LDA (VWN), DZ basis • Scalar Relativistic (SR) effects: ZORA • Code: ADF parallel (MPI) IBM SP6

  4. Relativistic effects in Au compounds Large relativistic contraction of the Au 6s shell 6s shell P. Pyykko and J. P. Desclaux, Acc. Chem. Res. 12 (1979) 276 Strong relativistic narrowing of the 5d – 6s gap J. P. Desclaux andP. Pyykko, Chem. Phys. Lett. 39 (1976) 300

  5. TDDFT electronic excitations • orbitals () and eigenvalues () obtained with: • DZ basis set • LB94 (correct asymptotic –1/r behavior) or LDA (VWN) • More stringent SCF convergence: |FP-PF|<10-8 • Closed shell electronic structure (charged clusters) Common VXC choices (LDA and GGA) do not obey to correct asymptotic –1/r behavior, this feature is important to obtain accurate excitation energies and intensities: LB94 is asymptotically correct. LB94: R. van Leeuwen and E. J. Baerends, PRA 49 (1994) 2421

  6. Gold clusters: optical activity Samples of large large nanoparticle exhibit an absorption band in visible region SPR (Surface Plasmon Resonance) Collective excitations of conduction band electrons Important optical property • Theoretical models: classical • electrodynamics for large size • Small size: quantum confinement effects: TDDFT Abs. spectrum of a sample of gold nanoparticles with aspect ratio di 2.6, 3.3, e 5.4 ( = 480 nm). Burda, C.; Chen, X.; Narayanan, R.; El-Sayed, M. A. Chem. Rev. 2005, 105, 1025-1102

  7. Structures of four gold clusters [Au146]2+ octahedral [Au146]2+ Octahedral [Au172]4+ Cubic [Au147]5+ Cube-octahedral [Au147]- Icosahedral N. Durante, A. Fortunelli, M. Broyer and M. Stener, J. Phys. Chem. C, 115 (2011) 6277 - 6282.

  8. Structural relaxation: [Au146]2+ octahedral Geometry: bulk (2.88 Å)

  9. Structural relaxation: [Au146]2+ octahedral Geometry: relaxed

  10. Estimate peak energy from exp.: 2.9 – 3.0 eV Cottancin, E.; Celep, G.; Lermé, J.; Pellarin, M.; Huntzinger, J. R.; Vialle, J. L.; Broyer, M. Theor. Chem. Acc. 2006, 116, 514 • LB94 better than LDA • Peak maximum more sensitive than peak center • Peak shape dependence

  11. Charge effect [Au147]Z+ Cube-octahedral TDDFT (LDA) relaxed geometry

  12. Structural relaxation effect [Au146]Z+ Octahedral TDDFT (LB94) relaxed and bulk (2.88 Å) geometry

  13. Alloys: nanoclusters • Built by chemical substitution of [Au147]5+ Cubo-Octahedral, keeping Oh symmetry • Two chemical compositions: [Ag55Au92]5+and[Au55Ag92]5+ • Three chemical ordering: core-shell, multi-shell and maximum mixing. [Ag55Au92]5+ core-shell [Ag55Au92]5+ multi-shell [Ag55Au92]5+ Maximum mixing

  14. Alloys, chemical compositon effect: [Au147]5+ Cubo-Octahedral shape, core-shell chemical ordering TDDFT (LB94) relaxed geometry M. Gaudry, J. Lermé, E. Cottancin, M. Pellarin, J. -L. Vialle, M. Broyer, B. Prével, M. Treilleux, and P. Mélinon, PRB 64 (2001) 085407 As Ag concentration increases: blue shift + intensity enhancement consistent with experiment

  15. Alloys, chemical ordering effect: [Ag55Au92]5+ and [Au55Ag92]5+Cubo-Octahedral shape core-shell, multi-shell, maximum mixing chemical ordering TDDFT (LB94) relaxed geometry • In both [Ag55Au92]5+ and [Au55Ag92]5+ • core-shell and multi shell resemble each other • maximum mixing looks different

  16. Shape effect: [M147]5+ and M120M=Au, Ag Cubo-Octahedral and Td shapes TDDFT (LB94) relaxed geometry Extreme shape effect is important for Au and dramatic for Ag, needs more investigation!

  17. Rationalization in terms of electronic structure Preliminar results on [Ag55Au92]5+ and [Au55Ag92]5+ core-shell Analysis of transitions in terms of initial and final states A: Au(6s)  Au (6p), Ag (5p) B: Au(6s,5d)  Au (6s,6p) C: Au(5d)  Au (6p) D: Au(6s), Ag(5s) Ag (5p) E: Au(5d)  Au (6s,6p), Ag(5s,5p) F: Au(5d)  Au (6s,6p), Ag(5s,5p) Increasing Ag concentration, Ag contributions start to populate final states.

  18. CONCLUSIONS AND PERSPECTIVES • Design: large systems, good compromise (efficiency) • Validation: LB94 seems to be better • Identification of trends, dramatic shape effects for Ag. For alloys? • Rationalization: only preliminar • Perspective: • Alloys with other metals (Cu, Pt, Pd, Fe) • Open-shell systems for magnetoplasmonics • Development of new computational schemes for larger systems (TB-TDDFT or a new TDDFT algorithm)

  19. ACKNOWLEDGEMENTS CNR Pisa Alessandro Fortunelli and Nicola Durante Funds: INSTM (Progetto PRISMA 2004) MIUR (FIRB 2001, PRIN 2004, PRIN 2006, PRIN 2008) CINECA for generous grants of computer time on SP6 IBM supercomputer and technical support: ISCRA projectsAu-SPR AuMixSPR

  20. Computational scheme: geometry GGA  2.97 Å Exp. Bulk:2.88 Å LDA  2.89 Å For Au, LDA is the best choice for geometry optimization O. Häberlen, S.-C. Chung, M. Stener and N. Rösch, J. Chem. Phys. 106 (1997) 5189.

  21. TDDFT electronic excitations The actual TDDFT equation solved by ADF is: The “ingredients” are KS orbitals () and eigenvalues ()

  22. TDDFT electronic excitations i and j run over Nocc a and b run over Nvirt • Davidson iterative diagonalization, extraction of the lowest n eigenvalues (n = 300 in our calculations) • W matrix is not stored, efficient density fit!

  23. Gold clusters Gold nanoparticles whose size and shape distributions are well defined • Conventional chemical synthesis • Structural characterization • at electron microscopy (TEM) Gold nanoparticles TEM images with SPR at: (a) 700, (b) 760, (c) 880, (e) 1130, e (f) 1250 nm. Bar scale 50 nm. Nikoobakht, B.; El-Sayed, M. A. Chem. Mater. 2003, 15, 1957-1962.

  24. DFT: the Kohn-Sham (KS) method The electron density  can be extracted from a system of non-interacting electrons: SCF iterative solution

  25. ADF program • LCAO formulation (STO basis set) • Numerical integrals • Density fitting

  26. i are spin-orbitals • The potential is local (at variance with HF) • VXC must be approximated in practice (LDA, GGA, …) • Total energy E[] and one-electron local operator properties of the systems can be calculated from density

  27. Relativistic effects: transformation • in ADF: ZORA (Zero Order Regular Approximation) • ZORA: well behaved over the nuclei • Two components: Spin-Orbit (SO) coupling included • If SO is neglected: Scalar Relativistic (SR)

  28. TDDFT: linear response In general, the density (1)induced by an external TD perturbative field v(1) is: Where  is the dielectric susceptibility of the interacting system, not easily accessible

  29. TDDFT justifies the use of the KS of the non-interacting system: Provided: • KS is easy to calculate • fXC (XC kernel) is unknown

  30. KS is expressed in terms of KS orbitals and energies: In practice fXC is approximated according to Adiabatic Local Density Approximation (ALDA):

  31. Therefore, dynamic polarizability xz() can be rigorously calculated at TDDFT level: The mean dynamic polarizability () is related to excitation energies EIand oscillator strengths fI : () has poles at EI and the residues are connected to the fI

  32. Gold bimetallic clusters: M@Au12 • Icosaedral bimetallic gold clusters: Au cage with encapsulated heteroatom WAu12 MoAu12 • First theoretically predicted, then synthesized and characterized by spectroscopy • Analysis of the spin orbit coupling on optical spectra

  33. WAu12: spin-orbit electronic structure Exp: photodetachment of WAu12-

  34. WAu12: Scalar Relativistic vs Spin-Orbit TDDFT

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