M. Alducin , R. Díez Muiño , J. I. Juaristi

1. M. Alducin, R. Díez Muiño, J. I. Juaristi

2. Contents • Lecture 1 INTRODUCTION: SURFACE CHEMISTRY AND HETEROGENEOUS CATALYSIS • Lecture 2 MOLECULAR STRUCTURE • Lecture 3 ELECTRONIC AND STRUCTURAL PROPERTIES OF SURFACES • Lecture 4 ELEMENTARY CHEMICAL PROCESSES AT SURFACES:POTENTIAL ENERGY SURFACES • Lecture 5 THEORY OF GAS/SURFACE DYNAMICS • Lecture 6 COMPUTATIONAL METHODS TO SIMULATE GAS/SURFACE DYNAMICS

3. LecturesonMolecular Dynamics at Surfaces: Friday May 7th: 9.00 --> 11.00 theoreticalbackground Tuesday May 11th : 9.00 --> 11.00 Wednesday May 12th : 9.00 --> 11.00 Friday May 14th : 9.00 --> 11.00 1stexercise: analysis of N2/W(110) PES 2ndexercise: dissociationdynamics of N2on W(110)

4. 2nd option!! LecturesonMolecular Dynamics at Surfaces: Friday May 7th: 9.00 --> 11.00 theoreticalbackground Tuesday May 11th : 9.00 --> 12.00 1st exercise: analysis of N2/W(110) PES Friday May 14th : 9.00 --> 12.00 2ndexercise: dissociationdynamics of N2on W(110)

5. I.- Theoreticalbackground

6. Simulation (computerexperiments): Experiment: a systemissubjectedtomeasurements and a result, in numericalform, isobtained. Theory: In thepast, a model of thesystemwasconstructed and latervalidatedbycheckingitsabilityto describe thebehavior of thesystem in somelimit cases (simplification understanding). Simulation: Theadvent of powerfulcomputationalresources has broughtthepossibilityto reduce theapproximations, reproduce thecomplexity of experimental conditions, and accurately compare with experimental results (study of regionsnot accesible experimentally).

7. Physical and chemicalprocesses at surfacesare dynamical in nature • Theoretically, staticproperties are usuallyaccuratelydescribed (groundstate): • DensityFunctionalTheory, Quantum Chemistry, Quantum Monte Carlo, etc. • Dynamicproperties still require furthertheoreticaldevelopment (mayinvolve • excitedstates)

8. gas/surface dynamics from the fundamental point of view, the goal is to understand how solid surfaces and nanostructures can be used to promote gas-phase chemical reactions dissociative adsorption molecular adsorption desorption some elementary reactive processes at surfaces

9. gas/surface dynamics Eley-Rideal recombination Langmuir-Hinshelwood Recombination

10. Physical and chemicalprocesses at surfacesare dynamical in nature • Theoretically, staticproperties are usuallyaccuratelydescribed (groundstate): • DensityFunctionalTheory, Quantum Chemistry, Quantum Monte Carlo, etc. • Dynamicproperties still require furthertheoreticaldevelopment (mayinvolve • excitedstates)

11. Lawrence Livermore National Laboratory

12. Molecular Dynamics Molecular dynamicsis a computersimulationtechnique in whichthe time evolution of a set of interactingatomsisfollowedbyintegratingtheirequations of motion.

13. Some nomenclature Classical Molecular Dynamics Simulation: A model of inteeractions between atoms is supplied as input before a simulation can be carried out. Quantum Molecular Dynamics Simulation: They do not require any a priori knowledge of interatomic interactions. Only the laws of quantum mechanics are used. Classical dynamics of nuclei Quantum dynamics of nuclei

14. gas/surface dynamics from the fundamental point of view, the goal is to understand how solid surfaces and nanostructures can be used to promote gas-phase chemical reactions dissociative adsorption molecular adsorption desorption some elementary reactive processes at surfaces

15. gas/surface dynamics Eley-Rideal recombination Langmuir-Hinshelwood Recombination

16. Theadiabaticapproximation A physical system remains in its instantaneous eigenstate if a given perturbation is acting on it slowly enough and if there is a gap between the eigenvalue and the rest of the Hamiltonian's spectrum Sketch: Potentialenergy curves of a neutral diatomic molecule R and itsnegative ion R-

17. Theadiabaticapproximation

18. Validity of theadiabaticapproximation Notes from Ballentine’s book

19. Ballentine’s book

20. Ballentine’s book

21. Ballentine’s book

22. Molecular Dynamics Molecular dynamicsis a computersimulationtechnique in whichthe time evolution of a set of interactingatomsisfollowedbyintegratingtheirequations of motion.

25. Born – Oppenheimerapproximation

26. Born – Oppenheimerapproximation

27. TheBorn-Oppenheimerapproximation

30. Quantum dynamics of nuclei are also possible (time-dependent wave-packet propagation, for instance) … but numericallyVERY demanding!

31. Quantum dynamics of nuclei are also possible (time-dependent wave-packet propagation, for instance) … but numericallyVERY demanding! Dissociation probability of H2/Pd(111) Díaz et al., PRB 72, 035401 (2005)

34. Classical dynamics: In practice…

35. Molecular Dynamics A list of molecular dynamicspackages, forthoseinterested: http://www.mrflip.com/resources/MDPackages.html

36. Classical Molecular Dynamics PotentialEnergySurface (PES) The PES providestheenergy (and itsderivatives!) forall positions of thenucleiRi. Itis a 3N dimensional function!

37. Classical Molecular Dynamics PotentialEnergySurface (PES) The PES providestheenergy (and itsderivatives!) forall positions of thenucleiRi. Itis a 3N dimensional function! Frozen Surface: In our case, everything is reduced to a 6D problem!

38. Howtocalculatethe forces (the PES)? ‘Classical’ calculation of the PES: - Forcefields, parametrizations, etc. Complete quantum calculation of the PES (previous to the dynamics): - Ab-initio methods (DFT, HF, etc.) with ensuing fitting On-the-fly methods: - Ab-initio molecular dynamics - Car-Parrinello

39. Howtocalculatethe forces (the PES)? ‘Classical’ calculation of the PES: - Forcefields, parametrizations, etc. Complete quantum calculation of the PES (previous to the dynamics): - Ab-initio methods (DFT, HF, etc.) with ensuing fitting On-the-fly methods: - Ab-initio molecular dynamics - Car-Parrinello All of them are adiabatic(ground-state) methods! Non-adiabaticmethods (TDDFT, forinstance) requiredforexcitedsystems.

40. Non-adiabatic processes Excitation of electron-hole pairs in a metal surface (no gap for excitations) bulk metal electrons at the surface can be excited

41. description of electronicexcitationsby a frictioncoefficient friction coefficient: effective medium approximation previously used for: bulk metal - damping of adsorbate vibrations: Persson and Hellsing, PRL49, 662 (1982) - dynamics of atomic adsorption Trail, Bird, et al., JCP119, 4539 (2003) classical equations of motion n(z) for each atom “i” in the molecule n0 mi(d2ri/dt2)=-dV(ri,rj)/d(ri) – h(ri)(dri/dt) z adiabatic force: 6D DFT PES friction coefficient n0 h=n0kFstr(kF) effective medium: FEG with electronic density n0

42. Non-adiabatic processes Desorption induced by electronic processes (DIET) MGR process: the molecule is excited to a repulsive PES without any change in the position and momenta of the molecule Antoniewicz process: the excited molecule moves towards the surface and decays into the ground state with higher kinetic energy available

43. II.- Particular case: dissociation of diatomicmoleculeson metal surfaces

44. A+B P CFM centro de física de materiales gas/solid interfaces and heterogeneous catalysis What is catalysis? The effect produced in facilitating a chemical reaction, by the presence of a substance, which itself undergoes no permanent change. A+B  P direct reaction A+B+C  P+C catalyzed reaction A and B are reactants C is the catalyst P is the reaction product

45. A+B P CFM centro de física de materiales gas/solid interfaces and heterogeneous catalysis What is catalysis? The effect produced in facilitating a chemical reaction, by the presence of a substance, which itself undergoes no permanent change. A+B  P direct reaction A+B+C  P+C catalyzed reaction A and B are reactants C is the catalyst P is the reaction product Heterogeneous catalysis: The catalyst is in a different phase  solid surfaces.

46. The chinese symbol for catalyst is the same as the one for marriage broker (matchmaker) A+B P CFM centro de física de materiales gas/solid interfaces and heterogeneous catalysis What is catalysis? The effect produced in facilitating a chemical reaction, by the presence of a substance, which itself undergoes no permanent change. Heterogeneous catalysis: The catalyst is in a different phase  solid surfaces.

47. CFM centro de física de materiales global context: chemical industry ammonia synthesis: 3H2(g) + N2 (g) ↔ 2NH3(g) (catalyzed by Fe surface) world production: 130 million tons (year 2000), ~200US$/ton

48. CFM centro de física de materiales global context: car industry Catalysis in car industry: In car engines, CO, NO, and NO2 are formed. Catalytic converters reduce such emissions by adsorbing CO and NO onto a catalytic surface, where the gases undergo a redox reaction. CO2 and N2 are desorbed from the surface and emitted as relatively harmless gases: 2CO + 2NO → 2CO2 + N2

49. Q Experimental techniques in Gas-Surfacedynamics Ei • Molecular beam techniques Stickingcoefficient of O2 on Ag(111): dependenceonenergy and polar incidenceangle  Sticking Coefficient The sticking coefficient, S , is a measure of the fraction of incident molecules which adsorb upon the surface i.e. it is a probability and lies in the range  0 - 1 , where the limits correspond to no adsorption and complete adsorption of all incident molecules respectively. In general, S depends upon many variables i.e. S = f ( surface coverage , temperature, crystal face .... )

50. Experimental techniques in Gas-Surfacedynamics • Molecular beam techniques Molecular beam scattering studies of H2–D2 exchange on Pt332 surface, showing that atomic steps on metal surfaces break chemical bonds, in this case, hydrogen-hydrogen bonds, with unit reaction probability (a) schematic defining the geometry of the incident angle polar and azimuthal of the molecular beam with respect to a stepped surface. (b) HD production as a function of angle of incidence of the molecular beam normalized to the incident D2 intensity.