Computational Catalysis by Aravind Asthagiri and Michael J Janik


5058e5ba7fbe642-261x361.jpg Author Aravind Asthagiri and Michael J Janik
Isbn 9781849734516
File size 9.4MB
Year 2013
Pages 276
Language English
File format PDF
Category chemistry


 

View Online RSC Catalysis Series . Published on 02 December 2013 on http://pubs.rsc.org | doi:10.1039/9781849734905-FP001 Series Editor: Professor James J Spivey, Louisiana State University, Baton Rouge, USA Advisory Board: Krijn P de Jong, University of Utrecht, The Netherlands, James A Dumesic, University of Wisconsin-Madison, USA, Chris Hardacre, Queen’s University Belfast, Northern Ireland, Enrique Iglesia, University of California at Berkeley, USA, Zinfer Ismagilov, Boreskov Institute of Catalysis, Novosibirsk, Russia, Johannes Lercher, TU Mu¨nchen, Germany, Umit Ozkan, Ohio State University, USA, Chunshan Song, Penn State University, USA Titles in the Series: 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: Carbons and Carbon Supported Catalysts in Hydroprocessing Chiral Sulfur Ligands: Asymmetric Catalysis Recent Developments in Asymmetric Organocatalysis Catalysis in the Refining of Fischer–Tropsch Syncrude Organocatalytic Enantioselective Conjugate Addition Reactions: A Powerful Tool for the Stereocontrolled Synthesis of Complex Molecules N-Heterocyclic Carbenes: From Laboratory Curiosities to Efficient Synthetic Tools P-Stereogenic Ligands in Enantioselective Catalysis Chemistry of the Morita–Baylis–Hillman Reaction Proton-Coupled Electron Transfer: A Carrefour of Chemical Reactivity Traditions Asymmetric Domino Reactions C–H and C–X Bond Functionalization: Transition Metal Mediation Metal Organic Frameworks as Heterogeneous Catalysts Environmental Catalysis Over Gold-Based Materials Computational Catalysis How to obtain future titles on publication: A standing order plan is available for this series. A standing order will bring delivery of each new volume immediately on publication. For further information please contact: Book Sales Department, Royal Society of Chemistry, Thomas Graham House, Science Park, Milton Road, Cambridge, CB4 0WF, UK Telephone: +44 (0)1223 420066, Fax: +44 (0)1223 420247 Email: [email protected] Visit our website at www.rsc.org/books View Online . Published on 02 December 2013 on http://pubs.rsc.org | doi:10.1039/9781849734905-FP001 Computational Catalysis Edited by Aravind Asthagiri Ohio State University, USA Email: [email protected] and Michael J. Janik Pennsylvania State University, USA Email: [email protected] . Published on 02 December 2013 on http://pubs.rsc.org | doi:10.1039/9781849734905-FP001 View Online RSC Catalysis Series No. 14 ISBN: 978-1-84973-451-6 ISSN: 1757-6725 A catalogue record for this book is available from the British Library r The Royal Society of Chemistry 2014 All rights reserved Apart from fair dealing for the purposes of research for non-commercial purposes or for private study, criticism or review, as permitted under the Copyright, Designs and Patents Act 1988 and the Copyright and Related Rights Regulations 2003, this publication may not be reproduced, stored or transmitted, in any form or by any means, without the prior permission in writing of The Royal Society of Chemistry or the copyright owner, or in the case of reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency in the UK, or in accordance with the terms of the licences issued by the appropriate Reproduction Rights Organization outside the UK. Enquiries concerning reproduction outside the terms stated here should be sent to The Royal Society of Chemistry at the address printed on this page. The RSC is not responsible for individual opinions expressed in this work. Published by The Royal Society of Chemistry, Thomas Graham House, Science Park, Milton Road, Cambridge CB4 0WF, UK Registered Charity Number 207890 For further information see our web site at www.rsc.org . Published on 02 December 2013 on http://pubs.rsc.org | doi:10.1039/9781849734905-FP005 Preface The RSC Catalysis Book Series has been publishing books focused on many aspects of catalysis since the 1970’s, but to date there has not been a book in the series that has solely focused on computational modeling of heterogeneous catalysis. The importance of computational catalysis has grown over the past two decades and there are an increasing number of young researchers entering this area. The aim of this book is to provide a pedantic presentation of select methods in computational catalysis. Our hope is that this book will prove useful to the graduate student or other researchers already familiar with computer simulations, but interested in applying specific methods to their catalysis research. In the first chapter, Lars Grabow (University of Houston) discusses the screening of catalysts through the use of first-principles methods. Using density functional theory (DFT), key descriptors and scaling relationships can be identified and incorporated with an appropriate microkinetic model. Such an approach allows for the rapid screening of materials based on DFT calculations. One of the key challenges in modeling catalysts is the need to predict the appropriate surface structure at reaction conditions. Jason Bray and Bill Schneider (Notre Dame) present a detailed example of a first-principles based thermodynamic model for oxygen adsorption on Pt surfaces. They derive a cluster expansion model, fit to DFT data, which allows for exploring the complex heterogeneous oxygen phase as a function of temperature and oxygen partial pressure using Monte Carlo simulations. These types of simulations also allow for exploring surface reaction behavior under reaction conditions. In the third chapter, Kuan-Yu Yeh and Mike Janik (Penn State University) present a detailed review of DFT-based modeling of electrocatalysts. The electrochemical interface is one of the more challenging environments to model, and several different models that vary in accuracy and computational expense RSC Catalysis Series No. 14 Computational Catalysis Edited by Aravind Asthagiri and Michael J. Janik r The Royal Society of Chemistry 2014 Published by the Royal Society of Chemistry, www.rsc.org v View Online . Published on 02 December 2013 on http://pubs.rsc.org | doi:10.1039/9781849734905-FP005 vi Preface are presented. With these methods potential dependent reaction energies and barriers can be calculated for elementary steps. Specific examples are presented to illustrate how to apply these various models. Another important area of computational catalysis is modeling the metal/ oxide interface, which is discussed by Tom Senftle, Adri van Duin, and Mike Janik (Penn State). They review several applications, such as the water-gas shift reaction and hydrocarbon activation, and the stability of oxide phases, that applies both DFT-based calculations and charge transfer potentials. Thomas Manz (New Mexico State University) and David Sholl (Georgia Tech) present the details and application of their charge partitioning method called the density derived electrostatic and chemical (DDEC) method. This method can be used to obtain chemically relevant atomic charges and spin moments for both periodic and non-periodic systems. Such output can assist in understanding the relationship between electronic structure and material properties, and can also be used as input into the fitting of classical potentials. The last two chapters present details of two classical potentials that incorporate charge transfer. Adri van Duin and co-workers present the details of the ReaxFF potential and discuss several applications. Susan Sinnott and coworkers from the University of Florida present the charge optimized many body (COMB) potentials and its application to molecules and metals on oxide surfaces. We appreciate the efforts made by the authors to present a wide range of important methods in computational catalysis at a level that can benefit a researcher learning these methods for their research. Aravind Asthagiri Michael J Janik . Published on 02 December 2013 on http://pubs.rsc.org | doi:10.1039/9781849734905-FP007 Contents Chapter 1 Computational Catalyst Screening Lars C. Grabow 1 1.1 1 1.2 1.3 1.4 1.5 1.6 1.7 Introduction 1.1.1 A Walk through a Computational Catalyst Design Process: Methanation Starting from the Electronic Structure 1.2.1 Density Functional Theory 1.2.2 The d-Band Model Identifying the Right Descriptor Set 1.3.1 Scaling Relations for Surface Intermediates 1.3.2 Scaling Relations for Transition States: The Brønsted–Evans–Polanyi Relationship The Sabatier Principle and the Volcano Curve 1.4.1 Sabatier Analysis Sabatier Analysis in Practice 1.5.1 First Example: Ammonia Synthesis 1.5.2 Second Example: CO Oxidation Notes on Microkinetic Modeling 1.6.1 Numerical Solution Strategies 1.6.2 Entropy and Enthalpy Corrections 1.6.3 Microkinetic Model Analysis CO Oxidation Catalyst Screening 1.7.1 Numerical Microkinetic Model 1.7.2 Degree of Rate and Catalyst Control 1.7.3 Two-dimensional CO Oxidation Volcano 1.7.4 Effect of Lateral Interactions RSC Catalysis Series No. 14 Computational Catalysis Edited by Aravind Asthagiri and Michael J. Janik r The Royal Society of Chemistry 2014 Published by the Royal Society of Chemistry, www.rsc.org vii 3 4 4 6 8 9 13 17 18 20 20 25 27 29 31 32 35 35 41 44 45 View Online . Published on 02 December 2013 on http://pubs.rsc.org | doi:10.1039/9781849734905-FP007 viii Chapter 2 Contents 1.8 Conclusions Appendix References 47 48 55 First-principles Thermodynamic Models in Heterogeneous Catalysis J. M. Bray and W. F. Schneider 59 2.1 Introduction 2.1.1 Background 2.1.2 Background on Oxygen Adsorption on Platinum 2.2 Setting up the System 2.2.1 Developing a Slab Model 2.2.2 Identifying and Characterizing Adsorption Sites 2.2.3 Increasing Coverage 2.3 Developing a Self-consistent Cluster Expansion Model 2.3.1 Cluster Expansion Fundamentals 2.3.2 Self-consistent Fitting Approach 2.4 Applying the Model to Obtain Physical Insight 2.4.1 Analysis of the DFT Fitting Database 2.4.2 Analysis of Ordered Ground States 2.4.3 Monte Carlo Simulations 2.4.4 Kinetic Properties from CE/GCMC Methods 2.5 Conclusions Acknowledgments References Chapter 3 59 59 62 63 63 65 69 72 72 74 80 80 83 93 109 112 112 113 Density Functional Theory Methods for Electrocatalysis Kuan-Yu Yeh and Michael J. Janik 116 3.1 116 3.2 Introduction 3.1.1 A Motivating Example: H2 Oxidation/H2 Evolution 3.1.2 Electrode Potential Effects on Reaction Energies and Activation Barriers 3.1.3 Electrochemical Double-layer Theory 3.1.4 Overview of DFT Models for Electrocatalysis Examples Applying DFT Methods to Electrocatalysis 3.2.1 Simulating the Vacuum–Metal Interface 3.2.2 Simulating an Aqueous–Metal Interface 3.2.3 Linear Sweep Voltammetry Simulations 117 121 122 124 128 129 137 146 View Online ix Contents . Published on 02 December 2013 on http://pubs.rsc.org | doi:10.1039/9781849734905-FP007 3.2.4 Calculation of Surface Reaction Free Energies 3.2.5 Potential Dependent Activation Barriers 3.3 Conclusions References Chapter 4 Application of Computational Methods to Supported Metal–Oxide Catalysis Thomas P. Senftle, Adri C.T. van Duin and Michael J. Janik 4.1 4.2 Introduction Computational Approaches to Supported Metal–Oxide Catalysis 4.3 Selected Applications 4.3.1 Application of DFT to WGS 4.3.2 Ab Initio Thermodynamics 4.3.3 Classical Atomistic Modeling 4.3.4 Combined Application: Hydrocarbon Activation over Pd/CeO2 4.4 Conclusions References Chapter 5 Computing Accurate Net Atomic Charges, Atomic Spin Moments, and Effective Bond Orders in Complex Materials Thomas A. Manz and David S. Sholl 5.1 5.2 Introduction Net Atomic Charges and Atomic Spin Moments 5.2.1 The Charge Partitioning Functional 5.2.2 The Spin Partitioning Functional 5.2.3 Example using VASP Software 5.2.4 Examples using GAUSSIAN Software 5.2.5 VASP Non-collinear Magnetism Example 5.3 Modeling the Electrostatic Potential Surrounding a Material 5.3.1 Atom-centered Distributed Multipole Expansion 5.3.2 Applications to Force-fields used in Atomistic Simulations 5.4 Effective Bond Orders 5.5 Conclusions Acknowledgments References 147 151 153 153 157 157 158 159 161 167 174 178 185 186 192 192 194 194 196 198 201 205 209 209 211 212 219 219 220 View Online x . Published on 02 December 2013 on http://pubs.rsc.org | doi:10.1039/9781849734905-FP007 Chapter 6 Chapter 7 Contents A Reaxff Reactive Force-field for Proton Transfer Reactions in Bulk Water and its Applications to Heterogeneous Catalysis Adri C.T. van Duin, Chenyu Zou, Kaushik Joshi, Vyascheslav Bryantsev and William A. Goddard 223 6.1 6.2 Introduction Methods 6.2.1 Quantumchemical Methods 6.2.2 Force-field Optimization 6.3 Results and Discussion 6.3.1 Force-field Development 6.3.2 Molecular Dynamics Simulations 6.3.3 Heterogeneous Catalysis 6.4 Conclusions References 223 226 226 226 226 226 233 238 240 240 Charge Transfer Potentials Yu-Ting Cheng, Tao Liang, Simon R. Phillpot and Susan B. Sinnott 244 7.1 7.2 244 Introduction Variable Charge Reactive Potentials: COMB Potentials 7.2.1 A General Form of the COMB Potentials 7.2.2 Electrostatic Energies 7.2.3 Short-range Interactions 7.2.4 van der Waals Interactions 7.2.5 Correction Terms 7.2.6 Parameterization of the COMB Potential 7.3 Applications 7.3.1 Ethyl Radical Deposition on the Cu(111) Surface 7.3.2 Cu/ZnO Heterogeneous System 7.4 Conclusions Acknowledgments References Subject Index 247 247 247 249 251 251 251 255 255 256 257 258 258 261 . Published on 02 December 2013 on http://pubs.rsc.org | doi:10.1039/9781849734905-00001 CHAPTER 1 Computational Catalyst Screening LARS C. GRABOW Chemical & Biomolecular Engineering, University of Houston, Houston, Texas, 77204-4004, USA Email: [email protected] 1.1 Introduction Brute-force attacks are known in cryptography as (typically illegal) attempts to hack into encrypted data by systematically trying all possible key combinations of letters, digits and special characters until the correct access key or password has been found. Although a brute-force attack is guaranteed to be successful, its application is limited to very small problems because of the time required to generate and test all possible key combinations. For example, a standard 128-bit encryption key has 2128 possible permutations. If we simply assume that a typical central processing unit (CPU) can generate 109 bit flips per second (B1 GHz), then the total time that is required to test all possible permutations is 2128/ 109 ¼ 3.41029 seconds or 1022 years! For obvious reasons a brute-force attack is most likely going to fail for this problem and a more targeted strategy is needed. The above example illustrates the shortcomings of a brute-force attack, but a variation of it is still one of the most widely used strategies for the development of heterogeneous catalysts in practice. By using a combinatorial chemistry approach with completely automated, high-throughput experimentation equipment, one can synthesize and test enormous libraries of catalysts for their catalytic activity for a specific reaction. A good example is the search for advanced water–gas shift catalysts, in which Yaccato et al. have synthesized over 50 000 catalysts and RSC Catalysis Series No. 14 Computational Catalysis Edited by Aravind Asthagiri and Michael J. Janik r The Royal Society of Chemistry 2014 Published by the Royal Society of Chemistry, www.rsc.org 1 View Online . Published on 02 December 2013 on http://pubs.rsc.org | doi:10.1039/9781849734905-00001 2 Chapter 1 tested them in more than 250 000 experiments for low, medium and high temperature water–gas shift conditions.1 Their effort led to a proprietary noble metal catalyst that can reduce the reactor volume by an order of magnitude without increasing the reactor cost. Although this trial-and-error approach almost always leads to an acceptable catalyst, the search space is restricted by the amount of time and resources available and many, possibly far better, candidates can be missed. The quickly evolving alternative to experimental high-throughput catalyst testing is computational catalyst screening. This approach relies on the fact that the catalyst activity for many catalytic reactions is usually determined by a small number of descriptors, which can be calculated from first-principles density functional theory (DFT) simulations and stored in a large property database. Populating this property database with DFT data is the most time-consuming step in this process, but the resulting database is applicable to any reaction and only has to be generated once. With a comprehensive database in place, it becomes a very easy task to screen thousands of database records in a short amount of time to identify catalyst candidates that possess descriptor values within the optimal range for a given reaction. Although the computational screening process can still be interpreted as a brute-force attack, the complexity of the problem has been greatly reduced. Hence, the number of materials that can be screened computationally increases drastically when compared with the experimental counterpart. The list of catalysts that fall into the desired range of descriptor values may be narrowed down further by using cost, stability, environmental friendliness, or any other applicable criteria.2,3 The remaining materials can then be synthesized and experimentally tested under realistic reaction conditions. In general, not all computationally screened candidates will be good catalysts, but good catalysts will usually be included in the candidate list. Somorjai and Li have recently reviewed the major advances in modern surface science that only became possible through the successful symbiosis of theory and surface sensitive experimental techniques.4 The recent literature also contains several examples where a descriptor-based approach, both theoretically and experimentally, has led to the discovery of new catalytic materials. The following list should not be understood as an exhaustive review, but is meant to serve as inspiration to the reader and to demonstrate the wide applicability of this method. Early on, Besenbacher et al. discovered graphite resistant Ni/Au alloy catalysts for steam reforming,5 Jacobsen et al. found an active Co/Mo alloy for ammonia synthesis by interpolation in the periodic table,6 and Toulhoat and Raybaud showed that the metal–sulfur bond strength can correctly predict trends in hydro-desulfurization activity on metal–sulfide catalysts.7 These initial successes were followed by other prominent examples that include CO-tolerant fuel cell anodes,8,9 Cu/Ag alloys as selective ethylene epoxidation catalysts,10 near-surface alloys for hydrogen activation11 and evolution2,12, Ru/Pt core–shell particles for preferential CO oxidation,13 Ni/Zn alloys for the selective hydrogenation of acetylene,14 Sc and Y modified Pt and Pd electrodes15 and mixed-metal Pt monolayer catalysts16 for electro-chemical oxygen reduction, and the rediscovery of Pt as the most active and selective catalyst for the production of hydrogen cyanide.17,18 View Online Computational Catalyst Screening 3 . Published on 02 December 2013 on http://pubs.rsc.org | doi:10.1039/9781849734905-00001 1.1.1 A Walk through a Computational Catalyst Design Process: Methanation The most comprehensive example of a success story in computational catalyst design comes from the group of Jens Nørskov, who has pioneered the descriptorbased design approach and has applied it to numerous reactions.19,20 In several publications his group has studied the methanation reaction (CO þ 2H2 - CH4 þ H2O), starting from a detailed electronic structure analysis and leading to the development of a patented technical methanation catalyst based on a Fe/Ni alloy.21–25 In the beginning of any descriptor-based design study one must first answer the question: ‘‘What is the most suitable reactivity descriptor for the reaction?’’ This question is typically answered by thoroughly studying the underlying reaction mechanism and identifying the rate-limiting step and most abundant surface intermediates. However, intuition can sometimes replace a detailed mechanistic study and a descriptor can be found through an educated guess. In the case of the methanation reaction, CO dissociation is the most critical step in the reaction mechanism. For weakly interacting metal catalysts, the dissociation is rate limiting, whereas for strongly interacting catalysts, the surface is poisoned by adsorbed C and O atoms. This leads to the volcano curve in Figure 1.1(a), which shows the experimentally measured methanation activity as a function of the calculated CO dissociation energy. The top of the volcano corresponds to the maximum methanation activity and indicates the optimal value of the CO dissociation energy, which is the activity descriptor in this case. The next step in the catalyst design process is to screen a database of CO dissociation energies and search for catalysts with CO dissociation energies near the optimum. This screening may be combined with a cost estimation of the resulting material and can further be linked to a stability test. Figure 1.1(b and c) show pareto plots of binary transition metal alloys for which the CO dissociation energy was estimated through a simple interpolation scheme owing to the lack of an existing database. The most active catalysts, characterized by CO dissociation energies close to the optimum, lie to the left of the graph and are connected with a solid line indicating the paretooptimal set. The pareto-optimal set of Figure 1.1(b) contains the cheapest catalysts for a given value of CO dissociation energies and, similarly, Figure 1.1(c) can be used to screen for alloy stability. Only alloys with a negative alloy formation energy are stable and their stability increases as the alloy formation energy becomes more negative. Upon careful inspection, one notices that FeNi3 is not only contained in both sets, but it is also located at the ‘‘knee’’ of the activity pareto-optimal set, which indicates that neighboring solutions are worse with respect to either activity or cost. Clearly, FeNi3 is a very promising catalyst candidate for the methanation reaction. This catalyst identification step concludes the theoretical design process and experimental verification of the theoretical prediction is necessary. Experimentally obtained methanation rates of Fe/Ni alloys as a function of Ni content are displayed in Figure 1.1(d) and clearly show that the computationally predicted FeNi3 alloy is significantly more active than its components. As an outcome of this tour de force in computational catalyst design, a process based on Fe/Ni alloys has been patented for the hydrogenation of carbon oxides.24 View Online . Published on 02 December 2013 on http://pubs.rsc.org | doi:10.1039/9781849734905-00001 4 Chapter 1 (a) (b) (c) (d) Figure 1.1 Computational design of a technical methanation catalyst. (a) A characteristic volcano curve is obtained when the experimentally determined methanation activity is plotted as a function of the CO dissociation energy. (b) and (c) Pareto-optimal bimetallic catalysts in terms of cost and stability. Ediss(optimal) refers to the optimal CO dissociation energy corresponding to the maximum of the activity volcano in panel (a). (d) Measured methanation activity of binary Fe/Ni alloys at T ¼ 548 K, 2% CO in 1 bar H2 as a function of Ni content. [(a), (b), (d) are reprinted by permission from Macmillan Publishers Ltd: Nature Chemistry, Ref. 15, 2009, (c) is from ref. 25] In the remainder of this chapter, the background information that leads to the identification of appropriate catalyst descriptors (e.g. d-band model, scaling relationships) is reviewed and the basic strategy for successful catalyst screening using various levels of detail (e.g. Sabatier rate vs. microkinetic model) is outlined. A step-by-step illustration of the method will be given using ammonia synthesis and CO oxidation as examples. The interested reader is encouraged to work through the examples independently at her/his own pace. 1.2 Starting from the Electronic Structure 1.2.1 Density Functional Theory Computational catalyst screening would not be possible without the existence of a theory that enables us to calculate the chemical properties of the catalyst View Online 5 . Published on 02 December 2013 on http://pubs.rsc.org | doi:10.1039/9781849734905-00001 Computational Catalyst Screening and the reaction of interest. Fortunately, in the mid 1960s Hohenberg, Kohn and Sham published two seminal papers formulating two theorems, which led to the development of density functional theory (DFT).26,27 The contributions of Walter Kohn to the development of this theory were later honored in 1998 with the Nobel Prize in Chemistry. DFT is nowadays widely used in many different areas of science and engineering, including computational chemistry, catalysis, materials science, physics, and geology. The two theorems can be summarized as: 1. The ground state properties of a many-electron system are uniquely determined by the electron density. 2. The total energy of a system has a minimum for the ground state electron density. DFT provides a solution to the Schro¨dinger equation: ^ ¼ EC HC ð1:1Þ and is in principle an exact theory, but in practice the exact formulation of the kinetic energy term for a system of interacting electrons is unknown. In the Kohn–Sham approach, the kinetic energy is therefore approximated with the kinetic energy of a system of non-interacting electrons and a correction term, EXC, which accounts for exchange and correlation effects in the interacting system. Although approximations for the description of the exchangecorrelation energy must be made, DFT has the huge advantage over wave function based methods that the electron density is a function of only three spatial coordinates, while the many-body wave function for N electrons depends on 3N coordinates. Thus, DFT significantly reduces the computational intensity of the problem and enables the treatment of systems of several hundred atoms. From the electron density, n(r), all other properties of the system are determined (Theorem 1) and the total energy E is calculated using Z ZZ 1 nðrÞnðr 0 Þ 0 E ½nðrÞ ¼ TKS ½nðrÞ þ þ vnucl ðrÞnðrÞdr þ EXC ½nðrÞ ð1:2Þ drdr 2 jr  r 0 j The first term, TKS[n(r)], is the kinetic energy of fictitious, non-interacting electrons and is obtained from the single-electron Kohn–Sham equations  2   h r þ veff ci ¼ ei ci ð1:3Þ 2m where veff is the effective field defined by the nuclei and the current electron density. The second and third term in the total energy equation describe the electrostatic electron–electron interactions (Hartree energy) and the electron– nuclei interactions, respectively. The last term, EXC, in the total energy equation depends on the unknown exchange-correlation functional, for which several approximations exist. The simplest approximation is the local density approximation (LDA), which can be derived from the case of a homogeneous View Online . Published on 02 December 2013 on http://pubs.rsc.org | doi:10.1039/9781849734905-00001 6 Chapter 1 electron gas and only depends on the electron density at a single point. In this case, the exchange contribution in the LDA is exact, but the correlation still has to be approximated. The LDA works remarkably well for bulk materials where the electron density varies slowly, but has insufficient accuracy for most applications in chemistry, including atoms, molecules, clusters, and surfaces. An obvious extension to the LDA is the generalized gradient approximation (GGA), which depends not only on the local density but on the density gradient. Because the gradient correction can be implemented into a GGA functional in many different ways, there exist a variety of different GGA flavors. The most widely used GGA functionals are the Perdew–Wang 91 (PW91)28,29 and the Perdew–Burke-Ernzerhof (PBE)30 functional. Both GGA functionals have good accuracy for a wider range of problems than the LDA because they contain more physical information; however, they are not necessarily always better. The PBE functional was later revised by Hammer, Hansen and Nørskov (RPBE), in order to improve the accuracy of chemisorption energies of atoms and small molecules on transition metal surfaces.31 These GGA functionals are very good general-purpose functionals and may be used as a starting point for computational catalyst design. However, the GGA still fails for problems such as the accurate prediction of band gaps in semiconductors, systems where van der Waals interactions are dominant, or for electronic structure calculations in materials with strongly correlated electrons, where self-interaction errors can be encountered. Several improvements to the GGA have been suggested (e.g. DFT þ U, DFT-D, meta-GGA, hybrid-GGA), but many of these functionals are problem specific or contain adjustable parameters that need to be fitted for each system. This empirical nature, along with the increased computational effort, renders these functionals generally unsuitable for computational catalyst screening. Work to improve XC functionals further is ongoing in the community, and in the next few years faster computers and new functionals will have a positive impact on the quality of DFT calculations. Although DFT calculations are at the heart of computational catalysis, it is not strictly necessary to perform your own calculations for a catalyst design project. DFT calculations for many reactions have already been published and efforts are undertaken to make these data easily available to the whole catalysis community, even on mobile devices. Yes, there is an app for that!32 But even a non-DFT expert should understand the basic principles that underlie the theoretical results, before using them in a research project. For those readers that have a deeper interest in DFT and want to perform their own calculations, the tutorial-style book Density Functional Theory – A Practical Introduction by David S. Sholl and Janice A. Steckel is a highly recommended starting point.33 1.2.2 The d-Band Model Computational catalyst screening relies on the prediction of correct trends across different catalysts rather than the prediction of quantitative rates and selectivities for each catalyst. Understanding the origin of the observed trends in terms of the underlying electronic structure can therefore be very helpful View Online . Published on 02 December 2013 on http://pubs.rsc.org | doi:10.1039/9781849734905-00001 Computational Catalyst Screening Figure 1.2 7 Schematic density of states (DOS) illustration of the d-band model. The interaction of an adsorbate state with a transition metal can be thought of as a two-step process. The interaction with the broad s-band leads to a broadening and downshift of the adsorbate states. The adsorbate states split into bonding and anti-bonding states upon interaction with the narrow transition metal d-band. Anti-bonding states that are above the Fermi level remain empty and do not weaken the chemisorption. (Taken from ref. 20) during the screening process. For transition metal surfaces, trends in reactivity can be very well described and understood in terms of the d-band model (Figure 1.2) developed by Hammer and Nørskov.34,35 Many of us have likely seen a schematic drawing of the bonding structure in a hydrogen molecule in one of our previous chemistry classes. Upon bond formation, the two atomic orbitals form two new molecular orbitals and they can be distinguished as a bonding and an anti-bonding orbital. In the case of a hydrogen molecule, two electrons can distribute into these orbitals and since each orbital can accommodate up to two electrons, naturally both electrons occupy the lower-lying bonding orbital. The energy that is gained by stabilizing the electrons in this process is the bond energy. The interactions of adsorbates with transition metals are a bit more complicated but conceptually similar. A transition metal does not possess atomic orbitals, but has a continuous range of available states called a ‘‘band’’. In a simplified picture of the band structure in transition metals (Figure 1.2, right) we can imagine that they have a broad s-band (turquoise) and a narrow band of localized d-electrons (red). Assuming that we can separate the coupling between the adsorbate level and the s- and d-bands of the transition metal, we can write the chemisorption energy as the sum of both interactions. DEChem ¼ DEs þ DEd ð1:4Þ The interaction of the adsorbate state with the broad s-band, DEs ; leads to a broadening of the state and a downshift in energy. Since all transition metals have broad and half-filled s-bands, the contribution DEs ; is approximately the same for all transition metals. In the next step, the broadened molecular state can couple to the narrow d-band of the transition metal, which causes a split View Online . Published on 02 December 2013 on http://pubs.rsc.org | doi:10.1039/9781849734905-00001 8 Chapter 1 into bonding and anti-bonding states, just as in the case of the molecular orbitals of a hydrogen molecule. However, in contrast to the molecular system, where a fixed number of electrons is available to occupy the new orbitals, a transition metal has a large reservoir of electrons. These electrons will fill up all states located below the Fermi level and, consequently, the more anti-bonding states are located below the Fermi level, the weaker the resulting chemisorption bond. For stronger bonds it is desirable that all the anti-bonding states are high in energy and above the Fermi level. The location of the anti-bonding states relative to the Fermi level and, in turn, the strength of the resulting bond, is largely determined by the position of the d-band. Since the d-band spans a range of energies, we need to find a convenient way to define the term ‘‘position’’, and therefore introduce the d-band center. The d-band center, Ed , is the energy-weighted average of the density of d-states r. It sounds complicated, but it is the same equation that you use to calculate the center of mass (just substitute rCOM ¼ Ed , r ¼ E and m ¼ r). R rEdE Ed ¼ R ð1:5Þ rdE The d-band center varies across the transition metals and according to the dband model this will cause a variation in the interaction strength, DEd. If we recall that DEs is constant, the variations in chemisorption energy across transition metals can be attributed to changes in DEd and, thus the d-band center. Transition metals with higher-lying d-bands have stronger chemisorption properties. Numerous examples supporting the d-band model theory exist in the literature (ref. 20 and references 22–37 therein) but, as with most rules, there are some exceptions. In systems including electronegative adsorbates with nearly filled valence shells (e.g. OH, F, Cl) on surfaces with almost fully occupied d-bands (d9 and d10 metals) there can be a significant repulsive interaction between the transition metal d-band and the adsorbate states, which leads to a local reversal of the d-band model trend.36 For computational screening studies, however, we can safely neglect this exception, because it only affects the local fine structure and general trends are preserved. 1.3 Identifying the Right Descriptor Set If you have ever played the party game ‘‘Taboo’’ you have experienced how hard it can be to describe a word or object without using the five most closely related words listed on the card. On the other hand, if you were allowed to mention only the five forbidden words, your teammates would probably guess the hidden word immediately. Think of these five taboo words as the descriptors that we need to guess the performance of our catalyst. Choosing the right descriptors is the key to a successful descriptor-based catalyst design study and it needs to be done carefully. The ideal set of descriptors needs to fulfill two conflicting requirements. First and foremost, the descriptor set has to be large enough to enable predictions that View Online . Published on 02 December 2013 on http://pubs.rsc.org | doi:10.1039/9781849734905-00001 Computational Catalyst Screening 9 are accurate enough to serve the purpose of the study. For simple reactions, a single descriptor may be sufficient to describe qualitatively the activity trends across different catalyst materials. However, product selectivity, for example, is often more sensitive to the input parameters and may require additional descriptors. If quantitative results are desired, then the number of required descriptors quickly approaches the total number of enthalpy and entropy parameters in a reaction network, which defeats the purpose of reducing the problem complexity by introducing the concept of descriptors. In fact, reducing the complexity is the second most important requirement that the descriptors must meet. The set of descriptors should be as small as needed to capture catalytic trends and enable fast and efficient screening for new catalyst materials. There is no strict rule for the ‘‘correct’’ choice of descriptors; in fact, for most cases there is more than one set of descriptors and all of them may be equally viable. A descriptor can be any measurable intrinsic quantity of the catalyst (e.g. the d-band center), but most often descriptors are binding energies of key intermediates inferred from the detailed knowledge of the dominant reaction mechanism and the kinetically relevant steps. This information can be obtained from mechanistic studies using DFT in combination with kinetic measurements and modeling. Alternatively, the existence of scaling relations for surface intermediates and transition states can guide the descriptor selection process. These scaling relations find their physical roots in the d-band model and are discussed next. 1.3.1 Scaling Relations for Surface Intermediates The binding energy of an adsorbed molecule is determined by the number and strength of the chemical bonds that it forms with the surface. To a first approximation we can consider these bonds to form independently of each other and assume that the bond strength only depends on the two types of atom involved in the bond formation. In this simple picture, it would be sufficient to know through which atoms a molecule binds to the catalyst surface in order to predict its adsorption energy. Indeed, it has been shown that the adsorption energies of adsorbates within a family of similar adsorbates can be predicted using this simple idea. The resulting linear scaling relationships can be used to predict unknown adsorption energies from the adsorption energies of related surface species.37,38 The accuracy of linear scaling relations is generally adequate to predict catalytic trends correctly, but the average errors (0.2–0.3 eV) are too large for quantitative predictions. However in the context of computational screening, in which we are only interested in the relative order between different transition metal catalysts, these errors are acceptable. 1.3.1.1 Hydrogen-containing Molecules The discussion in this section is fully based on the scaling papers by AbildPedersen et al.37 and Fernandez et al.,38 which are highly recommended references on this topic. Each of the four panels in Figure 1.3 shows the View Online 10 Chapter 1 . Published on 02 December 2013 on http://pubs.rsc.org | doi:10.1039/9781849734905-00001 3 2 2 Figure 1.3 Linear scaling relationships on close-packed terraces (black), step sites (red) and the FCC(100) surface (blue) of hydrogen-containing molecules of the type AHx with A ¼ C, N, O, S. Reprinted with permission from F. Abild-Pedersen, J. Greeley, F. Studt, J. Rossmeisl, T. R. Munter, P. G. Moses, E. Sku´lason, T. Bligaard and J. K. Nørskov, Phys. Rev. Lett., 2007, 99, 016104–016105. Copyright 2007 by the American Physical Society. Available at: http://link.aps.org/doi/10.1103/ PhysRevLett.99.016105.37 adsorption energies, DEAHx, of the hydrogen-containing intermediates AHx (A ¼ C, N, O, S) plotted as a function of the adsorption energy, DEA of the central atom A for a range of typical transition metal surfaces. The adsorption energies were obtained from periodic DFT calculations on close-packed terraces (black), step sites (red) and, additionally, on the face-centered cubic [FCC(100)] surface (blue) for OHx. It can be seen that the adsorption energies DEAHx are linearly correlated with DEA and given by DE AHx ¼ gDE A þ x: ð1:6Þ There is certainly some scatter around the linear scaling lines, but the general trend is correctly captured and the absolute errors are within the 0.2–0.3 eV

Author Aravind Asthagiri and Michael J Janik Isbn 9781849734516 File size 9.4MB Year 2013 Pages 276 Language English File format PDF Category Chemistry Book Description: FacebookTwitterGoogle+TumblrDiggMySpaceShare The field of computational catalysis has existed in one form or another for at least 30 years. Its ultimate goal – the design of a novel catalyst entirely from the computer. While this goal has not been reached yet, the 21st Century has already seen key advances in capturing the myriad complex phenomena that are critical to catalyst behaviour under reaction conditions. This book presents a comprehensive review of the methods and approaches being adopted to push forward the boundaries of computational catalysis. Each method is supported with applied examples selected by the author, proving to be a more substantial resource than the existing literature. Both existing a possible future high-impact techniques are presented. An essential reference to anyone working in the field, the book’s editors share more than two decade’s of experience in computational catalysis and have brought together an impressive array of contributors. The book is written to ensure postgraduates and professionals will benefit from this one-stop resource on the cutting-edge of the field.     Download (9.4MB) Nanoscience: Volume 2: Nanostructures through Chemistry Chemical Reagents for Protein Modification (4th Edition) Lanthanum: Compounds, Production and Applications Heterogeneous Catalysis for Today’s Challenges: Synthesis, Characterization and Applications Photochemistry: Volume 44 Load more posts

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