Theoretical description of H 2 Eley-Rideal recombination on W(110)

Transcription

1 Theoretical description of H 2 Eley-Rideal recombination on W(110) Cédric CRESPOS, Pascal LARREGARAY, Ernesto QUINTAS, Rémi PETUYA Theoretical Chemistry Group Institut des Sciences Moléculaires Université Bordeaux 1 Quantum Modeling of electronic processes in Organic Optoelectronic Devices Bordeaux 7-8 Nov 2012

2 Contents! General aspects of the gas-surface reactivity! Context! Elementary processes! Experimental measurements! Theoretical background! Construction of the Potential Energy Surface (PES): time consuming step for the simulation of reaction dynamics! The Corrugation Reducing Procedure (CRP) for H 2 /W(110)! Extension of the CRP for H+H/W(110)

3 Context! Heterogeneous Catalysis 90% of the chemical industry production: ammonia synthesis (fertilizers and explosives)! Interstellar and Atmospheric Chemistry! Plasma-wall interactions Nuclear fusion reactor project ITER Atmospheric reentry

4 Elementary Processes! Atom-Surface Atomic adsorption Atomic reflection : elastic or inelastic Atomic desorption! Molecule-Surface Molecular dissociative adsorption Molecular adsorption Molecular reflection: elastic or inelastic

5 Elementary Processes! Recombination mechanisms Langmuir-Hinshelwood recombination Eley-Rideal recombination Hot-atom recombination

6 Experimental measurements! Molecular beam experiments Experimental conditions: - Ultra High Vacuum (clean surface) - Oriented Molecular beams - Single crystalline surface C. T. Rettner, L. A. DeLouise, and D. J. Auerbach, J. Chem. Phys. 85 (1986) P2 $" Yo. MS P1 Crystal I VP! %!! & "! #" P2 "" P4 P5!"

7 Molecular beams experiments DO NOT provide direct information of the scattering mechanisms! P diss (Ei), P diss (T S ) P diss (v,j) P diss ( i ) P ref ( f,v f,j f ) Simulations Reactive and non-reactive scattering mechanisms Dissociative adsorption probability, P diss Reflection probability, P ref P diss (Ei) P diss (v,j) P diss ( i ) P ref ( f,v f,j f ) Mechanism?! 1 ps E i v,j i i f? P diss (Ts) Surface

8 Theoretical background! Simplest approximations Born-Oppenheimer Static Surface approximation (BOSS) Electronic excitations are neglected! Potential Energy Surface (PES) Electronic structure calculations: DFT adapted to periodic systems Construction of PES : - global methods " fitting by analytical function - local methods " numerical interpolation! Dynamics simulations Numerical integration of quantum dynamic equations of motion: i!!"(r,t)!t = ˆ H n (R)"(R,t) Numerical integration of classical equations of motion: q k =!H n(q,p)!p k!p k =! H n (q, p)! q k

9 Exemple : Dynamics of N 2 scattering on W(100)! Scattered angle distributions! i = 45 In plane reflection Static Surface Model ( trajectories)! %! $"! & "! #" Experimental data: C. T. Rettner, E. K. Schweizer, and H. Stein, J. Chem. Phys.,93, 1442, (1990) ""!"

10 Theoretical background! Usual approximations Born-Oppenheimer Static Surface approximation (BOSS) Electronic excitations are neglected! Potential Energy Surface (PES) Electronic structure calculations: DFT adapted to periodic systems Construction of PES : - global methods " fitting by analytical function - local methods " numerical interpolation! Dynamics simulations Numerical integration of quantum equations of motion: i!!"(r,t)!t = ˆ H n (R)"(R,t) Numerical integration of classical equations of motion: q k =!H n(q,p)!p k!p k =! H n (q, p)! q k

11 Theoretical background! Usual approximations Born-Oppenheimer Static Surface approximation (BOSS) Electronic excitation are neglected! Potential Energy Surface (PES) Electronic structure calculations: DFT adapted to periodic systems! Potential Energy Surface (PES) Construction of PES : - global methods " fitting by analytical function - local methods " numerical interpolation! Dynamics simulations Numerical integration of quantum dynamic equations of motion: i!!"(r,t)!t = ˆ H n (R)"(R,t) Numerical integration of classical equations of motion: q k =!H n(q,p)!p k!p k =! H n (q, p)! q k

12 Construction of the Potential Energy Surface! Corrugation Reducing Procedure (CRP) Non Spin Polarized (NSP) Density Functional Theory (DFT) calculations within the Generalized Gradient Approximation (GGA) Functional : Perdew and Wang (PW91) (Phys. Rev. B 1992, 45, 13244) Software : Vienna Ab-initio Simulation Package (VASP) - Pseudopotentials - Plane wave basis set Slab supercell approach H 2 /W(110) H. F. Busnengo and A. E. Martinez J. Phys. Chem. C 2008, 112, #" W(110)!"

13 Construction of the Potential Energy Surface! Corrugation Reducing Procedure (CRP) V 6 D (X,Y,Z,r,!,") = V 3D (X A,Y A,Z A ) + V 3D (X B,Y B,Z B ) + I 6 D (X,Y,Z,r,!,") Calculation of the atomic term V 3D $" &" H B Z CM H A #" 13!"%#$ 520 DFT points %" Y CM!"#$ X CM!" Interpolation of V 3D

14 Construction of the Potential Energy Surface! Corrugation Reducing Procedure (CRP) Calculation of the molecular term V 6D DFT calculation for 2D-(Z cm,r) cut $" Z CM H A &" H B #" configurations 6240 DFT points Y CM %" X CM!" Subtraction of the atomic terms V 3D V 6 D (X,Y,Z,r,!,") # V 3D (X A,Y A,Z A ) # V 3D (X B,Y B,Z B ) = I 6 D (X,Y,Z,r,!,")

15 Construction of the Potential Energy Surface! Corrugation Reducing Procedure (CRP) From DFT calculation to a continuous representation of the PES : interpolation of I 6 D (X,Y,Z,r,!,") Interpolation over Z cm and r : 2D-cubic spline Interpolation over! and " : symmetry-adapted expansions of trigonometric functions Interpolation over X cm and Y cm : 2D-periodic cubic spline X=0, Y=0,!=45, "=0,r=0.75 Å V6D I6D -246 I6D -247 DFT Energy (in ev) DFT Energy (in ev) Z of the center of mass (in A) Z of the center of mass (in A)

16 Construction of the Potential Energy Surface! Corrugation Reducing Procedure (CRP) DFT Energy (in ev) DFT Energy (in ev) I 6 D (X,Y,Z,r,!,") Theta=0, Phi=0 Theta=45, Phi=0 Theta=45, Phi=180 Theta=45, Phi=270 Theta=45, Phi=54.74 Theta=45, Phi=90 Theta=90, Phi=0 Theta=90, Phi=54.74 Theta=90, Phi=90 X=a/4, Y=a#2/8, r=0.75 Å Z center of mass (in A) 1 1,5 2 2,5 Z of the center of mass (in A)

17 Construction of the Potential Energy Surface! Corrugation Reducing Procedure (CRP) PES constructed to study the dissociation of H 2 /W(110) Non Spin Polarized calculations Limit of the grid r > 2.3 Å Eley-Rideal recombination of H+H/W(110) Extend the grid: Spin Polarized calculations are required

18 Construction of a Spin Polarised 6D-PES with CRP (CRP-SP) H. Fabio BUSNENGO, Alejandra E. MARTINEZ, Rémi PETUYA Instituto de Fisica Rosario and Facultad de Ciencias Exactas, Ingenieria y Agrimensura Universidad Nacional de Rosario

19 Construction of the CRP-SP! Atom/surface DFT Spin Polarized calculations -246 position 12 NSP position 5 NSP position 1 NSP position 1 SP position 5 SP position 12 SP DFT Energy (in ev) !"%#$!"#$ SP DFT points 1,5 2 2,5 3 3,5 4 4,5 Z (in Angtroms)

20 Construction of the CRP-SP! Atom/surface DFT Spin Polarized calculations -246 position 12 NSP position 5 NSP position 1 NSP position 1 SP position 5 SP position 12 SP DFT Energy (in ev) V 3D NSP = V SP 3D! Z = 2.8A V 3D SP = V asymptotic! Z = 4.6A ,5 2 2,5 3 3,5 4 4,5 Z (in Angtroms)

21 Construction of the CRP-SP! H 2 in vacuum DFT Spin Polarized calculations 0-1 Potential (in ev) -2-3 NSP mag 1 0 mag 1 1 fit expo 2 final magnetization 1, , ,5 2 2, ,5 2 2,5 3 Interatomic distance r (in A)

22 Construction of the CRP-SP! H 2 in vacuum DFT Spin Polarized calculations 0-1 Potential (in ev) NSP mag 1 0 mag 1 1 fit expo 0 1 1,5 2 2, ,5 2 2,5 3 Interatomic distance r (in A) 1 0,5 final magnetization For r= 1.52 Å V NSP = V SP For r= 1.75 Å V 1,5 NSP # V SP For r= 3.0 Å V = V asymptotic

23 Construction of the CRP-SP! Molecule/surface DFT Spin Polarized calculations ;$89:$ $ #">%#$ &'($$ )*+($,'-./+012$ <?$1@A/.*'-.B'($8;C$/C$D:$ ) 3 4$ 5 6 7$ )*+($,'-./+012$ 2 Spin Polarised configurations: - Horizontal:!=90, "=90 r = 1.75;2.0;2.25;2.5,2.75 Å Z cm = 2.75;3.0; ;4.6 Å - Perpendicular:!=0 r = 1.75;2.0;2.25;2.5,2.75 Å Z cm = 1.25;1.5; ;5.975 Å V 6 D H 2 = V 3D H A + V 3D H B!"%#$ $="#$ =$!"##$!"%#$ <"=$$ /$89:$!"#$ 336 SP DFT points

24 Construction of the CRP-SP! Comparison CRP-SP/DFT for b=0 0-0,5 Potential (in ev) -1 13!"%#$ # $%&'()*+(" CRP-SP DFT-NSP DFT-SP -1, !"!"#$ #,-%.(," -2!"##$%& Z projectile (in A)

25 Construction of the CRP-SP! Comparison CRP-SP/DFT for b=0.25 X 0 Potential (in ev) -0,5-1!"!"##$%& CRP-SP DFT-NSP DFT-SP -1,5 $" %,-" -2 %&'()*"+" #" 1 1,5 2 2,5 3 3,5 4 4,5 5 Z projectile (in A)

26 Construction of the CRP-SP! Comparison CRP-SP/DFT for b=0.5 X 0 Potential (in ev) -0,5-1!"!"##$%& CRP-SP DFT-NSP DFT-SP -1,5 $" %,-" -2 %&'()*"+" #" 1 1,5 2 2,5 3 3,5 4 4,5 5 Z projectile (in A)

27 Construction of the CRP-SP! Comparison CRP-SP/DFT for b=0.25 Y 0 Potentiel (in ev) -0,5-1!"!"##$%& CRP-SP DFT-NSP DFT-SP -1,5 $" %,-" -2 %&'()*"+" #" 1 1,5 2 2,5 3 3,5 4 4,5 5 Z projectile (in A)

28 Construction of the CRP-SP! Comparison CRP-SP/DFT for b=0.5 Y 0-0,5 Potential (in ev) -1!"!"##$%& CRP-SP DFT-NSP DFT-SP -1,5 $" %,-" -2 %&'()*"+" #" 1 1,5 2 2,5 3 3,5 4 4,5 5 Z projectile (in A)

29 Construction of the CRP-SP! New configurations in the CRP-NSP V 6 D (X,Y,Z,r,!,") = V 3D (X A,Y A,Z A ) + V 3D (X B,Y B,Z B ) + I 6 D (X,Y,Z,r,!,") $" Z CM H A! r H A &"! r H B H B #" %" !"#$!"%#$ ;$89:$ $ #">%#$ &'($$ )*+($,'-./+012$ <?$1@A/.*'-.B'($8;C$/C$D:$ ) 3 4$ 5 6 7$ )*+($,'-./+012$ Y CM X CM!" $="#$ =$!"##$!"%#$ <"=$$ /$89:$ DFT calculation for 2D-(Z cm,r) cut 56 configurations NSP DFT points

30 Construction of the CRP-SP! Comparison CRP-SP/DFT for b=0 0-0,5 Potential (in ev) -1 13!"%#$ # $%&'()*+(" CRP-SP CRP-SP ultima DFT-NSP DFT-SP -1, !"!"#$ #,-%.(," -2!"##$%& Z projectile (in A)

31 Construction of the CRP-SP! Comparison CRP-SP/DFT for b=0.25 X 0 Potential (in ev) -0,5-1!"!"##$%& CRP-SP CRP-SP ultima DFT-NSP DFT-SP -1,5 $" %,-" -2 %&'()*"+" #" 1 1,5 2 2,5 3 3,5 4 4,5 5 Z projectile (in A)

32 Construction of the CRP-SP! Comparison CRP-SP/DFT for b=0.5 X 0 Potential (in ev) -0,5-1!"!"##$%& CRP-SP CRP-SP ultima DFT-NSP DFT-SP -1,5 $" %,-" -2 %&'()*"+" #" 1 1,5 2 2,5 3 3,5 4 4,5 5 Z projectile (in A)

33 Construction of the CRP-SP! Comparison CRP-SP/DFT for b=0.25 Y 0 Potentiel (in ev) -0,5-1!"!"##$%& CRP-SP CRP-SP ultima DFT-NSP DFT-SP -1,5 $" %,-" -2 %&'()*"+" #" 1 1,5 2 2,5 3 3,5 4 4,5 5 Z projectile (in A)

34 Construction of the CRP-SP! Comparison CRP-SP/DFT for b=0.5 Y 0-0,5 Potential (in ev) -1!"!"##$%& CRP-SP CRP-SP ultima DFT-NSP DFT-SP -1,5 $" %,-" -2 %&'()*"+" #" 1 1,5 2 2,5 3 3,5 4 4,5 5 Z projectile (in A)

35 Dynamics of the H 2 /W(110) ER recombination! Molecular dynamic simulations (Quasi)-classical trajectories method Static surface Generalized Langevin Oscillator (GLO) No electronic excitation (adiabatic ground PES)! " #! " # $! Initial conditions Single adsorbate (ZPE, Boltzmann distribution) Normal incidence for the projectile Various collision energy (0-5 ev) Target adsorbed in the hollow site - X target = a/2 - Y target = a$2/8 - Z target = 1.07 Å! "! #,"!"#"!"##$%& -" #*+" #$%&'(")"!"

36 Eley-Rideal dynamics study for H+H/W(110)! Exemple of Eley-Rideal Cross Section 0,12 Eley-Rideal Cross Section (in Å 2 ) Eley-Rideal Cross Section (in A^2) 0,1 0,08 0,06 0,04 0,02 Static Surface Etarget=Boltzmann + Ts=100K Etarget=Boltzmann + Ts=300K Kinetic Energy (in ev) Kinetic Energy (in ev)

37 Conclusion/Prospects! Construction of an accurate PES for the Eley-Rideal dynamics study of H 2 /W(110) Spin Polarized DFT calculations Addition of new configurations in the Non Spin Polarized region! Study of the Eley-Rideal dynamics! Study of Hot-Atom process dynamics More relevant to compare with the experiments Higher cross section Surface coverage necessary

38 Thank you for your attention

39 Dynamics of the H 2 /W(110) ER recombination! Exit channels definition!"#$%&'(#)"% &#*+,-'.)/+.%% Direct Eley-Rideal: one rebound of the center of mass H+H!"#$%&#'() *"(+',"-) Z target > 7 Å + Z proj > 7 Å + P Zcm > 0 + r HH < 2.0 Å!"#$%#"&'(")&%*"+'!"#"$%&'( Hot atom: n rebproj % 1 and r HH % 5.3 Å Bound-hot-atom: E proj < 0 Metastable-hot-atom: E proj > 0 and n rebproj %2 Z target < 7Å + Z proj > 7Å + r HH > 2.0 Å!"#$%&'$() Z < 1.25 Å (CRP)

40 Construction of the CRP-SP! H 2 in vacuum DFT Spin Polarized calculations 0-1 Potential (in ev) NSP mag 1 0 mag 1 1 expo potentiel H2 vide SP 0 1 1,5 2 2, ,5 2 2,5 3 Interatomic distance r (in A) 2 1,5 1 0,5 final magnetization