Introducing! Operando computational modeling in heterogeneous catalysis

I found the following article as the result of a Google Scholar email alert. Besides being a good review article, it has the additional benefit of being absolutely free. The link to the source appears at the end of the post.

TIP: Study the article’s introduction. It is better than the abstract at explaining the point of the review. Keep it in mind when you write your next article.

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Towards operando computational modeling in heterogeneous catalysis

Lukáš Grajciar ORCID (a), Christopher J. Heard ORCID (a), Anton A. Bondarenko (b), Mikhail V. Polynski ORCID (b), Jittima Meeprasert ORCID (c), Evgeny A. Pidko ORCID *(b)(c) and  Petr Nachtigall ORCID *(a)
a Department of Physical and Macromolecular Chemistry, Faculty of Science, Charles University in Prague, 128 43 Prague 2, Czech Republic. E-mail: lukas.grajciar@natur.cuni.cz ; petr.nachtigall@natur.cuni.cz ; heardc@natur.cuni.cz
b TheoMAT group, ITMO University, Lomonosova 9, St. Petersburg, 191002, Russia
c Inorganic Systems Engineering group, Department of Chemical Engineering, Faculty of Applied Sciences, Delft University of Technology, Van der Maasweg 9, 2629 HZ Delft, The Netherlands. E-mail: e.a.pidko@tudelft.nl
First published on 11th September 2018
DOI: 10.1039/C8CS00398J (Review Article) Chem. Soc. Rev., 2018, Advance Article

Abstract
An increased synergy between experimental and theoretical investigations in heterogeneous catalysis has become apparent during the last decade. Experimental work has extended from ultra-high vacuum and low temperature towards operando conditions. These developments have motivated the computational community to move from standard descriptive computational models, based on inspection of the potential energy surface at 0 K and low reactant concentrations (0 K/UHV model), to more realistic conditions. The transition from 0 K/UHV to operando models has been backed by significant developments in computer hardware and software over the past few decades. New methodological developments, designed to overcome part of the gap between 0 K/UHV and operando conditions, include (i) global optimization techniques, (ii) ab initio constrained thermodynamics, (iii) biased molecular dynamics, (iv) microkinetic models of reaction networks and (v) machine learning approaches. The importance of the transition is highlighted by discussing how the molecular level picture of catalytic sites and the associated reaction mechanisms changes when the chemical environment, pressure and temperature effects are correctly accounted for in molecular simulations. It is the purpose of this review to discuss each method on an equal footing, and to draw connections between methods, particularly where they may be applied in combination.

Lukáš Grajciar
Lukáš Grajciar received his MSc and PhD degrees in chemistry from the Charles University in Prague in 2009 and 2013, respectively, developing and applying dispersion-corrected DFT methods for adsorption in zeolites and metal–organic frameworks. At his postdoctoral position at Jena University in Germany, he became involved in development of high-performance algorithms for ab initio treatment of large molecules and periodic system within the TURBOMOLE program, including implementation of a new tool for global structure optimization of clusters in confinement. Currently, he is a researcher at the Charles University in Prague, investigating reactivity of zeolites using biased ab initio molecular dynamics.

1. Introduction
Most of the chemicals produced nowadays are obtained using processes based on catalysis. The on-going search for optimal process conditions and the most suitable catalyst is driven by various concerns, including (i) environmental impact, (ii) resource utilization, (iii) safety and (iv) overall process economy. While this has traditionally been the domain of experimental investigations, the input from computational investigations has been steadily increasing over the last 40 years. An increased synergy between theory and experiment has become apparent during the last decade, in particular, in the field of heterogeneous catalysis.
By definition a heterogeneous catalyst shifts the reference reaction onto a different free energy surface where the energy of critical transition states with respect to relevant intermediates becomes lower. Mechanisms of chemical reactions were traditionally explored within the concept of the potential energy surface (PES), considering simplified models of a catalytic system working under idealized conditions of, basically, infinite dilution. Such a heterogeneous catalysis model represents ultra-high vacuum conditions, for which calculations provide information at 0 K; we will refer to this model as the 0 K/UHV model. Strictly speaking, such a description corresponds to rather unrealistic reaction conditions and its validity decreases with increasing temperature and pressure. A great number of mechanisms have been proposed based on calculations with such a simplistic model and results were often at least in qualitative agreement with available experimental data. Computational results obtained with 0 K/UHV model correspond reasonably well with experimental data obtained for well-defined surfaces under UHV conditions. However, the overlap of such calculated data and catalytic experiments carried out under realistic conditions is rather small, and a good agreement between 0 K/UHV theory and catalytic experiments was often just fortuitous.

The success of the simple PES concept applied within the 0 K/UHV approximation can be expected only when the following assumptions hold: (i) the structure of the active site under realistic conditions is known (or correctly guessed), (ii) both the structure of the active site and the reaction mechanism do not depend on the surface coverage of individual reaction intermediates, (iii) the reaction mechanism found under nearly UHV conditions is not different from that at the realistic composition of the surrounding gas or liquid phase and (iv) temperature effects, including the transition from PES to free energy surface (FES), can be safely neglected. Unfortunately, all such assumptions are rarely satisfied at once. If the temperature is relatively low it follows that reactants, products and/or reaction intermediates are adsorbed on the surface; and in contrast, one can expect that the reaction proceeds on a clean catalyst surface only at elevated temperature.

A deeper atomistic insight into the reaction mechanisms, the catalyst structure/activity relationship and catalyst stability/transformation during the reaction greatly increases our chances to find the optimal catalyst for a particular process. The most detailed experimental evidence about the catalyst at the molecular level can be obtained by a combination of characterization techniques under UHV conditions. More and more information becomes available from experimental investigations gathered under the conditions of a model catalytic reaction – in situ conditions – and also under conditions where the applied catalytic process takes place – operando conditions. For details of experimental in situ and operando conditions see, e.g., ref. 1–3. A great development of in situ and in particular operando experimental techniques for studying catalytic reactions in the last 20 years has brought an increasing amount of information about the state of the catalysts under realistic conditions.4,5

Among the most important findings emerging from such studies is the evidence of the dynamic nature of the catalyst surface, whose structure constantly changes under the catalytic reaction conditions. For example, in oxidation catalysis by supported metal nanoparticles, in situ and operando techniques revealed the formation of ultra-thin oxide layers covering the metal nanoparticles in an oxidizing atmosphere, which provide the active sites for the target catalytic reactions. Obviously, such an active site model could not be proposed based on the UHV surface science experiments or computations carried out in the 0 K/UHV regime. A problem of how the structure of the catalyst depends on the realistic chemical environment and temperature that are relevant for a particular process is thus the key for a proper understanding of catalysis at the molecular level and for a design of improved catalysts.6–8

Similar to the shift of experimental investigations in catalysis from UHV to operando conditions, theoretical investigations in the field of catalysis are moving more and more from 0 K/UHV models to computational operando investigations. In analogy with the experimental operando conditions, a computational operando model is defined by the following conditions: the structure of the active catalyst surface and the reaction coordinates must reflect realistic conditions during the reaction and a complex reaction network must be established (see Fig. 1 and corresponding text for more details). However, a transition from the 0 K/UHV to operando model dramatically influences the complexity of the problem and increases computational demands. A number of methods have been developed in the past few decades that ease the 0 K/UHV ? operando transition and it is the goal of this review to discuss the current state of the computational investigations of catalysis, with the goal to enable the long-sought after paradigm of catalysis by design.

Fig. 1  Schematic of the various computational methods applied to heterogeneous catalysis, which lie between an idealised UHV model and a realistic, operando model. The traffic light key depicts the quality of each method with respect to catalyst model complexity (Cat), reaction coordinate accuracy (RCN) and reaction network complexity (RxN). Adapted with permission from Piccini et al., Journal of Physical Chemistry C, 2015, 119, 6128–6137, Copyright 2015, American Chemical Society, Vilhelmsen et al., Journal of Chemical Physics, 2014, 141, 044711, Copyright 2014, American Institute of Physics, Chen et al., Journal of Catalysis, 2018, 358, 179–186, Copyright 2018, Elsevier, Pavan et al., Journal of Chemical Physics, 2015, 143, 184304, Copyright 2015, American Institute of Physics, Heard et al., ACS Catalysis, 2016, 6, 3277–3286, Copyright 2016, American Chemical Society. 

A huge gap between the 0 K/UHV models on one side and operando models on the other side cannot be overcome by a single computational method that would explicitly account for the whole complexity of the underlying phenomena. A multiscale modeling approach can be followed to construct a composite methodology that includes all the crucial physical phenomena. In our opinion, the following five methods appear to be the most important for bridging this gap: (i) global optimization techniques, (ii) ab initio constrained thermodynamics, (iii) biased MD simulations, (iv) microkinetic models of reaction networks. The fifth class of methods is a conceptually different approach that does not necessarily imply the explicit account of the complex physics of a catalyst system and yet holds great promise as a tool to enable catalysis by design. This class is the broad family of machine learning methods. The latest development of each of these five techniques is addressed individually in the following five sections of this review.

A transition from the 0 K/UHV to operando model is schematically depicted in Fig. 1. The 0 K/UHV model corresponds to the situation at the lower left corner, corresponding to vanishing partial pressures of reaction components (expressed in terms of chemical potentials) and low temperature. The operando model corresponds to the upper right corner. Going from bottom to top of the figure the reaction environment (in terms of chemical potentials and temperature) becomes more realistic. Any model improvement results in the increased complexity of the problem (from left to right), mostly in the number of configurations that are considered. Basics of the 0 K/UHV model include the following approximations: (i) idealized catalyst surface (denoted as Cat in Fig. 1), (ii) idealized reaction coordinates with minimum number of reactants on the PES at 0 K (reaction coordinate environment – RCE) and (iii) elementary reaction steps are considered (reaction network – RxN). All these approximations must be lifted to move forward to an operando model.

Methods presented in Fig. 1 from left to right start with Hessian-based thermal corrections, followed by a global optimization approach, ab initio constrained thermodynamics and biased MD; microkinetic modeling and machine learning techniques are taken off this order since they can be used at any level of the 0 K/UHV ? operando transition. The order presented in Fig. 1 is motivated by the fact that if all extensions are applied for a particular system, they would be applied in the order presented in the figure, with the exception of Hessian-based thermal corrections. Hessian-based thermal corrections allow a proper transition from potential- to free-energy surfaces while the complexity of the system remains unchanged; they can be used either to improve the 0 K/UHV model or in combination with global optimization or ab initio constrained dynamics (improving the quality of partition functions). It is important to note that it is common to apply just one or two extensions (or even three in some cases) and by no means does it have to be the first methods from left to right. For example, it is rather common to combine Hessian-based thermal corrections directly with microkinetics. It depends on the particular problem under investigation as to which of the extensions is crucial. Global optimization techniques mostly help in finding relevant configurations when these are difficult or impossible to obtain from relevant experimental data. Ab initio thermodynamics is critically important for the investigation of catalyst surfaces that are changed in the reaction environment. Biased molecular dynamics (MD) techniques become essential for the localization of transition states in complex environments when these are strongly affected by the surrounding molecules. Microkinetic modeling of the reaction network is essential for situations in which a large number of reaction intermediates exist. Last but not least, machine learning techniques are emerging as a useful tool in rationalization of the system descriptors and finding important correlations in large data sets.

Each of the methods presented in Fig. 1 is designed to overcome part of the gap between 0 K/UHV and operando conditions. Each method is discussed in the following sections and each of the methods has been reviewed separately in recent years in a comprehensive way. It is the purpose of this review to discuss them on an equal footing with respect to the gap between 0 K/UHV and operando. It should be stressed that the simultaneous application of all these extensions is computationally prohibitive in a general sense. But it should be noted that it is often not necessary to apply all these model extensions for a particular catalytic system; instead it is important to identify which of the extensions is critical for the problem investigated.

Free full text source: https://pubs.rsc.org/en/content/articlehtml/2018/cs/c8cs00398j
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