tddft computational study of optical photoabsorption in au n and au n ag m nanoclusters mauro stener...

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