xiii international conference on the applications of dft in chemistry and physics
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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. - PowerPoint PPT PresentationTRANSCRIPT
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XIII International Conference on the applications of DFT in Chemistry and Physics
Lyon 2nd September 2009
Juan María García LastraJuan María García Lastra
Kristian Sommer ThygesenKristian Sommer Thygesen
Ángel RubioÁngel Rubio
GW renormalization of DFT molecular GW renormalization of DFT molecular electronic levels at the vicinity of a surface: electronic levels at the vicinity of a surface:
The image charge effectThe image charge effect
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Outline
1.Introduction
2.Motivation
3.Our work
4.A simple model to explain the results
5.Outlook
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1.Introduction Image charge
2
0
( )4( )img
qV z
z z
Metal
)1(
)1(
)(4)(
0
2
r
rimg zz
qzV
Semiconductor
Is it possible to reproduce this effect
within DFT?
C60 on Ag(111)
R. Hesper, L.H. Tjeng and G.A. Sawatzky, Europhys. Lett. 40, 177
(1997)
q
-q
z
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1.Introduction Some definitions and equivalences in DFT
Ionization Potential (IP) X IP X e
Electron affinity (EA) X EA X e
Gap () IP EA
HOMO
LUMOLUMO
HOMO
Vacuum
HOMOIP Exact Vxc
LUMOEA
LUMO HOMO C
DFT
C is the derivative discontinuity
J.P. Perdew and M. Levy Phys. Rev. Lett. 51, 1884 (1983)
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1.Introduction SCF
IP
EA
=IP-EA + -2
Problem: EXTENDED SYSTEMS
HOMO
LUMO
Alternative : SCF
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1.Introduction Many Body Perturbation Theory
The combination of a particle and its influence on the local environment
Propagators
R.D. Mattuck, A guide to Feynman Diagrams in the Many-Body Problem
Self-energy
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1.Introduction GW approximation
,DFT DFTi i
0G i
P i
i
W i i
,QP QPi i
0 ,G G GSE G
G. Onida, L. Reining and A. Rubio, Rev.Mod.Phys. 74, 601 (2002)
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)
0 0G G G G
Good enough
Initial guess
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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.
Hartree-Fock exchange Screening correction
Schilfgaarde, Kotani, and Faleev, PRL 96, 226402 (2006)
1. Introduction DFT vs. GW
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2.Motivation Theoretical interest
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2.Motivation STM
D. G. de Oteyza, J.M. García-Lastra et al., Adv. Func. Mater., accepted
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2.Motivation Molecules and layers on surfaces
D. G. de Oteyza, J.M. García-Lastra et al., Adv. Func. Mater., in press
DIP and F16CuPc on Cu(111)
Aromatic molecules on Cu(110)
N. Atodiresei, V. Caciuc et al., PRL 102, 136809 (2009)
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2.Motivation Conductance at molecular junctions
SY Quek et al., Nano Lett 7, 3477 (2007)
Amine-Gold Linked Single-Molecule Circuits
K. Kaasbjerg and K. Flensberget, Nano Lett 8, 3809 (2008)
S D
SiO2
Image Charge by dielectrics
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2.Motivation Conductance at molecular junctions
SY Quek et al., Nano Lett 7, 3477 (2007)
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9 Å >Z>4 Å
DFT calculations performed with PWSCF code (#)
G0W0 calculations performed with the Yambo code(*).
Yambo:
G0W0 LDA, Plane wave basis, norm-conserving pseusopotentials, plasmon pole approximation.
(*) 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)
3.Our work First-principles GW calculations: Physisorbed benzene
(#) S. Baroni et al. (2009), QUANTUM ESPRESSO package, www.quantum-espresso.org/
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3.Our work Benzene Molecule
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)
= 10.4 eV
•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
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3.Our work Substrates
CaO(001) BaO(001)MgO(001)NaCl(001)
Insulator and semiconductor
BaO(111)•Same structure (fcc)
•Varying the gap
•Varying the surface
8.9 eV 7.7 eV 6.3 eV 4.0 eV
Metallic surface!
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3.Our work Substrates
Metals
Pt(111) Rh(111) Ti(001) Li(001)Al(111)
sd sd sd sp s
•Different DOS at Fermi Level
•Similar interatomic distances
•Except Li: Electrons outer of the surface
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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
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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)
J.M.G-L, A. R. and K.S.T., submitted
4.5 Å
3.Our work GW and LDA benzene HOMO-LUMO gaps
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)1(
)1(
)(4)(
0
2
r
rimg zz
qzV
Best-fit values for and z0:
Electrostatic energy of point charge above a polarizable medium:
Classical model describes the physics of the gap reduction qualitatively.
3.Our work Classical image charge model
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
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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)
3.Our work Variation of HOMO and LUMO levels
Vacuum
Vacuum
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Gap reduction increases with decreasing substrate band gap
3.Our work General trends in level shifts
Insulator and semiconductor
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Gap reduction increases with increasing substrate DOS at EF
Li and BaO(111) deviate from general trend!
3. Our work General trends in level shifts
Metals
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Renormalization of single electronic level, , by non-local
interactions with substrate electrons:
4. A simple model to explain the resultsGW to second order in V
Hartree-Fock exchange Screening correction
We truncate the expansion in the second order term
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4. A simple model to explain the results Semiconductors
Effective interaction strength
Substrate joint density of states weighted by particle-hole transitions
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A simple model to explain the results Metals
proportional to JDOS
Slope of JDOS at =0 proportional to
DOS at EF
The correction increases if DOS at
EF increases
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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.
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A simple model to explain the results Metals