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 and P. 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. Important optical property
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,

7. Structures of four gold clusters [Au147]5+ Cube-octahedral
[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)

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.:
system
peak
position (eV)
centre (eV)
height (f)
147-CO LB94
3.2
3.25
1.20
146-Oh LB94
3.4
1.80
172-CU LB94
2.95
3.00
147-Ih LB94
0.65
147-CO LDA
2.3
2.55
0.47
146-Oh LDA
2.6
2.50
0.55
172-CU LDA
2.1
2.35
0.30
147-Ih LDA
2.5
0.35
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. [Au147]Z+ Cube-octahedral TDDFT (LDA)
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 [Ag55Au92]5+ core-shell [Ag55Au92]5+ multi-shell
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)
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. TDDFT (LB94) relaxed geometry
Shape effect:
[M147]5+ and M120 M=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 projects Au-SPR AuMixSPR

21. 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.

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

23. 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!

24. Gold nanoparticles whose size and shape distributions are well defined
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,

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

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

27. 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

28. 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)

29. 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

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

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

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

33. 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

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

35. WAu12: Scalar Relativistic vs Spin-Orbit TDDFT