xiv etsf workshop Évora 17 th september 2009 juan maría garcía lastra kristian sommer thygesen...
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XIV ETSF Workshop
Évora 17th September 2009
Juan María García LastraJuan María García Lastra
Kristian Sommer ThygesenKristian Sommer Thygesen
Ángel RubioÁngel Rubio
Classical and Many-Body Theory of Image Classical and Many-Body Theory of Image Potentials at Solid-Molecule InterfacesPotentials at Solid-Molecule Interfaces
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
z0
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)
1.Introduction SCF
IP
EA
=IP-EA + -2
Problem: EXTENDED SYSTEMS
HOMO
LUMO
Alternative : SCF
In practice the KS orbital gap is taken as the gap
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
2.Motivation STM
D. G. de Oteyza, J.M. García-Lastra et al., Adv. Func. Mater., accepted
User’s project
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)
2.Motivation Conductance at molecular junctions
SY Quek et al., Nano Lett 7, 3477 (2007)
Amine-Gold Linked Single-Molecule Circuits
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
2.Motivation Conductance at molecular junctions
SY Quek et al., Nano Lett 7, 3477 (2007)
Shift due to classical image potential+ Self
energy correction
2.Motivation Conductance at molecular junctions: Dielectrics
K. Kaasbjerg and K. Flensberget, Nano Lett 8, 3809 (2008)
S D
SiO2
r(SiO2) = 3.9( 1)
0.59( 1)r
r
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?
(SiO2) = 8.9 eV
3.Our work
ME
TA
L
Thygesen and Rubio, Phys. Rev. Lett. 102, 046802 (2009)
GW-TB Microscopic model of metal-molecule interface
3.Our work Weak physisorption limit
Small t Large metal DOS at EF Large density response Efficient screening
LUMO
HOMO
Free LUMO
Free HOMO
Static linear responseEnergy
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
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).
3.Our work First-principles GW calculations: Physisorbed benzene
(#) S. Baroni et al. (2009), QUANTUM ESPRESSO package, www.quantum-espresso.org/
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
PBE: 5.2 eV
PBE0:7.1 eV
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!
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
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
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
4
5
6
7
8
9
10
11V
acuu
m
NaC
l(001
)
MgO
(001
)
CaO
(001
)
BaO
(001
)
TiO
2(00
1)
Gra
phite
Al(1
11)
Pt(
111)
Rh(
111)
Ti(0
01)
Li(0
01)
BaO
(11
1)
HO
MO
-LU
MO
Ga
p (
eV
)
GW
LDA
4
5
6
7
8
9
10
11V
acuu
m
NaC
l(001
)
MgO
(001
)
CaO
(001
)
BaO
(001
)
TiO
2(00
1)
Gra
phite
Al(1
11)
Pt(
111)
Rh(
111)
Ti(0
01)
Li(0
01)
BaO
(11
1)
HO
MO
-LU
MO
Ga
p (
eV
)
GW
LDA
4
5
6
7
8
9
10
11V
acuu
m
NaC
l(001
)
MgO
(001
)
CaO
(001
)
BaO
(001
)
TiO
2(00
1)
Gra
phite
Al(1
11)
Pt(
111)
Rh(
111)
Ti(0
01)
Li(0
01)
BaO
(11
1)
HO
MO
-LU
MO
Ga
p (
eV
)
PBE0
LDA
)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
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
Gap reduction increases with decreasing substrate band gap
3.Our work General trends in level shifts
Insulator and semiconductor
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
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
4. A simple model to explain the results Semiconductors
Effective interaction strength
Substrate joint density of states weighted by particle-hole transitions
4. 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
Assumption: Vkk’ similar for all the systems
4. A simple model to explain the resultsBaO(111) and Li(001)
Li(001) Rh(111)
2
'kkV
Much bigger in Li and BaO(111) than in the other systems
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.