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

Outline

1.Introduction

2.Motivation

3.Our work

4.A simple model to explain the results

5.Outlook

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

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

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

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

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 Theoretical interest

2.Motivation STM

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

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

K. Kaasbjerg and K. Flensberget, Nano Lett 8, 3809 (2008)

S D

SiO2

Image Charge by dielectrics

2.Motivation Conductance at molecular junctions

SY Quek et al., Nano Lett 7, 3477 (2007)

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/

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

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

)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

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

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.

A simple model to explain the results Metals