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Page 1: P.M. Dinh, E. Suraud

P.M.Dinh, Workshop ESNT, Jan. 23th 2006

P.M. Dinh, E. SuraudLaboratoire de Physique Théorique (Toulouse)

P.G. Reinhard, F. FehrerInstitut für Theoretische Physik (Erlangen)

Time-Dependent Density Functional Theory

in metal clusters

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P.M.Dinh, Workshop ESNT, Jan. 23th 2006

• Nuclei vs. metal clusters

• DFT in metal clusters

• A cluster@substrate model

• Deposition of Na cluster on Ar surface

• Conclusion and perspectives

Outline

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P.M.Dinh, Workshop ESNT, Jan. 23th 2006

Nuclei Metal clusters

relevant length scale

R ~~ r0 N 1/3

Nuclei vs. Metal clusters

N < 300 nucleons 3 < N < 105-7 atomsR ~~ rs N 1/3

dense systemswith strong Pauli

quantummean field

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P.M.Dinh, Workshop ESNT, Jan. 23th 2006

MEAN

FIELD

... 8250282082

Short range (nuclear) + long range (Coulomb) interactions

Long range (Coulomb) interactions

Nuclei vs. Metal clusters

Free nucleons Nucleons IN nucleus Nucleus

Free atom Atom IN cluster Cluster

... 13892402082

Interactions

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P.M.Dinh, Workshop ESNT, Jan. 23th 2006

Nuclei vs. Metal clustersAlkalines

(Li, Na, K, Rb, Cs)

1 fs

100 fs

10 fs

Nuclei

10 fm/c

1000 fm/c

100 fm/c

Time scales

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P.M.Dinh, Workshop ESNT, Jan. 23th 2006

DFT in metal clustersValence electrons Ions = core electrons + atom

Degrees of freedom ?

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P.M.Dinh, Workshop ESNT, Jan. 23th 2006

3 groups : Dresden, Kyoto-Seattle, Erlangen-ToulouseSemi-classical versions (Grenoble, Erlangen-Toulouse)

DFT in metal clusters How to solve the problem?

« Exactly »Ab initio methods of quantum chemistryWave packets in molecular physicsBut very small systems

« Adiabatically»Born-Oppenheimer approximation= Electrons bound to ground state surfaceBut very weak excitations

« Effectively »Density Functional Theory (effective mean field )Level 1 : Electrons only (1984…) Shells, plasmon,…Level 2 : Electrons + ions (1994 …) Complete non-adiabatic treatment of electrons and ions

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P.M.Dinh, Workshop ESNT, Jan. 23th 2006

DFT in metal clusters

Hohenberg-Kohn (1964)for Coulomb system,GS energy = functional of

start from HF procedure

(local)

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P.M.Dinh, Workshop ESNT, Jan. 23th 2006

DFT in metal clusters ???

Local DensityApprox.

homogeneous electron gaz

Perdew, Wang(1992)

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P.M.Dinh, Workshop ESNT, Jan. 23th 2006

DFT in metal clusters

MD-TDDFT(LDA)

in LDA Adiab. LDA or TDLDA

non-adiab. dynamics(≠Born-Oppenheimer)

dynamics ?

IONS ?

TDDFT

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P.M.Dinh, Workshop ESNT, Jan. 23th 2006

TDDFT in metal clusters

Na9+ under laser irradiation

I = 5x1011 W/cm2

FWHM = 125 fs= 2.3 eVdelay = 50 fs

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P.M.Dinh, Workshop ESNT, Jan. 23th 2006

TDDFT in metal clusters

Calvayrac, Reinhard, Suraud (1998)

Na9+ Carbon chains

Optical response

exp.ab initio

TDLDA Yabana,Bertsch (1997)TDLDA Berkus,Reinhard,Suraud(2002)

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P.M.Dinh, Workshop ESNT, Jan. 23th 2006

A cluster@substrate modeleasier with embedded or deposited clusters

Na cluster + Ar substrate

DAr dynamically polarizable electron cloud

2 others classical d.o.f.

Need to model interaction with environment

DArRAr

Experiments...

RAr core

gaussians, width from ()

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P.M.Dinh, Workshop ESNT, Jan. 23th 2006

A cluster@substrate modelCoupling to valence electrons and ions

Coulombab initio

dipole-dipole

finalfine-tuning

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P.M.Dinh, Workshop ESNT, Jan. 23th 2006

Deposition of Na cluster on Ar surfaceBO surfaces

0,1-

0,05-

0

0,05

0,1

0,15

0,2

-7 -5 -3 -1 1 3 5 7 9Distance (a0)

Ener

gy (R

y)

Na@Ar384Na+@Ar384Na@383

Na and Na+@Ar384

Na @Ar383

surface

minimumin matrix !

a vacancy

atom

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P.M.Dinh, Workshop ESNT, Jan. 23th 2006

Deposition of Na cluster on Ar surfaceNa@Ar384

Ekin0 = 4.7 meV

mechanicalwave in matrix

atom

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P.M.Dinh, Workshop ESNT, Jan. 23th 2006

BO surfaces

0,1-

0,05-

0

0,05

0,1

0,15

0,2

-7 -5 -3 -1 1 3 5 7 9Distance (a0)

Ener

gy (R

y)

Na@Ar384Na+@Ar384Na@383

Deposition of Na cluster on Ar surfaceNa@Ar384

complex cross-overbetweenBO surfaces

contradiction with previous BO calculations ?Ekin0 = 4.7 meV

NO !≈ Na@Ar383

Na finally inside Ar matrix !

an Ar atom ejectedfrom firstlayer

atom

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P.M.Dinh, Workshop ESNT, Jan. 23th 2006

Deposition of Na cluster on Ar surfaceNa6@Ar87

Ekin0 = 2.2 meV

soft material

systematics on Ekin0 size of Na cluster size of Ar cluster deformation transfer of kin. E wave celerity ...

cluster

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P.M.Dinh, Workshop ESNT, Jan. 23th 2006

Conclusion

Other materials ... •In progress:

Ne, Kr substrates• In the future:

hard substrates (MgO, NaCl) water environment

Perspectives

• MD-TDLDA: powerful tool for metal clusters in agreement with experiments

• Interaction with polarizable Ar substrate quite cumbersome high computing-time very soft material

CNRS post-docsept/oct 2006

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P.M.Dinh, Workshop ESNT, Jan. 23th 2006

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P.M.Dinh, Workshop ESNT, Jan. 23th 2006

DFT in metal clustersSelf-Interaction Correction

less expensive