LYON permanent Team involved in MONET

• Marie-Laure Bocquet, CNRS Researcher, Lyon

• David Loffreda, CNRS Researcher,Lyon

+External Collaborator:• Nicolas Lorente, Professor IUF, Toulouse

Special Thanks to Herve Lesnard, 3rd Year PhD

Outline

Introduction to periodic DFT approach (VASP code)

I. Classical outputs in our group

II. New outputs in our group

III. Projects

Density Functional Theory (DFT):Kohn-Sham equations

€

−12∇2 +V(r ) +Vxc(r )

⎡

⎣ ⎢

⎤

⎦ ⎥ψ i(k, r )=ε i(k)ψ i(k, r )

V(r ) =Ve−n(ExternalorCoulomb) + J Hartree( ) : exact

Vxc(r ) :approximationbutsmall!

Vxc(r ) =Te−e −12∇2 +Ve−e −J

ψ i(k, r ) =e ikru(r ) = cGke i(k+G )r

G∑

‘The ‘orbital’ concept : one-electron wave function

if V( r) periodic

Various methods for solving Kohn-Sham equations

VERYEXPENSIVEcode:WIEN

FLAPWAugmented PW

Various choicesof basis sets

in both regions

All-electron Methodsmuffin-tin geometry

(spheres around atoms+interstitial region)

STABLEOPTIMIZED

codes: VASPCPMD, ABINIT,CASTEP

first and secondderivatives of

electronic energy

Plane-wavebasis sets

(PW)

Mixedbasis sets

EFFICIENTFOR LARGE SYSTEMS

code: SIESTA

order-Nmethods

NumericalAtomic Orbitals

(NAO)

PseudopotentialMethods

Treatment of ionic cores?

The surface model… slabs!

surface = 3D metallic slab (supercell approach)

coverage = adlayer + superstructure

Adsorption and surface energies

€

EadsDFT =Emol+met

DFT −EmetDFT −Emol

DFT

σ surfDFT =Emet

DFT −NmetEbulkDFT

2A

DFT: energy at T=0 K et P=0 atm

σsurf = energy loss due to surface formation

Eads = energy gain due to adsorption

Bridging (T,P) gaps!… Atomistic thermodynamics

free Gibbs energy G(T,P) Gas phase = large reservoir

imposing its temperature and pressure on the adsorbed phase……temperature effects on metal negligible

€

Ω=1A

Gmol+met− Niμi∑( )

γsurf =1A

Gmol+met−Nmetμbulk−Nmolμgas( )

ΔGads =1A

Gmol+met−Gmet−Nmolμgas( )

I. Classical outputs in our group

• STM simulations

• Vibration Analysis

• HREELS Spectra simulation

• Reactive pathways

STM simulations (Lorente)

• Workhorse

• Improvement: Matching procedure of DFT

sample ψs with analytical exp. decaying ψs.

€

2D periodicBlochwaveΨk //,m = ck //,G //

m ei(k// +G// ) r//f(z)G//

∑

withmbandindex,G// reciprocicalvectors, k// ∈ BZ,Φ surfaceworkfunction

withf(z) =f0e−(z−z0 ) (k// +G// )

2 +2 eΦ,z0 matchingheight

€

Tersoff Hamman:G =ρ ∝ ψν (r0 )ν∑

2

δ(E f −εν )

=>Plot density contours at realistic distances.

Ex: STM simulations of phenyl and benzyl species

Structures

Improved TH simulations

Vibration Analysis: normal modes

€

Evaluationof kij =∂2E∂xi∂xj

=−∂Fi

∂xj

=−∂Fj

∂xj

by finitedifferencesonFi

Mass−weightedcoordinate: xi© =xi mi

DiagonalizationofK ij =∂2E

∂xi© ∂xj

©=

kij

mi mj

⇒ λp =ωp

2andQp

δq1p

δqNp

⎡

⎣

⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥

,p mode index

so thatV =12

λkQk

2

k∑ (quadraticform)

Ex: CH modes for phenyl and benzyl species on Cu(100)

In and Out Decoupling

Coupling

IRAS and EELS intensity calculations

€

IIRk ∝ dΜz

dQk

⎛

⎝ ⎜

⎞

⎠ ⎟2

Infrared Reflection-Absorption Spectroscopy (IRAS)Electron Energy Loss Spectroscopy (EELS) in Specular Geometry

Selection rules: vibrational modes giving rise to an oscillating

dynamic dipole moment along the surfacenormal are active

Ex: Structure Recognition - HREELS croton/Pt(111)

(Haubrich, Loffreda et al, CPL 2006)

Transition State Search(Henkelman & Jonsson)

« Nudged-Elastic Band » (NEB) method

Set of n images linked with spring forces

‘Nudged’ force acting on each i image:

€

r Fi =−

r∇ V(

r Ri )/ ⊥

+ ki+1( r Ri+1−

r Ri )−ki (

r Ri −

r Ri−1)[ ]//

Ex: Successive Dehydrogenation on Cu(100)(Lesnard, Bocquet, Lorente, JACS in press 2007)

Benzene Benzyl + 2H

Phenyl + H

TS structures

II. New outputs in our group

• STM-IETS simulations

• Electrochemical phase diagram: water/Pd

Elastic and Inelastic Electron Tunneling(Stipe, Rezaei, Ho, 98)

IETS: theoretical strategy(Lorente, Persson et al, PRL 00,01)

€

Computeinelasticfractionof electron:

η =δ( ∂I∂V

)

∂I∂V

=δ(G)G

Tersoff Hamman:G =ρ∝ ψν (r0 )ν∑

2δ(E f −εν )

andη=δ(ρ)ρ

thensimilarly=>δ(ρ)∝ δψν (r0 )ν∑

2δ(E f −εν )

withδψν (r0 ) responsetoavibration?

Local density of one-electron states

€

1)VibrationalAnalysis⇒ MODES k(ωk,Qk) :

2)Compute: ψ(r+ =r0 + h2ωk

Qk) =ψ+ andψ(r− =r0 − h2ωk

Qk) =ψ−

€

3)Orthonormalisation(Löwdin) : ψ+ → S12ψ+ =ψ+ andS

12ψ−=ψ−

4)Finally∂ψ =ψ+ − ψ−

ψ+ / ψ−with ψ+ / ψ− =eiθ

δΨ response to a vibration k: 4-step procedure

finite difference

IETS: methodology(Lorente, Persson et al, PRL 00,01)

Ex: IETS experiments(Lauhon & Ho, SS 2000 and Komeda et al, JCP 2004)

CC66HH66 dis-Cdis-C66HH6 6 : benzyl : benzyl

Cu(100)

Pulse 2.9 V

Ex:IETS simulations(Bocquet, Lesnard, Lorente, PRL 06)

PhenylPhenyl(-1H)(-1H)

BenzylBenzyl(-2H)(-2H)

dis-Cdis-C66HH66

Rule out experimental assigment

The electrochemical approach(Filhol and Neurock, Angewandte 2006)

Electrochemical

energy

€

EDFT (ne,nbg) =E slab(ne) + E slab−bg(ne,nbg) +Ebg(nbg)[ ]

[ ] =− V(Q)q

∫ dQ, sampleelectrostaticpotentialV,

referencedtovacuum

E Free(ne) =EDFT (ne,nbg) + V(Q)q

∫ dQ−qV(=φ),

φ ne( )sampleworkfunction

H-up / Pd(111)

H-down / Pd(111)

Ex: water 1ML /Pd(111): charged interface!

(Filhol&Bocquet, CPL 2007 in press)

Pd disproportionation

Ex: Charge control of oxygen buckling(Filhol&Bocquet, CPL 2007 in press)

Monet Project: liquid+molecules/metal interface

(Fradelos’s PhD project)

Explicit water: multilayers

Insertion of

Large organic

Molecules

Image: Courtesy of JS Filhol

Monet Project: graphene/Ru interface(Wang’s PhD project)

STM image: J. Wintterlin’s group PRB 2007 in pressMoiré pattern 11x11

STM/STS simulations