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

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

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

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

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

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

DFT in metal clustersValence electrons Ions = core electrons + atom

Degrees of freedom ?

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

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)

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

DFT in metal clusters ???

Local DensityApprox.

homogeneous electron gaz

Perdew, Wang(1992)

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

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

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)

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 ()

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

A cluster@substrate modelCoupling to valence electrons and ions

Coulombab initio

dipole-dipole

finalfine-tuning

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

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

Deposition of Na cluster on Ar surfaceNa@Ar384

Ekin0 = 4.7 meV

mechanicalwave in matrix

atom

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

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

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

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

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

DFT in metal clustersSelf-Interaction Correction

less expensive