C–H bond activation in light alkanes: a theoretical perspective

Abstract

Alkanes are the major constituents of natural gas and crude oil, the feedstocks for the chemical industry. The efficient and selective activation of C–H bonds can convert abundant and low-cost hydrocarbon feedstocks into value-added products. Due to the increasing global demand for light alkenes and their corresponding polymers as well as synthesis gas and hydrogen production, C–H bond activation of light alkanes has attracted widespread attention. A theoretical understanding of C–H bond activation in light hydrocarbons via density functional theory (DFT) and microkinetic modeling provides a feasible approach to gain insight into the process and guidelines for designing more efficient catalysts to promote light alkane transformation. This review describes the recent progress in computational catalysis that has addressed the C–H bond activation of light alkanes. We start with direct and oxidative C–H bond activation of methane, with emphasis placed on kinetic and mechanistic insights obtained from DFT assisted microkinetic analysis into steam and dry reforming, and the partial oxidation dependence on metal/oxide surfaces and nanoparticle size. Direct and oxidative activation of the C–H bond of ethane and propane on various metal and oxide surfaces are subsequently reviewed, including the elucidation of active sites, intriguing mechanisms, microkinetic modeling, and electronic features of the ethane and propane conversion processes with a focus on suppressing the side reaction and coke formation. The main target of this review is to give fundamental insight into C–H bond activation of light alkanes, which can provide useful guidance for the optimization of catalysts in future research.

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Yalan Wang

Yalan Wang obtained her bachelor's degree (2011) and master's degree (2014) from East China University of Science and Technology (ECUST). She received her PhD from the Norwegian University of Science and Technology (NTNU) in 2019, where she is currently working as a postdoctoral fellow. Her main research interests include methane activation, CO hydrogenation, electrochemical CO2 reduction, and redox reaction cycles. She has strong expertise in density functional theory calculations and descriptor-based microkinetic modeling for rational design of catalysts in heterogenous catalysis.

Ping Hu

Ping Hu is currently a PhD student in the School of Chemical Engineering at East China University of Science and Technology (ECUST). She studied Chemical Engineering at Shanghai Normal University (SHNU) and graduated with an MSc in 2015. Her current research interest is to combine density functional theory calculations and microkinetic analysis to examine the kinetics of propane dehydrogenation and search for better catalysts.

Jia Yang

Jia Yang (born in 1983) is associate professor in the Department of Chemical Engineering, Norwegian University of Science and Technology (NTNU). She received her PhD in Heterogeneous Catalysts from NTNU in 2011. She carried out postdoctoral research in the same field and then worked as a research scientist in SINTEF for three years before joining the Department in 2016. Her main research interests include Fischer–Tropsch synthesis, biomass conversion to fuels and chemicals, electrochemical CO2 reduction, fuel cell catalysts, and photocatalytic H2 generation. She has strong expertise in mechanistic investigation with Steady-State Isotopic Transient Kinetic Analysis (SSITKA) and isotopically labelled gases.

Yi-An Zhu

Yi-An Zhu received his PhD from East China University of Science and Technology (ECUST) in 2007, where he is now Professor of Chemical Engineering. His research interest is focused on the kinetics and mechanisms of heterogeneous catalytic reactions over solid-state catalysts. His current research projects include descriptor-based microkinetic analysis combined with results from density functional theory calculations for rational catalyst design and molecular simulations based on classical and reactive force fields for determination of structures of complex solids.

De Chen

De Chen (born in 1962) has been a Full Professor in catalysis in the Department of Chemical Engineering, Norwegian University of Science and Technology (NTNU), since 2001. He holds a PhD in industrial catalysis at NTNU (1998). His scientific activity is mainly devoted to mechanistic and kinetic studies of heterogenous catalysis, multiscale modeling of catalytic processes for the conversion of various resources such as natural gas, biomass and plastic waste, and CO2 capture technologies. He developed new research methods to study dynamic redox reaction cycles in industrial catalytic processes by combining first-principles calculation and operando kinetic study.

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1. Introduction

Alkanes or paraffins (C_nH_2n+2) are acyclic saturated hydrocarbons and are the major constituents of natural gas and crude oil. Alkanes have the simplest structure among organic molecules, where each carbon atom is sp³-hybridized with four sigma bonds (either C–C or C–H), and each hydrogen atom joins to one of the carbon atoms (in a C–H bond). The efficient and selective activation of C–H bonds can directly convert abundant and low-cost hydrocarbon feedstocks into value-added products as commodity, intermediate, and fine chemicals, which have the potential to have a substantial economic impact. However, there is a formidable challenge for the sufficient activation of C–H bonds in alkanes into more sophisticated value-added architectures due to the thermodynamically strong C–H bonds and thus a high energy barrier to break the bonds. The bond strength of C–H bonds depends slightly on the structure, and the bond dissociation energies (BDEs) of the primary (1°), secondary (2°), and tertiary (3°) C sp³–H bonds of alkanes fall in the range of 4.16 to 4.38 eV, with the 1° C–H bonds being stronger than the 2° and 3° bonds.¹ Methane molecules, as the main constituent of natural gas, have four primary C–H bonds which are highly stable and thus are the most difficult to activate. Moreover, the C–H bonds of alkanes functionalized products (such as alkenes and oxygenates) are not as stable as alkanes, which presents a challenge for gaining a high selectivity in alkane conversions.

Catalysts play a privileged role in selective C–H bond activation and controlling the reaction pathways to improve the selectivity and lower the carbon footprint. Many catalytic routes have been developed to convert alkanes to high value-added chemicals, which form the technological foundation of the modern chemical industry and meet the demand of certain substances in a transition from petroleum to natural gas and shale gas and liquids. The global demand for light alkenes has increased due to the increasing demand of their corresponding polymers. The light olefin market across the globe is expected to reach USD 475.8 million at a compound annual growth rate of 5.85% by the end of 2027. Besides, with a shift of the feedstock from naphtha to natural gas feedstocks, the supply of certain chemicals such as propylene, butadiene, and BTX has become constrained. Their shortage in the market is the main driving force for the renewed interest in producing them from alkanes, as low-cost feedstocks for chemical production. Synthesis gas and hydrogen production via steam reforming, dry reforming, and partial oxidation from methane, and dehydrogenation reactions have been often used by industry for the on-purpose production of hydrogen and light alkenes like ethylene, propylene, and butylene. Catalytic dehydrogenation of light alkanes is becoming increasingly important with the exploitation of shale gas, which provides a significant amount of ethane and propane feedstocks. The dehydrogenation is one of the major routes to fill the lower olefin gap in terms of future production and demands.

Catalytic dehydrogenation reaction is an endothermic reaction, and high equilibrium conversion is favored by high temperature and low alkane pressure.² However, hydrogenolysis also occurs at the high temperature, forming methane and other lower carbon number species leading to low olefin selectivity. Both transition metals (TMs) and metal oxides are active for the dehydrogenation of light alkanes. Oxidative dehydrogenation (ODH) is an alternative process to break down the thermodynamic limitation. The main challenge is to control the consecutive oxidation of alkanes/alkenes to carbon oxides due to the much higher reactivity of products than the reactants. The critical issue in the development of catalysts is, therefore, how to selectively activate the C–H bonds of alkane molecules.³

During the last few decades, great progress has been made in developing catalysts and catalytic processes of alkane conversion to value-added chemicals. Amounts of reviews have been reported for homogeneous catalysis regarding C–H bond activation of alkanes on organometallic and/or inorganic complexes,^4–10 which are not covered in this review. In contrast, we focus on heterogeneous catalysis. So far, many comprehensive reviews on methane conversion^11–13 and ethane and propane conversion on metal,^2,14 oxide,^2,3,15–18 metal-free,^19,20 and bifunctional catalysts²¹ have been reported towards heterogeneous systems, covered mainly catalysts,^{2,12,17,21,22} kinetics,^3,15 and processes.^2,17 These reviews deal with progress in the experimental studies of chemistry and catalysis, focusing on key challenges related to light alkane activation in terms of activity, selectivity, and carbon formation. Despite their successful applications at an industrial scale, several central questions remain unanswered, such as active sites effectively activating C–H bonds, the detailed reaction mechanism of catalytic cycles, rate-determining steps (RDSs), and factors governing the selectivity and carbon formation in activation and conversion processes of methane and light alkanes.

A better understanding of the factors governing the fundamental aspects mentioned above is important to design more efficient catalyst systems to promote selective C–H activation. The design of new effective catalysts and/or improvement of industrial catalysts rely on a better understanding of the surface reactions at a molecular level. Great efforts have been devoted to assessing the structure–property–performance relationship. However, it is still challenging because the experimental approach can severely restrict the range of catalyst structures and compositions to be examined. An effective strategy for developing useful catalysts should involve simultaneous consideration of all structure–function relationships that are related to stability, activity, and selectivity in the design of catalyst and reaction systems.²³

Theoretical heterogeneous catalysis and surface science have witnessed significant development toward a molecular-level understanding of the working catalysts. Electronic structure calculations based primarily on ab initio density functional theory (DFT) calculations have been widely applied in heterogeneous catalysis.²⁴ Over the past decade, DFT combined with microkinetic modeling is widely used to provide vital fundamental data regarding the properties of the active sites, mechanisms of surface reactions, RDSs, trends in reactivity, etc.^25–28 The development and application of DFT in heterogeneous catalysis^29,30 as well as microkinetic modeling for catalyst design^31,32 have been reported in several excellent reviews. Generally, microkinetic models are constructed based on DFT estimated energetics of elementary steps involved in reaction mechanisms for targeted reactions. Particularly, in recent years, the rapidly developed scaling relationships^27,33–36 make the combination of microkinetic modeling with DFT more convenient due to much addressed computational complexity. That is, based on the DFT calculated energetics, the scaling relationships are obtained and used to predict the energetics of other adsorbates or on other catalyst surfaces, which are further employed as input parameters of the microkinetic model. DFT calculations have shown that the energetics of crucial reaction intermediates are linked by linear scaling relationships that have been applied for rationalizing trends in C–H bond activation of light alkanes across different catalyst surfaces. Gong and coworkers²⁹ reviewed the mechanistic insights into heterogeneous catalytic dehydrogenation of light alkanes obtained from DFT calculations in 2015. Owing to the rapid development of scaling relationship-based microkinetic modeling, the molecular level understanding of surface catalyzed reactions involved in C–H activation of light alkanes has been dramatically improved across metal, alloy, oxide, and metal–oxide hybrid catalysts. A comprehensive review of the theoretical heterogeneous catalysis of C–H activation of methane, ethane, and propane on various catalysts is highly desired to provide fundamental insights into industrial catalytic processes and guidelines for the rational design of new catalysts and/or improvement of industrial catalysts.

The purpose of this review is to describe the recent progress in computational catalysis that has addressed the C–H bond activation of light alkanes, such as methane, ethane, and propane by heterogeneous transition metal, oxide, and metal/oxide catalysts, with emphasis on activity, selectivity and coke formation in light alkane conversion. This review describes the detailed understanding of kinetic and mechanistic insights into catalytic dehydrogenation of light alkanes at atomic and molecular levels obtained from DFT calculations and microkinetic modeling across various catalyst surfaces. It unravels the basic electronic features of the C–H cleavage process to the targeted products. The results of the mechanistic studies depend on temperature, pressure, and reactant composition. Finally, the design of new catalysts and improvement of the catalysts are reviewed and proposed based on the fundamental understanding and theory-driven catalyst design.

The first part of the review addresses direct and oxidative C–H bond activation of methane via σ–d interaction on metals and oxides. The mechanistic insights obtained from DFT assisted microkinetic analysis into steam and dry reforming, and the partial oxidation dependence on metal/oxide surfaces and nanoparticle (NP) size are summarized and analyzed. The theory-driven catalyst design is reviewed and discussed. The second and third parts describe direct and oxidative activation of the C–H bonds of ethane and propane towards light alkene formation on various metal and oxide surfaces. The emphasis is on the elucidation of active sites, intriguing mechanisms, microkinetic modeling, and electronic features of the ethane and propane conversion processes with a focus on suppressing the side reaction and coke formation.

2. C–H bond activation in methane

Methane is the simplest hydrocarbon, which is the predominant constituent (approximately 70–90%) of natural gas.³⁷ Recent advances in hydraulic fracturing have led to the effective extraction of natural gas from shale rock and triggered the so-called ‘shale gas revolution’.^29,38,39 This increased supply of natural gas makes methane very attractive as both an energy source and feedstock to produce fuels and chemicals. Apart from natural gas reserves, methane is also a central component of biogas produced by the anaerobic digestion of organic materials.^38,40,41 Moreover, methane can be found in crystalline hydrates existing in permafrost areas as well as the continental slopes of many oceans.³⁸ In view of its abundant reserves and resources, and with the depletion of oil reserves, methane activation will play a key role in ensuring the supply of energy, fuels, and chemicals in the future.

Methane activation can be carried out through both direct and indirect conversion routes. To date, the industrial direct conversion routes of methane into fuels and chemicals have been limited. The challenges associated with these routes arise from the phenomenon that methane is very stable and requires very aggressive operating conditions to activate its C–H bonds, which facilitates undesirable reactions, thus resulting in a loss in activity, selectivity, and yields of desired products.³⁹ Moreover, the products are more reactive than methane, which necessitates the selective separation of the products and brings more challenges in the chemical process.⁴² Despite the great challenges, significant progress has been made in the direct conversion of methane to chemicals, especially in the production of hydrocarbons, such as olefins and aromatics. Direct conversion to olefins can be realized via oxidative coupling of methane (OCM),^43–45 and to aromatics can be realized via methane dehydroaromatization (MDA).⁴⁶ Since recently Schwach et al.¹² published an excellent review on direct conversion of methane into value-added chemicals, we will not include this in our review. They gave the fundamentals of C–H activation, analyzed the reaction pathways regarding selective routes of OCM, MDA, and MTOAH (methane conversion to olefins, aromatics, and hydrogen),⁴⁷ and provided insights into the reaction mechanisms. Readers who are specifically interested in direct conversion of methane are directed to this review article.

The indirect conversion routes of methane into more valuable chemicals via synthesis gas are economically feasible and currently industrially applied. The production of synthesis gas from methane can be realized through three reactions,^42,48,49 namely steam reforming (SRM, eqn (1)), dry reforming (DRM, eqn (2)), and partial oxidation (POM, eqn (3)), which are summarized as follows:

SRM: CH₄ + H₂O → CO + 3H₂ ΔH_298 K = 2.14 eV (1)

DRM: CH₄ + CO₂ → 2CO + 2H₂ ΔH_298 K = 2.56 eV (2)

POM: CH₄ + 0.5O₂ → CO + 2H₂ ΔH_298 K = −0.37 eV (3)

The differences between the three processes are based on the oxidant used, the energetics and kinetics of the reaction, and the synthesis gas produced with different H₂/CO ratios.^40,50 Among the three indirect processes, SRM is the conventional technology for methane conversion due to the highest hydrogen yield, from which approximately 75% of hydrogen is produced.⁵⁰ DRM and POM are not industrially mature processes. However, the considerable environmental benefit of DRM^49,51 and the thermodynamic advantage of POM³⁸ make them have great potential in the future. In view of the importance of these indirect processes in methane conversion, the development of effective catalysts to achieve high activity, selectivity, and stability has a great significance for further methane utilization.

All three processes are found to be active over noble metal catalysts such as Rh, Ru, Ir, Pt, and Pd, and over non-noble metal catalysts like Ni and Co. Moreover, the oxide is one of the crucial types of catalysts to promote methane conversion. So far, the catalyst performance, support effect, promoter effect, deactivation, and kinetics and mechanisms of SRM,^{38,39,52–58} DRM,^{40,49–51,59–65} and POM^48,66–71 over both noble and non-noble metal catalysts as well as oxide catalysts^{16,18,72–74} have been summarized in many reviews. However, these reviews are mostly introduced from experimental points of view, and a systematic understanding of these reactions from a theoretical perspective is still missing. Herein, we mainly review these reactions based on DFT calculations and microkinetic modeling, with the kinetic studies briefly introduced. C–H bond activation in methane is first elucidated.

2.1 Activation of C–H bonds in methane on metal and oxide surfaces

A methane molecule has four H atoms bonded to a single C atom in a tetrahedral orientation. The CH₄ molecule is geometrically highly symmetrical and nonpolar, and it is neither an electron donor nor acceptor. The unique structural and electronic features of the methane molecule make it weakly interact with catalytic surfaces. A high bond dissociation energy of the C–H bond makes methane a relatively unreactive starting material. The first C–H bond activation is the critical step in methane conversion, which has been reported to be the RDS for methane decomposition, oxidation, and steam and dry reforming on different catalysts (Ni, Pd, Ru, and Rh), according to the kinetic studies by Wei and Iglesia^75–80 and other researchers.^81–90 Therefore, understanding the mechanism for C–H bond activation is essential for further comprehending SRM, DRM, and POM reactions.

2.1.1 C–H bond activation on metal surfaces. On metal catalysts, the first C–H bond activation might take place via three pathways, namely direct CH₄ dissociation, O*-assisted CH₄ dissociation, and OH*-assisted CH₄ dissociation. Hibbitts et al.⁹¹ carried out DFT calculations to systematically explore the activation of the C–H bond in methane over group 8–10 (Ru, Rh, Pt, Pd, Os, and Ir) and group 11 (Cu, Ag, and Au) TMs. The three methane activation pathways, namely the direct C–H activation, and O* and OH*-assisted activation, were considered, where the transition-state structures on the Pd(111) surface are shown in Fig. 1(a).

Fig. 1 (a) Transition-state structures for the activation of the C–H bond in CH₄ over (A) metal–metal site pairs (direct), (B) metal–O* site pairs (O*-assisted), and (C) metal–OH* (OH*-assisted) on the Pd(111) surface. Reported bond lengths are given in pm. (b) Difference between the O*-assisted and direct CH₄ activation barriers (●) and the difference between OH*-assisted and direct CH₄ activation (▲) compared to the binding energy of O*. Activation barriers and reaction energies for the CH₄ activation via (c) direct CH₄ activation (■), (d) O*-assisted CH₄ activation (●), and (e) OH*-assisted CH₄ activation (▲). Points are colored by the trends in O* binding energy, where red refers to the most strongly bound O* and blue refers to the most weakly bound O* (BE^rad, eV). The data of Ni, Co, and Fe in (c), (d), and (e) were obtained from our previous work.^36,87,89,92 The others were reported by Hibbitts et al.⁹¹ Adapted from ref. 91 with permission from Elsevier, copyright 2016.

Fig. 1(b) gives the activation barrier differences between the three routes as a function of O* binding energy. The respective activation barriers as a function of reaction energy for the three routes are shown as Fig. 1(c–e), respectively. The data of Ru, Rh, Pd, Os, Ir, Pt, Cu, Ag, and Au were reported by Hibbitts et al.,⁹¹ and those of Ni, Co, and Fe were obtained from our previous work.^36,87,89,92 For group 8–10 metals (Ru, Rh, Pd, Os, and Ir), the DFT calculated activation barriers of O*-assisted CH₄ dissociation were much higher than those of OH*-assisted CH₄ dissociation, both higher than those of direct CH₄ dissociation. Hibbitts et al.⁹¹ also compared the activation barriers for CH₃* dissociation of the three pathways, where the direct route exhibited the lowest activation barrier for the above group 8–10 metals.

Similarly, Niu et al.⁹² also found that the first C–H bond activation via direct CH₄ dissociation (activation energy E_a: 1.21 eV) was more energetically favorable than O-assisted (E_a: 1.66 eV) and OH-assisted CH₄ dissociation (E_a: 3.39 eV) on a Ni(111) surface (Fig. 1c–e). Moreover, the C–H bond activation of CH₃* and CH₂* via direct dissociation was energetically preferred over the other two pathways. The observation is in good agreement with those reported by Zhu et al.⁹³ on a Ni(111) surface, by Fan et al.⁹⁴ on Ni(111), Ni(211), and Ni(100) surfaces, by Wang et al.^87,89 on Ni, Rh, Pd, and Pt(111), (211), and (100) surfaces, by Jørgensen et al.⁸⁶ on Pd(111) and Pd(100) surfaces, by Yoo et al.⁹⁵ on a Pd(111) surface, and by Wang et al.⁸⁸ on a Pt(111) surface. Like on Ni, the activation barriers of direct CH₄ dissociation on Co and Fe were also much lower than those of the other two pathways (Fig. 1c–e), and extremely high activation barriers of OH*-assisted CH₄ dissociation (3–4 eV) were observed (Fig. 1e).^36,89 It is worth mentioning that even though the direct CH₄ dissociation was also calculated as the energetically most favorable pathway on Co catalysts, Tu et al.⁹⁶ suggested that the O*-assisted route dominated CH₄ activation on Co and Ni–Co clusters because of their high oxophilicities, resulting in their surfaces covered with oxygen adatoms.

For group 11 metals, the O*- and OH*-assisted routes were energetically preferred over the direct CH₄ dissociation route for both CH₄ and CH₃* dissociation. However, the activation energies of O*- and OH*-assisted C–H activation are still higher than that of the direct dissociation of methane on other groups of metals (8–10). The promotional effects of O* and OH* in activating C–H bonds on the group 11 metals were related to the M–O/M–OH binding energy and their basicity when binding with metal. The weakly bound O* and OH* often participate and assist in C–H bond activation. As such, enhanced promotional effects were observed on the group 11 metal surfaces by O*/OH* over direct metal activation due to their weak M–O/M–OH bonding. Moreover, the O* and OH* are more negatively charged when binding with the group 11 metals, thus increasing their basicity and ability to promote C–H activation. In contrast, the basicity of O* and OH* over the group 8–10 metal surfaces is not strong enough to aid C–H bond activation. As a result, the presence of O* or OH* will reduce the overall reaction rate since they will block active surface sites.

The Pt(111) surface is an exception, where the activation barrier for OH*-assisted CH₄ dissociation was lower than those for the direct dissociation and the O*-assisted route.^91,92,97 On the Pt(211) surface, the direct CH₄ dissociation was the energetically most favorable pathway.⁹⁷ However, the preferred reaction pathways need to be determined based on the whole catalytic cycle. Chen and Vlachos⁹⁷ proposed that the reactions involving OH*-assisted C–H bond activation and addition were most probably the minor reaction pathways, because the OH coverage was low in methane reforming and oxidation and the direct CH₄ dissociation was suggested as a dominant pathway on both the Pt(211) and Pt(111) surfaces. Similarly, the recent DFT study of Niu et al.⁹² indicated that the OH*-assisted CH₄ activation was considered as an attractive alternative route for SRM on a Pt(111) surface. However, taking the coverage effect of OH* into account could reasonably lead to the direct CH₄ dissociation route being dominant.

C–H bond activation via direct CH₄ dissociation dominates methane activation on group 8–10 metals, which are active catalysts for SRM, DRM, and POM reactions. Gong and coworkers²⁹ gave a detailed review of the theoretical study of methane dehydrogenation over various transition-metal surfaces, including fcc(111), hcp(0001), fcc(100), and fcc(211). The difference in activation energy between different elementary steps was found to be related to electronic and geometric effects, and the difference between other metals could be associated with the metal d-band center. Therefore, we only give a brief overview here. For instance, the geometries of the transition states (TSs) for CH₄ dehydrogenation on close-packed Ni(111) and stepped Ni(211) surfaces are shown in Fig. 2(a and b), with the corresponding activation energies listed.⁹⁴ Among the four elementary steps, the step CH → C + H showed the highest activation barrier for both Ni(111) and Ni(211) surfaces, consistent with that summarized by Gong and coworkers.²⁹ The high barrier of CH → C + H results mainly from the stability of CH* (electronic effect) coupled with the perpendicular nature of CH* (geometrical effect). As shown in Fig. 2(c), CH* is perpendicular to the Ni(211) surface, where an energy penalty is required to bend the structure parallel to the metal surface in the transition state, and therefore geometrically not favorable for further dehydrogenation. The Ni(211) surface exhibits lower activation energies than the Ni(111) surface due to the existence of under-coordinated atoms on the stepped (211) surface, leading to higher binding strengths of surface intermediates and more stabilization of transition states and final states. Moreover, the geometric effect also influences the activation barriers between stepped and terrace surfaces. The partial charge densities projected onto the bonding states in Fig. 2(c and d) show that the CH species forms bonds with 4 Ni atoms, while 5-coordinated bonding is achieved between the C atom and Ni(211), demonstrating the strong binding of C on the stepped Ni(211) surface.⁹⁸

Fig. 2 Geometries of the transition states (TS) for CH₄ dehydrogenation on (a) Ni(111) and (b) Ni(211) surfaces. The values below the geometries are the activation energies of the corresponding elementary steps reported by Zhu et al.⁹³ and Fan et al.⁹⁴ Reproduced from ref. 93 with permission from Elsevier, copyright 2009. Reproduced from ref. 94 with permission from the American Chemical Society, copyright 2015. The densities of states (DOS) projected onto the sp states of CH (c) and C (d) and the d-band of stepped Ni(211) surfaces. “ads” and “clean” denote the surface with and without an adsorbate, respectively. The left inset figures show the side and bird's eye views of the partial charge density projected onto bonding states within an energy range bound by a dashed ellipse. The right inset figures show the geometries of CH and C on Ni(211) surfaces.⁹⁸ Adapted from ref. 98 with permission from Springer Nature, copyright 2017.

The activation energy of the C–H activation depends on the metal surfaces (Fig. 1) and the metal dependence follows the Brønsted–Evans–Polanyi (BEP) relationship that the activation energy of the elementary step scales linearly with reaction heat. Nørskov and co-workers found that the C binding energy can be used as a descriptor for the linear scaling relations (LSRs) of CH_x (x = 1, 2, 3) adsorption energies and transition-state energies with respect to their gas-phase energies over various transition-metal surfaces.^33,99,100 The linear relation could also be established between the activation energies and C adsorption energies, as shown in Fig. 3(a), based on our data.³⁶ CH* dissociation shows the highest activation energy among the dehydrogenation steps, with the energy barriers for CH₄, CH₃, and CH₂ dissociation gradually reduced on the close-packed surfaces. The C–metal binding energy can be simply characterized by the metal d-band center, as shown in Fig. 3(b). This underlines the theory that the binding energy of an adsorbate to a metal surface is strongly dependent on the electronic structure of the surface itself. When the C–H σ bond interacts with the metal d bond, the metal d-band hybridizes with the C–H bonding (σ) orbital to form bonding (d–σ) and antibonding (d–σ)* states. The metal–adsorbate interaction depends on the extent of filling of the (d–σ)* or the location of the d-band center. The energetically higher d-band center results in a higher C binding energy. The higher C binding energy leads to more negative CH_x adsorption energy and its transition-state energy and a lower CH_x dissociation barrier.

Fig. 3 (a) Activation energies of CH₄ dehydrogenation steps as a function of carbon adsorption energies on an fcc(111) surface, with the data obtained from our previous work.³⁶ (b) Relationship between C binding energy and the metal d-band center.²⁹ Published by the Royal Society of Chemistry, copyright 2015.

2.1.2 C–H bond activation on oxide surfaces. Apart from metal surfaces, metal oxides are one of the important classes of catalysts for C–H bond activation in oxidative methane C–C coupling,^13,101 low-temperature oxidation,¹² solid fuel cells,¹⁰² and chemical looping reforming. A physically adsorbed methane molecule on an oxide surface has a binding energy of only about 0.10 to 0.15 eV.¹⁶ Methane activation could occur via either the radical-like transition state (Fig. 4a) or the surface-stabilized transition state (Fig. 4b) on metal oxides.^103–105 The major difference between the two transition states is the distance between C (in CH₄) and the interacted surface metal atom, which illustrates the distinct interaction between CH₄ and the metal surface.¹⁰⁴ Many of the most promising catalysts stimulate alkane activation via radical-like TS, due to the energetically unfavorable interaction of the CH₃ with the surface. However, regardless of the transition states, the nucleophilic surface oxygen attacks the electrophilic H in the C–H bond to form an OH bond in C–H bond activation. The hydrogen affinity (E_H) has been shown to be a suitable descriptor of reactivity for radical-like hydrocarbon activation. Latimer et al.^103,106 presented a universal scaling relation to predict C–H activation barriers on heterogeneous catalysts, where a transition-state (TS) energy can be correlated with a single universal descriptor for various catalysts that proceed via a radical-like TS, as shown in Fig. 4(c). The TS energy is linearly correlated with H binding energy. In addition, all materials they explored that occurred through the surface-stabilized pathway seem to follow the TS scaling relationship which is linearly related to the final state energy, as shown in Fig. 4(d). The authors demonstrated that these scaling relations were valid for several reducible and irreducible oxides, sulfides, and promoted metals.

Fig. 4 Two activation mechanisms on rutile-type metal oxide (110) surfaces are exhibited: (a) the radical-like transition state (TS) and (b) the surface-stabilized transition state (TS).¹⁰⁴ Reproduced from ref. 104 with permission from the American Chemical Society, copyright 2019. Universal scaling relations for (c) the radical pathway (0.75E_H + 1.09) and (d) the surface-stabilized pathway (0.67E_FS + 1.04).¹⁰³ Reproduced from ref. 103 with permission from the PCCP Owner Societies, copyright 2017.

More interestingly, Latimer et al.^103,106 proposed a universal scaling relationship for C–H bond activation (E_TS) across reactants and catalysts that depends only on the hydrogen affinity of the catalyst (E_H) and the C–H bond energy of the reactant (E_C–H):

E_TS = 0.75E_H − 1.26E_C–H − 4.93 (4)

The relationship predicts well the C–H bond activation energies compared to the DFT-calculated ones across a wide variety of reactants and catalysts. The C–H activation energy of methane is the highest due to the more negative C–H bond energy.

Aljama et al. studied the role of alkaline metal oxides (MgO, CaO, and SrO)¹⁰⁷ and alkaline earth metal oxides (AEMOs) with an alkaline earth metal (AEM) or a TM as a dopant¹⁰⁸ in breaking the C–H bond in methane. The dopant can change the TS structure. Microkinetic modeling and analysis were performed using the binding energies of H and CH₃ as two descriptors, and a volcano plot was obtained. Even for the surface-stabilized TS on pure alkaline metal oxides, the hydrogen binding energy was found to be a more appropriate descriptor. This suggested that at weak H binding strength, the reaction was limited by C–H bond activation. However, at strong H binding strength, the reaction was limited by poisoning of the active site.

Perovskite oxides with the formula ABO₃ have gained increasing attention in applications in energy-related processes, such as solid fuel cells and chemical looping reforming of methane due to the massive family of combinations of A and B, well-defined structures, and excellent tunability of properties. Fung et al.¹⁰⁹ investigated a broad set of perovskite compositions via descriptors of O reactivity such as the H adsorption energy, vacancy formation energy, and first C–H activation energy of methane using DFT calculations. The cubic perovskite (001) surface has both ‘A’ and ‘B’ terminations, as shown in Fig. 5(a). On each model termination, one possible lattice O site exists for catalysis. On the ‘A’ termination surface, the O is fourfold-coordinated to the surface A cation and onefold-coordinated to the subsurface B cation. On the ‘B’ termination surface, the O is twofold-coordinated to both the surface B cation and subsurface A cation. The reactive lattice O activates the methane molecule via a homolytic C–H bond cleavage, as illustrated in the upper part of Fig. 5(a). The typical geometries of C–H activation transition states over the perovskite(001) surface A and B terminations can be found in the lower part of Fig. 5(a). A strong linear relationship between the H adsorption energy or hydrogen affinity and the O vacancy formation energy was observed, as shown in Fig. 5(b). Both parameters can be used as descriptors for C–H bond activation of methane, as shown in Fig. 5(c) and (d), in good agreement with the universal scaling relationship.^103,106 The stronger the hydrogen adsorption on the lattice O or the easier the O vacancy formation at the lattice-O site, the lower the C–H activation barrier of methane. The oxygen vacancy formation energy has been widely used as a descriptor of the C–H activation energy of methane on CeO₂(111) doped with TMs, TbO_x(111), ZnO, doped TiO₂, and doped MgO;¹⁰¹ on pure CeO₂(111), (100) and (110) surfaces and surfaces with Pd or Zr substituted in Ce lattice positions;¹¹⁰ on lanthanum oxides doped with Fe, Mg, Zn, Cu, Nb, Ti, Zr, and Ta; and on undoped catalysts.¹¹¹ Oxides doped with low-valence atoms decreased the oxygen vacancy formation energy, which enhanced C–H bond activation. The lowered methane activation barrier was also observed for La₂O₃ catalyst doped with Cu, Zn, or Mg¹¹² and for CeO₂ doped with Pt.¹¹³ It can be generally proposed that oxides doped with low-valence metals are better methane activation catalysts than the undoped oxides.

Fig. 5 (a) Top: CH₄ activation on the perovskite (001) A and B terminations. Bottom: The homolytic C–H pathway and the typical transition states (A, green; B, blue; O, red; C, grey; H, white). (b) Correlation between the hydrogen adsorption and vacancy formation energy of the lattice oxygen. Correlations between the homolytic C–H activation energy of CH₄ and (c) hydrogen adsorption energy and (d) oxygen vacancy formation energy. The black dotted line represents the linear best fit.¹⁰⁹ Reproduced from ref. 109 with permission from the Royal Society of Chemistry, copyright 2018.

2.2 Methane conversion on metal surfaces

Great efforts have been devoted to the first-principles study of the C–H bond-breaking step of methane in a multistep process,^{91,98,103,106,114–120} because the C–H bond activation is often the RDS of the methane conversion. However, studying only the C–H activation step is insufficient to gain insight into the reaction mechanism, carbon formation, and RDSs, which can change with catalysts and operating conditions. Calculating the energy profile for the entire catalytic cycle is a demanding task, but it provides the activation barriers for the elementary steps. Microkinetic modeling and analysis of the whole cycle allow us to assess the preferential reaction pathways, RDSs, and dominating surface intermediates. Besides, the scaling relationships related to the binding energies of a wide variety of catalytic intermediates across a range of catalyst surfaces enable us to conduct theory-driven catalyst design. In the next sections, we will review the progress in the first-principles study and descriptor-based microkinetic modeling and analysis of the entire catalytic cycles in steam and dry methane reforming and partial oxidation of methane across a range of catalyst surfaces and catalyst nanoparticles.

2.2.1 Steam reforming of methane.
Metal dependence of activity. Steam reforming of methane is one of the main processes for hydrogen production.¹²¹ To date, many efforts have been devoted to investigating the SRM reaction from both experimental^{75,76,78,122–129} and theoretical^{87,89,97,126–128,130–135} points of view. The reaction is active over various transition-metal catalysts. For these metals, most studies demonstrated an activity trend of Ru, Rh > Ni, Ir > Pt, Pd > Co, Fe with a temperature range of 673–1173 K and atmospheric pressure.^{87,123,124,127,136}Fig. 6(a) gives the microkinetic modeling results of SRM, reported by Jones et al.,¹²⁷ and plots log₁₀(TOF) as a function of C and O binding energies as two descriptors. The microkinetic model was built based on the energetics estimated by the linear scaling relationships and BEP relationships over the fcc(211) and bcc(210) surfaces. The descriptor-based microkinetic modeling provided a volcano curve as a function of C and O binding energies as descriptors. Ru, Rh and Ni(211) were found to be active for SRM and the activity is near the predicted optimum activity. It can be explored to design new catalysts with high performance.

Fig. 6 (a) Microkinetic modeling predicted log₁₀(TOF) as a function of C and O binding energies for SRM. Reaction conditions: T = 773 K, P = 1 bar, 10% conversion. (b) Experimentally measured TOF as a function of dispersion for SRM across Ru (○), 5 wt% Rh (▲), 1 wt% Rh (Δ), Ni (■), Pt (□), Ir (•) and Pd (♦) catalysts. Reaction conditions: T = 773 K, P_CH4 = 0.19 bar, P_H2O = 0.74 bar, P_H2 = 0.07 bar.¹²⁷ Reproduced from ref. 127 with permission from Elsevier, copyright 2008.

At 773 K, 1 bar, and 10% conversion, the model-predicted activity trend is Ru > Rh > Ni > Ir > Pt ∼ Pd. In addition to theoretical calculations, the authors also investigated the activity employing experimental measurements. By assuming that support effects were negligible, the obtained experimental activity trend at 773 K was Ru ∼ Rh > Ni ∼ Ir ∼ Pt ∼ Pd (Fig. 6b). Although the modeling results are not exactly the same as the experimental results, the general trends are consistent. The difference between the theoretical and experimental results might be caused by some sources of errors both in the modeling and in the experiments. The combined DFT, scaling relationship, and descriptor-based microkinetic modeling can effectively describe catalytic reactions at surfaces with the detail and accuracy required for the predicted activity tendency comparable to experiments.

It seems that among these pure metals, Ru and Rh are the most active catalysts, Ni and Ir are moderately active, and Pd and Pt are less active. However, the kinetic studies of Wei and Iglesia^75–80 illustrated a different result, with the activity order as Pt > Ir > Rh > Ru, Ni at 873 K. In their studies, Pt is the most active catalyst. Despite the controversy about the metal activity, Ni, Rh, Ru, Pt and Pd are among the focuses of research for SRM. Ni is the most studied catalyst due to its low cost, abundance, and relatively high activity, and is a commercial and mature industrial SRM catalyst.^58,137 Rh and Ru are normally studied because of their high reforming activity and coke-resistant performance.¹³³ Pt is also a potential SRM catalyst with high activity, according to Wei and Iglesia's work.⁷⁵ A better understanding of the SRM mechanism on these metal surfaces serves as an important step in revealing the nature of this reaction and in aiding the rational design of catalysts.

Metal dependence of the reaction mechanism. The reaction mechanism of steam methane reforming has been long studied both experimentally and theoretically, due to its industrial importance. The reaction mechanism of SRM typically involves methane activation (three C–H activation pathways as discussed above), and CH*/C* oxidation by OH* or O* to form CO. As a result, the mechanism involves many elementary steps, leading to many reaction pathways to form synthesis gas, as shown in Fig. 7.

Fig. 7 Reaction network for SRM over Ni catalyst and estimated net turnover frequency (TOF_Net) for elementary steps involved in the microkinetic model over the Ni(211) surface. The dominant reaction pathway is colored blue. Reaction conditions: 773 K, 1 bar, S/C = 3.5, and CH₄/H₂ = 1.0.⁸⁷ Reproduced from ref. 87 with permission from Elsevier, copyright 2019.

The activation of C–H bonds in methane generates surface CH_x (x = 1–3), and CH* and C* have been identified as the critical intermediates for CO formation. The CH*/C* may follow five routes to form CO by using O*/OH* as an oxidant (Fig. 7). They are (1) the direct C* and O* combination route (C–O route: CH* → C* → CO*), (2) hydrogen insertion via HCO* (CH–O route: CH* → HCO* → CO*) and (3) COH* (C–OH route: CH* → C* → COH* → CO*), and routes that involve the HCOH* intermediate like (4) the HCO–H route (CH* → HCOH* → HCO* → CO*) and (5) the H–COH route (CH* → HCOH* → COH* → CO*). The O* and OH* are provided by the dissociation of H₂O.

DFT calculations and microkinetic modeling are powerful tools for elucidating the reaction pathways for syngas formation via the complex reaction mechanism and identifying the RDS, as it is difficult or almost impossible to gain a full picture on the basis of only experimental work. However, due to the coverage or surface concentration effect, it is difficult to determine the dominating reaction mechanisms purely based on DFT-calculated barriers under reaction conditions.²⁹ The microkinetic modeling is therefore employed to clarify further the mechanistic scenario, which provides opportunities to directly acquire the reaction rate by taking into account both energy and coverage.^{87,94,130,132,138} Recently, Wang et al.⁸⁹ conducted comprehensive microkinetic modeling to gain unified insight into the SRM mechanism on different metal surfaces with energetics estimated by combining a DFT-modified UBI-QEP (unity bond index-quadratic exponential potential) method and BEP relationships. The unified 2D mapping of the dominant reaction pathway and the RDS as a function of C and O formation energies is shown in Fig. 8 at 773 K (a) and 1073 K (b). The lower formation energy corresponds to a higher binding energy. The map can be divided into three areas in terms of the dominant reaction pathways. The O*-assisted C–H activation can only be for the catalysts with high C formation energy and low O formation energy. For most of the catalysts, the direct C–H dissociation is the preferred pathway for methane activation. RDSs such as H–CH₃, H–CH₂, C–OH, and CH–O were observed. This clearly shows that the RDS can change with catalysts or conditions. Based on the 2D map, the dominant reaction pathway and the RDS on transition metals Ni, Pt, Pd, and Rh with different surfaces such as (111), (100) and (211) were analyzed. It was found that the direct CH₄ dissociation was the dominant pathway for methane activation for all the metal surfaces concerned, independent of temperature. CO formation mainly takes place via the C–OH route on the (100) surface due to the strong C binding strength and relatively weak binding of O, except for Ni(100) with H–CH₃ activation as the RDS. On Pt(111) and (211), CH–O (HCO* formation) is the RDS, while on Ni(211), H–CH₃ activation is the RDS. On Ni(111) and Rh surfaces, with increasing temperature, the RDS changes from HCO* formation to CH₄ dissociation. The change in RDS with temperature agrees with the microkinetic modeling results reported by Jones et al.¹²⁷

Fig. 8 Schematic diagrams of the dominant reaction pathways (divided by colors) and rate-determining steps (divided by the dashed lines) as functions of C and O formation energies on different metal surfaces for SRM (a) at 773 K, 1 bar, with 18.2% CH₄, 63.6% H₂O, 18.2% H₂, and (b) at 1073 K, 10 bar, with 18.2% CH₄, 63.6% H₂O, 18.2% H₂.⁸⁹ Adapted from ref. 89 with permission from the American Chemical Society, copyright 2020.

The reaction mechanism and microkinetics have been intensively studied on Ni, Rh, Ru, Pt, and Pd catalysts. We will review the recent progress in the understanding of the mechanism and RDS on these catalysts.

Ni catalysts. Ni catalyst is the most widely studied catalyst due to its importance in industry where the Ni(111) surface is the most studied surface. In 1997, Aparicio¹²⁵ carried out transient isotopic and microkinetic modeling to investigate the SRM mechanism over Ni catalysts. Direct dissociation of methane was experimentally demonstrated to be the main C–H bond activation pathway. The results suggested that there was no unified RDS for SRM. Both the first C–H activation and CO formation could all be kinetically relevant steps depending on the reaction conditions. In some cases, one of them can be the RDS, but in most cases, a combination of them determines the reaction rate. Later, Wei and Iglesia^75–80 conducted a series of kinetic investigations for SRM on a range of metal catalysts (including Ni), which indicated that the first C–H bond activation was the RDS at high temperature (823–1023 K). However, at relatively low temperatures (<773 K), CO formation was expected as the RDS for most metals (including Ni), according to the thermodynamic analysis reported by Jones et al.¹²⁷ The change in the RDS from CO formation to methane dissociation is caused by the increased reaction barrier of methane dissociation (related to entropy contribution) as the temperature increases.

More detailed theoretical studies relevant to SRM on Ni catalysts have been extensively carried out on Ni(211), Ni(111), and Ni(100) surfaces. In 2002, Bengaard et al.¹²⁶ combined DFT calculations, microkinetic and Monte Carlo simulations, kinetic measurements, thermogravimetric analysis (TGA), and extended X-ray absorption spectroscopy (EXAFS) to present a comprehensive mechanistic picture of the SRM process on a Ni catalyst. DFT calculations were performed on step Ni(211) and flat Ni(111) surfaces, based on which potential energy diagrams of the full reaction were obtained. The methane activation was considered to be among the RDSs on the Ni(211) surface,¹²⁵ which is consistent with the general RDS mapping in Fig. 8. Although Ni(111) exhibited a higher barrier, it has more available active sites because of more facet sites than step sites in a normal particle (except for extremely small particles). Therefore, the authors concluded that there are at least two types of active sites on a Ni catalyst: one is very active, related to certain step and surface defect sites; and the other is less active, related to the close-packed surfaces.

It is generally agreed that the CH–O route was energetically the most preferred pathway on the Ni(111) surface for CO formation.^{81,92,93,130,139–141} Wang et al.⁸⁷ also confirmed the CH–O route as an energetically favorable pathway on Ni(211) as well as Ni(100) and Ni(111) surfaces from 773 to 848 K by microkinetic modeling. However, Blaylock et al.¹³² illustrated by multi-facet microkinetic modeling of Ni NPs consisting of Ni(111), Ni(211), and Ni(100) that the favorable reaction pathway depends on the reaction temperature. The C–O route was the most preferred pathway at high temperatures; however, at low temperatures, CH–O and C–OH routes were predicted to be more important. Dissociative chemisorption of methane and CO*/HCO*/COH* formation were the RDSs. Xu et al.¹³³ compared the C–O route, CH–O route, and C–OH route on twelve TM stepped (211) surfaces by means of microkinetic modeling and demonstrated that the C–O route was the most favorable pathway owing to the highest estimated rates. CO formation was the RDS at 773 K. In summary, for Ni catalysts, direct CH₄ dissociation is accepted as a dominant route for methane activation, although the exact reaction mechanism for CO formation is still under debate. The RDS can change with temperature and with Ni surfaces.

Rh, Ru, Pt, and Pd catalysts. Mei et al.¹²⁸ obtained a lower activation barrier for the CH–O route (1.37 eV) than the C–O route (1.59 eV) on a Rh(111) surface. van Grootel et al.¹³¹ reported competition between the CH–O route and C–O route on a Rh(111) surface and that the CH–O route was slightly more favorable on a Rh(211) surface through a comparison of DFT calculated activation barriers. Inderwildi et al.¹⁴² observed a much lower activation barrier for the CH–O route (0.99 eV) than the C–O route (2.23 eV) on a Ru(0001) surface. Chen et al.⁹⁷ suggested a dominant pathway of the C–O route on Pt(111) and Pt(211) surfaces. Wang et al.⁸⁸ demonstrated a primary reaction pathway of the CH–O route involving HCOO* on a Pt(111) surface, while the route involving a CHOH* intermediate turned to be dominant in a moist environment, based on the DFT-calculated activation barrier. Since the SRM mechanism is controversial on different metal surfaces, and it is insufficient to determine the dominant pathway solely based on the activation barrier; microkinetic modeling was employed to further elucidate the mechanism by taking into account both energy and coverage effects.

The microkinetic modeling of steam and dry reforming by Maestri et al.⁸³ predicted that the direct dissociation of the C–H bond was the main pathway of methane activation on Rh catalyst. The microkinetic can describe well the experimental results over a wide range. The microkinetic analysis showed that the CO formation took place by oxidation of the surface C* via C* + OH* → CO* + H*, and the CH₃* dehydrogenation (CH₃* + * → CH₂* + H*) was the RDS for both steam and dry reforming.

Towards CO formation, the DFT calculations and microkinetic modeling study of Zhu et al.¹³⁴ showed that the C–O route was the dominant pathway on Rh(211), Rh(111), Pt(533), and Pt(111) surfaces. The microkinetic modeling of Xu et al.¹³³ indicated that the C–O route was more favorable on Ru and Rh(211) surfaces and that the C–OH route was more preferred on a Pt(211) surface. The DFT-based microkinetic modeling of Jørgensen et al.⁸⁶ illustrated that the C–O route was more favorable at high temperatures and the C–OH route involving COH* and OCOH* intermediates was more preferred at low temperatures on Pd(111) and Pd(100) surfaces. The DFT and microkinetic study of Yoo et al.⁹⁵ revealed that the HCO–H route dominated the reaction on a Pd(111) surface under mildly oxidizing conditions. Trinchero et al.⁸⁴ reported a C–O route on (111), (100), (211), and (321) surfaces of Pt and Pd using DFT and microkinetic modeling. All the analyses point out that C–H bond activation in methane is among the RDSs, although there is a difference in the exact RDS. As shown in Fig. 8, the RDSs on Rh surfaces change with operating temperature. At relatively high temperatures, the H–CH₃ could be the RDS, in accord with the microkinetic analysis by Maestri et al.⁸³ The microkinetic analysis results agree with the experimental observation reported in the literature.^{77,123,143,144}

To sum up, it seems that direct CH₄ dissociation dominates methane activation for Ni, Rh, Ru, Pt, and Pd. The OH-assisted CH₄ dissociation is limited by low OH* surface coverage, although sometimes it is energetically favorable. At the same time, the dominant routes for CO formation are dependent on the catalysts and the metal surfaces. The RDS of the total SRM reaction can change with temperature and with catalysts. The change in RDS with temperature is mainly caused by the large entropy loss of methane, which raises the reaction barrier of methane dissociation as the temperature increases. The change in the RDS with catalysts results from the distinct C–metal and O–metal binding energies on different metal surfaces, which are descriptors to probe the catalyst activity.

Size dependence of activity. In addition to mechanistic research, the metal particle size-dependent activity of SRM also attracted much attention in the previous study. The early work concerning the particle size effect on metal activity for SRM was mainly carried out through experimental measurements. Wei and Iglesia^75–78,80 investigated the effects of metal dispersion on CH₄ reforming turnover rates for Pt, Ir, Rh, Ru, and Ni catalysts. The forward CH₄ turnover rates were observed to increase monotonically with the metal dispersions. Similarly, Jones et al.¹²⁷ observed a linear relationship between the TOF and dispersion for Ru, Rh, Ni, Pt, Pd, and Ir catalysts, as shown in Fig. 6(b). Since dispersion is inversely proportional to particle size for not too small particles, the particle size effect on activity could be easily obtained; that is, the smaller the particle size, the higher the activity (turnover number) for the investigated metals. The activity was therefore considered to depend on the surface structure of the NPs, and the under-coordination sites (edges, kinks, and defects) were expected to be the active sites for SRM because of the larger fraction of under-coordinated surface sites exposed on small particles than larger particles.^127,145,146 The DFT-based microkinetic modeling was subsequently employed to investigate the size-dependent activity. DFT calculations provide the reaction mechanism and kinetic parameters on specific surfaces such as Ni(111), Ni(100), and Ni(211). The multifaceted microkinetic model brings the bridge between the DFT calculation and the kinetics of nanoparticles.^87,89,123

To gain insight into the size-dependent activity, Wang et al.^87,89 reported an approach that combined microkinetic modeling with a truncated octahedron model to calculate the total activity based on the surface fraction and individual surface activity. The schematic diagram of a truncated octahedron model is shown in Fig. 9, which consists of fcc(111) and fcc(100) surfaces, where steps, edges, and corners are treated as an fcc(211) surface. The total reaction rate () can be estimated by the sum of surface fraction (f_i) times individual reaction rate (TOF_i):

where f₁₁₁, f₁₀₀, and f₂₁₁ are the surface fractions of (111), (100), and (211), respectively, estimated by a statistical truncated octahedron model. TOF₁₁₁, TOF₁₀₀, and TOF₂₁₁ are individual turnover frequencies on the (111), (100), and (211) surfaces, predicted by microkinetic modeling.

Fig. 9 A truncated octahedron model consisting of fcc(111), fcc(100), and fcc(211) surfaces.⁸⁹ Adapted from ref. 89 with permission from the American Chemical Society, copyright 2020.

For Ni catalyst, the modeling well reproduced the size-dependent activity observed from the kinetic study, namely lower activity on larger sized Ni particles (Fig. 10b).⁸⁷ The size-dependent activity was found to result from the surface-dependent activity. Ni(211) was the most active surface for SRM (Fig. 10a), and the decreased Ni(211) surface fraction with increasing particle size resulted in reduced Ni activity (Fig. 10b). The Ni(111) activity was limited by a high energy barrier, and the Ni(100) activity was limited by surface blockage related to C* and CH* deposition (Fig. 11a). The study also demonstrated that stabilizing Ni catalysts with particle sizes ≤6 nm (Fig. 10b) could be a good strategy to achieve high activity for SRM reaction. The apparent activation energies calculated from the modeling were 1.13–1.21 eV with the Ni particle size in the range of 8 nm to 12 nm, which was in good agreement with the results measured by experiments, 1.06–1.17 eV for 8–12 nm. These values were also close to the experimental data reported by Wei and Iglesia (1.06 eV),⁸⁰ Nikolla et al. (1.05 ± 0.04 eV),¹⁴⁷ Zeppieri et al. (1.00 ± 0.02 eV),¹⁴⁸ and Niu et al. (1.08 eV).⁹² Moreover, the combined model predicted well the change in the apparent activation energy with Ni particle size, i.e., lower activation energy on larger sized Ni particles. Niu et al.⁹² reported an effective activation energy of 1.12 eV based on a DFT calculated G plot, also consistent with the experimental values on Ni catalysts. This demonstrated that microkinetic modeling and/or DFT are feasible approaches to characterize the real kinetic properties.

Fig. 10 Modeling predicted forward CH₄ turnover frequency as a function of (a) C and O formation energies in SRM on Ni(111), Ni(211), and Ni(100) surfaces at 773 K, and (b) Ni particle size (1.3–16 nm) at 773, 798, 823, and 848 K.⁸⁷ Reproduced from ref. 87 with permission from Elsevier, copyright 2019. (c) Predicted activity for H₂ production over M(111) (green), M(211) (black), and M(100) (blue) surfaces. M denotes Ni, Pd, Pt, and Rh. (d) TOF_H2 as a function of particle size for Ni, Pd, Pt, and Rh NPs. Reaction conditions: 773 K, 1 bar, S/C = 3.5, and CH₄/H₂ = 1.0.⁸⁹ Reproduced from ref. 89 with permission from the American Chemical Society, copyright 2020.

Fig. 11 (a) O* and (b) C* site coverages as functions of C- and O-metal formation energies in SRM. Reaction conditions: 773 K, 1 bar, 18.2% CH₄, 63.6% H₂O, 18.2% H₂.⁸⁹ Adapted from ref. 89 with permission from the American Chemical Society, copyright 2020.

The size-dependent activity of SRM on Rh, Ru and Pt catalysts follows the same trend as that on Ni, namely, the smaller the particle size, the higher the activity.^{75–77,80,127,149} Wang et al.⁸⁹ also provided a systematic and in-depth understanding of the size-dependent activity on Rh, Ni, Pd, and Pt catalysts by combining microkinetic modeling with a truncated octahedron model. The modeling predicted activity of H₂ production in SRM on each metal surface is shown in Fig. 10(c). It was found that the M(211) surface is most active for Rh, Ni, and Pd catalysts, while for Pt, the M(100) surface is most active. The total activity was estimated by the sum of individual TOF on each surface multiplied by the surface fraction, based on that, the total TOF against particle size is plotted in Fig. 10(d). The TOFs were observed to be inversely proportional to particle size and linearly related to dispersion, in good agreement with reported experimental results.^{75–77,80,127,149} The linear scaling between TOFs and dispersion was associated with a linear relationship between surface fractions and dispersion. M(211) was the active surface, and the increased M(211) surface fraction along with increased dispersion led to enhanced NP activity at smaller NP size. As for metal-dependent activity, the catalytic activity of SRM followed Rh > Ni > Pd ∼ Pt for both small and large particles. Compared to Rh, the activity of Ni was limited by surface blocking, and the activities of Pt and Pd were limited by high free energy barriers. Although Rh exhibits very high activity, other noble metals such as Ru, Pt, Pd, and Ir are also active for SRM, but these metals are usually too expensive to be applied in conventional industrial reformers. Developing appropriate methods to combine Ni-based catalysts with these noble metals to achieve both enhanced activity and catalyst resistance to carbon deposition seems like a cost-effective way and a promising subject of SRM study in the future.

Catalysts improving carbon formation resistance. Although the use of Ni-based catalysts for SRM is a relatively mature technology, catalyst deactivation through carbon formation, poisoning and sintering tends to occur on the Ni surface, which is an important challenge and is among the subjects of active research.¹³³ Among them, carbon formation is the most common and significant challenge for Ni-based catalysts. Several types of carbon have been reported on the catalysts towards methane reforming and decomposition,¹⁵⁰ with atomic carbon, encapsulating carbon, and filamentous carbon being the most important.¹⁵¹ It is generally accepted that the growth of filamentous carbon involves decomposition of the carbon-containing gas to carbon adsorbed on the metal surface, dissolution/segregation of carbon into the bulk, diffusion of carbon through Ni particles to surfaces that are suitable for filament growth, and precipitation of filaments.¹⁵² Chen et al.¹⁵¹ performed a microkinetic analysis of deactivation during DRM over Ni catalyst, where both filamentous carbon and encapsulating carbon were assumed to generate from a surface carbon (C*) precursor. The carbon formation was dependent on the concentration of surface C*, and different operating conditions affected the coking rate through changes in *C site coverage. It was suggested that the formation of monolayer encapsulating carbon blocked the active sites and hence deactivated the methane reforming, the filamentous carbon formation and the encapsulating carbon formation itself.

The C* site coverage is an important parameter to characterize carbon formation. Both experimental and DFT studies of Nørskov and co-workers^126,153 suggested that the nucleation of graphene on Ni catalysts was initiated at the stepped Ni(211) sites. If the surfaces or step edges are too small, the nucleation cannot proceed, thereby further inhibiting the graphene formation. This explains why very small particles cannot grow filamentous carbon under normal conditions. However, the recent microkinetic modeling of Wang et al.⁸⁹ demonstrated carbon deposition on a Ni(100) surface (Fig. 11a). The absence of graphene formation on very small particles is related to the very low surface fraction of Ni(100), which is an energetically preferred facet of Ni for the formation of carbon. The carbon deposition phenomenon on Ni(100) has also been reported by Schouten et al. towards methane decomposition reaction.^154,155 Moreover, Eizenberg and Blakely observed the formation of monolayer graphene on a Ni(100) surface in experiments.^156,157 According to Fig. 11(a), in addition to Ni(100), the Rh(100), Pt(100) and Pd(100) surfaces as well as Rh(211) and Pd(211) surfaces could also suffer from carbon deposition because of the strong carbon binding energy. In contrast, the Ni(211) surface is poisoned primarily by surface O* due to relatively strong O binding energy (Fig. 11b). The active surface for carbon formation is, therefore, still under debate.

High temperature and pressure are beneficial to the removal of carbon formation, based on the thermodynamic analysis.^158,159 It was found that for temperatures above 1100 K there is no possibility of carbon formation for the steam-to-methane ratios above unity. For temperatures below 1100 K, carbon formation removal could be done by increasing the pressure. Therefore, for large-scale hydrogen production through SRM, the pressure is above 10 bar.

Ni-based bimetallic catalysts by alloying Ni (the active metal) with another metal (e.g. Au,¹⁶⁰ Ru,¹⁶¹ Rh,⁵⁵ Co,¹⁶² Pt,^163,164 Ag,¹⁶⁵ and Sn¹⁶⁶) are generally used to reduce methane dissociation and enhance the surface reaction of carbon removal, which could effectively increase catalyst resistance to deactivation and improve catalyst stability. Besenbacher et al.¹⁶⁰ combined molecular beam scattering experiments, scanning tunneling microscopy (STM), and DFT calculations to design a surface alloy for steam reforming. It was demonstrated that alloying Au into the surface layer of Ni could effectively improve the catalyst performance, achieving high resistance to carbon formation, which was confirmed by experimental results. Nikolla et al.¹⁶⁶ conducted a DFT study to investigate the effect of a Ni-containing alloy on C deposition relative to monometallic Ni and indicated that the growth of carbon deposits was inhibited by Sn alloying of Ni.

Ni-Based bimetallic catalysts with alloy metals such as Ru, Rh, Pd, Ag, Pt, Cu, and Au were investigated by Fan et al.¹⁶⁷ for methane dissociation. The DFT-calculated potential energy diagrams are shown in Fig. 12. They demonstrated that the Cu- and Ag-modified surfaces were energetically more favorable than the bare Ni surface for dissociation reactions. For CH₄* dissociation, the activation barriers on Ru/Ni(111) (0.65 eV), Rh/Ni(111) (0.77 eV), and Cu/Ni(111) (0.88 eV) were lower than that on Ni(111) (0.92 eV). On the other hand, the DFT-calculated C adsorption energies on Pt/Ni(111), Pd/Ni(111), Au/Ni(111), and Rh/Ni(111) were less negative than that on Ni(111), indicating that coke formation was suppressed to a certain extent on these bimetallic catalysts. The Ni–Rh bimetallic catalyst was therefore suggested as a good candidate for methane dissociation due to improvement in both activity and stability, which has been verified by experimental observations.^168,169

Fig. 12 Potential energy diagrams for methane dissociation on Ni-based bimetallic surfaces. The chemisorbed H atoms required to balance adsorption states have been omitted to simplify the notation.¹⁶⁷ Reproduced from ref. 167 with permission from AIP Publishing, copyright 2012.

Xu et al.¹⁷⁰ studied the effect of Ag on the control of Ni-catalyzed carbon formation by DFT calculations. The addition of Ag into Ni catalysts reduced the catalytic activity towards SRM but enhanced coke formation resistance. Liu et al.¹⁷¹ reported that segregated NiCu was a good SRM catalyst to suppress coke formation, which displayed the highest carbon deposition resistance among Ni, Fe, Co, Cu, NiFe, NiCo, NiCu, and segregated NiCu catalysts via DFT study. Yoon et al.¹³⁵ compared Ni, Ni–Ru, and Ni–Rh bimetallic catalysts for SRM through DFT calculations, which demonstrated that alloying Ni with Ru could be an effective way to greatly enhance the catalytic efficiency and reduce carbon deposition. Niu et al.⁹² performed DFT studies on Ni, Pt, and Ni@Pt catalysts for SRM reaction, which revealed that core–shell structured Ni@Pt showed a lower activation barrier for CH and C oxidation but a higher activation barrier for CH dissociation to form C. The Ni@Pt catalyst was found to significantly inhibit carbon formation without sacrificing much activity. To summarize, the Ni–Rh, Ni–Ru, and Ni–Pt alloys are promising bimetallic catalysts to effectively increase catalyst resistance to carbon deposition without sacrificing much activity or even with enhanced activity for SRM reaction.

2.2.2 Dry reforming of methane. Dry reforming of methane is a promising technology to covert greenhouse gases (CH₄ and CO₂) to synthesis gas (H₂ and CO) for the manufacture of value-added products.^49,51,172 Dry reforming of methane has not been an industrially mature process so far. It is an extremely highly endothermic reaction (2.56 eV). Therefore, very high reaction temperatures (as high as 1173 K) are required to attain high synthesis gas yields. The high temperature leads to rapid carbon formation, and thus catalyst deactivation. Moreover, the requirement for pure CO₂ and the long reaction time make DRM still need further development.⁶² Ni-Based catalysts are commonly used for this reaction. However, these catalysts tend to undergo carbon deposition and sintering and lose their activity. To overcome this problem, the use of different supports, promoters, and Ni-based bimetallic catalysts has been investigated by many researchers. Here, we summarize the DRM mechanism from kinetic, DFT and microkinetic modeling points of view, with emphasis put on Ni-based catalysts.
Reaction mechanism of DRM. The mechanism of DRM over Ni catalysts has been extensively investigated experimentally. The isotopic kinetics study of Wei and Iglesia⁸⁰ indicated that the initial C–H bond activation of methane was the sole kinetically-relevant step for DRM on Ni catalysts. However, some other researchers argued that carbon oxidation,^173–175 the surface reaction between CH_x* and O*,¹⁷⁶ or CH_xO decomposition^177,178 could be the RDS for Ni-based catalysts. The controversial observation could be related to the factor that the mechanism is a function of operating conditions. Using transient isotopic approaches and microkinetic modeling, Aparicio¹²⁵ suggested that there was no single RDS in methane reforming over Ni catalysts. Under certain conditions, the availability of surface oxygen may play a key role in determining the rate. Bradford and Vannice¹⁷⁹ proposed a reaction model for DRM, where CH₄ dissociation and CH_xO decomposition were assumed as RDSs, which correlates experimental data successfully. The same RDSs were obtained by Nandini et al.¹⁸⁰ over the Ni–K/CeO₂–Al₂O₃ catalyst. The kinetic study of Cui et al.¹⁸¹ indicated that CH₄ dissociation was the RDS at low temperature, while the reaction between CO₂ and CH_x became the RDS at high temperature. Zhang et al.¹⁸² developed a Langmuir–Hinshelwood (L–H) model, assuming CH₄ dissociation and the reaction between activated CO₂ and the C species as RDSs over a Ni–Co/Al–Mg–O catalyst, which agrees well with the experimental data. Despite the numerous experimental studies devoted to investigating the mechanism of DRM, there are still arguments between different researchers. The theoretical studies were therefore employed to further elucidate the reaction mechanism of DRM.

The theoretical DRM mechanism is usually interpreted in terms of CH₄ activation, CO₂ activation, and CO formation. CH₄ activation was generally believed to take place via the direct dissociation route, which has been reviewed in detail in Section 2.1.1. CO formation pathways are the same as those in SRM reaction. CH* and C* are the critical intermediates for surface oxidation by O* or OH*. CO₂ activation is the key step that is different from SRM.

CO₂ activation. Concerning CO₂ activation, the direct decomposition (CO₂ → CO + O) and H-induced CO₂ decomposition (CO₂ + H → COOH → CO + OH) were considered by Zhu et al.⁹³ on a Ni(111) surface. The geometries of the initial states, intermediates, and transition states for CO₂ decomposition obtained from DFT calculations are shown in Fig. 13(a–f). The total energy and free energy diagrams for the two routes on the Ni(111) surface are given in Fig. 13(g). It was observed that the CO₂ direct decomposition was energetically more favorable than H-induced CO₂ decomposition. The CO₂ direct decomposition was also supported by Jiao and co-workers on both Ni(111) and Ni(211) surfaces.^{81,82,183,184}

Fig. 13 Geometries of (a) the physisorbed CO₂ on Ni(111), (b) the chemisorbed CO₂ on Ni(111), (c) the transition state for CO₂ decomposition via the direct pathway, (d) the transition state for the H-inducted CO₂ decomposition, (e) the intermediate for the H-induced CO₂ decomposition, and (f) the transition state for COOH dissociation to generate CO and OH, and (g) total energy and Gibbs free energy diagrams for the CO₂ direct decomposition and H-induced CO₂ decomposition on Ni(111).⁹³ Reproduced from ref. 93 with permission from Elsevier, copyright 2009.

CO₂ activation on other metals has also attracted some attention.^185,186 Ko et al.¹⁸⁵ systematically investigated CO₂ activation and dissociation on a series of pure metal surfaces and bimetallic alloy surfaces by using DFT calculations. The scaling relations (Fig. 14a) were obtained, where the reaction heat ΔE(CO₂^δ−) of CO₂ dissociation scaled linearly with the sum of the adsorption heats of CO and O over various pure metal surfaces. Meanwhile, the BEP relationships were suitable (see Fig. 14b), with the CO₂^δ− dissociation barrier linearly correlated with ΔE(CO₂^δ−). In light of this fact, the activation energies of CO₂ dissociation over pure metal and bimetallic surfaces could be rapidly predicted by combining the surface mixing rule, scaling relation, and BEP relationship, as illustrated in Fig. 14(c). The barrier increases from left to right and from top to bottom. Fe, Ru, Co, Ni, Rh, and Ir pure metals as well as Fe-, Ru-, Co-, Ni-, Rh-, and Ir-based bimetallic alloys exhibited relatively low E^act_a values (∼0.75 eV). Pd, Pt, and Cu pure metals as well as Ru-, Co-, Ni-, Rh-, Ir-, and Cu-based bimetallic alloys showed moderate E^act_a values (0.76–1.50 eV). Au and Ag pure metals as well as Pd-, Pt-, and Cu-based bimetallic alloys were observed to take high E^act_a values (1.51 eV).

Fig. 14 (a) Scaling relations between E_ads(CO) + E_ads(O) and ΔE(CO₂^δ−) on TM surfaces. (b) BEP relationships for CO₂^δ− dissociation. (c) CO₂ activation pathways and screening for E^act_a for CO₂ dissociation on pure metals and bimetallic alloys. Gray cells indicate that the bimetallic alloys are not preferred for the surface segregation of solute atoms. Here, E^act_a is estimated by combining the BEP relation, scaling relation, and surface mixing rule.¹⁸⁵ Reproduced from ref. 185 with permission from the American Chemical Society, copyright 2016.

Support and promoter effects are important factors in facilitating CO₂ activation. Kattel et al.¹⁸⁷ combined DFT calculations, kinetic Monte Carlo (kMC) simulations, and experimental measurements to investigate CO₂ hydrogenation over Pt, Pt/SiO₂, and Pt/TiO₂ catalysts. It was found that Pt NPs alone were not able to catalyze CO₂ activation due to the weak bonding with CO₂. Once CO₂ was stabilized, for example by using SiO₂ or defected TiO₂ with O vacancy as the support for Pt NPs, the overall CO₂ conversion would be enhanced via increased CO₂ binding. Pt/TiO₂ exhibited more significant enhancement than Pt/SiO₂ and thus higher activity. Yang et al.¹⁸⁸ studied the reduction of CO₂ by hydrogen over Au/TiO₂ and Au/CeO_x/TiO₂ surfaces. On Au₃/TiO₂, the reaction was suppressed by the relatively large barrier (1.23 eV) for the activation of *CO₂ to **CO₂, which was significantly promoted in the presence of CeO_x (0.16 eV). On Au/CeO_x/TiO₂, an electronic metal–support interaction resulted in a charge redistribution in the metal around the Au–ceria interface. Such surface electronic polarization at the metal–oxide interface enhanced both CO₂ adsorption and activation. Niu et al.¹⁸⁹ employed both kinetic studies and DFT calculations to investigate the effect of oxide additives (CeO₂, ZrO₂, ZnO) on hydrotalcite-derived Ni catalysts for DRM reaction. Regarding CO₂ activation, the apparent activation energies obtained from the Arrhenius plot for CeO₂–Ni (0.62 eV) and ZrO₂–Ni (0.64 eV) were lower than that of Ni (0.68 eV). In contrast, ZnO–Ni exhibited a higher activation barrier (0.77 eV) than Ni. It was suggested that the addition of CeO₂ and ZrO₂ could lower the CO₂ activation energy on Ni catalyst, thus promoting CO₂ dissociation to CO and O. The authors also calculated the TOF based on Gibbs free energy, which was 5.92 s⁻¹ at 1023 K for CO₂ activation on the support, very close to the experimental value (6.13 s⁻¹ at 1023 K), but much higher than that on the Ni surface (4.42 × 10⁻⁶ s⁻¹). This demonstrated that the oxides played a significant role in CO₂ activation in DRM reaction.

For the overall DRM reaction, DFT-based microkinetic modeling was applied to explore the mechanism on various metal surfaces such as Ni(111),^85,94 Ni(100),⁹⁴ Ni(211),⁹⁴ Pt(111),^85,190 and Pd(111).⁸⁵ Regardless of the catalyst surface, direct dissociation was favored for C–H bond activation of methane. Direct dissociation is a preferred route for CO₂ activation on Ni,^85,94 but the H-assisted route via the COOH* intermediate is preferred for Pt and Pd catalysts.^85,190 However, different preferred routes for CO formation such as C* + O* on Ni,⁹⁴ CH* + O* on Ni(111), Pt(111) and Pt(111),⁸⁵ and CH* + OH* on Pt(111)¹⁹⁰ were proposed by different studies. The mechanism is very similar to the one of SRM. The RDS was dependent on operating conditions. At high CH₄ and CO₂ partial pressures, carbon oxidation was suggested as the RDS, while at low pressures, both CH₄ dissociative adsorption and C oxidation would jointly determine the overall reaction rate for the DRM reaction.⁹⁴ Since DRM has attracted more and more attention due to environmental effects, the DRM mechanism is still under debate, and more theoretical studies are essential to gain insight into the reaction, further aiding the rational design of catalysts.

Metal dependence of activity. Like SRM, the DRM reaction is active on metal catalysts, such as Ni, Ru, Rh, Pt, Pd, Ir, and Co.^{123,191–193} As discussed above, the C–H activation and CH and/or C reaction with surface O* are kinetically relevant steps in DRM. Besides, the CO₂ activation leading to surface O* formation is a function of support. Therefore, the metal dependence of the dry reforming activity depends also on the support used. Rostrup–Nielsen and Bak Hansen obtained an activity tendency on a TOF basis as Ru > Rh > Ni > Ir > Pt > Pd on a MgO support¹²³ like SRM.¹²⁷ Solymosi et al. reported an activity (in terms of turnover number) trend in the order of Ru > Pd > Rh > Pt > Ir on an Al₂O₃ support for the DRM process.¹⁹³ Ferreira-Aparicio et al. observed a TOF tendency of Rh > Ni > Ir > Ru–Pt > Co on an Al₂O₃ support, and Ni > Ru > Rh–Ir > Co–Pt on a SiO₂ support.¹⁹¹ Although the metal performances have some differences among different supports and different studies, Ni catalyst is of particular interest in DRM because it is less expensive than noble metals and exhibits relatively high activity.⁶³
Size dependence of activity. The kinetic study of Wei and Iglesia^75,80 illustrated a positive size-dependent activity for DRM on Pt, Ir, Ni, Rh, and Ru catalysts, namely the smaller the metal NPs, the higher the activities. The size dependence of the activity of DRM is similar to the one of SRM, as discussed in Section 2.2.1. Similarly, Lustemberg et al.¹⁹⁴ reported that Ni–ceria systems involving the smallest highly dispersed Ni particles were more efficient for methane activation and reforming than larger particles. This is related to the strong metal–support interactions, which affect the charge transfer between Ni particles and ceria. Small Ni particles on stoichiometric ceria undergo large electronic perturbations, which lead to a relatively low activation barrier of the first C–H bond cleavage of methane, compared to extended Ni surfaces. However, recently, Vogt et al.¹⁹⁵ established a volcano behavior of size-dependent activity for SRM and DRM at 773 and 873 K, and 5 bar, where the optimal Ni particle size was approximately 2–3 nm. Ni particles smaller than 2.5 nm exhibited a different structure sensitivity from that expected from the above literature. CH₄ activation, CO₂ activation, and CO formation were possibly important kinetically limiting steps for DRM.
Catalyst improvement. Carbon formation on Ni-based catalysts is the main obstacle to the commercialization of DRM.¹⁴⁰ To investigate the carbon formation scheme on Ni-based catalysts, Wang et al.¹⁴⁰ compared the whole reaction network of DRM over flat Ni(111) and step Ni(211) surfaces, as well as flat Ni₃C(001) and step Ni₃C(111) by DFT calculations. The kinetic analysis illustrated an activity order of Ni(111) > Ni₃C(001) > Ni(211) > Ni₃C(111) for DRM. That is, flat surfaces were more active than step surfaces, and metallic Ni catalysts were more active than nickel carbide. Therefore, the formation of nickel carbide would reduce the catalytic activity on both flat and step surfaces. With respect to carbon formation, the authors suggested that the rate ratio of the CH oxidation route to the C oxidation route (r_CH/r_C) coupled with the CO dissociation barrier could be used to measure the carbon formation probability. Ni(111) was found to exhibit both the highest activity and the best carbon resistance.

In addition to pure metal catalysts, a few theoretical studies have been employed to investigate the mechanism on Ni catalysts with supports, promoters, and Ni-based bimetallic catalysts for DRM reaction with improved performance. The experimental and computational studies of Akri et al. revealed that Ni atomically dispersed over Ce-doped hydroxyapatite (HAP-Ce) was highly active and intrinsically coke-resistant due to strong metal–support interactions, which favor only the first C–H bond activation in methane and stabilize Ni single atoms towards sintering.¹⁹⁶ The DFT studies of Rodriguez and coworkers^194,197,198 indicated that the effective barrier of methane activation decreased from 0.9 eV over a Ni(111) surface to only 0.15 eV over a Ni/CeO_2−x(111) surface (Fig. 15). The electronic or chemical properties of Ni were modified with CeO₂ through strong metal–support interactions. The strong interactions enhanced the Ni reactivity for methane dissociation and probably prevented carbon deposition and deactivation during DRM.¹⁹⁷ Moreover, a decrease in the barrier of the first C–H bond activation of methane from 1.07 eV over the Co(0001) surface to 0.87 eV over the Co²⁺/CeO₂(111) surface, and to only 0.05 eV over the Co⁰/CeO_2−x(111) surface, was obtained by Liu et al.¹⁹⁸ through DFT calculations. This suggests that the reduction degree of the CeO₂ or oxygen vacancy is vital for the activity of Ni/Co sites. The Ni/Co cation on CeO₂ shows a much lower activity for C–H activation of methane compared to the Ni/Co cation on reduced CeO₂ (Ce₂O₃). CO₂ dissociation was observed to take place on the oxide surface at 700 K, under DRM conditions, and no coke deposition was found in the catalytic cycle. CeO₂ is an efficient support that can play an essential role in the DRM process. In contrast, single-site Ni₁/Mg(100) was not active for CO₂ and CH₄ dissociation, while Ni₄/MgO(100) enabled the formation of H₂, CO, and H₂O under DRM reaction, revealed by combined DFT, kMC simulation, and experimental studies.¹⁹⁹ The Ni cluster provided the active sites, and MgO offered the Mg_vac as an anchor for Ni clusters to prevent Ni aggregation. The study revealed that the oxygen vacancy enhanced the C–H activation of methane. However, the whole catalytic cycle involving the oxygen vacancy was not analyzed. It is highly desired to analyze the elementary reaction steps at the metal–oxide interface in the catalytic cycle to gain a better understanding of the role of the interface in DRM.

Fig. 15 Atomic structures of Ni adsorbed on (a) CeO₂(111) and (b) Ce₂O₃(0001). (c) Reaction energy profiles for the CH₄ → CH₃ + H reaction on Ni(111), Ni²⁺/CeO₂(111), and Ni⁰/Ce₂O₃(0001). The structures shown on the left and right of the reaction pathways correspond to the side views of the optimized initial (molecularly adsorbed) and final (dissociated) states used in search of the transition state. O_s = surface oxygen atoms, O_ss = subsurface oxygen atoms, and O_bulk = bulk oxygen atoms.¹⁹⁷ Reproduced from ref. 197 with permission from Wiley-VCH, copyright 2016.

Foppa et al.²⁰⁰ employed a multiscale (DFT and microkinetic) modeling approach to investigate the role of a Ni/Al₂O₃ interface in WGS (water–gas shift) and DRM. The Ni/Al₂O₃ interface provided the active site for WGS, while all Ni atoms were active for DRM, which was confirmed by the experimental measurements. Li et al.²⁰¹ combined DFT, CO₂-TPD, and in situ DRIFTS to investigate the interfacial synergism of Ni/La₂O₃ catalysts towards CO₂ activation in DRM. They proposed a mechanism that CH₄ activation occurred on the Ni surface to form H₂ and activated coke precursors. CO₂ activation took place at the Ni/La₂O₃ interface to generate bidentate carbonate. Then bidentate carbonate underwent a reaction with adjacent activated coke precursors to generate CO. Therefore, carbon deposition was avoided at the Ni/La₂O₃ interface. The more the Ni/La₂O₃ interface existed, the better the stability by inhibiting the coke deposition.

Li et al.²⁰² combined DFT and microkinetic modeling to investigate the DRM reaction mechanism on a Ni(111) surface with La and La₂O₃ as promoters. For La modified Ni(111), the dominant pathway was CH₄ + CO₂ → CH + 3H + CO + O → CHO + 3H + CO → 2CO + 2H₂, with CH + O → CHO as the RDS. For La₂O₃ modified Ni(111), CH₄ + CO₂ + La₂O₃ → CH + CO₂(La₂O₂–O) + 3H CHO + CO₂(La₂O₂) + 3H → 2CO + 2H₂ + La₂O₃ was the dominant reaction pathway, with CH₄ → CH₃ + H as the RDS. The modified catalysts improved the DRM reaction both thermodynamically and kinetically. Moreover, the carbon deposition was inhibited on La₂O₃ modified Ni(111) because of the lower reaction rate in CH → C + H, compared to that on La modified Ni(111).

For Ni-based bimetallic catalysts, NiSn was observed to favor methane dissociation,²⁰³ and reduce coke formation²⁰⁴ more than pure Ni catalysts for DRM via both theoretical and experimental studies. NiFe bimetallic catalysts suppressed coke deposition due to the increased energy barrier of CH → C + H, in comparison to that on a pure Ni(111) surface.²⁰⁵ Furthermore, under DRM conditions, Fe was oxidized partially to FeO, leading to a partial dealloying. FeO could react with surface carbon deposits to form CO, where the reduced Fe returned to the original NiFe alloy.^205,206 The FeO/Ni(111) interface exhibited easier C–O bond cleavage of CO₂ and dehydrogenation of CH_x (x = 1–3). Therefore, both improved DRM reactivity and coke resistance were obtained on NiFe catalysts. The Ni₂Cu(111) catalyst displayed superior carbon deposition resistance compared to Ni(111) and Ni₂Fe(111) due to the higher energy barrier of CH dissociation. It could also improve carbon elimination by enhancing C* + O* reaction, resulting in improved catalyst stability.²⁰⁷ NiPt bimetallic catalysts showed higher reaction barriers for CH cracking and lower carbon adsorption energy than that on pure Ni(111), which decreased the possibility of coke formation. It can be concluded that the use of supports, promoters, and Ni-based bimetallic catalysts can effectively suppress coke formation on Ni surfaces. Meanwhile, some supports, such as CeO₂, promoters such as La₂O₃, and Ni-based bimetallic catalysts such as NiSn and NiFe can improve the metal activity for DRM due to enhanced methane activation.

2.2.3 Partial oxidation of methane. Partial oxidation of methane is another process for synthesis gas production, which can also be used to produce methanol.^208,209 Herein, we only focus on the POM to synthesis gas. This process, like SRM, has a long history but has attracted much less attention until the 1990s.^48,69 Owing to its thermodynamic advantages and the produced H₂/CO ratio of 2, which is desired for downstream methanol and Fischer–Tropsch (FT) synthesis, POM may become increasingly important in methane conversion and as an attractive alternative to SRM which may applied in industry in the future.^38,210 Despite its exothermicity, high temperatures (1100–1200 K) are required to obtain H₂ and CO. The high temperatures make the reaction difficult to control. Moreover, the hot spots formed during this process are difficult to handle and might cause local overheating. These issues, coupled with the danger of a mixture of methane and oxygen, result in the main problems (safety issues) of POM. Additionally, catalyst stability is another factor that hinders this process from being industrialized.⁴² In this review, the POM mechanisms on TMs are summarized, mainly from theoretical points of view based on DFT calculations, microkinetic modeling, and kinetic analysis.
Metal dependence of the reaction mechanism. Although many studies have been carried out to elucidate the mechanism of POM reaction, the mechanism of synthesis gas formation is not yet completely clarified. In the literature, two reaction mechanisms have been proposed for POM reaction: one is the “direct partial oxidation” (DPO) mechanism, in which CH₄ and O₂ react on the catalyst surface to generate CO and H₂ directly; and the other is the “combustion and reforming reaction” (CRR) mechanism, which involves total methane combustion to form H₂O and CO₂ first, followed by SRM and DRM to produce CO and H₂.^{38,48,69,70,211,212} The latter mechanism was suggested by Prettre et al.²¹³ as early as 1945, but due to the highly desired direct selective route to produce synthesis gas, significant efforts have been made towards investigating whether this can be achieved in practice.⁶⁹

Rh and Pt are two of the most widely used catalysts in POM reaction.²¹⁴ The first simulations on POM over Pt and Rh surfaces were reported by Hickmann and Schmidt,^69,215,216 using a model with 19 elementary steps containing adsorption, desorption, and surface reactions. The reaction parameters were obtained from the literature or from fitting to previous experiments. The model results demonstrated that at high temperatures with CH₄-rich conditions, CO and H₂ were primary products of direct methane oxidation via a pyrolysis mechanism. The superiority of Rh over Pt towards the direct oxidation of methane to CO and H₂ was due primarily to the much lower activation barrier of OH formation from O* and H* on Pt than that on Rh (0.11 eV for Pt vs. 0.87 eV for Rh).

Boucouvalas et al.²¹⁷ conducted a kinetic study of POM over supported Rh catalysts. The calculated apparent activation energy of CO₂ formation was around 0.35 eV, which was close to that of methane conversion (∼0.39 eV). In contrast, the apparent activation energy of CO formation was 0.88–1.13 eV, close to those for CO production from SRM and DRM,^{123,217–219} and much higher than that for CO₂ formation. It was suggested that the POM followed an indirect (CRR) mechanism; namely, the reaction initially involved total oxidation of methane to CO₂ and H₂O, followed by reforming reactions to synthesis gas. The kinetic study reported by Kondratenko et al.²¹⁰ also illustrated that CO and H₂ were mainly produced through SRM and DRM at least in the case of complete oxygen conversion. Donazzi et al.¹⁴³ carried out a kinetic study of POM over a Rh/α-Al₂O₃ catalyst, with SRM, DRM, WGS, reverse-WGS, CO and H₂ combustion tests also conducted to refine the study. It was found that under the POM conditions the kinetic role of DRM is negligible; therefore SRM and CH₄ total combustion account for the consumption of methane.

Mallens et al.²²⁰ employed a transient kinetic study to investigate the reaction mechanism of POM to synthesis gas over Pt. The methane decomposition took place on reduced platinum and resulted in surface C* and H*, which produced CO and CO₂ in parallel by the involvement of different oxygen species. In the presence of both CH₄ and O₂ at a stoichiometric feed ratio, the major reaction pathways were the direct formation of H₂ and CO followed by their consecutive oxidation. Based on the study, a Mars–van Krevelen (MVK) redox cycle²²¹ was postulated for POM over Pt: the methane oxidation was accompanied by the reduction of platinum oxide, which was re-oxidized via incorporation of dioxygen into the catalyst.

In view of the controversy in the POM mechanism, it is of great significance to further elucidate the reaction from a microscopic perspective. Mhadeshwar and Vlachos²²² developed a thermodynamically consistent C1 microkinetic model for POM, SRM, DRM, and oxygenate decomposition on Rh using a hierarchical multiscale methodology with parameters obtained from combined UBI-QEP and DFT calculations. The model predicted distinct oxidation and reforming zones, where CO and H₂O were the primary products that existed in the oxidation zone. H₂ was produced from methane reforming by H₂O generated in the oxidation zone. Matteo et al.²²³ integrated a microkinetic model²²⁴ with detailed reactor models²²⁵ to investigate the dominant reaction pathways for syngas production in POM on Rh. Three reaction zones were suggested: deep combustion of a methane zone (O* is the most abundant reactive intermediate), followed by a zone where both direct formation of synthesis gas and catalytic combustion occur, and, finally, a SRM and WGS zone (oxygen is no longer available). Zone II and zone III were supported by the microkinetic study of spatially resolved autothermal POM experiments reported by Donazzi et al.²²⁶ over Rh-coated foams. Besides, the reaction pathway analysis of Donazzi et al.²²⁶ showed that methane was activated via pyrolytic decomposition, and the main oxidizer was OH* rather than O*. In the oxidation zone (zone II), OH* was generated from O* and H* combination, while in the reforming zone (zone III), OH* was formed by H₂O dissociation.

Mhadeshwar and Vlachos²¹⁴ developed a predictive CH₄ (C1) mechanism on Pt by using a hierarchical multiscale approach. They concluded that POM on Pt was indirect, where total oxidation occurred first to form CO₂ and H₂O, followed by SRM and DRM to generate CO and H₂, consistent with modeled experimental data. The combined kinetic and DFT studies of CH₄ oxidation on Pt and Rh clusters by Chin et al.²²⁷ confirmed that POM to CO and H₂ followed an indirect mechanism at the molecular scale. CO and H₂ were predominantly produced upon complete O₂ consumption from the sequential reforming steps. Based on the above kinetic and microkinetic studies, it is generally accepted that there is no unified mechanism of POM to synthesis gas and that even for the same catalyst the process might follow different reaction routes depending on the reaction conditions and the state of the catalyst.

Au et al.²²⁸ gave a detailed theoretical study of POM to synthesis gas on Ni, Pd, Pt and Cu catalysts, where adsorption energies were calculated using the Amsterdam density functional (ADF) program system, and activation energies were estimated by the UBI-QEP method. These metals were simulated by Ni₇, Pd₁₀, Pt₁₀, and Cu₁₀ clusters. The calculated total methane dissociation energies followed the trend of Ni < Pd ≈ Pt, corresponding to the experimental tendency in methane conversions as Ni > Pd ≈ Pt. The rather high activation energy of discrete dehydrogenation steps on Cu explains why Cu is not active for methane dissociation. C* + O* → CO* was the RDS on Ni due to the higher activation energy than those of dehydrogenations (CH_x,s → CH_x−1,s). On the other hand, on Pd, Pt, and Cu, CH* dissociation (CH* → C* + H*) was the RDS because of the highest activation energies. The calculation also indicated that gas-phase CO could easily combine with O* to form CO₂. The CO₂ selectivity was, therefore, dependent on the amount of adsorbed O* present on the surface. High CO selectivity can be obtained in an oxygen-depleted environment.

Metal dependence of the activity. Like SRM, POM reaction is active on noble metals such as Rh, Ru, Ir, Pt, and Pd, with Rh and Ru being the most active, and on non-noble metals like Ni and Co.^{38,42,70,210,211} For non-noble metal catalysts, Ni-based catalysts display the highest activity, which is even comparable to that of noble metal catalysts.⁴² Nevertheless, rapid catalyst deactivation caused by carbon deposition as well as loss and sintering of Ni under POM reaction conditions is a major problem that occurred on Ni-based catalysts.¹⁴¹ Consistent with the mechanism of POM with total oxidation followed with SRM, the activity order of POM on these metals is similar to that of SRM, namely Rh ≈ Ru > Ni ≥ Ir ≥ Pt, Pd,^48,127,210 which has been discussed in Section 2.2.1. The relative order of carbon formation was observed as Ni > Pd ≫ Rh, Ru, Ir, Pt, reported by Claridge and Battle et al.^48,229

Yoo et al.⁹⁵ employed DFT and microkinetic modeling to investigate methane oxidation to CO, CO₂, CH₂O, and CH₃OH over a Pd(111) surface under mildly oxidizing conditions. CO and CH₂O were found to be the main products. The CO selectivity was greater than 0.5 and normally increased with increasing temperature, while the CH₂O selectivity was less than 0.4 with a maximum at 550 K. In addition to Pd(111), the authors also extended the study to other metal fcc(111) surfaces by employing linear scaling relations in the microkinetic model. The obtained volcano plots of the product reaction rates are given in Fig. 16. Pd, Pt, and Rh(111) surfaces were selective to CO and/or CH₂O productions, where the metallic site led to CO production, and the surface O* site led to CH₂O production. Ag, Au, and Cu(111) surfaces were selective to CH₂O and/or CH₃OH productions, with the O*-assisted mechanism preferred for all dehydrogenation steps.

Fig. 16 Logarithms of the calculated production rates (s⁻¹ per site) of (a) CO₂, (b) CO, (c) CH₂O, and (d) CH₃OH during CH₄ oxidation at T = 523 K, P_CH4 = 0.91 bar, P_O2 = 0.11 bar, P_H2O = 0.02 bar, and P_H2, P_CH3OH, P_CH2O, P_CO, and P_CO2 = 10⁻³⁹ bar. ΔE_C and ΔE_O are taken relative to gas-phase CH₄, H₂O, and H₂.⁹⁵ Reproduced from ref. 95 with permission from the American Chemical Society, copyright 2018.

Catalysts improving carbon formation resistance. Like SRM and DRM, carbon deposition is a commonly encountered phenomenon occurring in the POM process that results in catalyst deactivation, especially for Ni-based catalysts. The application of bimetallic catalysts could effectively reduce the carbon deposition problem and sometimes also improve the catalyst activity. For instance, the DFT calculations of He et al.²³⁰ revealed an improved performance of Ni by alloying it with Co, which enhanced both catalyst activity and carbon formation resistance for methane oxidation. Alloying Ni with Cu could also improve the catalyst carbon formation resistance but with reduced activity as a cost.

Concerning direct partial oxidation to synthesis gas, theoretical studies mainly focus on single-atom alloy (SAA) catalysts rather than traditional bimetallic catalysts. Zhang et al.¹⁴¹ investigated the effect of Ni(111) alloying with Pt on this reaction via a DFT study. It was found that by doping Pt on Ni(111) methane dissociation was greatly promoted. However, the activation energy of CO formation (RDS: CH + O → CHO) and that of H₂ formation (H + H → H₂) were both observed to increase on the NiPt(111) surface, indicating that alloying Ni(111) with Pt might cause suppressed CO and H₂ production. The results demonstrated that NiPt bimetallic catalysts were beneficial to methane adsorption and dissociation and atomic C/H adsorption, but might be less favorable for synthesis gas formation.^71,141

Meng et al.⁹⁰ investigated POM to synthesis gas over a D-Pd/Cu(111) (doped Pd/Cu(111)) catalyst and over an A-Pd/Cu(111) (adsorbed Pd/Cu(111)) catalyst via DFT calculations. Through comparison, the D-Pd/Cu(111) catalyst showed more thermodynamic stability and exhibited a higher capacity for sintering resistance. In their other study,²³¹ Pt was doped on Cu(111) and Ni(111) surfaces to understand the bimetallic catalyst activity and coke-resistance during POM using DFT calculations. Fig. 17 gives a comparison of methane dissociation reaction pathways on Cu(111), Ni(111), Pt₁Cu(111) and Pt₁Ni(111) surfaces. The activation barriers of CH₄ dissociation were largely reduced by the introduction of a single Pt atom on the Cu(111) surface. Compared to Pt₁Ni(111) and Ni(111), Pt₁Cu(111) displayed similar activation barriers of CH₄ dissociation to CH₃, but a higher barrier of CH dehydrogenation to C. These results indicated that Pt₁Cu(111) can effectively promote methane activation, but not affect the excellent coke resistance. Towards CO formation, the dominant pathway was CH → CHO → CO on both Pt₁Cu(111) and Pt₁Ni(111), with CH + O → CHO as the RDS. The lower activation energy of CH + O → CHO on Pt₁Cu(111) than on Pt₁Ni(111) illustrated a higher potential of CO formation on Pt₁Cu(111), which prevented C formation and resulted in a better coke-resistance. The performance of the Pt single-alloy Cu catalyst was significantly enhanced, compared with that of commercial Ni-based catalysts.

Fig. 17 Comparison of methane dissociation reaction pathways on Pt₁Cu(111) and Pt₁Ni(111) surfaces.²³¹ Reproduced from ref. 231 with permission from the Centre National de la Recherche Scientifique (CNRS) and the Royal Society of Chemistry, copyright 2020.

In addition to bimetallic catalysts, the employment of supports could also effectively improve the performance of the catalysts. Guo et al.²³² investigated methane dissociation and partial oxidation on Rh₄/Ana-Ov (oxygen-defective anatase TiO₂ supported Rh) and Rh₄/Rut-Ov (rutile TiO₂ supported Rh) by DFT, with emphasis put on carbon deposition resistance. Rh₄/Ana-Ov showed a higher activation barrier of C–H bond breaking in methane decomposition and a lower energy barrier of CH₂ + O → CH₂O (RDS for CO formation) compared to that on Rh₄/Rut-Ov, implying a strong carbon deposition resistance and a high synthesis gas formation activity of the Rh₄/Ana-Ov catalyst. The microkinetic modeling of Rh₄/Ana-Ov illustrated a high (up to 90%) CO selectivity, which was increased with temperature. In another study of Guo et al.,²³³ DFT calculations were used to analyze the size-dependent carbon deposition resistance of Rh-clusters supported on anatase (Rh_x/Ana-Ov) for POM. Rh₁/Ana-Ov, Rh₄/Ana-Ov, and Rh₁₃/Ana-Ov were applied to simulate different cluster sizes. It was found that Rh₁/Ana-Ov displayed a much higher apparent energy barrier of methane dissociation and lower energy barrier of CH₂ + O → CH₂O (RDS for CO formation) among the three models, which could be the one owing to the strong carbon deposition resistance and high catalytic activity. Therefore, SAA catalysts were suggested as candidates to reduce carbon deposition for POM processes.

Size dependence of activity. The kinetic study of Kondratenko et al.²¹⁰ investigated the size effect on activity and selectivity for POM to synthesis gas over γ-Al₂O₃ supported Rh NPs. As the particle size increased, the methane conversion and H₂/CO ratio were decreased. Meanwhile, the apparent TOF of CO formation and CO selectivity were strongly reduced, indicating a size-dependent kinetics of this process on the supported Rh NPs. However, the overall mechanism of POM was size-independent, which mainly followed an indirect (CRR) mechanism through methane combustion and reforming to form CO and H₂.

According to the above kinetic, DFT and microkinetic studies, the mechanism of POM to synthesis gas is still under debate. The exothermic property of POM reaction makes it a challenge to elucidate the reaction mechanism. Nevertheless, owing to the potential of POM in methane conversion, there is a great possibility to attract more attention to this process in the future.

2.3 Methane conversion on oxides

There are extensive pieces of literature on methane activation over various oxide catalysts, some of which have been reviewed previously^{39,63,234–239} and among which methane oxidation was found to be the most studied reaction. Methane oxidation catalysis involves the introduction of methane and gaseous molecular oxygen into the reactor. Since both the adsorbed oxygen from the gas phase and lattice oxygen from the oxide catalyst can possibly participate in the reactions, it is essential to understand the relative role between them. It was earlier proposed that, instead of the adsorbed oxygen from the gas phase, the concentration of lattice oxygen controls the selectivity of the metal oxide catalyst for total oxidation.^239,240 This opinion is consistent with the MVK mechanism.

As early as 1993, Otsuka et al.²⁴¹ reported that CeO₂ could be used as an oxidant to transform methane into synthesis gas with a H₂/CO ratio of 2 at 873–1073 K. During the redox cycle of cerium oxide, methane was directly converted to CO and H₂, and CeO₂ was partially reduced to CeO_2−n, as shown in eqn (6):

CeO₂ + nCH₄ → CeO_2−n + nCO + 2nH₂ (6)

The reduced CeO_2−n could be used to convert CO₂ into CO, with oxygen recovery to CeO₂, as shown in eqn (7):

CeO_2−n + nCO₂ → CeO₂ + nCO (7)

The addition of Pt to CeO₂ accelerated the formation of synthesis gas, while the H₂/CO ratio became higher than 2 when the reduction of the Pt-doped CeO₂ catalyst was over 60 min, which implied coke formation on the cerium oxide surface after a period of reduction.

Encouraged by experimental results on CeO₂ oxides, methane oxidation has been studied by DFT calculations on CeO₂,^110,242 and CeO₂ doped with Zr or Pd,^110,242,243 and Pt.¹¹³ As discussed in Section 2.1.2, the C–H bond activation of methane is well correlated with the surface reducibility of CeO₂ measured by the formation energy of O vacancy. A comparative study of methane oxidation was performed by a DFT+U on Pd_xCe_1−xO₂(111), CeO₂(111) and PdO(100) surfaces.²⁴² The reaction mechanism is similar to that on transition-metal surfaces, where methane oxidation took place via CH₄ → CH₃* → CH₂* → CH* → HCO* → CO* → CO₂ at low coverage as shown in the free energy diagrams in Fig. 18. C–H bond activation in methane is the RDS on all three surfaces. Carbon formation was not favored over any surface, and the formation of POM products was also not thermodynamically favorable, which, however, was different from the results obtained by Otsuka et al.²⁴¹ that synthesis gas was the primary product on the CeO₂ surface.

Fig. 18 Reaction free energy diagrams for CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(g) over (a) Pd_xCe_1−xO₂(111), (b) CeO₂(111) and (c) PdO(100) at T = 298 K and P_CH4 = 0.01 atm, P_O2 = 0.04 atm, P_H2O = P_CO2 = 10⁻⁶ atm. Insets show the most stable intermediates in methane oxidation over the three surfaces. Ce is displayed as tan (light), Pd as light blue (gray), O as red (dark), and H as white.²⁴² Reproduced from ref. 242 with permission from Elsevier, copyright 2011.

Importantly, doping CeO₂ with Zr or Pd,^110,242,243 and Pt¹¹³ decreased the formation energy of O vacancy of the neighboring oxygen atoms and thus reduced the C–H activation energy barrier. Doping with metals is an effective method to increase the activity of C–H bond activation. The methane activation barrier was the lowest on the Pd_xCe_1−xO₂(111) surface, lower than those on CeO₂(111), PdO(100), and Pd*/CeO₂(111), and even lower than those on Pd(111) and stepped and kinked Pd(211) surfaces.²⁴³

Jin et al.²⁴⁴ conducted experimental and theoretical studies of oxidation of ventilation air methane on Fe₂O₃ and CuO catalysts. The mechanism schematics of CH₄ oxidation on the two surfaces are given in Fig. 19(a), together with calculated reaction energies. They implied that CH₄ dissociation was the RDS, with reaction energies as 2.76 eV for Fe₂O₃(0001) and 0.47 eV for CuO(110), due to the strong C–H bonding. It also revealed that the oxygen vacancy (OV) could recover quickly when additional O₂ molecules reached the metal oxide surface conducting adsorption and dissociation. Therefore, the reduction of Fe₂O₃ and CuO could rarely occur, which remained stable without transition to the reduced phase. The schematic configurations of surface bonding for methane oxidation on the O-terminated Fe₂O₃(0001) are presented in Fig. 19(b). An OV was generated when H₂O was released (Fig. 19b(A–C)), followed by O₂ filling in the OV to generate –Fe–O–O (Fig. 19b(D)). The formation of C–O bonding in Fig. 19b(F) was favorable to activate the C–H bond of CH_x due to the spontaneous transfer of the C–O single bond to the C=O double bond with the breakage of C–H. The DOS profiles in their work showed that OVs generated more local states over reduced metal surfaces, which were the active sites for O₂ adsorption and thus made the C–H activation and O₂ splitting more feasible. The under-coordinated metal atoms and OVs could stabilize CH_x radicals to promote CH₄ dissociation (RDS), which are therefore essential for potential high-performance CH₄ oxidation catalysts.

Fig. 19 (a) Mechanism schematics of CH₄ oxidation on the surfaces of Fe₂O₃ and CuO under the reaction atmosphere with abundant oxygen, together with calculated reaction energies in units of eV. Two values of the reaction energy are labelled for each elementary reaction: one is for Fe₂O₃, and the other given in the parentheses is for CuO. Red O indicates that the oxygen is from Fe₂O₃ or CuO, rather than adsorbed O₂. (b) Schematic configurations of surface bonding for CH₄ oxidation on the O-terminated Fe₂O₃(0001) surface. (A–C) show the generation of an OV, and (D–F) describe the recovery of the OV from O₂ dissociative adsorption. O_s represents the surface oxygen and OCO denotes one-coordinated oxygen.²⁴⁴ Reproduced from ref. 244 with permission from the PCCP Owner Societies, copyright 2015.

In addition to the above metal oxide catalysts, IrO₂ was also reported to be an effective catalyst to activate the C–H bond of methane.²⁴⁵ According to the DFT study of Yeh et al.,²⁴⁶ formaldehyde formation was the most favorable reaction for methane oxidation. The reaction was limited by formaldehyde desorption, with a desorption energy of 1.10 eV on an IrO₂(110) surface, and the reaction barrier was lower than 0.70 eV. An external electric field was employed to modify the reactivity of IrO₂(110), which was found to have no apparent influence on methane dehydrogenation and C–O coupling but could regulate the desorption energy of the adsorbates, especially promoting methane oxidation to formaldehyde over an O-rich IrO₂(110) surface.

Despite the most cases that lattice O was favorable for methane oxidation, surface oxygen adsorbed or “activated” O played an important role in the POM reaction on oxides with high formation energies of oxygen vacancy, such as MoO₃(100)²⁴⁷ and SiO₂ surfaces.²⁴⁸

Perovskite oxides (ABO₃) have stimulated interest in various redox cycle reactions (e.g. methane oxidation) due to their excellent crystal structure and redox reversibility.^249–251 Methane oxidation has been studied on LaFeO₃ based perovskites by DFT calculations focused on the active sites and oxygen mobility and their effects on catalyst activity and selectivity.^252,253 The mechanism and structure requirements of selective and total oxidation of methane in a chemical looping process are both experimentally and theoretically examined on La_0.5Sr_0.5Fe_1−xCo_xO_3−δ perovskites. The substitution of Sr for La at the A site and the substitution of Co for Fe at the B site of the ABO₃ perovskites significantly reduced the formation energy of oxygen vacancy. The lattice O diffusion rate and the activity of methane conversion increased, and the selectivity decreased upon decreasing the formation energy of oxygen vacancy. The formation energy of oxygen vacancy increased upon increasing the lattice oxygen charge. Recently, Zhang et al.²⁵² employed combined electrical conductivity relaxation measurements and DFT calculations to study the influence of FeO₆ octahedral distortion on lattice oxygen in La_1−xCe_xFeO₃ perovskites for POM coupled with a CO₂ splitting process. It was found that changing the content of Ce₃₊ substitution in La_1−xCe_xFeO₃ (x = 0, 0.25 0.5, 0.75, 1) resulted in a change in Fe–O bond-length variance, which could tune the FeO₆ octahedral distortion degree in La_1−xCe_xFeO₃, activate the lattice oxygen and significantly improve the catalysts’ performance in chemical looping POM-CO₂ splitting.

Methane oxidation on spinel structured oxides such as CaFe₂O₄²⁵⁴ and NiCo₂O₄²⁵⁵ was studied experimentally and theoretically. The deep reduction of calcium ferrite facilitated the production of synthesis gas through methane dehydrogenation and selective oxidation of C to CO. The mechanism difference of POM to form CO and H₂ with the CaFe₂O₄ carrier can be associated with the differences in the oxide phases existing during the reduction process, oxygen species concentration, and bonding in the lattice structure.²⁵⁴ The metal total combustion on NiCo₂O₄ was observed to follow (1) O₂ dissociation on surface O vacancies; (2) the dissociated O atoms filled into O vacancies and coupled with H atoms to form OH and H₂O; (3) CH₄ dissociation to form CH₃* on Ni cations with a subsequent oxidation to CH₃O*; (4) CH₃O* dehydrogenation to form CH₂O* with a subsequent ODH (with the O species of the nearby Co site) to form CHO*; and (5) transformation of CHO* to products (CO₂ and H₂O) via two subpathways including OCHO dehydrogenation and CO oxidation. The high activity of NiCo₂O₄ in CH₄ conversion to H₂O and CO₂ at a relatively low temperature together with its low cost leads to NiCo₂O₄ being very promising for the removal of CH₄ in the exhaust gas of a natural gas engine through complete oxidation.

Unlike the extensive literature reported for methane oxidation, only a few theoretical studies have been conducted for SRM and DRM reactions on oxide catalysts, such as SRM on a Ce_0.90Ni_0.05Ru_0.05O₂ (CNR) catalyst,²⁵⁶ and DRM on Rh-substituted lanthanum zirconate pyrochlore (LRhZ),²⁵⁷ NiO–MgO,²⁵⁸ and Ni–CaO.²⁵⁹ In SRM and DRM, the metal oxides are normally used as supports to favor possible H₂O^{92,200,260,261} or CO₂ activation^{40,189,262,263} coupled with methane activation on transition metal surfaces. The relatively high activity and low cost of Ni-based catalysts, as well as good performance of other metal catalysts for SRM and DRM, make the research mainly focused on metal surfaces.

3. C–H bond activation in ethane

Ethylene is the most critical chemical building block which could be applied to synthesize various downstream products. It can be produced by noncatalytic thermal dehydrogenation, catalytic dehydrogenation, and oxidative dehydrogenation. Steam cracking is still the dominating route for industrial production of ethylene, but other technologies have also gained increasing attention. Several excellent reviews have addressed the progress in ethane dehydrogenation and oxidative dehydrogenation of ethane.^3,264–273 Here we summarize the progress of theoretical catalysis on C–H activation of ethane.

3.1 Ethane dehydrogenation on metal surfaces

Ethane is physisorbed on various metal and metal oxide surfaces, and the composition of the catalyst changes the physisorption very much. The C–H bond activation of ethane is similar to the C–H activation of methane and follows the universal scaling relationship of the activation energy of C–H activation of light alkanes. The C–H activation of ethane deals with the secondary C sp³–H bond cleavage. The C–H activation energy of ethane is generally lower than the one of methane, due to the weaker strength of 2° than 1° C–H bonds.

3.1.1 Reaction mechanism. The exact reaction mechanism of dehydrogenation of ethane is still under debate, due to the fact that a large variety of materials can catalyze this reaction. The 4 step Horiuti–Polanyi mechanism is commonly used to describe the dehydrogenation mechanism on metal surfaces.²⁷⁴ It consists of 4 main steps: dissociative adsorption of alkanes, C–H cleavage of a second hydrogen atom, the formation of a hydrogen molecule, and subsequent desorption of both the hydrogen and the olefin. Both the dissociative adsorption of ethane and C–H cleavage of a second hydrogen atom^275–277 have been suggested as the RDSs. Pt is the most active pure metal for ethane dehydrogenation to produce ethylene, due to its superior activity towards C–H bond activation and low activity towards C–C bond cleavage.²⁷⁸ On the Pt surface, it is generally accepted that the reaction goes through ethane dehydrogenation to ethyl, CH₃CH₂*, then to ethylene, while the non-selective pathway to methane and deeply dehydrogenated species is predicted to go through dehydrogenation via CH₃CH*.

The geometries of the transition states for activation of ethane and ethyl C–H bonds on Pt(111) and Pt(211) surfaces are shown in Fig. 20, with the corresponding activation barriers summarized in Table 1.²⁷⁹ The C–H bond activation of ethane on both surfaces occurs through the simultaneous interaction of C and H with a surface Pt atom, forming a C–Pt–H three-membered ring structure (Fig. 20a and d). The C–Pt–H three-membered ring structures are also found in ethyl to ethylene on both surfaces (Fig. 20c and f) and ethyl to CH₃CH* on the Pt(211) surface (Fig. 20e). For the transition states of ethyl to CH₃CH* on the Pt(111) surface, ethyl is bonded to Pt surfaces via the C atom, where the H in C–H is bonded to adjunct Pt (Fig. 20b). The energy barriers of the three steps follow the order Pt(211) < Pt(111), as shown in Table 1. Similarly, the energy barriers of Pt(433) step < Pt(433) terrace,²⁸⁰ and Pt₅₅ < Pt(111)²⁸¹ are obtained. The stepped Pt surfaces (or small Pt particles) having coordinatively unsaturated Pt atoms are therefore kinetically more active for the dehydrogenation of ethane to form ethylene than the flat surfaces.

Fig. 20 Geometries of the transition states for the activation of ethane and ethyl C–H bonds on Pt(111): (a) CH₃CH₂–H, (b) CH₃CH–H, and (c) CH₂CH₂–H; and on Pt(211): (c) CH₃CH₂–H, (d) CH₃CH–H, and (e) CH₂CH₂–H.²⁷⁹ Reproduced from ref. 279 with permission from the American Chemical Society, copyright 2010.

Table 1 Calculated energy barriers (E_act) for ethane and ethyl dehydrogenation on different metal surfaces

Surface	E act (eV)			XC functional	k points	Unit cell	Ref.
	CH3CH3(g) → CH3CH2*	CH3CH2* → CH3CH*	CH3CH2* → CH2CH2*
Pt(111)	0.54	0.88	0.81	PBE	5 × 5 × 1	2 × 2	279
Pt(211)	0.08	0.27	0.44		3 × 4 × 1	2 × 1
Pt(110)-(1 × 2)	0.38	0.33	0.29	PW91	—	2 × 2	285 and 286
Pt(433) terrace	0.65	0.81	0.71	PW91	1 × 2 × 1	1 × 3	280
Pt(433) step	0.33	0.08	0.27
Al6O11 decorated Pt(433)	0.69	0.78	0.73
Pt(111)	0.84	—	0.67	PBE	3 × 3 × 1	4 × 4	281
Pt55	0.57	—	0.48		1 × 1 × 1	—
Pt(111)	0.91	0.91	0.89	PW91	6 × 6 × 1	2 × 2	282 and 283
Pt3Sn/Pt(111)	1.19	1.04	1.07
PtSn/Pt(111)	1.58	1.28	1.28
Pt(111)	0.90	0.95	0.88	PW91	6 × 6 × 1	2 × 2	284
Pt3Sn/Pt(111)	1.18	1.30	1.08
Pt3Sn(111)	1.08	0.84	0.88

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In addition to activity, ethylene selectivity is another important factor in characterizing ethane dehydrogenation. From Table 1, one can see that the energy barrier of CH₃CH₂* → CH₃CH* is lower than that of CH₃CH₂* → CH₂CH₂* for both the Pt(211) and Pt(433) steps. It means that these under-coordinated step sites preferably promote deep dehydrogenation, resulting in coke formation and catalyst deactivation.²⁸⁰ By decorating the step with AlO_x species (Al₆O₁₁ decorated Pt(433)), the step sites can be blocked, leading to suppression of deep dehydrogenation and coke formation. The deep hydrogenation can also be suppressed by doping Pt with Sn. As shown in Table 1, Pt–Sn surface alloys with different site coverages of Sn and Pt–Sn bulk alloy have been investigated for ethane dehydrogenation via DFT calculations.^282–284 The activation energies of the first and second C–H bond cleavage steps for ethylene formation were calculated as Pt(111) < Pt₃Sn(111) (bulk alloy) < Pt₃Sn/Pt(111) (surface alloy) < PtSn/Pt(111) (surface alloy). The addition of Sn into Pt increases the C–H and C–C bond cleavage barriers, which inhibits the catalyst activity but favors ethylene selectivity over carbon formation. A more detailed discussion on the site coverage of Sn and the location of the Sn on Pt catalyst for ethane dehydrogenation can be seen in Section 3.1.2.

Nørskov and co-workers²⁸⁷ developed a descriptor based microkinetic model for ethane dehydrogenation over close-packed metal surfaces and varied reaction conditions. The C₂H₄ turnover frequency and selectivity can be predicted as functions of the adsorption energies of two key intermediates CH₃CH* and CH₂CH₂*. The model results showed that Pt and Pt alloys were among the most active catalysts for ethane dehydrogenation, as shown in Fig. 21(a). The catalytic activity followed the order IrPt₃ ≈ Pt > Re > Ir > Ru > Rh > Ni, Co, while Cu, Zn, Au, In, and Ag were almost inactive. The Sn–Pt and Zn–Pt alloys showed reasonable activity, but it was lower than that of Pt. The Sn and Zn alloyed with Pt lowered the adsorption strength of CH₂CH₂*, and thus significantly enhanced ethylene selectivity, as shown in Fig. 21(b). The activity trend predicted by micro-kinetic modeling is in general agreement with experimental results.

Fig. 21 (a) Activity volcano for ethylene production at 873 K, 0.2 bar C₂H₆(g), 2 × 10⁻⁴ bar C₂H₄ (1% carbon conversion), 0.6 bar H₂(g), and 10⁻⁹ bar CH₄ and 10⁻¹² bar C₂H₂. (b) Map of carbon-specific selectivity.²⁸⁷ Reproduced from ref. 287 with permission from Elsevier, copyright 2019.

Bell and co-workers²⁸⁸ applied tetrahedral metal clusters in DFT calculations to represent metal NPs to study the elementary processes involved in ethane dehydrogenation. The DFT estimated free energy activation barrier for the dissociative adsorption of ethane to present activity trend followed Pt₃Sn > Pt₃Ir > Pt₄, which agreed relatively well with the experimentally measured activity order. The same group investigated the effects of intermetallic interaction on alkane dehydrogenation systematically using Pt-based, subnanometer-sized alloy cluster catalysts.²⁸⁹ The alloys were modeled with Pt₃X (X = Pd, Sn, Ge, Si, In, Ga, Au, Ag, Cu, and Ir). For all the alloy catalysts, the RDS was found to be the same, namely the first C–H bond cleavage. The activation energy of the first C–H cleavage on the alloy clusters was predicted to be in the order of Pt₃Si < Pt₃Ge < Pt₃Sn < Pt₃Ir < Pt. No significant BEP relationship could be found with respect to atomic H or CH₃ group binding energy for the Pt alloys. However, the catalyst activity correlated well with the HOMO–LUMO gap of the clean catalyst. Smaller HOMO–LUMO gaps indicated higher activity due to the increased flexibility of the valence electron at the active site.

3.1.2 Effect of promoters on selectivity and deactivation. Unpromoted Pt catalysts suffer from low alkene selectivity and rapid deactivation due to coking. Both undesired phenomena are mainly a consequence of deep dehydrogenation of surface C₂H₄*, leading to C–C bond breaking.^275–277 Improvements of catalyst activity, selectivity, and stability can be achieved by alloying Pt with Sn and by adding hydrogen to the alkane feed.^{277,282–284} Pt alloys have been widely studied both experimentally and theoretically. DFT calculations have been used to provide a molecular understanding of those promoters for improving ethylene selectivity and catalytic stability. Alloys of Pt with Sn, Zn, Ga, Ge, and In have been widely studied, and Pt–Sn is the most studied system. Experiments showed that Pt–Ir and Pt–Sn had higher ethylene selectivity than Pt, and Pt–Ir exhibited better stability to coke deposition than Pt–Sn.²⁸⁸ Microkinetic modeling²⁸⁷ and the cluster model^267,289 suggested a higher selectivity of Pt–Sn compared to Pt. However, the sub-nanometer cluster model^288,289 predicted the selectivity trend. The cluster model predicted a higher C–H cleavage activation energy of ethylene and thus high activation energy of C–C cleavage, which resulted in a high ethylene selectivity and better stability on Pt₃Ir than Pt, in good agreement with experimental observation.

The cluster model²⁸⁹ predicted relatively high ethylene selectivity on Pt-based catalysts due to their relatively high barriers for direct C–C bond cleavage compared to C–H bond breaking. A natural bond orbital analysis revealed that the d-orbital shape of the HOMO with its pronounced nodal features better facilitated the breaking of a C–H bond than that of a C–C bond due to better overlap with the C–H anti-binding orbital.

The site coverage of Sn and the location of the Sn on Pt catalyst do influence the catalyst performances for ethane dehydrogenation.^282–284 Kinetic reaction barriers were calculated for potential energy surfaces of C1 and C2 intermediates from C–H and C–C bond cleavage of ethane with ¼ and ½ surface monolayers of Sn.²⁸² Sn weakened the binding energies of all species at both coverages. At the lower Sn coverage (¼ monolayer), the effect was purely electronic since the binding geometries had not changed compared to those on the Pt(111) surface. At the higher coverage of Sn, a larger effect on reaction energies was observed due to the changes in the binding geometries as a result of the elimination of 3-fold hollow sites that consist of Pt atoms. In terms of the electronic effect, Sn can donate electrons to Pt atoms and reduce the binding energies of adsorbates to Pt and increase the barrier for C–H and C–C cleavage, as shown in Table 1. The increase in the barriers favors ethylene selectivity over carbon formation. The same group further studied the effect of tin in the bulk of PtSn alloys for ethane dehydrogenation.²⁸⁴ DFT calculations were performed on pristine Pt(111), a Pt₃Sn/Pt(111) surface alloy, and a Pt₃Sn(111) bulk alloy. The binding energies of adsorbates weakened on both Sn alloys. But on the bulk alloy, the binding energy was weaker than that on pure Pt but stronger than that on the surface alloy. Therefore, the activity trend for ethylene formation was predicted as pure Pt > bulk alloy > surface alloy based on the activation energies of the first and second C–H bond cleavage steps (Table 1). A selectivity descriptor was defined for ethane dehydrogenation as the energy difference between the activation energy for ethylene dehydrogenation (E_a, CH₂CH₂* → CH₂CH*) and the desorption energy of ethylene (ΔE_des, CH₂CH₂*) for several substitutional surface alloys. A smaller value indicates that further ethylene dehydrogenation is more favored over desorption and therefore predicts poor selectivity towards ethylene. The selectivity descriptor was calculated as −0.12, 0.04, and +0.36 eV for Pt, the bulk alloy, and the surface alloy, respectively. Therefore, the ethylene selectivity was highest on the surface alloy, followed by the bulk alloy and pure Pt.

The selectivity descriptor has been used to study a broader range of Pt–M surface alloys at low and high M coverages, including metals from groups 7–15.²⁸³ The Pt₃M/Pt(111) alloy surface was created by replacing one surface Pt atom with alloying element M, giving 1/4 ML surface coverage for M. There were two types of 3-fold hollow sites, namely Pt₃ and Pt₂M sites on Pt₃M/Pt(111) surfaces. A PtM/Pt(111) surface was created by replacing two surface Pt atoms with M, giving 1/2 ML surface coverage for M. On the PtM/Pt(111) surface, the 3-fold Pt₃ sites were removed, and 3-fold binding sites included Pt₂M and PtM₂ sites. 27 elements (M) were selected for this study, which comprised the TMs from groups 7–11 and the post-transition (P-T) metals from groups 12–15. The P-T metals included Zn, Cd, Hg, Al, Ga, In, Tl, Ge, Sn, Pb, Sb, and Bi. The TMs were further classified as nonpreferred transition (NT) metals and carbon-preferred transition (CT) metals based on the preferred binding site of a carbon atom (Fig. 22a). NT metals were transition metals where a carbon atom placed on Pt₃M/Pt(111) preferred to bind on Pt₃ sites. Conversely, the transition metals where C preferred to bind on Pt₂M sites over Pt₃M/Pt(111) were labeled CT metals. The NT metals included Mn, Fe, Co, Ni, Pd, (Pt), Cu, Ag, and Au. The CT metals included Tc, Re, Ru, Os, Rh, and Ir. On P–T and NT alloys, C, H, and CH preferred to bind to Pt₃ at 1/4 ML coverage and Pt₂M at 1/2 ML coverage. CH₃ preferred to bind to top sites of Pt at both coverages. On CT alloys, C, H, and CH preferred to bind to Pt₂M at 1/4 ML coverage and PtM₂ at 1/2 ML coverage. CH₃ preferred to bind to top sites of the M atom at both coverages. The scaling relationship was established between the desorption energy of ethylene and methyl binding energy (BE_CH3) (Fig. 22b and c) as well as the activation energy of ethylene dehydrogenation and the methylidyne dehydrogenation reaction energy (ΔE_CH) plus the methyl binding energy (BE_CH3) (Fig. 22d) on various Pt₃–M alloys. It indicated that alloying Pt with Pb, Bi, Tl, Sn, Sb, Hg, and In decreased the ethylene desorption energy and increased the activation energy of C–H activation of ethylene, thus resulting in higher ethylene selectivity.²⁸³

Fig. 22 (a) Binding site preferences of carbon atoms on three categories of alloying elements: post-transition (P-T) metals, nonpreferred transition (NT) metals, and carbon-preferred transition (CT) metals. Relationships between the methyl binding energy (BE_CH3) and the desorption energy of ethylene (ΔE_des) at (b) ¼ ML and (c) ½ ML coverage. (d) Relationships between the methylidyne dehydrogenation reaction energy (ΔE_CH) plus methyl binding energy (BE_CH3) and the ethylene dehydrogenation barrier (E_a, ethylene) for alloys at ¼ ML coverage. NT alloys in blue, P–T alloys in black, and CT alloys in red.²⁸³ Reproduced from ref. 283 with permission from the American Chemical Society, copyright 2017.

Cybulskis et al.²⁹⁰ investigated Zn promotion of platinum for ethane dehydrogenation by combining DFT, kinetic, and in situ spectroscopies. DFT calculations could accurately predict the electronic structure of Pt 5d valence orbitals in Pt/SiO₂ and PtZn/SiO₂. Zn lowers the energy of filled states of the Pt surface and weakens the binding energy between adsorbates and the Pt surface as well as increases the turnover rate of the reaction. In addition, Zn has a geometric effect, leading to the formation of a Pt₁Zn₁ intermetallic alloy with uniformly isolated Pt surface sites, which effectively suppresses hydrogenolysis and cracking reactions.

Ko et al.²⁹¹ investigated the influence of P doping into Ni-based catalysts on ethane dehydrogenation by combined DFT and experimental study. DFT calculations revealed that a Ni₂P(001) surface exhibited a similar CH₃CH₂–H activation barrier to, but a much greater CH₂CH–H activation barrier (an indicator of the coking tendency) than a Ni(111) surface. Meanwhile, the experimental study demonstrated a much higher ethylene selectivity (<80%) and less carbon deposition on the Ni₂P(2)/SBA-15 catalyst compared to Ni/SBA-15 (<1% ethylene selectivity). This highlights the potential of using metal phosphides as robust and selective catalysts for alkane dehydrogenation.

Ge is another promising promoter. It can enhance the catalyst selectivity without decreasing the catalytic activity. DFT calculations were performed on MgO-supported Pt₃ and Pt₇ with Pt₂Ge and Pt₇Ge clusters.²⁷⁸ It was found the Pt₂Ge could elongate the C–H bond more than Pt and had a lower activation barrier of 0.05 eV compared to 0.17 eV for pure Pt. Therefore, the activity of ethane dehydrogenation was not negatively affected by Ge. On the other hand, Ge quenched the unpaired electrons in the metal clusters, which were needed to activate alkenes for dehydrogenation. Ge in alloys made Pt interact less strongly with ethylene and therefore increased ethylene selectivity. For the smallest cluster size, the C binding energy was significantly reduced and increased catalyst resistance to deactivation due to coking.

3.1.3 Effect of Pt and Pt alloy particle size. Pt and PtSn alloy particle size effects were studied experimentally on ethane dehydrogenation by Bell and co-workers.²⁹² It was found that the ethane TOF increased monotonically with increasing particle size in the range of 1.5–8.5 nm, whereas the ethylene selectivity remained constant across all particle sizes. Their result suggested that ethane dehydrogenation was favored over flatter surfaces on large particles. The authors attributed the high TOF on large particles to the favored desorption of ethylene due to the lower binding energy of ethylene on terrace sites. The dehydrogenation and hydrogenolysis reactions have been studied on Pt(111) and Pt(211) with DFT calculations.²⁷⁹ On the Pt(211) surface, CH₂CH₂* and CH₃CH* can be generated very rapidly from ethane with low activation barriers (Table 1). However, the stronger CH₂CH₂* adsorption energy on Pt(211) makes the desorption of ethylene more difficult compared to Pt(111). On Pt(111), CH₃CH* can be dehydrogenated rapidly to form CH₃C*. The C–C bond cleavage takes place most possibly via CH₃CH₂, CH₃CH, and CHCH. More quantitative data on reaction pathways require detailed microkinetic modeling. More recent work showed that under-coordinated step edge sites bonded C₂H_x and CH_x species more strongly than terrace sites.²⁸⁰ These under-coordinated step edge sites promote deep dehydrogenation, resulting in coke formation and catalyst deactivation. Atomic layer deposition (ALD) of alumina on Pt step edge sites significantly suppresses unselective deep dehydrogenation and coke formation (Table 1). The experiment of decorating Pt with ALD of alumina results in a 4-fold increase in the TOF of ethylene formation.

Carbon deposition is also dependent on the particle size of Pt and PtSn alloy, as well as the Sn content. In general, carbon deposition under reaction conditions increases with increasing particle size, but higher Sn content suppresses carbon formation.²⁹²

3.2 Oxidative dehydrogenation of ethane

Oxidative dehydrogenation, which couples the endothermic dehydration of ethane with the strongly exothermic oxidation of hydrogen, exhibits higher ethane conversion and lower operation temperature compared to steam cracking, which leads to growing interest in this process. However, major practical challenges with ODH reaction still occur, which are (1) additional safety measures associated with O₂ in the feed and (2) the development of highly active and selective catalysts due to the high reactivity of olefins compared with the corresponding paraffins.²⁶⁵ The ODH of ethane has not been practiced on a large scale yet. The relatively higher reactivity of olefins is attributed to the direct interaction of the olefin with catalytic surfaces. Typical undesired side reaction involves total oxidation to form CO, CO₂, and water. The reaction occurs through oxygen insertion into the C–H bond or from the addition of oxygen to olefins.

The only feedstock that can achieve high selectivity to olefins is ethane because ethylene is sufficiently unreactive towards oxygen compared to ethane. This is evidenced by the bonding strength difference in paraffins and olefins. The weakest C–H bond in ethane has a bond energy of 4.35 eV, whereas the weakest C–H bond in ethylene has an energy of 4.60 eV. For propane and propylene, the weakest C–H bond has a bond energy of 4.16 and 3.74 eV respectively. A more significant difference exists for C–C bond energy; the weakest C–C bond in ethylene is a double bond with a bond energy of 7.46 eV compared to 4.29 eV in propylene, in which the weakest C–C bond is a single bond. In general, to achieve high selectivity, the weakest C–H or C–C bond in the olefin has to be less than 0.31 eV weaker than the weakest C–H bond in the reacting paraffin.²⁹³ This is true for ethane and ethylene, but not for propane and propylene.

3.2.1 Reaction mechanism with oxygen as an oxidant on metal oxides. According to the analysis at the molecular level, the ODH of ethane with O₂ as an oxidant takes place by the way that dissociated O species that originated from gas-phase O₂ reacts with H species dissociated from ethane on the surface to form H₂O and ethylene, as shown below.²⁹⁴

C_nH_2n+2 + 1/2O₂ → C_nH_2n + H₂O (8)

ODH normally accompanies the combustion of hydrocarbons, producing CO and CO₂. To avoid over-oxidation of hydrocarbons, lattice oxygen in metal oxides can be used as the alternative oxygen supplier for the ODH process, which is often called a chemical looping ODH process. Most of the catalysts that are active for the ODH of ethane fall into redox-active metal oxides such as V₂O₅,²⁹⁵ MoO₃,²⁹⁴ MoVTeNb mixed metal oxides,²⁹⁶ Co oxides,²⁹⁷ Ni oxides,²⁹⁸ and IrO₂.²⁹⁹ There is a general consensus that ODH of ethane on such materials follows a MVK²²¹ mechanism and the reactivity of oxygen plays a vital role in the C–H activation of ethane. That is, the lattice oxygen of metal oxides interacts with hydrocarbons to form oxygen vacancies (eqn (9)), followed by the regeneration process (eqn (10)).

C_nH_2n+2 + M_xO_y → C_nH_2n + M_xO_y−1 + H₂O (9)

M_xP_y−1 + 1/2O₂ → M_xO_y (10)

V₂O₅ catalysts. The most prominent redox metal oxides for ethane ODH are supported V₂O₅ catalysts. The oxide support does not participate in the reaction, but it does influence the reactivity and stability of the oxygen bonded to V.³⁰⁰ Three types of metal–oxygen bond have been identified in the surface vanadium species as illustrated in Fig. 23, including terminal V=O bonds, bridging O atoms between V and the support (V–O–S), and bridging O atoms between two V cations (V–O–V).³⁰¹ The isolated VO₄ species on the support contains the first two types of V–O bonds, while the polymeric VO₄ species contains all three V–O bonds.

Fig. 23 Isolated and polymeric VO₄ species in supports.³⁰¹ Reproduced from ref. 301 with permission from the Royal Society of Chemistry, copyright 2011.

Ethane ODH pathways on vanadium oxide catalysts were elucidated by kinetic and isotopic tracer and exchange measurements.³⁰² The lack of exchange products (C₂H_6−xD_x or C₂H_4−xD_x isotopomers) revealed that the first C–H bond cleavage in ethane and ethylene was an irreversible and kinetically relevant step in ODH and combustion reactions. ¹⁶O₂–¹⁸O₂–C₂H₆ reactions on supported V¹⁶O_x domains led to the initial appearance of ¹⁶O from the lattice in the products H₂O, CO, and CO₂, evidencing the involvement of lattice oxygen in C–H bond activation steps. The emerging paradigm is that the development of suitable catalysts requires fundamental insight into the reaction mechanism on a molecular level, including the details of the interactions with the catalytic surfaces and the associated gas-phase reactions. The theoretical calculation has been used to provide a molecular understanding of active sites and reaction mechanisms on vanadium-based oxides. Similar activity of oxygen species and reaction mechanisms of C–H bond activation have been found on ethane ODH²⁹⁵ as well as propane ODH³⁰³ on the V₂O₅(001) surface. The most favorable pathway occurred on the O(1) (V=O) site through a radical mechanism with an activation energy of 1.52 eV;²⁹⁵ V–O–V was less active toward C–H bond activation (1.63 eV) through an oxo-insertion mechanism but much more selective towards ethylene formation. However, the terminal O site exhibited a more favorable side reaction leading to acetaldehyde than to ethylene. The first C–H activation step was the RDS, in good agreement with the experimental observation.³⁰² Water and acetaldehyde would desorb from the surface to create vacant O(1) sites easily. The oxygen molecule can re-oxidize the reduced vanadium, which is exothermic by 3.77 eV, with a barrier of 1.52 eV. Obviously, the surface of the catalyst can be re-oxidized easily at high temperatures when it is exposed to O₂. A more detailed discussion on the active sites, the reactivity of surface oxygen species, and the reaction mechanism of C–H bond activation of light alkanes can be seen in Section 4.2.

MoO₃ catalysts. The surface stability and equilibrium morphology of MoO₃ have been investigated by DFT calculations.³⁰⁴ The (010) surface has the lowest surface energy among the surfaces exposed to the gas.³⁰⁴ The ethane ODH mechanism on the MoO₃(010) surface was investigated by the first-principles study using the on-site Coulomb correction.²⁹⁴ There are three types of surface oxygens, namely terminal O and symmetric and unsymmetric Mo–O–Mo, and the terminal O is the main active site. Two stable configurations of ethylene adsorption on the MoO₃(010) surface, namely horizontally and vertically adsorbed ethylenes, were identified. The horizontal adsorption favors ethylene formation with a barrier of 1.36 eV, which is lower than that of V₂O₅. The vertical adsorption of ethane favors acetaldehyde formation along the α-ODH pathway, and the ethylene oxide formation along the β-ODH pathway. The β-ODH pathway may also produce ethylene from the CH₂CH₂O intermediate, with the second C–H bond activation of ethane as the RDS. Towards horizontal C₂H₆ ODH reaction (the dominant ethylene formation pathway), the first C–H bond activation of ethane is the RDS. This is in agreement with the kinetic study that irrespective of the oxidant's chemical identity (O₂, CO₂ or H₂O), ethane activation occurs via the kinetically relevant C–H activation of C₂H₆ on the lattice O of MoO_x, forming ethylene.³⁰⁵
MoVTeNb mixed metal oxides. MoVTeNb mixed metal oxides have exhibited high selectivity and yields to C₂H₄. The catalyst is typically composed of two compounds Mo_7.8V_1.2Te_0.937NbO_28.9 and Mo_4.31V_1.36Te_1.81Nb_0.33O_19.81, which are referred to as M1 and M2 phases, respectively.³⁰⁶ The structure of the M1 phase is illustrated in Fig. 24(a). It is generally accepted that the M1 crystalline phase is responsible for high activity and selectivity due to its ability to catalyze the initial homolytic H abstraction from alkanes.³⁰⁷ Both the basal [001] plane³⁰⁸ and lateral surface^309,310 have been reported to be responsible for the activation of alkanes. The S2–S4–S7 metal positions were proposed as the catalytic centers for alkane activation. The crystal termination of the M1 phase did have an impact on the intrinsic activity of ethane ODH.²⁹⁶ A quantitative correlation was found between the sum of the surface areas of facets (001), (120), and (210) at the surfaces of the M1 crystals and the activity, demonstrating that multiple facets were involved in the reaction. Different facets would have different degrees of exposed active sites, and therefore different catalytic activities. The number of different facets can be tuned by changing the crystal morphology of the M1 phase of MoVTeNbO_x catalysts.

Fig. 24 (a) Two-dimensional diagram of the MoVTeNbO_x M1 unit cell viewed in the [001] direction with 13 cation sites labelled as in the literature.³¹¹ Active site centers are composed of metal positions S2–S4–S7 (red and green), located between unit cells.²⁹⁶ Reproduced from ref. 296 with permission from Wiley-VCH, copyright 2016. (b) Accessibility of surface catalytic sites to reactants on VO_x/SiO₂ and MoVTeNbO as well as C₂H₆/C₆H₁₂ rate ratios on MoVTeNbO relative to the corresponding values on VO_x/SiO₂. (c) vdW-DF2 derived electronic energies and (d) structures of transition states for C₂H₆ ODH (TS1, TS2), parallel O-insertion in ˙C₂H₅ (TS3) and sequential O-insertion in C₂H₄ (TS4) at O-atoms exposed in heptagonal pores of double-layer MoVTeNbO.³¹² Reproduced from ref. 312 with permission from the American Chemical Society, copyright 2018.

In addition to the surface reaction, C₂H₆ ODH can also occur on M1 phase MoVTeNb mixed oxides’ micropores, which was considered to be the reason for the high ethylene yields at moderate temperatures.^312,313 Deshlahra and co-workers³¹² assessed the role of the M1 phase heptagonal channel micropores in regulating reactivity and selectivity using reactant size-dependent kinetic probes and DFT treatments for C₂H₆ and C₆H₁₂ (cyclohexane) activations inside and outside the micropores and compared with nonmicroporous vanadium oxides (VO_x/SiO₂). As shown in Fig. 24(b), both C₂H₆ and C₆H₁₂ activations can take place on the VO_x/SiO₂ surface and MoVTeNbO external surfaces. Inside the MoVTeNbO micropores, C₂H₆ activation is possible due to a tight guest–host fit, while C₆H₁₂ cannot access intrapore sites because of the large kinetic diameter. The measured C₂H₆/C₆H₁₂ activation rate ratios on MoVTeNbO were much higher than those measured on VO_x/SiO₂ and estimated by DFT calculations on the external surfaces, demonstrating that most C₂H₆ activations on MoVTeNbO occur inside the micropores under typical conditions. MoVTeNbO and VO_x/SiO₂ exhibited similar product selectivities for C₆H₁₂ oxidation, while for C₂H₆ oxidation, the ethylene selectivity was much higher on the former oxide. This suggested that the external surfaces of MoVTeNbO displayed a similar ability to activate C–H bonds and prevent O-insertion in products with VO_x/SiO₂, but the micropores in MoVTeNbO are more selective for C–H activation, which was confirmed by DFT calculations. The DFT calculated electronic energies and structures of transition states for C–H activation and O-insertion in C₂H₆ and C₂H₄ inside the heptagonal pores of MoVTeNbO are shown in Fig. 24(c) and (d), respectively. C₂H₆ ODH is the dominant reaction pathway, with the first C–H activation as the RDS and ethylene as the product. The C–O bond formation via two O-insertion pathways is hindered due to steric hindrances, which require much bulkier CH₂ groups in close contact with concave pore walls (top views of TS3 and TS4 in Fig. 24d). Therefore, the heptagonal pores of MoVTeNbO enhance ethylene selectivity by enhancing C–H activation and suppressing O-insertion reactions via a combination of van der Waals (vdW) and steric effects.

Fig. 25 DFT calculated energy profiles of reforming and ODH of ethane on (a) Pt-terminated CoPt(111) and (b) mixed FeNi(111).³²³ Reproduced from ref. 323 with permission from Elsevier, copyright 2016.

The same group investigated lattice O atom coordination effects and pore confinement on selectivity limitations for ethane ODH catalyzed by vanadium–oxo species.³¹³ DFT was used to calculate C–H activation and C–O formation in ethane ODH on (001) surfaces of V₂O₅ and MoVTeNb oxides and in pores of MoVTeNb oxides. High C₂H₄ selectivity depended strongly on the O atom coordination and H atom addition energies of the oxides. C–O formation preferably occurred at V=O terminal O atoms due to their significantly lower energy than V–O–V, V–O–Mo bridging or V₂–O–V tri-coordinated O atoms. In contrast, the C–H activations on MoVTeNbO(001) surfaces exhibited similar activation energies between bridging O atoms and terminal O atoms. Terminal O atoms are inaccessible in MoVTeNbO bulk oxide micropores, which leads to high ethane activation rates and ethylene selectivity.

Co oxides. Co₃O₄ is a good oxidation catalyst. Its high activity has been attributed to the weak metal–O bond among other transition metal oxides³¹⁴ and the easy formation of oxygen vacancies at the catalyst surfaces.³¹⁵ Co₃O₄ is also active for ODH. Surface termination can have an impact on the catalyst activity and selectivity of ODH. Experimental and theoretical calculations have identified several stable Co₃O₄ surfaces, such as (110), (111), and (100). Fung et al. developed a full catalytic cycle of ODH based on first-principles calculations on a thermodynamically stable Co₃O₄(111) surface.²⁹⁷ The full catalytic cycle includes the first and second C–H bond activations, hydroxyl clustering, water formation, water desorption, and lattice oxygen-site regeneration. On the most stable terminal surface, there are two types of lattice oxygen: O^A, which is triply coordinated to the subsurface cobalt (Co³⁺); and O^B, which is not only doubly coordinated to the subsurface Co but also singly coordinated to the surface Co. There are also two types of C–H activation of ethane, namely the homolytic pathway where the lattice O is the active site, and the heterolytic pathway where the O and Co pair is the active site. The C–H activity depends on the lattice oxygen reactivity. The formation energy of oxygen vacancy and Bader charges are good descriptors to predict well the higher reactivity of O^A. The first C–H activation was more favorable on more reactive lattice oxygen and had a lower barrier for the homolytic pathway (∼0.62 eV), but the barrier for the second C–H activation was lower for the heterolytic pathway. The water formation step of the catalytic cycle on the pure (111) surface was found to be the RDS, possibly due to the highly oxyphilic nature of the Co surface.

The same group investigated the effects of Co₃O₄ doping on oxygen reactivity and ethane C–H activation energies over Co₃O₄(111) and (311) surfaces for a series of dopants.³¹⁶ The DFT calculations illustrated that the O vacancy formation energy and H adsorption energy were descriptors for oxygen reactivity, which were directly correlated with the ethane C–H activation energy and the TS geometry. The group also discovered that the surface orientation had a significant influence on dopant efficacy.

Ni oxides. The reaction mechanism of ODH of ethane has also been studied on nickel-based oxides, namely Ni₃O_x (x = 1, 2, 3) by DFT calculations using the cluster model.²⁹⁸ Ethylnickel species have been identified as main reaction intermediates through a concerted mechanism involving two sites for the C–H bond activation step. Subsequent pathways include beta-H elimination, alpha-H abstraction, C–C bond cleavage, and isomerization to ethoxide species. The selectivity of ethylene depends on the relative rates of the four pathways. According to the calculation, the S_C2H4 selectivity increases from 37% to over 99% with decreasing x value. The oxygen vacancy has a significant influence on the selectivity and more oxygen vacancies in Ni oxides enhance remarkably the ethylene selectivity. An important issue for transition-metal catalyzed oxidation of hydrocarbons is the type of primary species generated from the C–H bond activation step and the types of species directly responsible for the initial product selectivity observed in the experiment.¹⁴ The adsorbed ethane on oxygen sites forms ethoxide, which leads to ethylene formation. The high selectivity in the Ni₃O₁ case is due to the absence of a bare O atom nearby the α-Ni site and block isomerization from ethyl-nickel to ethoxide, which is more likely to undergo C–C bond cleavage.

Doping of NiO with Sn, Ti, and W has been shown to increase the catalytic activity and selectivity.³¹⁷ DFT calculations show that doping these metals into the NiO structure are thermodynamically feasible. The dopant, on the one hand, can decrease the particle size of NiO and open up more active sites. The incorporation of these metals into the NiO lattice, on the other hand, reduces the number of holes (h⁺), resulting in a significant decrease of nonstoichiometric oxygen (O˙⁻) in the NiO structure. The low concentration of nonstoichiometric oxygen contributes to the improved catalytic selectivity (O˙⁻ is known to favor complete ethane oxidation to CO₂). Based on this study, a design criterion has been proposed; an optimum concentration of nonstoichiometric oxygen at the NiO surface exists. A too high oxygen concentration leads to total oxidation of ethylene to CO₂, while a too low oxygen concentration leads to difficulty in activating ethylene at a lower temperature.

Doping of NiO with Nb in ethane ODH was found to form NbO₂ groups, considered to be the dopant, predicted by DFT calculations.³¹⁸ The NbO₂ groups were created because the Nb-doped NiO adsorbed oxygen very strongly from the gas phase and dissociated it to generate two chemisorbed O atoms, with each making an Nb–O–Ni bond. The calculated activation energies of dissociative adsorption of ethane on the NbO₂-doped oxide were substantially lower than that on undoped NiO. This is because the NbO₂-doped oxide was more reactive in breaking the C–H bond of ethane than undoped NiO. However, this is different from the experimental results^319,320 in that even adding a small amount of Nb decreased the ethane conversion per unit area and per unit time for NiO catalysts. The difference between the experimental observation and the DFT prediction might be due to the formation of NbO_x clusters on the surface or NiNb₂O₆ (instead of NbO₂ groups used in the model) during the calcination in oxygen for catalyst preparation. Experiments found that the slow deactivation of the catalyst was attributed to the formation of NiNb₂O₆.

IrO₂ catalysts. In contrast to most metal oxides, where initial C–H bond activation is the RDS of ethane ODH, the first C–H bond activation of ethane is a fast reaction over IrO₂ catalysts. A DFT study of ethane activation over an IrO₂(110) surface reported by Pham et al.³²¹ indicated that ethane was most stably adsorbed on IrO₂(110) by interacting with two adjacent Ir_cus (five-fold coordinated Ir) atoms, and ethane activation on IrO₂(110) was both thermodynamically (ΔE, PBE: −1.12 eV; optB88-vdW: −1.13 eV) and kinetically (E_a, PBE: 0.50 eV; optB88-vdW: 0.57 eV) favorable, which was expected to occur at low temperature. Similarly, the temperature-programmed reaction spectroscopy (TPRS) and DFT results reported by Bian et al.²⁹⁹ showed that ethylene desorption was the RDS in the conversion of ethane to ethylene over IrO₂(110) during the TPRS. The DFT calculated barrier of ethane C–H bond cleavage over clean IrO₂(110) (0.39 eV) was much lower than that of ethylene desorption (1.96 eV). However, the DFT calculation predicted that the oxygen vacancy plays a significant role in ethane conversion. Partial hydrogenation of IrO₂(110) was found to enhance ethane conversion to ethylene while suppressing ethane oxidation to CO_x species. According to DFT, hydrogenation of reactive O atoms of IrO₂(110) to OH groups effectively inhibited these sites as H atom acceptors, resulting in ethylene desorption being favored over further dehydrogenation. The study revealed that IrO₂(110) displayed an exceptional ability to promote C₂H₆ dehydrogenation to C₂H₄ near room temperature, and controlled deactivation of reactive O atoms was an effective way to facilitate ethylene production from ethane on IrO₂(110).

3.2.2 Reaction mechanism with CO₂ as an oxidant. CO₂ can also be used in ODH of ethane as a soft oxygenate.

C₂H₆(g) + CO₂(g) → C₂H₄(g) + CO(g) + H₂O(l) ΔH₂₅° = 1.39 eV (11)

The advantage of this approach is that overoxidation of the reactants and products can be reduced and therefore the olefin selectivity can be enhanced.²⁶⁸ The effect of the support nature on the catalytic activity and stability has been investigated on CrO_x catalysts supported on γ-Al₂O₃, ZrO₂, CeO₂, and Ce_xZr_(1−x)O₂.³²² The nature of the support influences the oxidation state of chromium species. The reaction pathway, catalytic activity, and stability of the catalyst depend on both the chromium state and support properties, in particular, on its acid–base and redox properties. On CrO_x/γ-Al₂O₃ catalysts, ethylene is formed by a direct dehydrogenation (DDH) of ethane accompanied by RWGS, while on CrO_x/ZrO₂, ethylene is formed by selective ODH. Besides the oxide surface, bimetallic catalysts also appear to be active for this reaction.

In addition to producing ethylene via an ODH pathway through C–H bond scission, the interaction of ethane with CO₂ can also produce synthesis gas via a dry reforming pathway through C–C bond scission. High ethylene selectivity can be achieved by using different catalysts to selectively promote the C–H bond scission and preserve the C–C bond scission. Chen and co-workers have done a lot of work on it.^323–326 They studied the dry reforming and ODH of ethane with CO₂ as a soft oxidant on CeO₂ supported bimetallic catalysts.³²³ It was found that CoPt/CeO₂, CoMo/CeO₂, and NiMo/CeO₂ bimetallic catalysts favored the reforming pathway to produce synthesis gas via the C–C bond cleavage, while FeNi/CeO₂ favored the ODH pathway to produce ethylene via the C–H bond cleavage. The DFT calculated energy profiles shown in Fig. 25 clearly demonstrate different pathways on the CoPt/CeO₂ catalyst compared to the FeNi/CeO₂ catalyst.

The most likely active sites over CeO₂-supported NiFe catalysts were further elucidated by the same group by combining in situ characterization with DFT calculations.³²⁴ Both the experimental and theoretical results revealed that the Ni–FeO_x interfacial sites could selectively break the C–H bonds and preserve the C–C bond of C₂H₆ to produce ethylene, while the Ni–CeO_x interfacial sites efficiently cleaved all of the C–H and C–C bonds to produce synthesis gas. Similar work has been done on non-precious FeNi and precious NiPt catalysts supported on CeO₂ for ODH of propane by CO₂ of propane and dry reforming.³²⁷ DFT was performed on three representative surfaces: Fe₃Ni, FeO/Ni(111), and Ni₃Pt. The FeO/Ni(111) surface was used to represent potential FeO–Ni interfacial active sites due to the observation of the FeO layer on the Ni surface during the reaction conditions. DFT results revealed that on bulk-terminated-Fe₃Ni(111) the ODH reaction (ΔE = 0.29 eV and E_a = 1.02 eV) had lower reaction energy and activation energy than *O insertion reaction (ΔE = 0.43 eV and E_a = 3.30 eV). Therefore, the ODH reaction is more favorable along the C–H bond cleavage pathway than the *O insertion reaction along the C–C bond cleavage pathway. Similarly, on the FeO/Ni(111) surface, ODH reaction is favored over the C–C bond cleavage dry reforming reaction. However, on the Ni₃Pt catalyst, the C–C bond cleavage is favored over C–H bond cleavage dehydrogenation reaction.

Chen and co-workers also found that the Mo₂C/γ-Al₂O₃ catalyst preserved the C–C bond cleavage of ethane to produce ethylene, while Pt/CeO₂ preferably produced synthesis gas.³²⁵ These findings agreed with DFT results that the Mo₂C(001) surface led to ethylene formation, and the CeO₂/Pt(111) surface preferentially generated synthesis gas. Besides, the authors demonstrated that a MoO_x modified Mo₂C surface was related to ethylene formation in ethane ODH with CO₂.³²⁶ Oxygen modification was able to inhibit the C–C bond cleavage and reduce coke formation. The Fe promoter could accelerate the formation of the surface MoO_x layer and stabilize it, leading to a higher ethylene yield and improved stability.

An ab initio microkinetic model (MKM) was constructed to investigate the reactivity trends of transition metal catalysts for ethane dehydrogenation with CO₂ as a mild oxidant.³²⁸ Both direct ethane dehydrogenation and O-assisted ethane dehydrogenation on terrace (111) and step (211) surfaces were studied. Ethane was predominantly converted to ethylene via direct dehydrogenation on both surfaces. Towards O-assisted ethane dehydrogenation (CO₂ consumption), Co, Ru, Ni, and Rh were more active than other transition metals on both surfaces (Fig. 26a and b). In an attempt to screen bimetallic alloys to achieve greater CO₂ consumption activity with reduced coke formation, three potential bimetallic alloys (Ni₃Fe, Ni₃Co and Pt₃Co) were selected (Fig. 26c). Out of them, two were tested experimentally, and FeNi/CeO₂ has shown some promise for ethane dehydrogenation along with CO₂ reduction.

Fig. 26 Elementary reaction rate for oxygen assisted ethane dehydrogenation (C₂H₆ + O → C₂H₅ + OH) over the (a) (111) surface and (b) (211) surface of transition metal catalysts; and (c) screened alloy candidates.³²⁸ Reproduced from ref. 328 with permission from the Royal Society of Chemistry, copyright 2020.

4. Activation of C–H bonds of propane and propylene

Propylene is one of the vital petrochemical building blocks for producing various chemical products, such as propylene oxide, polypropylene, and acrylonitrile. The conventional production processes of propylene are mainly steam cracking and fluidized catalytic cracking of light diesel, naphtha, and other oil byproducts.^329,330 Along with the large-scale revolution of shale gas and the growth of the global propylene demand (which is expected to increase to 130 million metric tons by 2023), on-purpose propylene production, specifically propane dehydrogenation (PDH), seems to be a promising alternative.³³¹ The PDH process is an endothermic reaction, and successfully commercialized PDH catalysts can be categorized into two groups: Pt- and Cr-based catalysts. The reaction is normally performed at around 600 °C on Al₂O₃ supported Pt–Sn or CrO_x catalysts. Pt-Based catalysts are commonly used commercial catalysts for PDH because of their high catalytic activity. Still, they suffer from unsatisfactory propylene selectivity, fast deactivation, and poor catalyst stability caused by coke formation and catalyst sintering at high reaction temperatures.^{277,289,292,332} Thus, significant efforts have been devoted to improving the performance of Pt-based catalysts, generally by doping with additional promoters, such as late TMs and main-group metals (including Ga and Sn) and by modifying carriers.^333,334

The oxidative dehydrogenation of propane generally follows the MVK mechanism,^221,335,336 also known as the lattice oxygen mechanism. This mechanism holds that reactants with reducing properties react with highly reactive oxygen atoms in the catalyst surface to generate oxidation products and thus form oxygen vacancies on the surface. Then, followed by O₂ or CO₂ adsorption at the oxygen vacancy sites, the sites can be oxidized or filled with oxygen, forming a catalytic cycle. Besides, in order to break the thermodynamic limitations of the propane dehydrogenation reaction, an oxidant that is added to the reaction feed or system will react with the intermediate species hydrogen or the product H₂ to produce water, releasing a large amount of heat.^337,338 However, for the ODH of propane, the reaction products are easily oxidized to produce CO and CO₂, so the reaction has to be carried out at a lower temperature in order to obtain a higher selectivity.³³⁹ Also, propane dehydrogenation is a kinetically controlled reaction, and the activation of the C–H bond in propane is usually a rate-determining step, which requires the reaction at a higher temperature.³⁴⁰

Currently, in the PDH and ODH systems, the nature of the reaction mechanisms and reaction pathways on the catalysts remains elusive, and many side reactions such as deep dehydrogenation, C–C bond cleavage, H migration, and H₂O formation also need to be taken into consideration. By DFT calculations, the surface electronic structures of catalysts can be studied, mainly for exploring the active sites, stability, and modulation mechanism on the surface. Then, the elementary steps of dehydrogenation reaction involved in the network of the main and side reactions, together with the migration of H on the catalyst surface, are investigated to identify a favorable reaction pathway. Besides, the kinetic analysis can further convert the rate constants of the elementary steps calculated with DFT to the corresponding turnover rates under the reaction conditions, and consequently, it can determine the activity trend and rate-determining steps. It is therefore of great interest to employ theoretical calculations as a tool for investigating how the PDH and ODH catalysts function on an atomic scale. We will see that, by using microkinetic analysis combined with results from DFT calculations, the crucial roles of different active sites, promoters, and supports, and reaction pathways and RDSs²⁹ can be explained, which guides the investigation toward a more effective catalyst for PDH and ODH. The progress in computational catalysis of PDH and ODH is reviewed in Sections 4.1 and 4.2, respectively.

4.1 C–H bond activation in propane on metals

4.1.1 Adsorption of propane and propylene on metal surfaces. In the last few decades, the activation of C–H bonds of propane over transition-metal and alloy surfaces has been extensively studied both theoretically and experimentally.^341–346 The surface reaction of PDH can lead to numerous fragments ranging from C1 to C3 species adsorbed on these surfaces. As for the C3 species, propane and propylene are the reactant and the desired main product, respectively,^347,348 and their adsorption on metal surfaces has been the subject of extensive research.^349–351 Generally, because the propane molecule is a saturated compound and has no unpaired electron, there is no hybridization between propane and metal d states, and therefore propane is physisorbed on the metal surfaces.^347,349,352 The lengths of the C–H and C–C bonds of adsorbed propane are found to be almost the same as those of the isolated propane (C–H: 1.10–1.11 Å, C–C: 1.53 Å).^349,351 The equilibrium adsorption distances between propane and metal surfaces are in the range from 2.5 to 4.5 Å, suggesting that this is mainly an intermolecular interaction.^{348,350,352,353} On flat surfaces such as Pt(111), the GGA-PBE adsorption energies of propane at different adsorption sites fall within the range of −0.02 to −0.06 eV, as presented in Table 2.^349,354 The small variation in adsorption energy from site to site indicates that propane does not favor any particular site on the flat metal surfaces. The adsorption energies of propane are generally underestimated by the PBE functional because the standard GGA fails to account for long-range vdW interactions between propane and metal surfaces. With the vdW correction considered, the adsorption energy of propane becomes much more negative.³⁵³ For the stepped metal surface, propane preferably adsorbs at the hollow site below the step edge, and the adsorption energies are in the range from −0.39 to −0.46 eV.^331,355 Clearly, the propane molecule experiences more attractive interactions from the stepped surface than those from the flat surface because there exists a larger contact area between them, and the strength of dispersion forces tends to increase with increasing molecular size. Moreover, alloying of Pt with metals such as Sn did not alter the adsorption energy (Table 2).³⁵⁰

Table 2 Adsorption energies and geometries of propane and propylene on different Pt surfaces

Surface		Propylene					XC functional	Ref.
	Propane	di-σ				π
	E ads (eV)	E ads (eV)	d C1=C2 (Å)	d Pt–C1 (Å)	d Pt–C2 (Å)	E ads (eV)
Pt(111)	−0.34	−0.83	1.501	2.145	2.178	—	vdW_DF	350
Pt3Sn/Pt(111)	−0.39	−0.48	1.504	2.159	2.174	—
Pt3Sn(111)	−0.28	−0.54	1.497	2.159	2.193	—
PtSn2(111)	−0.24	−0.23	—	—	—	—
Pt(111)	—	−0.64	1.48	2.12	2.14	0.06	B3LYP	356
Pt(111)	−0.06	−0.93	1.50	2.11	—	−0.66	PBE	349
Pt(100)	−0.04	−1.22	—	—	—	−1.07	PBE	357
Pt(111)	−0.04	−0.97	—	—	—	−0.67
Pt(211)	−0.04	−1.43	—	—	—	—	PBE	347

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A crucial point in the dehydrogenation reaction is the examination of the competition between propylene dehydrogenation and desorption, which provides the key to understanding how the selectivity of catalyst surfaces can be tuned.³⁵⁸ Compared to propane, propylene has a half-saturated double bond (C=C), which could be readily decomposed on metal surfaces. Valcárcel et al. proposed a schematic representation of adsorbed propylene on Pt(111), where these surface structures mainly depend on coverage and temperature.³⁵⁹ At temperatures below 230 K, propylene is undissociated to adsorb on the metal surface, as is the case for ethylene. The di–σ and π models are the most common propylene chemisorption configurations on metal surfaces, as shown in Fig. 27(a). The adsorption configuration depends on the site coverage of propylene, and the di–σ mode through its unsaturated C=C bond at a short bridge site is predominant below half-saturation coverage, with the C=C bond being nearly parallel to the surface, and the methyl group would tilt away from the surface as the site coverage is close to saturation. The adsorption energy of the di–σ adsorption is generally more negative than that of the π adsorption.^{349,350,353,357,359} This can be explained by the larger valence charge density between the C and metal surface in the di–σ bond than in the π adsorption, indicating a stronger C–metal bond, as shown in Fig. 27(b). The strong adsorption weakens the C=C bond.³⁶⁰ Upon the di–σ adsorption over metal surfaces, the length of the double C=C bond in propylene increases from 1.36 (in gas-phase propylene) to about 1.50 Å,^349,351,353 which is close to the single C–C bond length of propane. This change, together with the fact that propylene loses its “planarity” as the C–H bonds bend away from the surface plane, indicates the rehybridization of the C atom from sp² to sp³, and the C=C bond is therefore weakened by forming covalent bonds with Pt atoms. On Pt(100)³⁵⁷ and Pt(211) surfaces,³⁴⁷ propylene adsorption also prefers the di–σ mode to the π mode. The adsorption energy of propylene follows the order of Pt(211) > Pt(100) > Pt(111), as can be seen in Table 2. Although the estimated adsorption energy depends on the functionals used, it does not change the trend on the different surfaces. The adsorption energy on Pt(111) obtained with the vdW–DF functional agrees well with the experimental desorption energy determined using temperature-programmed desorption (TPD) measurements.³⁵⁰

Fig. 27 (a) Adsorption modes of propylene on Pt surfaces.³⁵⁷ Reproduced from ref. 357 with permission from Elsevier, copyright 2014. (b) The valence charge densities calculated for different propylene adsorption modes.³⁴⁹ Reproduced from ref. 349 with permission from Elsevier, copyright 2010.

Alloying Pt(111) with less reactive metal Sn leads to weaker propylene adsorption, as can be seen in Table 2.³⁵⁰ Propylene binds preferentially to the Pt₃Sn(111) surface in the di–σ mode, similar to that on Pt(111), but the adsorption is weak on the PtSn₂(111) surface and dominated by vdW interactions. This result is mainly attributed to the geometric effect of introduced Sn, which reduces the number of Pt–Pt di–σ sites accessible by propylene, whereas the electronic effect that originated from the interaction energy of the Pt–Pt di–σ sites was found to be small.

4.1.2 Activation of the first C–H bond of propane. The propane dehydrogenation process involves a relatively complex reaction network and a large number of reaction intermediates and the elementary steps involved are mainly the C–H and C–C bond-breaking reactions. These elementary steps can be divided into three categories, as shown in Fig. 28(a): (1) the dehydrogenation steps from propane to propylene (steps 1–4), (2) the deep dehydrogenation steps from propylene to 1-propenyl and 2-propenyl (steps 5 and 6), and (3) the C–C bond cleavage reactions of propane, 1-propyl, 2-propyl, and propylene (steps 7–10).³⁵⁷ The initial C–H bond cleavage at the methyl (step 1) or methylene (step 2) groups of physisorbed propane is often the RDS that governs the rate law of the overall dehydrogenation reaction, leading to the 1-propyl or 2-propyl species.³⁵⁸

Fig. 28 (a) Reaction network for propane dehydrogenation to propenyl and (b) geometries of the transition states for the initial activation of the propane C–H bonds at the methyl and methylene groups on Pt(111), Pt(100), and Pt(211). The detached H atoms are not included for clarity. The numbers signify the sequence numbers of the elementary steps.^347,357 Reproduced from ref. 347 with permission from the PCCP Owner Societies, copyright 2011. Adapted from ref. 357 with permission from Elsevier, copyright 2014.

The C–H bond dissociation energy of propane is 4.35 and 4.17 eV for the primary and secondary C–H bond scission, respectively. In the catalytic system, the energy barriers for the initial activation of the propane C–H bonds at the methyl and methylene groups are 0.69 and 0.70 eV on Pt(111), respectively, which indicates that there is no particular preference for the activation of C–H bonds on the surface.³⁴⁷ For the transition states of propane activation on Pt surfaces, propane is bonded to Pt surfaces via the C atom, where the H in C–H is bonded to adjunct Pt. The C–H bonds at the methyl group are stretched by 1.50 Å (see Fig. 28b), as compared to the C–H bond length in gas-phase propane (1.10 Å). The geometries of the transition states on Pt(111), Pt(100), and Pt(211) are almost identical, as shown in Fig. 28(b). The C–H bond activation follows the universal scaling relationship, as shown in eqn (4). The lower C–H bond energy leads to a lower activation energy of propane activation than ethane and methane activation. The activation energies of the first dehydrogenation steps on Pt(211) are lower than those on Pt(100) and Pt(111) due to the higher hydrogen affinity on the unsaturated surfaces, where the lower activation energies for propane give higher dehydrogenation activity on these three surfaces. The activated C–H bonds are stretched by 0.36–0.41 Å. The energy barriers for the activation of C–H bonds occurring at the two groups are calculated to be 0.32 and 0.28 eV on stepped Pt(211), and 0.43 and 0.42 eV on Pt(100), respectively.³⁵⁷

The addition of one or more main-group metals or TMs is an effective way to modify Pt-based catalysts.^350,361,362 DFT calculations revealed that the Sn component could broaden the d-band of Pt, giving rise to a downshift of the d-band center, and the dehydrogenation activity ranked in the descending order is: Pt(111) > Pt₃Sn(111) (bulk alloy) > Pt₃Sn/Pt(111) (surface alloy) > PtSn₂(111) (bulk alloy) > Pt₂Sn/Pt(111) (surface alloy).³⁴⁸ In addition to Pt-based catalysts, other metal catalysts, such as metal Ni, intermetallic Pd–Zn, and Pd–Cu, have also been studied for the activation of C–H bonds.^351,363,364 Saelee et al. reported that the activation energy for the first dehydrogenation of propane on Ni(111) (0.69 eV) is close to that on Pt(111) (0.70 eV). Single Pd atoms at the edge site of Cu₅₅ clusters can facilitate the first C–H bond cleavage, and the energy barrier predicted using the PBE functional is 1.06 eV, approximately 0.25 eV lower than the corresponding barrier on pure Cu₅₅ clusters. With the correction of the vdW–DF functional, this energy barrier is increased to 1.17 eV.³⁶⁴

4.1.3 Mechanism of propane dehydrogenation to propylene on metal surfaces. Pt is one of the most commonly used commercial catalysts for PDH.² It is generally accepted that the dehydrogenation of propane over Pt catalyst follows the reverse Horiuti–Polanyi mechanism.²⁷⁴ The dehydrogenation steps from propane to propylene is shown in Fig. 28(a) (steps 1–4), and the energy barriers for these four steps can describe the catalytic activity of metal surfaces for propylene production.³⁵⁷Table 3 summarizes some of the calculated energy barriers of PDH over Pt(111), Pt(100), and Pt(211) surfaces.^{340,347,353,357} From the table, one can see that the energy barriers for both the first and second C–H bond activations of propane follow the order Pt(211) < Pt(100) < Pt(111). The stepped Pt surfaces having coordinatively unsaturated Pt atoms are kinetically more favorable for the dehydrogenation of propane to form propylene than the flat surfaces. Recently, however, Xiao et al.³⁶⁵ suggested that although PDH over Pt(111) follows the generally accepted reverse Horiuti–Polanyi mechanism, as shown in Fig. 29, an unexpected non-reverse Horiuti–Polanyi mechanism over Pt(211) is proposed to dominate the kinetics.

Table 3 Calculated energy barriers (E_act) for propane and propyl dehydrogenation on different Pt surfaces

Surface	E act (eV)				XC functional	k points	Unit cell	Ref.
	C3H8 → 1-C3H7	C3H8 → 2-C3H7	1-C3H7 → C3H6	2-C3H7 → C3H6
Pt(111)	0.69	0.70	0.70	0.68	PBE	7 × 7 × 1	3 × 3	347
Pt(211)	0.32	0.28	0.34	0.33	PBE	4 × 2 × 1	1 × 3	347
Pt(100)	0.43	0.42	0.39	0.39	PBE	7 × 7 × 1	3 × 3	357
Pt(111)	0.59	—	0.66	—	PBE	5 × 5 × 1	3 × 3	331
Pt(111)	0.92	0.92	0.90	0.94	BEEF-vdW	3 × 3 × 1	3 × 3	353
Pt(111)	0.75	0.60	0.74	0.78	opt-PBE vdW–DF	3 × 5 × 1	4 × 2	340

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Fig. 29 Flux analysis of PDH under experimental reactor inlet conditions (723.15 K, 0.03 bar propane, and 0.04 bar hydrogen) over (a) Pt(111) and (b) Pt(211) with adsorbate–adsorbate interactions considered. The arrows which are labelled with the percentage of the total reaction flux indicate the direction in which the reversible elementary steps actually proceed. The percentage of the reaction flux is calculated as the absolute value of the net rate for that elementary step divided by the rate for propane consumption. (c) Simplified reaction networks for PDH over Pt(111) and Pt(211).³⁶⁵ Reproduced from ref. 365 with permission from the American Chemical Society, copyright 2020.

In addition, the strongly endothermic nature of PDH (Δ_rH° = 1.28 eV, under standard conditions at 298 K) requires high reaction temperature (800–980 K) to achieve a reasonable propane conversion.³⁶⁶ However, side reactions, such as cracking, hydrogenolysis, deep dehydrogenation, oligomerization, cyclization, and coke formation, can be promoted even more dramatically by the increase in temperature.^332,367 As a result, ethylene (or ethane), methane, and coke are often produced in the PDH reaction as byproducts. The critical challenge for the catalysis of PDH is to reduce the selectivity to byproducts and to maintain the catalytic stability of the catalyst. It is thus essential to include not only the C–H bond activation but also the C–C bond cleavage in the whole catalytic cycle of PDH for the kinetic analysis. Yang et al. systematically investigated the PDH process on flat and stepped Pt surfaces, including Pt(111), Pt(100), and Pt(211).^347,349,357 They focused on the kinetics of the C–H bond activation of all the C3 intermediates in PDH, containing 17 dehydrogenation elementary reactions (see Fig. 30) and 12 C–C bond-breaking steps. As an example, the energy profile for PDH on Pt(111) is shown in Fig. 30(b). The insights provided by these studies are summarized as follows:

Fig. 30 (a) The network of surface reactions of PDH, not including the adsorption reactions of gases and dissociation of H₂. All elementary reactions are reversible, and asterisks indicate surface adsorbed species.³⁵³ Reproduced from ref. 353 with permission from the American Chemical Society, copyright 2018. (b) Energy profile for propane dehydrogenation on Pt(111) including both the dehydrogenation steps (the solid lines) and the C–C cracking steps (the dotted lines).³⁴⁷ Reproduced from ref. 347 with permission from the PCCP Owner Societies, copyright 2011.

(1) A good scaling relation was found between the transition-state energy and the final-state energy for C₃H_x (x = 3–9) dehydrogenation. C–C bond cleavage steps have higher transition state energy and hence higher activation energy than C–H activation.³⁴⁷ The adsorption strength of the intermediates is the key parameter in tuning the activity and selectivity. The stepped Pt surfaces are kinetically more favorable than the flat surfaces for the dehydrogenation of propane because of the stronger adsorption of intermediates on Pt(211).^347,368

(2) The activation energy difference between propylene dehydrogenation and desorption was identified as the selectivity descriptor. Lowering the desorption energy and increasing the C–H bond activation barrier of propylene are crucial for increasing the propylene selectivity. Both quantities are closely related to the adsorption strength of propylene. The selectivity towards propylene is substantially lowered in the presence of the coordinatively unsaturated surface Pt atoms due to the strong adsorption of propylene, which has recently been widely used to screen promising candidates as the catalysts for PDH.^{331,345,354,369}

(3) The deeply dehydrogenated intermediate of propyne (CH₃CCH*) was identified as an important surface species for the C–C bond breaking because it is the sole C3 species that energetically prefers the cleavage of the C–C bond to the C–H bond breaking, which has also been determined by the microkinetic analysis on Pt(111).^340,353

(4) PDH to propylene follows the generally accepted reverse Horiuti–Polanyi mechanism over Pt(111), while over Pt(211), a non-reverse Horiuti–Polanyi mechanism dominates.³⁶⁵ The experimental³⁵⁴ and theoretical analyses of Gibbs energy profiles of the PDH reaction^340,353 suggest that the first C–H bond activation is the RDS on Pt(211) and Pt(100) for smaller Pt cluster sizes, while the second C–H bond activation is the RDS on Pt(111). The first C–H activation of propane was identified as the RDS on the Pt(111) by a microkinetic analysis.³⁴⁰ It should be noted that the energy barriers for the first and second C–H bond activations are quite close on Pt(111). The RDS could change with the reaction conditions.

So far, there have been only three microkinetic studies of PDH based on a relatively full description of the reaction pathway of dehydrogenation to propylene, deep dehydrogenation, and C–C bond cracking over Pt(111) surfaces, which were carried out by Saerens et al.,³⁴⁰ Lian et al.,³⁵³ and Xiao et al.,³⁶⁵ respectively. The DFT-based kMC simulations by Lian et al. reveal that there are quick deactivation and steady states during the PDH process.³⁵³ The precursor of coke is mainly formed during the rapid deactivation, which originates from the coverage of cracking products at the active sites. Then, the surface species and active sites covered by the hardly removed coke lead to the steady-state after quick deactivation. Saerens et al.³⁴⁰ focused their studies on the influence of hydrogen co-feeding on the reaction mechanism of PDH. They pointed out that the increasing the co-feeding hydrogen pressure can decrease the coverage of deeply dehydrogenated coke precursors and increase the number of free sites on the Pt(111) surface; moreover, this increase in free sites can lead to higher catalytic activity. The modeling results rationalized the experimental observation of the reduced coke formation and enhanced propylene selectivity by co-feeding hydrogen in PDH.^340,353 By using microkinetic analysis in combination with results from DFT calculations, Xiao et al.³⁶⁵ found that a non-reverse Horiuti–Polanyi mechanism accounts for more than half the propylene production at the under-coordinated active sites that dominate the kinetics of PDH (see Fig. 29), which consists of three dehydrogenation steps that have two β-H and one α-H atoms removed from propane, followed by the hydrogenation of CH₃CCH₂, and at this species the deep dehydrogenation reaction competes with the production of propylene.

The microkinetic modeling of the side reactions of C–C bond cracking and deep dehydrogenation, and coke formation indicates that the catalyst deactivation is due to the formation of CH₃CC* and C*, which lead to cracking and eventual coke formation, respectively.^340,353 The formed C1 and C2 species could desorb to form ethane, ethylene, and methane or serve as coke precursors.³⁴⁰ Then, the formation of coke could block the active sites of the catalyst, impede the catalytic activity, and eventually deactivate the catalyst.^331,353 Lian et al. studied the detailed reaction pathway of propylene formation, deep dehydrogenation, and C–C bond cracking for understanding the origin of coke formation.³⁵³ The deep dehydrogenations are via R6 → R11 and R10 and finally lead to the cracking of C3 species, mainly starting from propyne (see Fig. 30). The coke precursors are mainly formed during the quick deactivation, and the active sites are mainly occupied by C2 and C1 species, which are hardly removed from the surface. However, the covered active sites, after quick deactivation, can lead to a stable state, which can hinder the side reactions to achieve a stable selectivity. Besides, the co-adsorption of carbon can shift the d-band centers of the surface Pt atoms further below the Fermi level, leading to a decrease in the catalytic activity for PDH.³⁴⁰ Zhu et al. proposed that coke formation is not structure-sensitive, as coke can be formed by all Pt facets and can preferentially cover the under-coordinated active sites.³⁵⁴ The higher coking rate on small Pt clusters is due to the larger Pt surface area, and the faster coke formation resulted in faster deactivation. Therefore, the rational construction of a Pt surface structure can be a crucial factor in improving catalytic selectivity and controlling coke formation.³⁵³

4.1.4 Guidelines for improving the selectivity and coke resistance. The DFT studies by Zhu et al. identified propylene as the precursor for the formation of byproducts such as coke.³⁵⁴ Strong adsorption of propylene means that the surface-adsorbed propylene molecule prefers dehydrogenation to desorption, leading to the deep dehydrogenation and cracking of the subsequent C3 derivatives. The formation of ethane, methane, and coke would lower selectivity to propylene. The critical challenge to gain a high selectivity to propylene and stable catalysts is to weaken the propylene adsorption strength and suppress the deep dehydrogenation on Pt-based catalysts. This provides a guideline for design of PDH catalysts with enhanced catalytic performance.

Under high-temperature reaction conditions, the interaction between Pt and propylene is strong, and side reactions readily occur to form coke and deactivate the catalyst, so the propylene selectivity is around 60–80%, and the catalyst stability is poor.³⁷⁰ To increase the selectivity toward propylene at relatively high catalytic activity, various attempts have been made to modify the geometrical and electronic structures of Pt-based catalysts,^2,371,372 such as controlling the size and shape of Pt NPs, alloying Pt with TMs or main-group metals, and selecting appropriate catalyst supports. For example, Zhu et al. reported that the Pt catalysts of larger cluster sizes with (111) dominating the surface have higher selectivity toward propylene and better stability than the smaller clusters where (211) is dominant on the surface. This is due to the weakened binding strength of propylene and the higher energy barrier for deep dehydrogenation on Pt(111). Yang et al.^354,357 proposed that the introduction of H can decrease the desorption barrier for propylene, and therefore, the selectivity toward gaseous propylene is improved. The Gibbs free energy of the dominant reaction pathways of propane to propynyl (CCCH₃) on Pt(111) shows that with increasing H coverage the propylene adsorption strength decreases, while the energy barrier for the further dehydrogenation of propylene increases, leading to a higher catalytic selectivity.³⁴⁰

Previous studies have proved that alloying of Pt with one or more TMs, such as Sn, Ti, Ga, Cu, Co, Zn, Ir, and In, is an effective way to improve the catalytic performance in PDH.^{2,290,373–377} Among them, Sn is most widely studied due to its application in the industrial process. Yang et al.³⁴⁸ reported that with the increase in Sn content in Pt–Sn alloys, the d-band centers of surface Pt atoms are shifted farther below the Fermi level, as shown in Fig. 31(a), which changes the adsorption properties of Pt. According to the d-band model,³⁷⁸ downshifting the d-band center of surface atoms would reduce the interaction strength between the surface and adsorbates, whereas upshifting the d-band center of surface atoms may cause the antibonding states to, at least in part, shift up through the Fermi level and become empty, which eventually leads to a stronger binding strength of the adsorbate to the metal surface. Therefore, from the figure, one can see that an upshift of the d-band center gives rise to stronger binding of 1-propyl to the surface and a lower energy barrier for PDH to 1-propyl, which lowers the catalytic activity for PDH. Moreover, the step sites of Pt modified by adding Sn show more profound electron transfer from Sn to Pt on the Pt–Sn alloy surfaces. In addition, the authors also investigated the competition between propylene dehydrogenation and propylene desorption. They found that the introduction of Sn into Pt(111) can lower the energy barrier for propylene desorption and simultaneously increase the activation energy for propylene dehydrogenation (see Fig. 31b). The electronic effect, i.e., the decrease in the interaction energy of the available Pt–Pt di–σ sites, and the geometric effect of the introduced Sn reducing the number of Pt–Pt di–σ sites accessible by propylene can weaken propylene adsorption, leading to a lower desorption barrier than the dehydrogenation barrier of propylene, and thus higher propylene selectivity than Pt(111).³⁷⁹ By considering the compromise between the catalytic activity and selectivity, the Pt₃Sn bulk alloy is proposed to be the best candidate for PDH. The related experiments also proved that the Sn component added as a promoter in the Pt/γ-Al₂O₃ catalyst can achieve higher propylene selectivity and minimize coke formation.^{334,373,380,381} The work also reported that the addition of Sn can help Pt re-disperse in the catalyst regeneration by providing nucleation sites on the γ-Al₂O₃ surface to achieve superior catalyst stability.³⁸¹

Fig. 31 (a) Plots of the binding energies of 1-propyl (red dots) and the energy barriers for propylene dehydrogenation to 1-propyl (green dots) against the d-band centers over Pt(111) and PtSn surfaces. (b) Energy barrier difference (E_diff) between propylene dehydrogenation and propylene desorption. Blue and red bars indicate pathways to 1- and 2-propenyls, respectively.³⁴⁸ Reproduced from ref. 348 with permission from the American Chemical Society, copyright 2012. (c) DFT calculated projected DOS for the 5d orbitals of Pt in the top-layer Pt₃Ti(111) and Pt(111). (d) Optimized structures as numbered in (e) from the side and top views (H* is not shown). (e) Free energy diagrams of relevant (side-)reaction steps in PDH on Pt₃Ti(111) and Pt(111) surfaces. The dotted lines denote the C–C cracking of C₃H₆*, C₃H₅*, and C₃H₄*, and the dashed-dotted lines denote the deep dehydrogenation of C₃H₆* and C₃H₅*.³⁸² Reproduced from ref. 382 with permission from Springer Nature, copyright 2018.

Similarly, an improved catalytic performance was also reported on the Pt₃Ti catalyst.³⁸² As shown in Fig. 31(c), the d-band center of Pt(111) is located at −1.97 eV relative to the Fermi level, whereas that of Pt₃Ti(111) downshifts to −2.37 eV due to the strong Pt–Ti d–d orbital coupling, giving rise to weaker adsorption of reaction intermediates and changes in the relative free energy and barriers of the reaction steps during dehydrogenation and side reactions (see Fig. 31d and e). From the figure, one can see that the barrier for propylene desorption on Pt₃Ti(111) is 0.25 eV lower than that on Pt(111), but the energy barrier for deep propylene dehydrogenation is increased by the introduction of Ti into Pt. Moreover, on the Pt₃Ti(111) surface, the C–C bond cracking steps are all endergonic and hence are hindered compared to Pt(111), where C₃H₅* and C₃H₄* cracking are exergonic and much more favorable. These results indicate that Pt₃Ti has higher selectivity toward propylene for PDH compared to pure Pt. Wang et al. also studied the effect of Ga as a promoter of Pt/CeO₂–Al₂O₃ catalysts on PDH, indicating that introduced Ga can decorate Pt NPs by forming Pt–Ga alloys and, meanwhile, the Ga component can be incorporated into the cubic fluorite structure of CeO₂. The metal Ga promoter on Pt–Ga alloys can decrease the size of Pt ensembles or block the low-coordinated defect active sites, lower the desorption barrier of propylene and coke precursors by donating electrons to Pt atoms, and thus suppress undesirable side reactions to achieve better propylene selectivity. Besides, the promoter towards CeO₂ can enhance both lattice oxygen storage capacity and surface oxygen mobility to increase the reducibility of CeO₂ and consequently reduce the coke deposition and improve the catalyst stability.³⁷⁶

Besides, the addition of one or more main-group metals or TMs, such as Sn, In, Cu, and Ga, is also an effective way to reduce the tendency to form coke.^{343,350,361,362} The dopants can promote the dispersion of Pt particles and thus prevent their sintering, suppress the structure-sensitive side reactions including hydrogenolysis and deep dehydrogenation to reduce the rate of carbon deposition, and promote the migration of carbon deposition from active metal components to the carrier, etc.^380,383,384

In addition, some novel core–shell Pt-based catalysts can not only improve the catalytic performance but also effectively increase the utilization efficiency of precious metals. Note that near-surface alloys (NSAs) having a host metal (such as Pt) as the subsurface and solute metals as the overlayer exhibit unique chemical and physical properties distinct from those of their constituent metals. Xiao et al.³³¹ reported that by substituting late TMs for the Pt atoms in the core region, the adsorption and catalytic properties of the surface Pt atoms in M@Pt core–shell catalysts could be tuned, which is attributed to the modification of the electronic structure of metal surfaces through the strain effect and electron transfer. The core–shell catalysts were found to have less negative propylene adsorption energies and higher activation energies for the dehydrogenation reactions than Pt, thus giving rise to lower catalytic activity and a higher selectivity toward propylene, as shown in Fig. 32(a). This figure also indicates that higher catalyst selectivity toward propylene can be attained at the expense of a lower catalytic activity for PDH. Co@Pt is proposed to be the best core–shell catalyst for PDH if a compromise is made between catalytic activity and catalyst selectivity. Cesar et al.³⁷⁰ prepared bimetallic Pt–Co NPs for PDH with and without added H₂ and studied the effect of the Co loading amount on the core structure from Pt to Pt₃Co to PtCo. The result shows that bimetallic NPs have significantly better olefin selectivity than either single metal, suggesting that Co that acts as a less active promoter can utilize the geometric effects to enhance the selectivity by breaking up large Pt ensembles in the bimetallic catalysts. Therefore, through the experimental exploration for Pt–Co alloy catalysts, it is found that the catalysts exhibit superior PDH performance, especially catalytic selectivity, consistent with the results obtained by Xiao et al.³³¹ Besides, Sun et al.³⁸⁵ pointed out that the isolated Pt atoms dispersed in Cu NPs can break the PtM alloy scaling relationship, which is different from the scaling for conventional Pt alloys during the PDH (see Fig. 32b). In other words, the Pt/Cu single atom alloy maintains a reasonable dehydrogenation activation barrier and at the same time displays quite a high selectivity, which is reflected by the low free energy barrier difference between the propylene desorption and deep dehydrogenation. Therefore, the use of dopants can improve the selectivity of Pt-based catalysts, suppress catalyst deactivation, and extend the use time of catalysts.

Fig. 32 (a) Linear scaling relation between catalytic activity and selectivity for PDH over 12 core–shell alloy catalysts.³³¹ Reproduced from ref. 331 with permission from Elsevier, copyright 2019. (b) Screening of Pt-based bimetallic catalysts for PDH, where SAA denotes the single atom alloy.³⁸⁵ Reproduced from ref. 385 with permission from Springer Nature, copyright 2018. (c) Profiles of the potential-energy surface for PDH on Rh₁₃-L_s, Rh₁₃-L_s/UGO and Rh₁₃-L_s/TiO₂, where Rh₁₃-L_s is the low-symmetry Rh₁₃ cluster and UGO is the unzipped graphene–oxide.³⁸⁶ Reproduced from ref. 386 with permission from the PCCP Owner Societies, copyright 2017.

Moreover, selecting suitable catalyst supports is also an effective way to modify the catalytic performance of metal catalysts for PDH.^387,388 Chang et al.³⁸⁶ investigated the PDH over Rh₁₃-L_s (low-symmetry Rh₁₃ cluster), Rh₁₃-L_s/UGO (Rh₁₃-L_s cluster supported on a sheet of unzipped graphene oxide), and Rh₁₃-L_s/TiO₂ catalysts. They found that although electrons flowed from the Rh₁₃ cluster towards both supports, the UGO support induced an electronic redistribution of the Rh₁₃ cluster rather than just abstracting electronic charge from the Rh₁₃ cluster to the support, as compared with the TiO₂ counterparts. UGO would induce an electronic accumulation onto the top area of the Rh₁₃ cluster, while TiO₂ induced electronic depletion, which dictates different results for PDH. As shown in Fig. 32(c), for the Rh₁₃-L_s/UGO system, the energy barrier for the dehydrogenation of propane to propyl is 0.22 eV, and the calculated energy barrier for the dehydrogenation of propyl is 0.16 eV. UGO as a support could lower the energy barriers for both two dehydrogenation steps of propane, but TiO₂ as a support increased the energy barriers for both dehydrogenation steps, indicating that the UGO sheet is a more suitable support for the Rh₁₃-Ls cluster and for activation of the C–H bond in PDH. Besides, Jiang et al.³⁸⁹ found that the addition of an appropriate amount of TiO₂ in Pt/TiO₂–Al₂O₃ catalysts can improve propylene selectivity and catalyst stability. The reasons are that the electrons could be transferred from the partially reduced TiO_x (x < 2) to the Pt atoms, and the partial coverage of the metal surface by TiO_x species, and thus the increased electron density of Pt can hinder propylene adsorption on active metal sites and facilitate coke migration from the active sites to the carrier.

4.2 C–H oxidative activation on metal oxides

Although the direct dehydrogenation of propane to propylene (PDH) is a rather promising solution, the ODH of propane has some advantages: ODH is thermodynamically favored even at low temperatures and can avoid the formation of coke.^303,390,391 Besides, unlike the PDH reaction, the ODH of propane is mainly based on the following two mechanisms: first, lattice oxygen is involved in the reaction, and then the oxygen vacancies formed can be filled by the added oxidants (removal of lattice oxygen anions and their reinsertion); second, lattice oxygen is not involved in the reaction; however, the oxidants can be adsorbed on the surface to react with the reactants or intermediates.^392,393 Supported vanadium oxides are known to be one of the best catalysts for the ODH reaction with high thermal stability and a relatively large surface area. Several research groups have studied the mechanism of ODH reaction on metal oxide catalysts, usually following the MVK redox mechanism involving lattice oxygen in C–H bond activation.^394–396 This redox mechanism mostly occurs on transition-metal oxide catalysts with relatively high reducibility. It can be generally described as a two-step mechanism: (1) the reduction of the oxide surface by the dehydrogenation of the hydrocarbon – the catalyst in the oxidation state activates the C–H bond and therefore the dissociated H atoms combine with the lattice oxygen atoms to desorb in the form of H₂O; and (2) the subsequent reoxidation by gas-phase oxygen – the generated oxygen vacancies complete the circulation process of the catalyst surface under the action of oxygen.^29,397,398 The C–H bond activation in propane on (un)supported metal oxides such as VO_x, Cr₂O₃, ZnO, V₂O₃, and Ga₂O₃^{2,303,339,391,399–406} has been studied theoretically by using DFT calculations in which the active sites and reaction mechanism were focused. The reduction step has comprehensively been studied, and the full catalytic cycle is not considered because the oxidation of the substrate is typically a fast step.³³⁶

4.2.1 VO_x catalysts. The V₂O₅(001) surface is the most stable surface exposed in crystalline V₂O₅ formed at high vanadium loadings. It is generally accepted that there are three types of lattice oxygen on V₂O₅(001), which are singly coordinated terminal oxygen (O1), twofold-coordinated oxygen (O2), and threefold-coordinated oxygen (O3), as shown in Fig. 33. Previous experimental and theoretical studies have proposed that the terminal O1 and the bridging lattice O2 serve as the active sites assisting in the C–H bond activation in propane,^399,407 which is in good agreement with the DFT calculations by Fu et al.³⁰³ They reported three possible C–H activation mechanisms for the oxygen-assisted first C–H bond activation over the V₂O₅(001) surface, including oxo-insertion, concerted, and radical mechanisms (see Fig. 34a). The reaction mechanism depends on the identity of the active sites. It was found that both the radical and oxo-insertion mechanisms are feasible at the O1 sites, while only the oxo-insertion mechanism is preferred at the O2 sites. In addition, the activation energies for C–H activation for the secondary C–H bond are lower than those for the primary C–H bond, in agreement with the order of the C–H bond dissociation energies in propane.

Fig. 33 V₂O₅ bulk surface.⁴⁰⁸a, b, and c of the orthorhombic unit cells are parallel to the (100), (010), and (001) directions, respectively. V atoms are depicted as the white circles and O atoms as the smaller gray circles. O₁, O₂, and O₃ denote the single, 2-fold, and 3-fold coordinated oxygen atoms, respectively. Bond lengths in Å. Reproduced from ref. 408 with permission from the American Chemical Society, copyright 2005.

Fig. 34 (a) Three homolytic cleavage mechanisms for the C–H bond activation of propane: an oxo-insertion mechanism (A), a concerted mechanism (B), and a radical mechanism (C); and (b) lowest-energy pathways of the propane ODH process that occurred on O₁ and O₂ on the V₂O₅(001) surface.³⁰³ Reproduced from ref. 303 with permission from the American Chemical Society, copyright 2006.

The reactivity of O sitting on V₂O₅(001) follows the order of O₁ > O₂ > O₃. The energy barriers of activation of the first C–H bond in propane are 1.18 and 1.32 eV at the O₁ and O₂ sites, respectively, as shown in Fig. 34(b). The threefold-coordinated oxygen (O₃) is the least active for C–H bond activation and almost inert.³⁰³ The i-propoxide can much more easily further decompose into propylene at the O₂ site, releasing an H atom to a neighboring O₂ or O₃ atom, and the corresponding energy barrier is 0.95 eV lower than that at the O₁ site (>1.30 eV). The H₂O formation through the recombination of two OH groups at the O₁ site is facile, and H₂O desorption is endothermic with a relatively low reaction energy of 0.56 eV, leading to the formation of oxygen vacancies on the oxide surface. As the lattice oxygen is removed, the structure of the catalyst may collapse, indicating that the V₂O₅(001) surface is fully dynamic.

For the second H abstraction step, the reaction energy is −1.58 eV, and the estimated activation barrier is 0.65 eV, where the surface reconstruction is not taken into account.^399,409 Gas-phase reactions of propane with VO₂⁺ and V₃O₇⁺ have also been studied.^410,411 When considering the more complex reaction conditions of vanadium oxide catalysts involving supports and O₂ adsorption, some of the energy barriers could be affected, such as propane adsorption and H₂O elimination. However, the terminal O₁ is too active to release propylene and therefore shows poor propylene selectivity.

4.2.2 Supported VO_x catalysts. For supported VO_x catalysts, the effect of supports and VO_x dispersion for propane ODH has been widely studied.^15,404,412 The binding strength of the surface lattice oxygen in the VO_x surface species is a key parameter that governs the activities and selectivities for propane ODH.⁴⁰⁶
Active sites. Depending on the loading of VO_x on the support, the VO_x can present as an isolated monomer, dimer, and polymer (sub-monolayer, a monolayer) and crystalline structure.^404,413 Three types of lattice O are identified, such as (a) terminal V=O sites, (b) bridging V–O–V sites, and (c) V–O–support sites.^403,414 The active sites depend on the catalyst structure on the surface. On the supported monomeric VO_x, there are two different types of available active O sites, namely terminal V=O sites and V–O–support interface sites. For the dimer and polymer VO_x, there are additional bridging V–O–V sites. Activation of propane requires a pair of oxygen sites denoted as O_A–O_B as the active sites, where V is inert.⁴¹⁴ The active sites are highly dynamic, and there are a large number of combinations of two oxygen sites among the three O sites.
Activation of propane and propylene. The activation of propane has been studied on the isolated monomeric O=V(O–)₃ supported on SiO₂,⁴⁰¹ a VO_x monolayer on TiO₂(001),⁴⁰³ and monomeric and dimeric VO_x species supported on the (001) and (100) surfaces of anatase TiO₂.⁴¹⁴ Regardless of the supports, propane undergoes preliminary weak physical adsorption on the surface prior to dissociation. Unlike the non-selective activation on the metal surfaces, the secondary C–H bond activation is energetically preferred compared to the primary C–H bond activation, in agreement with the order of the C–H bond dissociation energies in propane. C–H bond activation follows similar mechanisms on the unsupported V₂O₅(001). The activation energies for hydrogen abstraction are almost the same at the different active sites of the unsupported catalyst, i.e., O1 ≈ O2 ≈ O3, while they increase in the order O1 < O2 < O3 on the supported catalyst.⁴⁰³

On the supported VO_x monolayer on TiO₂(001), the C–H bond activation in propane is via a concerted mechanism at the V–O site, leading to the formation of the metal hydride and adsorbed propoxide.⁴⁰³ The vanadyl site (V=O) is the most active site on V₂O₅(001) and V₂O₅/TiO₂, while the bridging V–O–V sites are more selective towards propylene. The rate-limiting step of oxidative PDH is the activation of propane via a direct H abstraction from the methylene C–H, based on the reaction path analysis at 0 K. The TiO₂ support enhances the C–H bond activation as compared to unsupported V₂O₅ by lowering the activation energy of the RDS as shown in Fig. 35 and influences the selectivity of the supported monolayer VO_x catalyst towards propylene production rather than propanol and acetone.

Fig. 35 (a) Investigated pathways for propane oxidation over the vanadia surface; the corresponding energy diagrams for propane oxidation to propylene on (b) V₂O₅ and (c) V₂O₅/TiO₂.⁴⁰³ Reproduced from ref. 403 with permission from Elsevier, copyright 2012.

The VO_x monomers and dimers supported on SiO₂ have also been studied by Rozanska et al.⁴¹⁵ The first H abstraction from propane is the RDS and yields activation barriers at 750 K, which are lower for dimeric VO_x (1.18 eV) than for monomeric VO_x (1.29 eV). Using the reaction energy as a reactivity descriptor, the energy barriers for propane ODH decrease with increasing VO_x coverage from dimers to larger oligomers. Besides, V^V/V^IV redox cycles are preferred over V^V/V^III cycles.

Dependence of activity on supports and cluster size. Various oxides such as TiO₂, SiO₂, CeO₂ and γ-Al₂O₃ have been studied as the supports of VO_x.^{394,416–418} The activity of the active sites in VO_x depends strongly on the supports, which is ascribed to the electronic modification of active oxygen sites.⁴¹⁴ TiO₂ is the most widely studied support owing to the highest activity of VO_x/TiO₂. Du et al. observed that propane ODH activity can be tuned by supporting on anatase TiO₂ surface and changing VO_x dispersion.⁴¹⁴ The activation energy of the first C–H activation and the formation energy of propylene on the monomeric and dimeric VO_x species supported on the anatase TiO₂(001) and (100) surfaces are summarized in Table 4.

Table 4 A summary of the active oxygen sites and energetics for the most feasible pathways of propane ODH reaction on the four catalysts^a.⁴¹⁴ Adapted from ref. 414 with permission from Elsevier, copyright 2013

	VOx/TiO2(001)		VOx/TiO2(100)
	First C–H activation	Propylene formation	First C–H activation	Propylene formation
a R represents the radical propyl mechanism and C represents the concerted propoxide mechanism. Values in the brackets for the monomeric and dimeric VOx/TiO2(100) surfaces are ZPE corrected (unit: eV).
Monomer	OV–Ti (1.58)	R: OV–Ti (1.83)	OV= (1.37)[1.14]	R: OV–Ti (1.86)[1.65]
		C: OV–Ti (1.85)	OV–Ti (1.36)[1.19]	C: OV–Ti (1.86)[1.69]
Dimer	OV= (1.62)	C: OV–Ti (2.02)	OV= (1.05)[0.86]	C: OV–Ti (1.19)[1.08]

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By comparing the energy barrier of the first C–H activation step and the overall energy barrier of propylene formation on TiO₂(001) and (100) surfaces given in Table 4,⁴¹⁴ it can be seen that the catalysts supported on the (100) surface show higher activity than those on the (001) surface. For the monomer, dimer, and monolayer of VO_x, the valence bond formed at the interface of VO_x and support surfaces. The interface electronic transfer resulted in the modification of the electronic structure of VO_x species, as evidenced by the projected p-DOS plots where the centers of the valence bands of the VO_x/TiO₂(100) surfaces are closer to the Fermi level than those of the VO_x/TiO₂(001) surfaces. This is also reflected in more negative Bader charges of oxygen sites on the (100) than (001) surfaces. This indicates that the oxygen sites are the nucleophilic centers to attack the positively charged H atoms and activate the C–H bond. The stronger basic oxygen sites with more negative charges in VO_x supported on (100) attack more efficiently the acidic C–H bond, and thus result in higher activities than those on the (001) surfaces. In addition, the support changed the relative charge of the oxygen sites. For example, the higher activity of the terminal V=O sites than that of the V–O–Ti interface sites on the dimeric VO_x/TiO₂(001) can be ascribed to the more negatively charged O on the former sites.

A comparative study of PDH on monomeric and dimeric VO_x supported on γ-Al₂O₃ and V₂O₅ crystal, as shown in Fig. 36, revealed that the cluster size has a remarkable influence on the relative activity of oxygen sites and the rate-determining step.⁴⁰⁴ The first C–H bond activation has a lower activation barrier than the secondary C–H activation on the supported V₂O₅, while both C–H bond activations have similar energy barriers on the supported VO₃. Besides, the O p-band center could correlate with the dehydrogenation barrier of the O sites to predict the dehydrogenation activity. Luo et al. also reported that mixed CaO and γ-Al₂O₃ supported VO_x is beneficial to the propylene formation compared to pure CaO supported VO_x, which is attributed to the moderate level of acidity and metal–support interaction.⁴¹⁹

Fig. 36 Reaction energy profiles of C₃H₆* formation and CH₃COCH₃* formation by two successive H ruptures of C₃H₈* over (a) supported monomeric VO₃/Al₂O₃, (b) supported dimeric V₂O₅/Al₂O₃, and (c) slab V₂O₅(001) surfaces. (d) Proposed reaction mechanisms over the different degrees of vanadium polymerization in different periods of reaction. The structures of transition states and adsorbed C₃H₆* are shown in the diagram. The black line denotes the C–H rupture by the V=O bond, while the red line denotes the C–H rupture by V–O–Al (or by the V–O–V bond). The blue line denotes the CH₃CO*CH₃ formation catalyzed by the V=O bond. The structures of transition states and adsorbed C₃H₆* are shown in the diagram. Color scheme: H white; Al green; V gray; O red; C gray.⁴⁰⁴ Reproduced from ref. 404 with permission from the American Chemical Society, copyright 2019.

Moreover, p-DOS analysis suggests that the electronic structure depends on the VO_x cluster size or dispersion, which rationalizes the activity dependence of the cluster size of VO_x on the support. The monomer dispersed VO_x is more active than the dimer dispersed VO_x on the TiO₂(001) surface, while the dimer dispersed VO_x is more active than the monomer dispersed VO_x on the TiO₂(100) surface.⁴¹⁴ Cheng et al.⁴²⁰ reported that the coordination number of the vanadium atom was the key structural parameter in predicting the catalytic activity, showing that the activation energy of the first dehydrogenation step for propane on anatase-supported vanadium oxide monomers and dimers is 1.73 eV and 1.91 eV, respectively.

The above discussion reveals that the support surface and the dispersion of the VO_x catalyst change the electronic properties of the oxygen sites and thus change their activity in activating the C–H bond of propane. The oxygen activity in VO_x seems to be of vital importance for C–H bond activation.

The activity of the lattice oxygen can also be described by the formation energy of the oxygen vacancy. The formation energy of surface oxygen vacancy can be identified as a dominant parameter in determining the adsorption mode and the catalytic activity of metal oxides.⁴²¹ Li et al. reported that the formation energy of surface oxygen vacancy could be used as a descriptor to explain the adsorption behaviors, which is more sensitive to the change in the electronic structure of perovskites, arising from the fact that the actual partial charges the oxygen and transition-metal ions carry determine the adsorption behaviors of the oxygen and transition-metal ions.⁴²² The estimated formation energies of oxygen vacancy of VO_x are summarized in Table 5.

Table 5 Calculated oxygen vacancy formation energies (eV) on unsupported and supported VO_x. O₁, singly coordinated vanadyl O; O₂ or O₂–support, doubly coordinated bridging O; O₃ or O₃–support, triply coordinated bridging O

Model	O* → * + 1/2O2(g)
	O1	O2	O3	O2–support	O3–support	Ref.
V2O5(001)	2.04	3.37	3.78	—	—	403
V2O5/TiO2	2.44	4.50	3.49	—	—
V2O5(001)	1.67	3.30	—	—	—	413
VO3/TiO2	1.86	—	—	0.77	—
V2O5/TiO2	2.63	—	—	2.76	2.23
V3O6/TiO2	2.86	4.16	—	2.85	4.29
V4O8/TiO2	2.68	3.92	—	—	—
1 mL VOx/TiO2	2.89	4.77	—	—	—
Monomeric OVSi7O12H7	2.98	—	—	—	—	423
Dimeric O2V2Si6O12H6	2.87	—	—	—	—
Octameric V8O20	2.65	—	—	—	—

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When going from monomeric through dimeric and eventually to octameric VO_x species, the reaction energy for VO_x species yielding an O defect site changes from 2.98 through 2.87 and eventually to 2.65 eV, as shown in Table 5, while the reaction energy for H abstraction in propane at the corresponding V=O site decreases from 1.06 through 0.90 and eventually to 0.52 eV.^415,423 The lower formation energy of oxygen vacancy corresponds to a higher oxygen activity. Likewise, the TiO₂ support lowered the formation energy of oxygen vacancy, thus increasing the activity. The formation energy of the oxygen vacancy can therefore be used as a descriptor when searching for new catalysts for ODH of propane.

Dependence of activity and selectivity on the cluster size and valence state. The selectivity of propylene remains a challenge in ODH of propane. A study of deep oxidation of propane to CO₂ on V₂O₅(001)⁴²⁴ revealed that the terminal V=O sites are the active sites for the formation of acetone from i-propoxide and the further combustion of acetone to CO₂. The V–O–support is the main active site for propylene formation. It provides a guideline for the rational design of new catalysts with improved selectivity. The ratio of the terminal V=O to the other two oxygen sites is a key parameter in the catalyst design. Small cluster VO_x with a low V=O ratio could increase the propylene selectivity at the expense of lowering the activity, while polymeric VO_x with a high V=O ratio could lower the propylene selectivity. The cluster size needs to be compromised between the activity and selectivity, and sub-monolayer VO_x could provide a high propylene yield, which has been very recently confirmed experimentally by Gong and coworkers.⁴¹³

Very recently, Xiong and co-workers found that the PDH reaction can be divided into two periods in the VO_x reduction by propane: the initial ODH dominant period leading to propylene, water and CO₂ formation and the non-ODH dominant period (see Fig. 36d).⁴⁰⁴ Over γ-Al₂O₃ supported VO_x, the V=O mainly contributes to H₂O and CH₃CO*CH₃ formation and deep oxidation to CO₂ in the ODH dominant period. With the consumption of the V=O during the reaction, the Al–O–V sites become dominating active sites for propylene formation. Note that the PDH ability should be related to their corresponding valence state.^420,425 It has been illustrated that the oxygen vacancy modified the electronic structure of active species and even change the reaction mechanism.⁴²⁶

Gas-phase O₂ in the reactant mixture reoxidizes the reduced V species and removes carbon deposits. The lattice O of VO_x species provides pathways toward desired propylene formation, while the surface O mainly forms undesired CO_x species. Propane conversion and the propylene yield could be described by a kinetic model including propane ODH, parallel propane combustion, and sequential propylene combustion. Propylene is the most abundant primary product. CO and CO₂ are formed by the secondary combustion of propylene, which is the main source of carbon oxides in the studied reaction, and CO₂ also forms by direct combustion of propane.^335,427,428 The activation energies of CO and CO₂ formation from secondary propylene combustion are less than the activation energy for propylene formation on TiO₂/SiO₂-supported VO_x catalysts, leading to the inverse conversion versus selectivity relationship.⁴²⁹ This result is different from the energy profiles for propane ODH and propylene combustion over VO_x/Al₂O₃ catalysts, as shown in Fig. 37.¹⁵ The C–H bond activation and the recombination of the remaining OH groups to form H₂O are irreversible.^427,428 For the propane ODH reaction over VO_x involving the participation of the O₂ molecule, the energy barriers for H₂O elimination on the surface can be reduced.⁴⁰⁹ The rate of propane ODH reaction is proportional to C₃H₈ partial pressure and independent of O₂ partial pressure in the limit of very low H₂O concentrations, and therefore propane activation is a kinetically relevant step. However, the rates acquire a more complex dependence on C₃H₈ and O₂ pressures when H₂O is present at higher concentrations. On V₂O₅ powders and supported VO_x, the dependencies of reaction rates on C₃H₈, O₂, and H₂O concentrations are identical, indicating that both surfaces have similar active centers.⁴²⁷

Fig. 37 Energy profile for propane ODH (left) and rate determining step of propene combustion over VO_x/Al₂O₃ catalysts.¹⁵ Reproduced from ref. 15 with permission from the American Chemical Society, copyright 2014.

In addition to these studies, significant efforts have been devoted to improving the activity of the different O sites for propane ODH of the supported VO_x catalyst. Alkali metal additives have been found to improve the propylene selectivity for propane ODH on V-based and Mo-based catalysts; the effect is explained by a modification of the acid–base properties of the catalysts.^{335,430–432} On VO_x/SiO₂ catalysts, the potassium additive by blocking active centers on the catalyst surface exhibits a strong inhibitory effect on the consecutive propylene and parallel propane combustion and has a lower influence on ethylene and ethane combustion.³³⁵ Thus, potassium does not change the ethylene selectivity but has a distinct influence on the propylene selectivity, and thus leads to high initial selectivity (−95%). Zhao et al.⁴³³ also reported that OH groups on supported VO_x catalysts can lead to lower PDH activity and less coke formation by combined experimental and calculational studies, but the fresh VO_x catalysts under a C₃H₈ atmosphere are directly reduced to V₂O₃.

4.2.3 Other catalysts. Other types of catalysts, such as Cr-based catalysts, Ga-based catalysts, Mo-based catalysts, and mixed metal oxides, have also been studied in the ODH of propane, and these catalysts generally permit the redox mechanism to occur without structural collapse.^72,393 However, most of these studies mainly involve experimental findings due to the complexity of the metal oxides, including the different crystal structures, the oxidation states, and the surface facets.^{337,338,434–437} Liu et al.⁴⁰² studied PDH on perfect Ga₂O₃(100) by DFT calculations. The bridge-bound surface O sites are active for cleaving the C–H bonds in propane, and thus rather stable OH groups are formed on the surface. The initial C–H bond activation of propane energetically prefers the radical mechanism and shows a rather low energy barrier (0.78 eV) at the surface O sites. Propylene can be formed through H abstraction from physically adsorbed propyl radicals or from propoxide and propylgallium intermediates. Besides, propylene at the surface O sites has high adsorption energy, which tends to be further dehydrogenated or oligomerized, leading to catalyst deactivation. Once the surface O ions are blocked or consumed by the H atoms, the Ga sites will become the main reaction sites to catalyze the further dehydrogenation reactions and H abstraction by Ga sites needs to overcome high energy barriers to form gallium hydrides (GaH). However, the formation of H₂ from the GaH and OH groups is much easier. Therefore, the RDS changes from H abstraction by oxygen sites at the initial reaction stage to H abstraction by Ga sites from various propyl sources to form GaH. On the Ga₂O₃(100) surface, it is difficult for the H atoms in the OH groups to form H₂ or H₂O. Since it is also possible to generate gaseous H₂O at high temperatures, the reaction would follow an ODH mechanism comprising H₂O at the initial stage and follow a PDH mechanism forming H₂ at the steady stage.

Fu et al.⁴⁰⁰ also reported that the initial propane activation on molybdenum oxides follows the same ODH mechanism as V-based catalysts in that lattice oxygens participate the C–H activation, where 6 possible mechanisms of the C–H bond activation on metal oxides are considered on Mo₃O₉, leading to 17 transition states involving C–H activations from the methyl and methylene groups in propane. For example, this activation step can specifically take place at M–O ion pairs by a heterolytic mechanism or at O–O pairs by a homolytic mechanism or at the terminal M=O site by an oxygen insertion mechanism. On the surface, it is found that the most feasible reaction pathway for the initial propane activation is H abstraction by the terminal Mo=O site and the C–H activation for methylene is 0.20 eV more favorable than that for the methyl C–H bond. The calculated activation enthalpy and entropy for the methylene C–H bond are 32.3 kcal mol⁻¹ and −28.6 cal (mol K⁻¹)⁻¹, respectively.

Also, for MoO_x catalysts, similar active centers are present on supported MoO_x, MoO₃, and ZrMo₂O₈.⁴²⁸ Surface O and OH groups are the most abundant surface intermediates that can lead to a rate expression to accurately describe the measured kinetics of propane ODH.^427,428 On MoO_x and VO_x catalysts, similar kinetic rate expressions confirm that propane ODH occurs via similar pathways, using lattice oxygen atoms to abstract hydrogen atoms from propane in the RDS of irreversible C–H bond activation.³³⁹ For the transition state for this elementary step, the electrons are transferred from lattice oxygens to metal centers as an i-propoxide and an OH group from propane.⁴³⁸ Propane ODH activation energies (1.03–1.31 eV) are higher than those for propylene combustion (0.53–0.67 eV), where the measured difference in activation energy (0.50–0.63 eV) between the both is larger than the difference in the weakest C–H bond dissociation enthalpy between propane and propylene (0.42 eV).

The activation energies for propane primary dehydrogenation and propylene secondary combustion increase as the Lewis acidity of the cations increases (V⁵⁺ < Mo⁶⁺ < W⁶⁺), while the corresponding reaction rates decrease. Therefore, metal oxides having high redox properties exhibit high catalytic activity, and less acidic metal oxides lead to higher propylene yields.³³⁹ Chen et al. also reported that VO_x catalysts are much more active than MoO_x catalysts with similar H₂ reduction rates.⁴³⁸

Zhu et al.^{358,391,405,439} systematically studied the catalytic performance of PDH on Cr₂O₃, ZnO, V₂O₃, and Ga₂O₃. There are oxygen vacancies that can exist on the ZnO surfaces, also implying that the reaction path of the ODH mechanism could occur in the initial reaction stage.⁴⁰⁵ Besides, oxygen vacancies may modify their electronic structure, thereby positively affecting the reactivity of α-Cr₂O₃, but negatively affecting ZnO mainly due to the weaker Lewis acid–base interaction on ZnO(10−10). Therefore, for the dehydrogenation reaction over some transition metal oxides without oxidants (such as O₂ and CO₂) introduced into the reaction gas mixture, active lattice oxygen can participate in the C–H bond activation, possibly following an ODH mechanism in the initial stage of the reaction before the oxide surfaces reach a steady state. However, if oxidants are introduced into the reaction gas, the dehydrogenation reaction could follow the ODH mechanism to remove the H atoms absorbed on the surface.^337,440,441 For example, Atanga et al.⁴⁴² proposed that CO₂ as a mild oxidant for the ODH of propane can reactivate deactivated redox catalysts caused by metal oxide reduction, and the introduction of CO₂ can also overcome the problems of over-oxidation and low propylene selectivity.

4.3 C–H activation on single atom–oxide hybrids

Single-atom catalysis is an area of intense current research.^443–445 On the one hand, single-atom catalysts (SACs) exhibit properties that are distinctly different from those of supported nanoclusters. On the other hand, single-atom catalysts have well-defined local structures, and therefore provide an opportunity for establishing the structure–reactivity relationship.^446–448 However, because of the low coordination environment, the surfaces of SACs have a high surface free energy, and single atoms tend to migrate and aggregate to form clusters. Recently, several research efforts have been devoted to synthesizing thermally stable SACs, such as the proposal of strong metal–support interactions (SMSI), which can play a role in keeping single atoms from sintering on the surface.^446,449 Lang et al. found that isolated Pt atoms or PtO₂ units can be trapped on an Fe₂O₃ support through SMSI during high-temperature calcination (800 °C, 5 h).⁴⁵⁰

Single metal atoms have been deposited onto transition metal, graphene, and metal oxides, among which singly dispersed metal atoms on metal oxides have received much attention in catalyzing PDH.^{364,385,451–455} As has been observed by Xiong et al.,⁴⁵¹ isolated single atoms of Pt can be steadily trapped on CeO₂ catalysts, while the catalyst is not selective towards propylene. DFT calculations show that the strongly adsorbed propylene is expected to undergo further reactions, leading eventually to C–C bond cleavage. To prevent a further reaction, Sn is added to the Pt single-atom catalyst. They found that propylene showed much lower adsorption energy on small Pt–Sn clusters than that on single Pt atoms. Consequently, a higher selectivity is obtained on Pt–Sn–CeO₂. Sun et al.³⁸⁵ directly dispersed single Pt atoms on Cu NPs to form SAA catalysts, which exhibit high propylene selectivity (∼90%) and great stability at 520 °C. In addition to the use of SAA catalysts, other SACs that provide excellent catalytic performance for PDH are still under theoretical research.

Some supports have been considered to anchor single metal atoms by theoretical calculations.^{358,391,405,439} For instance, Pt₁–Cr₂O₃(0001) and Pt₁–ZnO(10−10) oxides were constructed by Chang et al.,⁴⁰⁵ and show higher activity than their pristine surfaces by lowering the activation energy for the RDS and promoting H₂ desorption, and on these two types of oxide surfaces single Pt atoms act as promoters (see Fig. 38). These findings are in line with experimental and DFT studies by Liu et al. and Sattler et al.,^333,456 which clearly showed that the addition of a trace amount of Pt could accelerate H₂ desorption over ZnO/Al₂O₃ catalysts and affect the distribution of Ga³⁺, thereby leading to a higher activity than the pristine surfaces.^2,456 This may be attributed to the interactions between Pt and ZnO (or TiO₂). On the Pt₁–Ga₂O₃(100) surface, a Pt-doped Ga₂O₃ catalyst shows a bifunctional character in PDH where the Pt–O site brings about dehydrogenation, while the Ga–O site is active for desorbing H₂.⁴³⁹

Fig. 38 Energy profiles for PDH on pristine, oxygen-deficient, and Pt-doped (a) Cr₂O₃ and (b) ZnO surfaces. All the potential energies are referenced to gas-phase propane.⁴⁰⁵ Reproduced from ref. 405 with permission from the American Chemical Society, copyright 2019.

The kinetics of the PDH reaction over M₁–V₂O₃ (M = Mn–Cu, Ru–Ag, and Os–Au) were studied by Zhang et al.³⁹¹ In their model, surface V and O atoms are replaced with single atoms, including M₁–(V_vac)–V₂O₃(0001) (M = Mn, Fe, Co, Ni, and Cu) and M₁–(O_vac)–V₂O₃(0001) (M = Pd, Pt, and Au). Moreover, it shows that the V–O(o) site is the dominant active site over V₂O₃(0001). These findings agree well with the experimental studies by Liu et al. who found that V³⁺ was more active for PDH over VO_x/Al₂O₃, which, to some extent, explains why a VO_x catalyst without H₂ reduction shows higher initial activity.³⁹⁴ Besides, on M₁–(V_vac)–V₂O₃(0001), the active site for PDH is V–O(o) and M acts as the promoter, while on M₁–(O_vac)–V₂O₃(0001) the M and V ion pairs act as the active site. Apart from the work by Zhang et al., Ma et al. systemically examined the structural stability, catalytic activity and selectivity of 13 M₁–ZnO (M = Mn, Fe, Co, Ni, Cu, Ru, Rh, Pd, Ag, Os, Ir, Pt, and Au).³⁵⁸ By applying linear scaling relations of chemisorption energy and transition-state energy, it is found that the formation energies of H and 2-propyl can be used to measure the binding strengths of all the reaction intermediates and activated complexes and can therefore be used as descriptors to describe the kinetics of PDH over M₁–ZnO. As indicated in Fig. 39, theoretical calculations predict that most of the single-atom-doped ZnO catalysts except for Fe- and Os-doped ZnO exhibit higher activity than pristine ZnO. Such a study can not only offer new opportunities to develop a more cost-effective heterogeneous catalyst but also help guide future experiments.

Fig. 39 TOFs for propane dehydrogenation to propylene as a function of the formation energies of adsorbed H at the O site and adsorbed 2-propyl at the M site on the (a) first and (b) second groups of doped oxide surfaces.³⁵⁸ Reproduced from ref. 358 with permission from the Royal Society of Chemistry, copyright 2020.

5. Conclusions and perspectives

The paper reviews the computational catalysis of the C–H bond activation of light alkanes such as methane, ethane, and propane towards synthesis gas and light olefins, as the important building blocks of the chemical industry. Quantum chemical calculations have grown into a technique of extraordinary power that pervades all current discussions of heterogeneous catalysis. In particular, computational approaches that use results from DFT calculations combined with descriptor-based scaling relationships as inputs to microkinetic analysis or kinetic Monte Carlo simulations not only play a significant role in developing a step-by-step, molecular-level view of the pathway leading to products but also provide an effective way to rationally screen potential catalyst candidates for a given catalytic reaction. A highly integrated approach using DFT, linear scaling relations, and microkinetic modeling successfully accounts for the way catalyst compositions like various metals, alloys, single atoms, metal–oxide interfaces, and locally coordinated oxygen in oxides modify the electronic properties of the active sites and their relations to the catalytic performance of alkane conversion. DFT-based microkinetic analysis extends the computational catalysis from model surfaces to industrially relevant catalysts. In this review, we attempted to illustrate the recent substantial progress made by using such theoretical methods in understanding the effects of geometrical and electronic structures on the activation of C–H bonds of light alkanes and in the discovery of new and more effective catalysts for light alkane conversion on metal and metal oxides. Special efforts have been devoted to recognizing the patterns of catalytic activity and selectivity for a class of substances applied in commercially important reactions.

Despite the fact that many different reactions and different types of catalysts have been applied to convert light alkanes to valuable products, it is common that the light alkane transformation initiates from C–H cleavage. The C–H bond activation of methane, ethane, and propane on metal and metal oxides was summarized and compared. A universal scaling relationship of C–H bond activation across C1–C3 alkanes and various catalysts was discussed.

Some mechanistic insights into methane conversion to synthesis gas are common for steam reforming, dry reforming and partial oxidation, involving C–H bond cleavage to form CH_x followed by subsequent oxidation of CH* or C* by O* or OH*. The preferred reaction pathways and rate-determining step depend on the catalysts and operating conditions. DFT calculations and microkinetic modeling provide a guideline to manipulate the catalyst surface to reduce the carbon formation by lowering the surface carbon coverage. The lowered surface carbon coverage benefits from the enhanced CH* oxidation and the reduced CH* formation and its decomposition to surface carbon.

The critical challenges in ethane and propane dehydrogenation and oxidative dehydrogenation are the selectivities to olefins and coke formation. The DFT calculations and kinetic analysis unravel useful fundamental insights into these key challenges at the molecular level, where the difference in the desorption energy of olefins and the activation energy of deep dehydrogenation of surface intermediates is used as the descriptor. Computational catalysis suggested Pt-based alloys as the best candidates for industrial catalysts by lowering the olefin desorption energy.

Oxidative dehydrogenation on oxides is an attractive alternative for light alkane dehydrogenation to olefins due to the breaking of the thermodynamic limitation and in situ supply of heat for highly endothermic dehydrogenation reactions. However, the critical challenge in olefin selectivity still remains due to the high reactivity of olefins. DFT calculations elucidated the active sites and surface reactions responsible for the formation of olefins, CO_x, and other byproducts. The lattice oxygen is the main active site. It significantly adds complexity in DFT modeling, where the activity of oxygen depends on the local structure and coordination as well as oxygen vacancy. However, it also provides huge opportunities to tune the oxygen activity to reduce the C–C bond cleavage and oxidation to CO_x. Oxides are a large family and present numerous oxide structures. The experimental and theoretical studies revealed the catalyst's activity dependence on the oxide identity, doping, cluster size, and supports. The formation energy of oxygen vacancy or hydrogen affinity was identified as the descriptor to describe the oxygen activity. However, a thorough screening of a huge number of oxide structures to find appropriate catalyst candidates for a given reaction remains a formidable challenge. Most of the studies have been performed only addressing the C–H bond activation. DFT calculations of elementary steps involved in the whole catalytic cycle, including by-product formation, are essential to address the selectivity. In addition, the active sites are highly dynamic on oxides due to their redox nature, with generation and filling of the oxygen vacancy. The oxygen vacancy in the steady-state can be changed with reaction conditions. Full modeling of reactions accounting for active site dynamics is also extremely challenging. Better scaling relationships for adsorption energy and activation energy on oxides need to be explored based on a big dataset. Machine learning and artificial intelligence could be explored to significantly accelerate catalyst development.

There is generally a strongly constrained relation between the C–H bond activation of light paraffins, olefin desorption, and deep C–H bond activation, which presents a challenge in catalyst design to maintain high activity, selectivity, and stability with a high coking resistance, simultaneously. The alloy of Pt with a second metal and a core–shell structure is an effective way to lower the ethylene and propylene desorption energy and increase the olefin selectivity and lower the coking potential, but at the expense of lower activity. The single metal or metal clusters on oxides could be explored to break down the constrained relation to enhance the catalytic performance. However, the active sites at the metal–oxide interface largely increase the complexity of the modeling. There are much more possible sites for adsorption and elementary reactions compared to the metal and oxide alone.

There remain several challenges in theoretical catalysis, which makes it difficult to discuss the chemistry of light alkane conversion in a more quantitative way. First, DFT has its complexity and a lot of physics hidden inside the approximate exchange–correlation functional. This term works surprisingly well given its simplicity and holds the key to the success of the theory. However, it is still challenging to quantitatively reproduce the reaction rates obtained from experiments, since the values of the calculated reaction heat and activation energy obtained by DFT calculations have an uncertainty of 0.1–0.2 eV.^457,458

Second, the structure of active sites on catalysts is generally represented by simple low-index surfaces in computational studies. A gap still exists between realistic catalysts under reaction conditions and model surfaces. In situ characterization of working catalysts can provide more detailed structural information to help build more reliable structures close to industrial catalysts. Even though computational modeling of the surface structure of industrial catalysts needs to be carried out with caution, there is no doubt that DFT calculations are able to suggest mechanisms and structure–activity–selectivity relations, and rationalize a considerable amount of experimental observations, which are often difficult to understand. Finally, the microkinetic analysis of reactions is necessary to present the experimental conditions appropriately to understand important industrial reactions. The DFT calculations and microkinetic modeling need to be even more tightly associated with multiscale modeling at catalyst pellet and reactor levels, as well as the experimental study for searching for new catalysts and improving industrial catalysts.

Despite many challenges, with advances in density functional theory, scaling relationships, and descriptor-based microkinetic modeling, it is now possible to describe catalytic reactions at surfaces with the detail and accuracy required for computational results to compare favorably with experiments.²⁸ The computational approach has become an effective tool for the design of catalysts with high activity, selectivity, and stability. It is interesting to note that the advanced computational catalysis approach has predicted the most active pure metals for methane and propane activation, and some bimetallic alloys are screened based on the volcano curve obtained from pure metals for ethane activation. The highly integrated computational and experimental approach will be explored to accelerate the development of next-generation catalysts for alkane conversion.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The supports from NTNU energy, the Centre for Industrial Catalysis Science and Innovation (iCSI), which receives financial support from the Norwegian Research Council, the Natural Science Foundation of China (No. 91645122 and 22073027), and the Natural Science Foundation of Shanghai (No. 20ZR1415800), as well as the computational time provided by the Notur project (nn4685k), are gratefully acknowledged.

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