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XIII International Conference on the applications of DFT in Chemistry and Physics

XIII International Conference on the applications of DFT in Chemistry and Physics Lyon 2 nd September 2009. GW renormalization of DFT molecular electronic levels at the vicinity of a surface: The image charge effect. Juan María García Lastra Kristian Sommer Thygesen Ángel Rubio. Outline.

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XIII International Conference on the applications of DFT in Chemistry and Physics

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  1. XIII International Conference on the applications of DFT in Chemistry and Physics Lyon 2nd September 2009 GW renormalization of DFT molecular electronic levels at the vicinity of a surface: The image charge effect 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 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. 1.Introduction DSCF Alternative : DSCF LUMO IP HOMO EA D=IP-EA + -2 Problem: EXTENDED SYSTEMS

  6. The combination of a particle and its influence on the local environment S Self-energy 1.Introduction Many Body Perturbation Theory Propagators R.D. Mattuck, A guide to Feynman Diagrams in the Many-Body Problem

  7. L. Hedin, Phys. Rev. 139, A796 (1965) B. I. Lundqvist, Phys. Kondens. Mater. 6, 193 (1967) F. Aryasetiawan and O. Gunnarsson, Rep. Prog. Phys. 61, 237 (1998) G. Onida, L. Reining and A. Rubio, Rev.Mod.Phys. 74, 601 (2002) 1.Introduction GW approximation Good enough Initial guess

  8. 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

  9. 2.Motivation Theoretical interest

  10. 2.Motivation STM D. G. de Oteyza, J.M. García-Lastra et al., Adv. Func. Mater., accepted

  11. 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)

  12. 2.Motivation Conductance at molecular junctions Amine-Gold Linked Single-Molecule Circuits SY Quek et al., Nano Lett 7, 3477 (2007) Image Charge by dielectrics K. Kaasbjerg and K. Flensberget, Nano Lett 8, 3809 (2008) S D SiO2

  13. 2.Motivation Conductance at molecular junctions SY Quek et al., Nano Lett 7, 3477 (2007)

  14. 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). See also: J. B. Neaton et al. Phys. Rev. Lett. 97, 216405 (2006)

  15. 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 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

  16. 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!

  17. 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

  18. 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

  19. 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)

  20. 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:

  21. 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)

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

  23. 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!

  24. 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

  25. 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 L

  26. L A simple model to explain the results Metals L proportional to JDOS Slope of JDOS at w=0 proportional to DOS at EF The correction increases if DOS at EF increases

  27. 5.Outlook • DFT 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.

  28. A simple model to explain the results Metals

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