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12. Introduction to First-Principles Modeling of Catalysis at Surfaces

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12. Introduction to First-Principles Modeling of Catalysis at Surfaces Introduction to first-principles modeling of catalysis at surfaces Bryan R. Goldsmith Fritz-Haber-Institut der Max-Planck-Gesellschaft Theory Department Catalysis is a multibillion-dollar industry and has a profound influence in everyday life Catalysts lower the activation barrier of a reaction without being consumed Images from presentation of Prof. Martin Wolf Early Nobel prizes for catalysis Paul Sabatier Wilhelm Ostwald “ for discoveries that confer the “for his method of hydrogenating "investigations into the fundamental greatest benefit on mankind” principles governing chemical organic compounds in the presence of equilibria and rates of reaction”, 1909 finely disintegrated metals", 1912 Irving Langmuir “for his discoveries and investigations Cyril Hinshelwood Fritz Haber, Berlin-Dahlem in surface chemistry”, 1932 "for researches into the mechanism “for the synthesis of ammonia of chemical reactions”, 1956 from its elements”, 1918 Some 21st-century Nobel prizes for catalysis What contributions can ab initio modeling provide to the catalysis field? Yves Chauvin, Lyon, France, 2005 Gerhard Ertl Fritz-Haber-Institut, Berlin “for his studies of chemical processes on solid surfaces”, 2007 CO + ½ O2 CO2 Pt Robert Grubbs, Richard Schrock Pasadena, CA, 2005 Boston, MA, 2005 → "for the development of the metathesis method in organic synthesis” Outline of this block course 1) Introduction to computational catalysis and first-principles modeling 2) Cluster models, slab models, ab initio thermodynamics and its applications 3) Transition state theory and potential energy surfaces --- 10 minute break 4) Computational screening of catalysts and the use of ‘descriptors’ 5) Topical Examples • Disintegration and redispersion of noble metal nanoparticles • Modeling isolated catalyst sites on amorphous supports Computational modeling can assist in understanding catalysis CO oxidation at RuO2 [1] K. Reuter, et al. Phys. Rev. Lett. 93, 116105 (2004) Many opportunities for improving catalysts remain Single atoms Nanoclusters Nanoparticles Metal-organic frameworks Single Pt atoms Rh6 nanocluster Gold nanoparticle The MOF-5 dispersed on FeOx supported by a zeolite supported by CeO2 lattice structure The dream: computational catalyst design Catalyst Catalyst design characterization Computational spectroscopy Active sites First-principles Ascertained thermochemistry & Reaction mechanism kinetic parameters First-principles Mechanistic understanding microkinetic modeling descriptor Computational screening Toward realistic time scales via simulation m space Continuum Equations, mm density- Rate Equations functional and Finite Element theory Modeling μm ab initio ab initio kinetic Monte Carlo nm Molecular Electronic Dynamics Structure Theory time f s p s n s μ s m s s hours years Image from presentation of Karsten Reuter The electron density contains all the information and is more tractable than the wave function Electronic structure theory approaches Potential energy for fixed nuclear positions {RI}: e E0 ({RI }) = MinΨ <Ψ| H {RI} |Ψ> Wavefunction based methods (Quantum Chemistry) Hartree-Fock, post Hartree-Fock (MP2, coupled cluster,…) Density-functional theory Ψ = Ψ[n(r)] (Hohenberg-Kohn, 1964) E ({R }) = Min E [n] 0 I n(r) {RI} XC = 3 ε XC ELDA [n] ∫ d r n(r) (no ) no =n(r) XC = 3 ε XC ∇ EGGA[n] ∫ d r n(r) (no , no ) (Kohn-Sham, 1965) no =n(r) Density functional theory (DFT) is widely applied to model catalysis at surfaces the choice of the exchange-correlation (XC) functional is critical for accurate predictions! Practitioner level GGA (metals) Hybrids (molecules, insulators) Major problems Self-interaction error Van der Waals interaction Inaccuracies in binding energies and activation barriers of order 0.2 − 0.4 eV! J. P. Perdew and K. Schmidt, AIP Conf. Proc., 577, 1 (2001) EP ● meta-GGA ● HSE … Theorists and experimentalists should work closely together from the beginning of a project. Theory can facilitate the development of catalysts and the understanding of reactions. R Schlögl - Cattech, 2001 Understanding the full catalytic cycle for even ‘simple’ surface reactions is challenging CO + H2O CO2 + H2 on Rh(111) ⇌ Microscale [CO]Rh + [OH]Rh CO Macroscale 1100 + [H]Rh T catalyst COOH*+* → CO*+OH* 1000 CO*+OH* → COOH*+* 900 → COOH*+* CO2*+H* 800 CO *+H* → COOH*+* 2 700 CO2* + H2O* → COOH* + OH* 600 T gas COOH* + OH* → CO2* + H2O* [H]Rh +[OH]Rh + Rh Temperature [°C] 500 CO2*+H* → HCOO** [CO2]Rh +2[H]Rh 400 HCOO** → CO2*+H* 2 CO2* + OH* + *→ HCOO** + O* HCOO** + OH* → CO * + H O* H 2 2 RDS 1.5 CH 2 CH* + H* → CH * + * 4 2 O CH* + * → C* + H* 1 2 CO CO2 C* + H* → CH* + * mmol/s H O CO [H O] + 2Rh 2 2 CH3* + O* → CH2* + OH* 2 Rh 0.5 CH2* + OH* → CH3* + O* CH* + OH* → CH * + O* 0 2 0 2 4 6 8 10 CH2* + O* → CH* + OH* Axial length [mm] … H2 H O ~ 102 potential steps 2 @ different coverages [1] M. Maestri and K. Reuter, Chem. Eng. Sci. 74, 296 (2012) Phenomenological models k1 CO + * CO* k -1 Determine rate constants k2 by fitting to experimental kinetic data O2 + 2* 2O* k-2 … A multiparameter fit problem kn COOH* + * CO * + H* k 2 -n Challenges Measure rates most sensitive to rate-determining steps (RDS) Perform experiments under wide range of operation conditions Different rate-determining step? Different surface structure and composition? Insufficient data (in particular on intermediates) to fully determine mechanism Branched/multi-step mechanisms From phenomenological models to ab initio Different reaction mechanisms can fit existing data equally well (more the norm than exception) Nullifies the objective of microkinetic modeling to generate mechanistic understanding Derived rate constants then have no microscopic meaning (effective parameters) Use quantitative calculations to determine rate constants and test reaction mechanisms Quantum Elementary Calculations Rate constants processes ~2000-2005: Stoltze/Nørskov, Neurock/van Santen, Reuter/Scheffler, … The effective site to atomistic gap * vs. Generic active site Atomistic active site model Independent of operation conditions Every atom counts One site model Generally insufficient characterization Distribution of active site types On which one to focus? Consider how many? The crucial ingredients toward first-principles microkinetics Quantum Elementary Calculations process Rate constant {Ri} → Etot Active site model Reaction rate theory + stat. mech., G(T,P,N) Level of theory M. Sabbe, M. F. Reyniers, K. Reuter, Catal. Sci. Technol. 2, 2010 (2012) Active site models Cluster Ionic insulators Embedded Cluster MgO, zeolites, … Non-ionic insulators Localized electrons Supercell TiO2, Al2O3,… Metals or metal-oxides Pt, Pd, RuO2… Use periodic boundary conditions to capture metallic band structure Simple examples of active site models Theoretical surface science approach Neglect facet edge effects Assume ideal terraces fcc(111) top bridge hollows More advanced examples of active site models Maarten et al. Catal. Sci. Technol. 2, 2010 (2012) Thermochemical calculations: Adsorption sites, lateral interactions, desorption enthalpies tot tot tot Ebinding = − [ E ( ) − E ( ) − E ( ) ] 1 Oxygen adsorption 2 on RuO(2x1)(0001) O(1x1) O(2x2) 3O(2x2) C. Stampfl and M. Scheffler, Phys. Rev. B 54, 2868 (1996) Mind the materials gap! STM images during high pressure ethylene hydrogenation on Rh(111) Model catalysts active inactive G. Rupprechter and Ch. Weiland, NanoToday 2, 20 (2007) K.S. Hwang, et al., J. Mol. Catal. A: Chem. 204, 499 (2003) Real vs. model materials: The materials and pressure gaps A DFT calculation corresponds to T = 0 K Real materials may be full of defects (vacancies, dislocations, dopants) Material’s structure and composition can strongly depend on preparation Impurities and adsorbates can influence the surface morphology A surface cannot be separated from a gas (or liquid) above it p ν = Requires p ≤ 10-12 atm to 2πmkT keep a “clean” surface clean For T = 300 K, p = 1 atm v ≈ 108 site-1 s-1 Bridging the pressure and temperature gap Theory: Development and use of first-principle statistical mechanics approaches ab initio thermodynamics Experiment: Awareness and diligent experiments… Development and use of in situ techniques Nanometer and sub-nanometer thin oxide films at surfaces of late transition metals, K. Reuter, in: Nanocatalysis: Principles, Methods, Case Studies, (Eds.) U. Heiz, H. Hakkinen, and U. Landman, Springer (Berlin, 2006) Ab initio thermodynamics provides a connection between the microscopic and macroscopic regimes Predict the preferred structure of a material as a function of environmental conditions µ (T, p ) O2 O2 equilibrium G(,) T p=+− Etotal F vibration TSconfigurational + pV DFT [1] C.M. Weinert and M. Scheffler, Mater. Sci. Forum 10-12, 25 (1986) [2] G.-X. Qian, R.M. Martin, and D.J. Chadi, Phys. Rev. B 38, 7649 (1988) [3] K. Reuter and M. Scheffler, Phys. Rev. B 65, 035406 (2002) Example of ab initio thermodynamics: Pd(100) metal surface in contact with O2 gas p(2x2) O/Pd(100) (√5x√5)R27o PdO(101)/Pd(100) [1] M. Todorova et al., Surf. Sci. 541, 101 (2003) [2] K. Reuter and M. Scheffler, Appl. Phys. A 78, 793 (2004) Ab initio thermodynamics: constrained equilibria µO (T, pO ) µ 2 2 X CO (T, pCO ) constrained equilibrium G(T, p) = E tot + F vib −TS conf + pV DFT [1] C.M. Weinert and M. Scheffler, Mater. Sci. Forum 10-12, 25 (1986) [2] E. Kaxiras et al., Phys. Rev. B 35, 9625 (1987); [3] K. Reuter and M. Scheffler, Phys. Rev. B 65, 035406 (2001) Surface phase diagram for the Pd(100) surface with an environment consisting of O2 and CO Pd: large blue spheres, O: small
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