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Time-Dependent Density Functional Theory in
metal clusters
P.M. Dinh, E. Suraud
Laboratoire de Physique Théorique (Toulouse)
P.G. Reinhard, F. Fehrer
Institut für Theoretische Physik (Erlangen)
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Outline

• Nuclei vs. metal clusters
• DFT in metal clusters
• A cluster_at_substrate model
• Deposition of Na cluster on Ar surface
• Conclusion and perspectives

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Nuclei vs. Metal clusters
Nuclei
Metal clusters
N lt 300 nucleons
3 lt N lt 105-7 atoms
R r0 N 1/3
R rs N 1/3
relevant length scale
dense systems with strong Pauli
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Nuclei vs. Metal clusters
Interactions
Short range (nuclear) long range (Coulomb)
interactions
... 82 50 28 20 8 2
MEAN FIELD
Long range (Coulomb) interactions
... 138 92 40 20 8 2
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Nuclei vs. Metal clusters
Time scales
Alkalines (Li, Na, K, Rb, Cs)
Nuclei
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DFT in metal clusters
Degrees of freedom ?
Valence electrons
Ions core electrons atom
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DFT in metal clusters
How to solve the problem?
 Exactly  Ab initio methods of quantum
chemistry Wave packets in molecular physics But
very small systems
 Adiabatically Born-Oppenheimer
approximation Electrons bound to ground state
surface But 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
3 groups Dresden, Kyoto-Seattle,
Erlangen-Toulouse Semi-classical versions
(Grenoble, Erlangen-Toulouse)
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DFT in metal clusters
start from HF procedure
(local)
for Coulomb system,
Hohenberg-Kohn (1964)
GS energy functional of r
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DFT in metal clusters
Local Density Approx.
Perdew, Wang (1992)
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DFT in metal clusters
dynamics ?
TDDFT
? Adiab. LDA or TDLDA
non-adiab. dynamics (?Born-Oppenheimer)
IONS ?
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TDDFT in metal clusters
I 5x1011 W/cm2 FWHM 125 fs w 2.3 eV delay
50 fs
Na9 under laser irradiation
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TDDFT in metal clusters
Optical response
Carbon chains
Na9
Calvayrac, Reinhard, Suraud (1998)
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A cluster_at_substrate model
easier with embedded or deposited clusters
Experiments...
Need to model interaction with environment
Na cluster Ar substrate
2 others classical d.o.f.

• RAr core

• DAr dynamically
• polarizable
• electron cloud

DAr
RAr
? gaussians, width from a(w)
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A cluster_at_substrate model
Coupling to valence electrons and ions
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Deposition of Na cluster on Ar surface
atom
Na and Na_at_Ar384
minimum in matrix !
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Deposition of Na cluster on Ar surface
atom
Na_at_Ar384
Ekin0 4.7 meV
mechanical wave in matrix
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Deposition of Na cluster on Ar surface
atom
Na_at_Ar384
Ekin0 4.7 meV
NO !
contradiction with previous BO calculations ?
Na_at_Ar383
complex cross-over between BO surfaces
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Deposition of Na cluster on Ar surface
cluster
Na6_at_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
• ...

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Conclusion

• MD-TDLDA powerful tool for metal clusters
• in agreement with experiments
• Interaction with polarizable Ar substrate
• quite cumbersome
• high computing-time
• very soft material

Perspectives

• Other materials ...
• In progress
• Ne, Kr substrates
• In the future
• hard substrates (MgO, NaCl)
• water environment

CNRS post-doc sept/oct 2006
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DFT in metal clusters
Self-Interaction Correction