P.M. Dinh, E. Suraud
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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