Alain Darte Compsys Project : Compilation and Embedded Systems CNRS, LIP, ENS-Lyon , France
LYON permanent Team involved in MONET Marie-Laure Bocquet, CNRS Researcher, Lyon David Loffreda,...
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Transcript of LYON permanent Team involved in MONET Marie-Laure Bocquet, CNRS Researcher, Lyon David Loffreda,...
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