XIV ETSF Workshop Évora 17 th September 2009

1. XIV ETSF Workshop Évora 17th September 2009 Classical and Many-Body Theory of Image Potentials at Solid-Molecule Interfaces Juan María García Lastra Kristian Sommer Thygesen Ángel Rubio

2. Outline • Introduction • Motivation • Our work • A simple model to explain the results • Outlook

3. z q Semiconductor C60 on Ag(111) -q R. Hesper, L.H. Tjeng and G.A. Sawatzky, Europhys. Lett. 40, 177 (1997) 1.Introduction Image charge Metal z0 Is it possible to reproduce this effect within DFT?

4. 1.Introduction Some definitions and equivalences in DFT Ionization Potential (IP) Electron affinity (EA) Gap (D) DFT Vacuum Exact Vxc LUMO C is the derivative discontinuity HOMO J.P. Perdew and M. Levy Phys. Rev. Lett. 51, 1884 (1983)

5. D=IP-EA + -2 1.Introduction DSCF Alternative : DSCF LUMO IP HOMO EA Problem: EXTENDED SYSTEMS In practice the KS orbital gap is taken as the gap

6. 1. Introduction DFT vs. GW DFT + local xc-functionals underestimate HOMO-LUMO gaps Hartree-Fock is good for small molecules (SI-free), but overestimates the gap for extended systems GW includes screening in the exchange and this solves the gap problem. Schilfgaarde, Kotani, and Faleev, PRL 96, 226402 (2006) Hartree-Fock exchange Screening correction

7. 2.Motivation Theoretical interest

8. 2.Motivation STM User’s project D. G. de Oteyza, J.M. García-Lastra et al., Adv. Func. Mater., accepted

9. 2.Motivation Molecules and layers on surfaces DIP and F16CuPc on Cu(111) D. G. de Oteyza, J.M. García-Lastra et al., Adv. Func. Mater., in press Aromatic molecules on Cu(110) N. Atodiresei, V. Caciuc et al., PRL 102, 136809 (2009)

10. 2.Motivation Conductance at molecular junctions Amine-Gold Linked Single-Molecule Circuits SY Quek et al., Nano Lett 7, 3477 (2007) Transmission peaks: Resonances at frontier orbitals energies Resonance at Zero-Bias potential: Tail of the peaks Error in the position of the peaks Huge error in the conductance at Zero-Bias

11. 2.Motivation Conductance at molecular junctions SY Quek et al., Nano Lett 7, 3477 (2007) Shift due to classical image potential+ Self energy correction

12. 2.Motivation Conductance at molecular junctions: Dielectrics K. Kaasbjerg and K. Flensberget, Nano Lett 8, 3809 (2008) S D SiO2 er(SiO2) = 3.9 D(SiO2) = 8.9 eV Authors use a classical model to explain a reduction of 0.5 eV in the gap Is it correct or a microscopic description is needed?

13. 3.Our work GW-TB Microscopic model of metal-molecule interface METAL Thygesen and Rubio, Phys. Rev. Lett. 102, 046802 (2009)

14. 3.Our work GW-TB Microscopic model of metal-molecule interface

15. Free LUMO LUMO HOMO Free HOMO 3.Our work Weak physisorption limit Energy Static linear response Small t Large metal DOS at EF  Large density response  Efficient screening

16. 3.Our work Now my work starts… • DFT vs. GW for image potential • Bulk dielectric constant: Is a good descriptor? • Check the GW-TB findings: Image charge proportional to DOS at Fermi Level

17. 3.Our work First-principles GW calculations: Physisorbed benzene DFT calculations performed with PWSCF code (#) G0W0calculations performed with the Yambo code(*). Yambo: G0W0 LDA, Plane wave basis, norm-conserving pseusopotentials, plasmon pole approximation. 9 Å >Z>4 Å (#) S. Baroni et al. (2009), QUANTUM ESPRESSO package, www.quantum-espresso.org/ (*) A. Marini, C. Hogan, M. Grüning, D. Varsano, Comp. Phys. Comm. 180, 1392 (2009).

18. 3.Our work Benzene Molecule • Previously obtained by Neaton et al. • LDA underestimates the gap by a factor of 2 (mainly due to Self-interaction) • GW HOMO-LUMO gap agrees with experiment (IP-EA) • LUMO predicted to be above the vacuum level in GW, in agreement with experiment 5.2 eV 10.5 eV PBE: 5.2 eV PBE0:7.1 eV Experiment: IP = 9.25 eV L. Klasinc et al., Pure Appl. Chem. 55, 289 (1983) EA = -1.15 eV B.T.Hill, J. Chem. Soc. Perkin Trans. II 1027 (1998) D = 10.4 eV

19. NaCl(001) CaO(001) BaO(001) MgO(001) BaO(111) 3.Our work Substrates Insulator and semiconductor 7.7 eV 6.3 eV 4.0 eV 8.9 eV • Same structure (fcc) • Varying the gap • Varying the surface Metallic surface!

20. 3.Our work Substrates Metals Li(001) Pt(111) Rh(111) Ti(001) Al(111) sd sp s sd sd • Different DOS at Fermi Level • Similar interatomic distances • Except Li: Electrons outer of the surface

21. 3.Our work Substrates Semimetallic • Benzene on Graphite(0001) • Previously studied by Neaton, Hybertsen and Louie, PRL 97, 216405 (2006) • Neaton et al. z = 3.25 Å • Our work 4 Å < z < 9 Å

22. 3.Our work GW and LDA benzene HOMO-LUMO gaps 4.5 Å J.M.G-L, A. R. and K.S.T., submitted • LDA gaps are independent of substrate and distance • Same result with other functionals (GGA, hybrid or exact exchange) • GW gaps show large variation across different surfaces • GW gap sensitive to atomistic details, e.g. surface plane (BaO)

23. 3.Our work Classical image charge model Electrostatic energy of point charge above a polarizable medium: Classical model describes the physics of the gap reduction qualitatively. Fitted for the gap: Different values if HOMO or LUMO are fitted independently Dynamic interaction between benzene orbitals and surfaces: Bulk Dielectric Constant is not a good descriptor Best-fit values for  and z0:

24. 3.Our work Variation of HOMO and LUMO levels Vacuum Vacuum GW: Symmetric effect on HOMO and LUMO. Exceptions Li and BaO(111) LDA: HOMO level agrees better with GW than does LUMO Very good agreement between LDA and GW for HOMO at metallic surfaces (error cancellation in LDA between self-interaction and image charge)

25. 3.Our work General trends in level shifts Insulator and semiconductor Gap reduction increases with decreasing substrate band gap

26. 3. Our work General trends in level shifts Metals Gap reduction increases with increasing substrate DOS at EF Li and BaO(111) deviate from general trend!

27. 4. A simple model to explain the results GW S to second order in V Renormalization of single electronic level,  , by non-local interactions with substrate electrons: Hartree-Fock exchange Screening correction We truncate the expansion in the second order term

28. L L L L Substrate joint density of states weighted by particle-hole transitions 4. A simple model to explain the results Semiconductors Effective interaction strength

29. L 4. A simple model to explain the results Metals Assumption: Vkk’ similar for all the systems L proportional to JDOS Slope of JDOS at w=0 proportional to DOS at EF The correction increases if DOS at EF increases

30. L 4. A simple model to explain the results BaO(111) and Li(001) Li(001) Rh(111) Much bigger in Li and BaO(111) than in the other systems

31. 5.Outlook • DFT (local xc-functionals) is not able to reproduce image charge effect • GW includes dynamic correlation (polarization) and solves the problem • Classic image potential describes the effect phenomenologically • However microscopic description is required • Renormalization of the gap in molecules follows the band gap in semiconductors • Renormalization of the gap in molecules follows the DOS at Fermi level in metals • It is possible to understand the results truncating at second order the self energy.