Post on 20-Jan-2016
TDDFT computational study of optical photoabsorption in Aun and AunAgm nanoclusters
Mauro StenerMauro Stener1,21,2, Nicola Durante, Nicola Durante33 and Alessandro Fortunelli and Alessandro Fortunelli33 1Università degli Studi di Trieste, Dipartimento di Scienze Chimiche2INSTM, Consorzio Interuniversitario per la Scienza e la Tecnologia dei materiali3CNR-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 MP0903Nanoalloys as advanced materials: from structure to properties and applicationsJoint Working Group Meetings, Faculty of Chemistry, Universitat de Barcelona
April 14-16, 2011
Objectives
1. Design of a DFT/TDDFT computational scheme to describe photoabsorption of alloyed nanoclusters
2. Validation with respect to experimental data
3. Identification of trends in alloys (composition, chemical ordering, cluster shape)
4. Rationalization of trends in terms of electronic structure
Computational scheme: geometry
1. Cluster geometry: DFT geometry optimization or experimental bulk interatomic distances (2.88 Å for Au)
2. Standard DFT-KS method: LDA (VWN), DZ basis
3. Scalar Relativistic (SR) effects: ZORA
4. Code: ADF parallel (MPI) IBM SP6
Relativistic effects in Au compounds
J. P. Desclaux and P. Pyykko, Chem. Phys. Lett. 39 (1976) 300
P. Pyykko and J. P. Desclaux, Acc. Chem. Res. 12 (1979) 276
6s shell Large relativistic contraction of the Au 6s shell
Strong relativistic narrowing of the 5d – 6s gap
• 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)
LB94: R. van Leeuwen and E. J. Baerends, PRA 49 (1994) 2421
TDDFT electronic excitations
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.
Samples of large large nanoparticle exhibit an
absorption band in visible region
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
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
Gold clusters: optical activity
Structures of four gold clusters [Au146]2+ octahedral
[Au147]- Icosahedral
[Au172]4+ Cubic
[Au147]5+ Cube-octahedral
[Au146]2+ Octahedral
N. Durante, A. Fortunelli, M. Broyer and M. Stener, J. Phys. Chem. C, 115 (2011) 6277 - 6282.
Geometry: bulk (2.88 Å)
Structural relaxation: [Au146]2+ octahedral
Structural relaxation: [Au146]2+ octahedral
Geometry: relaxed
Excitation Energy (eV)
0 1 2 3
f
0.0
0.5
Excitation Energy (eV)
0 1 2 3 4
f
0.0
0.2
0.4
f
0.0
0.5
1.0
f
0.0
0.5
1.0
1.5
f
0.0
0.5
1.0
1.5
f
0.0
0.2
0.4
f
0.0
0.2
0.4
f
0.0
0.2
0.4
0.6
[Au147]5+ CO (a)
[Au146]2+ Oh (b)
[Au172]4+ CU (c)
[Au147]- Ih (d)
LB94 LDA system peak position
(eV)
peak centre (eV)
peak height
(f)
147-CO LB94 3.2 3.25 1.20
146-Oh LB94 3.4 3.25 1.80
172-CU LB94 2.95 3.00 1.20
147-Ih LB94 2.95 2.95 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 2.35 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
1. LB94 better than LDA
2. Peak maximum more sensitive than peak center
3. Peak shape dependence
Charge effect[Au147]Z+ Cube-octahedral TDDFT (LDA)
relaxed geometry
Excitation Energy (eV)
0 1 2 3 4
f
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Z = 5Z = 1
LDA
Structural relaxation effect[Au146]Z+ Octahedral TDDFT (LB94) relaxed and bulk (2.88 Å) geometry
Excitation Energy (eV)
0 1 2 3 4
f
0.0
0.5
1.0
1.5
2.0
Relaxed geom.Unrelaxed (bulk) geom.
Alloys: nanoclusters
1. Built by chemical substitution of [Au147]5+ Cubo-Octahedral, keeping Oh symmetry
2. Two chemical compositions: [Ag55Au92]5+ and [Au55Ag92]5+ 3. Three chemical ordering: core-shell, multi-shell and maximum mixing.
[Ag55Au92]5+ core-shell
[Ag55Au92]5+ multi-shell
[Ag55Au92]5+ Maximum mixing
Excitation Energy (eV)
1 2 3 4 5
f
0
1
2
3
4
5
Au147
Ag55Au92 (core-shell)
Au55Ag92 (core-shell)
Ag147
Alloys, chemical compositon effect:[Au147]5+ Cubo-Octahedral shape, core-shell chemical ordering
TDDFT (LB94) relaxed geometry
As Ag concentration increases:blue shift + intensity enhancement consistent with experiment
M. Gaudry, J. Lermé, E. Cottancin, M. Pellarin, J. -L. Vialle, M. Broyer, B. Prével, M. Treilleux, and P. Mélinon, PRB 64 (2001) 085407
Excitation Energy (eV)
1 2 3 4 5
f
0
1
2
3
4
2 3 4
f
0
1
2
3
4
5
Core - shellMulti - shellMaximum mixing
Ag55Au92
Au55Ag92
Alloys, chemical ordering effect:[Ag55Au92]5+ and [Au55Ag92]5+ Cubo-Octahedral shape
core-shell, multi-shell, maximum mixing chemical orderingTDDFT (LB94) relaxed geometry
In both [Ag55Au92]5+ and [Au55Ag92]5+
• core-shell and multi shell resemble each other
• maximum mixing looks different
Excitation Energy (eV)
1 2 3 4 5 6
f
0
10
20
30
40 [Ag147]5+ CO
Ag120 Td
2 3 4 5
f
0.0
0.5
1.0
1.5
2.0
2.5
3.0
[Au147]5+ CO
Au120 Td
Aun
Agn
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!
Rationalization in terms of electronic structurePreliminar results on [Ag55Au92]5+ and [Au55Ag92]5+ core-shell
Analysis of transitions in terms of initial and final states
[Au55Ag92]+5
Excitation Energy (eV)
0 1 2 3 4 5
f
0
1
2
3
4
[Ag55Au92]+5
1 2 3 4
f
0.0
0.5
1.0
1.5
2.0
D
C
B
A
E F
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.
CONCLUSIONS AND PERSPECTIVESCONCLUSIONS AND PERSPECTIVES
1. Design: large systems, good compromise (efficiency)
2. Validation: LB94 seems to be better
3. Identification of trends, dramatic shape effects for Ag. For alloys?
4. Rationalization: only preliminar
Perspective:
1. Alloys with other metals (Cu, Pt, Pd, Fe)
2. Open-shell systems for magnetoplasmonics
3. Development of new computational schemes for larger systems (TB-TDDFT or a new TDDFT algorithm)
ACKNOWLEDGEMENTSACKNOWLEDGEMENTS
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
Computational scheme: geometry
O. Häberlen, S.-C. Chung, M. Stener and N. Rösch, J. Chem. Phys. 106 (1997) 5189.
LDA 2.89 Å
GGA 2.97 ÅExp. Bulk: 2.88 Å
For Au, LDA is the best choice for
geometry optimization
III E FF 2
)()(2 ,2
, jbjbiaiaiaabijjbia K
''''
1', rrrrr
rrrrrr lk
ALDAxcjiklij fddK
TDDFT electronic excitations
The actual TDDFT equation solved by ADF is:
The “ingredients” are KS orbitals () and eigenvalues ()
III E FF 2
Davidson iterative diagonalization, extraction of the lowest n eigenvalues (n = 300 in our calculations)
matrix is not stored, efficient density fit!
jbia , i and j run over Nocc
a and b run over Nvirt
TDDFT electronic excitations
• Conventional chemical synthesis
• Structural characterization
at electron microscopy (TEM)
Gold nanoparticles whose size and shape
distributions are well defined
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.
Gold clusters
DFT: the Kohn-Sham (KS) method
The electron density can be extracted from a system of non-interacting electrons:
rVrr
rdr
Rr
ZH XC
N N
NKS
2
2
1
niH iiiKS ,...,1
occ
iiiin * SCF iterative solution
ADF program
1. LCAO formulation (STO basis set)
2. Numerical integrals
3. Density fitting
k
kiki Crr
k
kakkikai OwO rrr
n
nn faocc
iiiin '~*
r
rdan2~min:
1. i are spin-orbitals
2. The potential is local (at variance with HF)
3. VXC must be approximated in practice (LDA, GGA, …)
4. Total energy E[] and one-electron local operator properties of the systems can be calculated from density
Relativistic effects: transformation • in ADF: ZORA (Zero Order Regular Approximation)
pp
Vmc
cVH ZORA
2
2
2
• ZORA: well behaved over the nuclei• Two components: Spin-Orbit (SO) coupling included• If SO is neglected: Scalar Relativistic (SR)
TDDFT: linear response
In general, the density (1) induced by an external TD perturbative field v(1) is:
','',,, )1()1( rrrrr dv
Where is the dielectric susceptibility of the interacting system, not easily accessible
TDDFT justifies the use of the KS of the non-interacting system:
','',,,)1()1( rrrrr dvSCFKS
Provided:
','',,''
,',, )1(
)1()1()1(
rrrrrrr
rrr dfdvv XCSCF
KS is easy to calculate
fXC (XC kernel) is unknown
occ
i
unocc
a ia
iaaiocc
i
unocc
a ia
iaaiKS i
rrrr
i
rrrrrr
****
,,
KS is expressed in terms of KS orbitals and energies:
In practice fXC is approximated according to Adiabatic Local Density Approximation (ALDA):
'
'
'',, rr
r
rrr
d
dVf
LDAXC
XC
Therefore, dynamic polarizability xz() can be rigorously calculated at TDDFT level:
rr xdzxz ,1
The mean dynamic polarizability () is related to excitation energies EI and oscillator strengths fI :
I I
I
E
ftrace
223
1
α
() has poles at EI and the residues are connected to the fI
• 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
Gold bimetallic clusters: M@Au12
WAu12: spin-orbit electronic structure
Exp: photodetachment of WAu12-
KS
-16
-14
-12
-10
-8
-6
-4
-2
0
5e1g(1/2)
4hg
7hg
8hg
5t2u
6ag
4ag
5t1u
5ig(5/2) + 4gg(3/2)6gu(3/2)+4e1u(1/2)
9gg(3/2) + 12ig(5/2)
8gg(3/2) + 11ig(5/2)
8e1g(1/2)11iu(5/2)
LUMO
HOMO
SR SO
1.43 eV1.43 eV
1.09 eV1.09 eV
X. Li, B. Kiran, J. Li, H.-J. Zhai and L.-S. Wang, Angew. Chem. Int. Ed. 41, 4786 (2002)
X. Li, B. Kiran, J. Li, H.-J. Zhai and L.-S. Wang, Angew. Chem. Int. Ed. 41, 4786 (2002)
1.81.8 eVeV0.90.9 eVeV
Excitation Energy (eV)
3 4 5 6 7 8 9 10 11 12
f
0
1
2
3
4
5
6
f
0
1
2
3
4
5
6 SR WAu12
SO WAu12
Figure 4
WAu12: Scalar Relativistic vs Spin-Orbit TDDFT