1. P.M.Dinh, Workshop ESNT, Jan. 23th 2006 P.M. Dinh, E. Suraud Laboratoire de Physique Théorique (Toulouse) P.G. Reinhard, F. Fehrer Institut für Theoretische Physik (Erlangen) Time-Dependent Density Functional Theory in metal clusters

2. 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

3. P.M.Dinh, Workshop ESNT, Jan. 23th 2006 NucleiMetal clusters relevant length scale ~ R ~ r 0 N 1/3 Nuclei vs. Metal clusters N < 300 nucleons3 < N < 10 5-7 atoms ~ R ~ r s N 1/3 dense systems with strong Pauli quantum mean field

4. P.M.Dinh, Workshop ESNT, Jan. 23th 2006 MEANFIELDMEANFIELD... 82 50 28 20 8 2 Short range (nuclear) + long range (Coulomb) interactions Long range (Coulomb) interactions Nuclei vs. Metal clusters Free nucleons Nucleons IN nucleusNucleus Free atom Atom IN clusterCluster... 138 92 40 20 8 2 Interactions

5. P.M.Dinh, Workshop ESNT, Jan. 23th 2006 Nuclei vs. Metal clusters Alkalines (Li, Na, K, Rb, Cs) 1 fs 100 fs 10 fs Nuclei 10 fm/c 1000 fm/c 100 fm/c Time scales

6. P.M.Dinh, Workshop ESNT, Jan. 23th 2006 DFT in metal clusters Valence electronsIons = core electrons + atom Degrees of freedom ?

7. P.M.Dinh, Workshop ESNT, Jan. 23th 2006 3 groups : Dresden, Kyoto-Seattle, Erlangen-Toulouse Semi-classical versions (Grenoble, Erlangen-Toulouse) 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

8. 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)

9. P.M.Dinh, Workshop ESNT, Jan. 23th 2006 DFT in metal clusters ??? Local Density Approx. homogeneous electron gaz Perdew, Wang (1992)

10. 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

11. P.M.Dinh, Workshop ESNT, Jan. 23th 2006 TDDFT in metal clusters Na 9 + under laser irradiation I = 5x10 11 W/cm 2 FWHM = 125 fs  = 2.3 eV delay = 50 fs

12. P.M.Dinh, Workshop ESNT, Jan. 23th 2006 TDDFT in metal clusters Calvayrac, Reinhard, Suraud (1998) Na 9 + Carbon chains Optical response exp. ab initio TDLDA Yabana,Bertsch (1997) TDLDA Berkus, Reinhard,Suraud(2002)

13. P.M.Dinh, Workshop ESNT, Jan. 23th 2006 A cluster@substrate model easier with embedded or deposited clusters Na cluster + Ar substrate  D Ar dynamically polarizable electron cloud 2 others classical d.o.f. Need to model interaction with environment D Ar R Ar Experiments...  R Ar core  gaussians, width from  (  )

14. P.M.Dinh, Workshop ESNT, Jan. 23th 2006 A cluster@substrate model Coupling to valence electrons and ions Coulomb ab initio dipole-dipolefinal fine-tuning

15. P.M.Dinh, Workshop ESNT, Jan. 23th 2006 Deposition of Na cluster on Ar surface Na and Na + @Ar 384 Na @Ar 383 surface minimum in matrix ! a vacancy atom

16. P.M.Dinh, Workshop ESNT, Jan. 23th 2006 Deposition of Na cluster on Ar surface Na@Ar384 E kin0 = 4.7 meV mechanical wave in matrix atom

17. P.M.Dinh, Workshop ESNT, Jan. 23th 2006 Deposition of Na cluster on Ar surface Na@Ar 384 complex cross-over between BO surfaces contradiction with previous BO calculations ? E kin0 = 4.7 meV NO ! ≈ Na@Ar 383 Na finally inside Ar matrix ! an Ar atom ejected from first layer atom

18. P.M.Dinh, Workshop ESNT, Jan. 23th 2006 Deposition of Na cluster on Ar surface Na 6 @Ar 87 E kin0 = 2.2 meV soft material systematics on E kin0 size of Na cluster size of Ar cluster  deformation  transfer of kin. E  wave celerity ... cluster

19. 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-doc sept/oct 2006

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

21. DFT in metal clusters Self-Interaction Correction less expensive