Direct Methane to Methanol - ACS Publications - American Chemical

Research Article Cite This: ACS Catal. 2018, 8, 6894−6907

pubs.acs.org/acscatalysis

Direct Methane to Methanol: The Selectivity−Conversion Limit and Design Strategies Allegra A. Latimer,†,§ Arvin Kakekhani,†,§ Ambarish R. Kulkarni,† and Jens K. Nørskov*,†,‡ †

Downloaded via UNIV OF TOLEDO on June 29, 2018 at 18:05:30 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

SUNCAT Center for Interface Science and Catalysis, Department of Chemical Engineering, Stanford University, 450 Serra Mall, Stanford, California 94305, United States ‡ SUNCAT Center for Interface Science and Catalysis, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, United States S Supporting Information *

ABSTRACT: Currently, methane is transformed into methanol through the two-step syngas process, which requires high temperatures and centralized production. While the slightly exothermic direct partial oxidation of methane to methanol would be preferable, no such process has been established despite over a century of research. Generally, this failure has been attributed to both the high barriers required to activate methane as well as the higher activity of the CH bonds in methanol compared to those in methane. However, a precise and general quantification of the limitations of catalytic direct methane to methanol has yet to be established. Herein, we present a simple kinetic model to explain the selectivity−conversion trade-off that hampers continuous partial oxidation of methane to methanol. For the same kinetic model, we apply two distinct methods, (1) using ab initio calculations and (2) fitting to a large experimental database, to fully define the model parameters. We find that both methods yield strikingly similar results, namely, that the selectivity of methane to methanol in a direct, continuous process can be fully described by the methane conversion, the temperature, and a catalyst-independent difference in methane and methanol activation free energies, ΔGa, which is dictated by the relative reactivity of the C−H bonds in methane and methanol. Stemming from this analysis, we suggest several design strategies for increasing methanol yields under the constraint of constant ΔGa. These strategies include (1) “collectors”, materials with strong methanol adsorption potential that can help to lower the partial pressure of methanol in the gas phase, (2) aqueous reaction conditions, and/or (3) diffusion-limited systems. By using this simple model to successfully rationalize a representative library of experimental studies from the diverse fields of heterogeneous, homogeneous, biological, and gas-phase methane to methanol catalysis, we underscore the idea that continuous methane to methanol is generally limited and provide a framework for understanding and evaluating new catalysts and processes. KEYWORDS: methane to methanol, selective oxidation, density functional theory, partial oxidation, methanol collector, heterogeneous protecting groups, selectivity−conversion limit theory (DFT)-predicted barriers.5−8 However, solutions to the second problem, that of product reactivity, have proven more elusive. Even if methanol can be locally produced by a catalyst at low temperatures, it is difficult to stop its CH bonds, which have a 0.4 eV lower bond dissociation energy (BDE) than those in methane, from being further oxidized.3,9 Indeed, an example of a continuous process able to simultaneously achieve both high methane conversion and high methanol selectivity has yet to be established, pointing to a robust selectivity−conversion trade-off.10 In light of this challenge, many efforts have shifted focus from catalytic to stepwise processes, in which reactant consumption and product collection are decoupled. These systems bypass the aforementioned selectivity−conversion

1. INTRODUCTION Currently, there exists no industrial process capable of directly converting methane to methanol. While many processes have been explored, none to date has proven cost-effective. A consequence of the paucity of catalysts for the direct oxidation of methane to methanol is the annual flaring of 140 billion cubic meters of natural gas at remote oil drilling locations around the world, accounting for 1% of global CO2 emissions with no associated energy gains.1 Two distinct problems are often cited as being responsible for the lack of catalysts available for such a process: the large barriers associated with activating the nonpolar and highly symmetric methane molecule and the higher relative reactivity of the desired products.2,3 Regarding the first problem, while methane activation barriers on transition metals are generally high (ΔGa(300 K, 1 bar) > 1.2 eV),4 several publications have highlighted nontransition metal catalysts able to activate methane at low temperatures or with low density functional © XXXX American Chemical Society

Received: January 17, 2018 Revised: June 1, 2018

6894

DOI: 10.1021/acscatal.8b00220 ACS Catal. 2018, 8, 6894−6907

Research Article

ACS Catalysis

Figure 1. Selectivity vs conversion trade-off for varying (a) temperature (at ΔGa = 0.4 eV) and (b) ΔGa (at T = 500 K) using eq 1.

similar results, namely, that ΔEa is normally distributed around a mean value of 0.55 (theory) or 0.59 (experiment) eV with a standard deviation of 0.08 (theory) or 0.09 (experiment) eV. Having recognized a significant limitation to direct methane to methanol processes, i.e., that methanol selectivity is independent of the catalyst chosen and depends solely on methane conversion and temperature, we conclude by identifying and exploring design strategies for overcoming this constraint. We introduce the concept of a “collector”, a material with strong methanol adsorption potential that can help lower the partial pressure of methanol in the gas phase. Including such a collector in a semicontinuous process should allow the high methanol selectivities associated with stepwise processes to be maintained while accessing higher methane conversions and minimizing the need for temperature cycling or water flushing. Additionally, we explore the effects of aqueous reaction conditions, diffusion-limited materials, and nonradical methane activation.

trade-off by producing a protected methanol derivative that is less prone to further oxidation compared to free methanol. Examples in homogeneous catalysis are often quasi-catalytic, i.e., turnover number (TON) > 1, and proceed through the use of small-molecule protecting groups. For example, Periana et al. oxidized methane to a stable methyl bisulfate product that could later be hydrolyzed to yield methanol and sulfuric acid.11,12 However, these systems are limited by expensive oxidants and the cost of recycling protecting groups. Similarly, it was found that metal-exchanged zeolites, which had previously achieved methanol yields of ∼3% (64% CH3OH selectivity; 5% CH4 conversion) in the catalytic process,13 could unlock higher methanol selectivities (∼98%) when used as heterogeneous protecting groups to oxidize methane to methanol stoichiometrically (TON = 1).14−18 Such processes typically involve three steps: zeolite activation at high temperatures (∼450 °C), stoichiometric methane oxidation at lower temperatures (∼150 °C), and methanol recovery by flowing water (∼150 °C).15 Unfortunately, this energyintensive temperature cycling in combination with the expensive oxidizing agents required to reactivate the catalyst and low methanol yields per cycle tend to limit the practical application of these approaches.10 Herein, we aim to understand the limitations of direct methane to methanol catalysis, and we propose strategies to overcome these limitations. While this work does not address the difficult design problem of methane conversion, i.e., finding a catalyst able to activate oxygen and methane and locally produce methanol, it does address the critical question of how to keep the produced methanol safe. We begin by describing a simple kinetic model to quantify the selectivity−conversion trade-off that hinders continuous partial methane oxidation processes. This model possesses a single unknown parameter, ΔGa, i.e., the difference in methane and methanol activation free energies. To understand the variability of this parameter, we employ two distinct approaches. First, building on our previous theoretical work,19 we calculate the components that make up ΔGathe electronic energy (ΔEa), entropy, heat capacity, and zero-point energies (ZPEs)via first-principles methods for a large library of materials. Second, we fit ΔEa to a large library of representative experimental data using the material-independent entropy, heat capacity, and ZPE components obtained from theory. We find that ab initio (DFT) methods and fitting to experiment yield strikingly

2. MODELING THE SELECTIVITY−CONVERSION LIMIT 2.1. Kinetic Model. Building on previous work,9,20,21 we invoke a simple two-step reaction mechanism in which both steps are irreversible to model the selectivity−conversion limit in direct methane to methanol continuous processes. k1

k2

CH4 → CH3OH → CO2

Here, the desired product, methanol, is a transient intermediate. The rate constants, k1 and k2, correspond to the microscopic rate constants of the rate-determining step in the potentially multistep processes of CH4 → CH3OH and CH3OH → CO2. Presently, we assume that hydrogen abstraction from methane or methanol is rate-limiting in both processes, as is often found to be the case.9,22−25 We posit that any oxygenates formed by hydrogen abstraction from methanol, proceeding with rate constant k2, are undesirable products. We can express the selectivity for the transient intermediate, CH3OH, (SCH3OH) solely as a function of methane conversion (X) and relative rate constants (k2/k1) as follows (details in SI section S1) SCH3OH =

1 − X − (1 − X )k 2 / k1 X[(k 2/k1) − 1]

(1)

Further, the rate constant ratio (k2/k1) can be rewritten as 6895


Research Article

ACS Catalysis a

k 2/k1 = eΔG / kbT

(2)

a a ΔGa = GCH − GCH 4 3OH

(3)

GaCH4

GaCH3OH

where and are the activation free energies of methane and methanol. Hence, the maximum methanol selectivity can be fully described by conversion, temperature, and the difference in methane and methanol activation free energies, ΔGa. Notably, in the derivation of eq 1, we made the assumption that each activated methane would turn over to methanol. We stress that this constitutes a “best-case scenario” for our catalyst; one can imagine many other pathways following methane activation that do not involve methanol production (for example, methyl radical formation, methyl adsorption to the catalyst and its subsequent dehydrogenation, etc.). Additionally, we made a second assumption that any produced methanol could be activated by CH bond cleavage once more. Again, while alternative pathways certainly exist for methanol activation, they can only result in a situation in which methanol is more easily activated than we predict here. Therefore, we stress that eq 1 represents the selectivity− conversion limit, i.e., an upper bound to the selectivity possible at a given conversion. Evidently, high temperatures and small or even negative values for ΔGa (corresponding to a larger activation barrier for methanol compared to methane) are desirable for the selective oxidation process (Figure 1). In the following sections, we explore the variability of ΔGa across catalysts through the lenses of both our first-principles calculations (section 2.2) and experimental observations from the published literature (section 2.3). 2.2. Determining ΔGa from First-Principles. CH bond cleavage may occur through either a surface-stabilized or a radical-like mechanism.19,26 In the transition state of the surface-stabilized pathway, the carbon atom forms a partial bond to the catalyst, while in the radical-like pathway, it does not.19,26 The radical-like pathway is of most relevance for single-site catalysts, such as zeolites,3,14,16,19,27,28 whose low concentrations of active sites have helped make them some of the most successful direct methane to methanol catalysts to date.14,15,17,29−32 Therefore, we focus first on methane activation via the radical-like mechanism. If we assume gases behave ideally and transition states harmonically (details in SI section S2), we can write ΔGa(T) as a function of electronic energies and ZPEs, vibrational heat capacity, and vibrational and rotational entropy as follows a ΔGa(T ) = ΔEa + ΔEZPE + a − T ·ΔSvib,rot (T )

∫0

T

Figure 2. Electronic activation energies for methane vs those for methanol on a given active site. Dashed lines correspond to the standard deviation of the population mean. BEEF-vdW principle component ellipses are shown on several materials, and HSE calculations are shown in light green. The inset shows a histogram of differences between methane and methanol activation energies on all catalysts.

vdW) on doped boron nitrides, porphyrins, and graphene layers (for details, see SI section S9). By examining this trend on many different types of catalysts, including oxides, metals, zeolites, metal−organic frameworks, doped boron nitrides, porphyrins, and graphene layers, we hope to capture a complete picture of the materials dependence of ΔEa. In line with our previous work,19 we see that ΔEa is essentially catalyst-independent. The near-unity slope of the line of best fit in Figure 2 suggests a constant mean difference between methane and methanol activation energies across catalyst morphologies. To quantify the DFT uncertainty, we examine the principal component ellipses of the ensemble of exchange−correlation functionals generated by BEEF-vdW.34 Additionally, to ensure that our conclusions are not limited to the GGA level, we have supplemented the BEEF-vdW calculations in this data set by using a hybrid functional (HSE06-D3,35,36 light green circles) on a subset of zeolites. Encouragingly, we find that (1) the principal component ellipses of the reduced 1σ BEEF ensembles show maximum variability along the direction of the scaling line and (2) the hybrid functional calculations are consistent with those achieved using a GGA functional. Therefore, while individual calculations of CH activation barriers will possess a potentially significant DFT uncertainty (approximated by the spread of the BEEF ensemble), the associated dif ference between methane and methanol activation energies, ΔEa, is more robust (Figure S4). We also quantify the morphology-dependent uncertainty in the inset of Figure 2. We see that ΔEa is normally distributed about 0.55 eV with a small standard deviation of 0.08 eV. We have included a brief discussion on the spread of the data in the SI (section S3). Interestingly, for several materials, like boron nitride and graphene, we find that bringing the molecule closer to the surface can stabilize the transition states by up to ∼0.2 eV through a combination of vdW and electrostatic interactions (Figure 3; see section S4 for details). We have included only the lowest-energy transition states in our analysis, and we caution that an unrealistic ΔEa can be calculated if care is not taken to calculate the lowest-energy radical transition state for both methane and methanol.

a ΔCv,vib dT

(4)

We begin by exploring the electronic energy component, a ΔEa = EaCH4 − ECH . It has recently been shown that in many 4OH systems where CH bonds are activated via the radical-like pathway the CH bond activation energy is well-described by two descriptors: the catalyst’s hydrogen abstraction energy (EH) and the BDE of the broken CH bond.19,33 Consequently, the activation energies of radical CH bond breaking in methane and methanol are highly linearly correlated, as shown by DFT transition state calculations for a large number of systems (Figure 2, Table S3). This data consists of calculations from our previous work,19 as well as new nudged elastic band (NEB) transition state calculations using the Bayesian error estimation functional with van der Waals corrections (BEEF6896


Research Article

ACS Catalysis

ΔGa(T ) ≈ ΔEa − (3.942 × 10−4) ·T − 0.0289

(5)

2.3. Determining ΔGa from Experimental Data. Having determined a material- and functional-independent ΔGa from theory (henceforth referred to as ΔGaDFT), we would like to verify our findings by determining a value for ΔGaexp from experimental data. First, to corroborate the functional form of the model given in eq 1, we examine a small set of experimental data collected on Fe-ZSM-5 between 543 and 573 K (red points, Figure 4a) and compare it to the sigmoid obtained by substituting the catalyst-independent ΔGaDFT(558 K) = 0.3 eV into eq 1 (black line, Figure 4a).37 The shaded region indicates a ±1σ error of the population distribution generated by our DFT calculations (originally shown in the inset of Figure 2). The model seems to describe the experimental data strikingly well, in both its functional form and inflection point. We note that only the inflection point is a function of the value assumed for ΔGaDFT; the sigmoidal shape is derived from the kinetic model proposed in eq 1 and not dependent on the ab initio calculations discussed in section 2.2. The correspondence in Figure 5a is particularly satisfying, keeping in mind that that no parameters have yet been fit to experiment. We reemphasize that ΔGaDFT(558 K) = 0.3 is calculated using ΔEaDFT and eq 5 to account for temperature effects. Encouraged by this result, we expand our analysis to a larger library of previously published experimental data (Table S5).13,31,37−66 Unlike the data in Figure 4a that was limited to one material tested by a single group at near-constant temperatures, the complete experimental data set is quite diverse and includes examples from heterogeneous, homogeneous, and radical gas-phase catalysis, temperatures from 273 to 903 K, oxidants including N2O, O2, and H2O2, and active sites composed of Cu, Fe, Co, Au, Pd, Rh, and Mo. We note that this analysis does not include data from cyclic oxidation processes as they are not expected to be well-described by eq 1. Furthermore, we have excluded all catalysts lacking single sites (Table S5, single-site = no) as our analysis is limited to radicallike CH bond activation and the transition state geometry in such catalysts is not well-known.26 Given the vastly different temperatures that characterize the experiments in this database, direct comparison of the entire set of raw data yields minimal catalytic insight. Instead, we

Figure 3. Comparison of high- and low-energy transition states for CH3OH and CH4 C−H bond cleavage on O*Pd@BN (oxygen adsorbed on palladium-doped boron nitride (with a B vacancy)).

To obtain the remaining components of ΔGa from eq 4, we calculate vibrational frequencies for a subset of the materials shown in Figure 2 and approximate their free energies using the harmonic approximation for transition states and the ideal gas approximation for gas-phase methane and methanol (see SI section S2). We find that the additional components of ΔGa are also normally distributed (Figure S1). This finding strongly indicates that, in addition to the difference in the electronic activation energies (ΔEa), the difference in the f ree energy of activation of methane and methanol is approximately constant at a given temperature. We emphasize that, while ΔEa and ΔGa are both material-independent quantities, the mean value of ΔGa and its standard deviation depend on temperature, as described in eq 4. While ΔGa is not precisely a linear function of temperature, we find that for the relevant temperature ranges (250−900 K) ΔGa can be successfully approximated as such (Figures S2 and S3). Therefore, for simplicity and ease of reproducibility, we approximate ΔGa(T) in the remainder of this work as its linear best fit

Figure 4. (a) Data taken from ref 37 (red) and corresponding reaction temperatures overlaid on the sigmoid described by eq 1 at 558 K using ΔGaDFT (black line) including a ±1 σ error (gray lines and shading). (b) Comparison of distributions of ΔEaexp (fitted to experiment using eq 1, red) and ΔEaDFT (calculated, black). 6897


Research Article

ACS Catalysis

Figure 5. Experimental selectivities and conversions of single-site catalysts. The central image shows data whose selectivities have been extrapolated to the gas phase at 700 K. The surrounding images show real experimental selectivities, grouped by similar experimental conditions, overlaid on the selectivity−conversion limit predicted by eq 1 and ΔGaDFT at those conditions. Colors denote different catalyst morphologies; diamonds are aqueous experimental reaction conditions, and circles are gas-phase. An interactive figure is available online.68

theory (see eq 5), and an arbitrary new temperature (needed to compare all data at equivalent conditions; we have arbitrarily chosen 700 K) are plugged into eq 1, yielding new experimental selectivities that have been “extrapolated” to the gas phase at 700 K. These extrapolated selectivities are shown in the central image of Figure 5 along with the prediction from ΔGaDFT and eq 1 at 700 K in black and its 68% confidence interval in gray. Additionally, the smaller plots surrounding the central image show all data in their nonextrapolated forms (i.e., the original selectivities at the original temperatures and either aqueous or gas-phase reaction conditions) along with the corresponding model prediction from ΔGaDFT and eq 1 every 50 K (cyan). These may be useful for comparing new results to previous experimental work done under similar conditions. We see that, in general, experiment and theory look quite comparable. Only a few data points lie to the right of the −1 σ boundary, indicating the robustness of the predicted selectivity−conversion limit. Additionally, the points lying to the left of the +1σ boundary are not unexpected; as noted in section 2.1, eq 1 represents an upper bound to the selectivity rather than a fixed trade-off. Notably, these findings provide us with the ability to predict the selectivity−conversion limit of direct methane to methanol catalysis with limited understanding of the active site composition or coverage. In Cu-exchanged zeolites, for example, the exact speciation of Cu under reaction conditions can be both variable and difficult to determine (i.e., [Cu− OH]+ ,32,69,70 [Cu(μO) 2Cu]2+ ,15 [Cu−O−Cu] 2+ , 14,71 or [Cu3(μO)3]2+).32,72 While predicting the absolute rate of methane oxidation will certainly require extensive analysis of this type, we stress that an estimation of the maximum selectivity at any given methane conversion can be quickly deduced for any single-site catalyst using the framework developed above. This estimation may be useful in determining whether a new catalytic process is worth optimizing before

would like to determine a non-temperature-dependent parameter, i.e., ΔEaexp, which would allow us to compare the intrinsic catalytic ability of each material simultaneously. In section 2.2, we demonstrated that ΔGaDFT depends linearly on temperature, changing from 0.4 to 0.15 eV as the temperature increases from 300 to 900 K. Because determining the temperature dependence of ΔGaexp is nontrivial, we assume that the experiments possess the same linear temperature dependence determined for ΔGaDFT (eq 5). Having made this assumption, we fit an effective ΔEaexp to each experiment such that the selectivity and conversion reported experimentally match the predictions from the kinetic model given by eq 1. In essence, we are assuming that the kinetic model describes the selectivity conversion trade-off, and we seek to determine the corresponding ΔEaexp. Furthermore, to compare experiments run in liquid water to gas-phase data, we correct all aqueous ΔEaexp values by the experimentally derived solvation free energy of methanol at 298 K (−0.22 eV).67 In other words, after fitting ΔEaexp to aqueous experiments, its value is increased by 0.22 eV to yield a gas-phase ΔEaexp equivalent that can be compared to the rest of the data. The distribution of values for ΔEaexp that we achieve as a result of this process are compared in Figure 4b (red) to the equivalent ΔEaDFT distribution originally shown in Figure 2 (black). These distributions are strikingly similar (experiment: 0.59 ± 0.09 eV vs theory: 0.55 ± 0.08 eV), suggesting both the relevance of the simple kinetic model given in eq 1 and a reasonable ab initio quantification of ΔEaDFT. While the wide range of temperatures in the experimental data set previously prevented us from visualizing all experiments and their agreement with the model simultaneously, the fitted ΔEaexp values (Figure 4b) and the temperature dependence of ΔGaDFT determined via theory (eq 5) now allow us to do so. Each experiment’s individual fitted ΔEaexp, the original experimental conversion, the free energy correction from 6898


Research Article

ACS Catalysis expending the effort of studying or synthesizing new catalysts. However, we note that our value of σ = 0.08 eV can correspond to several orders of magnitude uncertainty in the selectivity−conversion limit at low temperatures. This finding suggests that a precise value of the free energy difference on a particular catalyst may be desirable for quantitative applications. This analysis seems to be a disheartening one; catalysts that obey the selectivity−conversion limit that we have quantified herein can only be expected to achieve near-100% selectivity at methane conversions below 0.01% in the gas phase at temperatures below 700 K, corresponding to methanol yields that would be unacceptable in realistic applications.73 This brings us to a simple question: by understanding the limitations of direct methane to methanol catalysis, can we identify strategies to overcome them? In the following sections, we explore such strategies and note previous literature examples that support them. We organize these strategies as (1) collectors, (2) aqueous reaction conditions, (3) diffusionlimited materials, and (4) nonradical methane activation. Note that these strategies do not suggest specific catalysts or reactor configurations; rather, they provide a guiding principle for future experimental design.

Figure 6. Collector method. (a) Schematic to represent active site formation, methanol production, and methanol collection in the collector method. The lower surface represents a single-site methane to methanol catalyst, and the upper surface represents a potential collector. This schematic is meant to represent the proximity of the two surfaces, not the actual geometry. (b) Model of presaturation selectivity as a function of temperature and methanol binding energy to the collector assuming ΔPt=0 CH4 = 1 bar. Vertical lines represent the experimental value for ZnO(101̅0) and computational values for dry Al-term α-Al2O3(0001) and GeO2(110) (relevant experimental values not available). The values for GeO2 and α-Al2O3 correspond to a dissociated adsorption mode, while for ZnO, it corresponds to a molecular mode. (c) Schematic showing the maximum TON possible depending on the ratio of methanol collector sites to methane activation sites. S.A. refers to surface area.

3. STRATEGIES 3.1. Collectors. In the derivation of eq 1, we assumed a continuous catalytic process in which selectivity toward methanol is coupled to the methanol partial pressure. This assumption gave rise to the selectivity−conversion limit. However, for stepwise processes like those mentioned in section 1,11−18 this assumption no longer holds. Because methanol in these systems is trapped on the catalyst during the oxidation phase, the methanol partial pressure is not coupled to methane conversion. While these systems are not limited by the selectivity−conversion limit, they do tend to be limited by low methanol yields, presumably because the protected methanol poisons the catalyst active site.18,58,70,74,75 This phenomenon was highlighted in a recent account by Tomkins et al., showing that isothermal methane to methanol in several copper-exchanged zeolites follows a Langmuir adsorption isotherm, indicating stoichiometric conversion (TONs approaching 1).76 Parfenov et al. have demonstrated that an ironexchanged ZSM-5 zeolite can possess quasicatalytic behavior, reaching TONs as high as 3.5.37 Still, the methanol yields achieved in these systems remain far too low for industrial application.73 Ravi et al. have suggested that multicomponent systems, in which one component is used to activate methane and another is used to protect methanol, may facilitate higher yields.77 In this section, we expand on this idea and identify real materials that can act as methanol “collectors”. We define collectors as materials that pull methanol from the gas phase via strongly exothermic adsorption, thereby inducing a constant, low partial pressure of methanol (given by the Langmuir adsorption isotherm) in the reactor until the collector’s surface has been saturated. We envision that methane oxidation could be run continuously until the surface of the collector is fully saturated with methanol (Figure 6a), at which point this methanol could be removed and the collector recycled. Compared to zeolites, the benefit of using different materials as the activator and collector is two-fold. First, decoupling activation and collection allows for greater freedom in designing new catalysts as the active site must no longer preserve the methanol that it produces. Second is the potential

for higher TONs. If the active site is able to strongly bind methanol, TONs will be close to unity. However, if methanol binds not to the active site but to a collector, higher TONs and conversions can be achieved during each activation phase, potentially rendering temperature cycling more cost-effective. Once could increase the TON by having many collector sites per active site, i.e., by using high surface area (per weight) materials as collectors. In this section, we model the selectivity possible in the presence of a collector material. Assuming that gas-phase methanol is in equilibrium with adsorbed methanol on the collector surface and approximating the Langmuir isotherm to be a step function at 50% coverage (setails in SI section S5), we write the methanol partial pressure as a function of temperature (T) and binding free energy of methanol (G°CH3OH) at standard pressure (P°CH3OH) PCH3OH = P°CH3OH e−G°CH3OH / kBT

(6)

If methanol is the only product, the effective gas-phase conversion will be equal to the methanol partial pressure, and we can write an effective gas-phase conversion (X′) as X′ =

P°CH3OH e−G°CH3OH / kBT t=0 PCH4

(7)

Pt=0 CH4

where is the starting pressure of methane. Plugging this effective conversion into eq 1, we see that selectivity is now a 6899


Research Article

ACS Catalysis Table 1. Calculated Adsorption Energiesa of Relevant Intermediates on Potential Collectorsb α-Al2O3(0001) ZnO(101̅0) GeO2(110)

E(O)c

E(CH3+H)c

E(CH3OH)d

E(OCH3+H)d

E(OCH3) + E(H)d

experimental E(CH3OH)

0.81 0.94 1.97

−0.07 −0.13 −0.35

−1.32 −1.15 −1.18

−1.58 −1.15 −1.24

2.49 1.18 0.82

na −1.4685 na

a The adsorption energy is defined as the reaction energy of adsorption such that an exothermic process corresponds to a negative adsorption energy. bEnergy values are in eV. cGas-phase references are O2 and CH4. dThe gas-phase reference is CH3OH.

SI section S7) due to a difference in binding mechanisms.80 Promising collectors are listed in Table 1. We note that on some of these (GeO2(110) and Al-term α-Al2O3(0001)), methanol will dissociate to form a methoxyl and hydroxyl (EOCH3+H < ECH3OH). Fortuitously, diffusion of this hydroxyl is highly unfavorable (EOCH3 + EH > EOCH3+H) due to the strong acid−base stabilization of these species on insulating and semiconducting oxides,80−83 suggesting that the methoxyl will be locally trapped and bound to its hydrogen pair. Recently, Castelli et al.84 determined a correlation between band gap size and the extent of this Lewis acid base attraction. A sizable band gap is also associated with (a) weak affinity for oxygen (result of small charge transfer from the surface) and (b) more ionic nature, which ensures stronger surface Lewis acid sites (electron-pair acceptor) to adsorb methanol (electron-pair donor). Table 1 also demonstrates that the dissociation of CH4 is not favorable on the proposed collectors. Even for the most negative CH4 dissociation energy among these materials (GeO2(110): −0.35 eV), gas-phase entropy contributions (−0.6 at 300 K and 1 bar CH4 partial pressure) render CH4 dissociation thermodynamically unfavorable under relevant conditions. The reaction is further limited by kinetics as the barrier predicted by scaling relations is 1.4 eV at 300 K.26 As can be seen in Table 1, we have compared our DFTderived values for E(CH3OH) with experimental values in the literature where available. For ZnO(101̅0), we underestimate the binding energy by ∼0.30 eV. This is likely due to an underestimation of vdW interactions, not fully captured by our current XC functional (BEEF-vdW). The magnitude of this effect has been shown to be up to ∼0.18 eV for H2O;86−89 thus, for CH3OH (almost twice in size), a discrepancy of ∼0.30 eV is reasonable.90−93 Regardless, this deviation is advantageous because a stronger methanol affinity is desirable to enhance selectivity. For methanol adsorption on dry Al-term α-Al2O3(0001), we could not find a credible experimental value, but the corresponding value for H2O (which we expect to have very similar chemistry) matches our DFT value with only 7% error.85,94 It should be noted that Al-term α-Al2O3(0001) under a hydrogen-rich environment may tend to fully hydroxylate (gibbsite-like structure),78,95 thus becoming significantly less active toward methanol adsorption. Nevertheless, with proper treatment, the full hydroxylation can be avoided and/or the dry Al-term structure regenerated (details in SI section S8). In general, the similarities between H2O and CH3OH chemistries80 require that exposure of the collector to water before or during use be minimized so as not to poison the collector surface. We re-emphasize that the geometry in Figure 7a is merely a schematic, depicting some proximity between the collector and the activator. In practice, one has the freedom of using many different geometries to achieve this proximity. Three of these possibilities are (i) single-site activator catalysts (e.g., doped

function of the methanol binding strength of the collector, as opposed to conversion, assuming the availability of unoccupied collector sites for methanol to adsorb. Figure 6b shows the methanol selectivity that can be expected for a given temperature and collector binding strength, assuming Pt=0 CH4 = 1 bar and ΔGa = ΔGaDFT, overlaid with three potential collectors (white). With increasing temperature, selectivity eventually drops due to the increasing chemical potential of gas-phase methanol. The temperature that dictates this dropoff in selectivity will be higher for stronger binding collectors. For example, we predict that, when paired with an effective methane to methanol catalyst, dry Al-term α-Al2O3(0001)78 may be used as a collector to achieve 100% methanol selectivity at temperatures up to 600 K until its surface becomes saturated with methanol. Notably, this model can be applied to both true multicomponent systems possessing separate sites for methane activation and methanol adsorption and isothermal single-component systems like zeolites, in which methanol poisons the site of methane activation. The second case differs in that only a single turnover is possible (Figure 6c), but the selectivity toward methanol will remain a function of temperature and methanol adsorption energy (i.e., at high enough temperatures, methanol bound at zeolite active sites will desorb and be further oxidized). While changing the total pressure does not affect the model in eq 1, changing Pt=0 CH4 in the presence of a collector does affect the selectivity (shown in Figure S10). This directly stems from the fact that most of the produced methanol is adsorbed rather than gas-phase. Increasing the methane pressure can increase the temperature at which the selectivity drop-off occurs. In cases where methane activation requires higher temperatures, this possibility could be exploited. Once methanol occupies most sites on the collector surface, the oxidation reaction should be stopped and methanol can be removed by heating. Thus, a collector can be thought of as a heterogeneous protecting group that can be easily “recycled”. However, care must be taken to remove the methanol at temperatures low enough that its degradation to hydrogen and formaldehyde remains unfavorable (details in SI section S6). An alternative procedure could be flowing water, which would allow methanol to be removed at a lower temperature but would also require later drying the collector to reactivate the surface. We posit that a successful collector should have the following properties: (a) low reactivity for CH4 activation, (b) low reactivity toward oxidizing agents, and (c) strong methanol adsorption. These properties ensure that the surface does not participate in oxidation reactions and only provides sites for preferential methanol adsorption. While the realization of a material able to strongly bind methanol without binding oxygen may initially appear to be hindered by traditional scaling relationships among oxygen-bound adsorbates,79 in general we find that the binding energy for methanol is not correlated to other unsaturated oxygen-bound adsorbates (see 6900


Research Article

ACS Catalysis

experimental data obtained under aqueous conditions are plotted in Figure 7. Because the temperature range of this data set (273−423 K) is much smaller than that for the full library of experimental data, the selectivities plotted in Figure 7 are the real (not extrapolated) experimental selectivities; a version of this plot with selectivities extrapolated to 323 K (akin to Figure 5) can be found in the SI (Figure S13). We find that, in general, these data agree well with the model, but they seem to achieve systematically higher selectivities than predicted. This may suggest that more effects than solvation alone make liquid water advantageous. For example, the use of peroxides as oxidants in these studies may lead to aqueous-phase radical reactions besides those we’ve considered, potentially complicating the analysis. Nevertheless, we generally conclude that reactions run in aqueous media clearly and consistently outperform those conducted in the gas phase. Especially if the peroxides that seem to be required for low-temperature active site formation could be generated in situ, perhaps electrochemically, this may be a promising avenue for achieving high methanol yields at ambient temperatures. 3.3. Diffusion-Limited Materials. Methane monooxygenase (MMO) is an enzyme able to selectively convert methane to methanol using molecular oxygen at ambient conditions.51,96−98 In fact, it is MMO’s Cu and Fe dinuclear active sites that have helped inspire much of the research on methane to methanol in Cu- and Fe-exchanged zeolites.14,16 Intriguingly, however, in the realm of biological enzymes, the soluble variant of MMO (sMMO) is known to possess much lower substrate selectivity than many other oxygenases.98−100 For example, work carried out as early as the 1970s explored the substrate selectivity of sMMO isolated from Methylococcus capsulatus on various derivatized methanes, oxygenates, and hydrocarbons having as many as eight carbon atoms and found that, for almost every substrate explored, sMMO was able to selectively insert a single oxygen into the substrate.98 In fact, methanol itself is oxidized with an activation free energy effectively equal to that of methane (0.68 vs 0.67 eV).98,101 Detailed kinetic isotope studies have been conducted to understand the mechanism of hydroxylation for different substrates. Intriguingly, a strong kinetic isotope effect is found for methane, acetonitrile, and methyl nitrate, but no effect is found for methanol or ethane, suggesting that methanol and ethane are the only of these substrates not limited by CH bond cleavage.101,102 Considering molecular BDEs and the presence of allylic bonds, methane, acetronitrile, and nitromethane are expected to have higher CH bond breaking activation energies than methanol and ethane (Table S6).19,33,103 Assuming similar diffusion kinetics for all species, this agrees with the theory that diffusion to the enzyme active site is the limiting process for the substrates with weaker CH bond activation energies (ethane and methanol).101 Further, because the observed rates for diffusion-limited ethane and methanol activation are quite similar to those for CH bond cleavagelimited methane activation, it has previously been noted that the activation barriers for molecular diffusion to the active site and CH bond cleavage in methane may be “fortuitously similar”.101 While in the formulation of our model we assumed CH bond breaking to be rate-limiting for both methane and methanol oxidation, we can now consider diffusion to be ratelimiting simply by changing ΔGa. Namely, assuming similar diffusion barriers for methane and methanol, ΔGa will approach zero as diffusion becomes increasingly difficult.

Figure 7. Comparison of eq 1 at 323 K for gas- (blue) and aqueous(cyan) phase reactions using ΔGaDFT, with a correction on the cyan line equal to the solvation free energy of methanol at 298 K (−0.22 eV). Only the experimental data from reactions conducted in aqueous conditions are plotted.

nanoparticles or 2D materials) dispersed on a collector support, (ii) doping the inert collector with a low concentration of reactive metal atoms to create a combined activator−collector material, or (iii) a physical mixture of one of the suggested collectors (Table 1) with a known catalyst able to locally convert methane to methanol catalytically (i.e., those in Figure 5). The gas phase acts as a bridge between the activator and collector sites. As long as there is facile gas-phase diffusion of methanol from the activator to the collector sites, the activator and collector can be separate materials. 3.2. Aqueous Reaction Conditions. As demonstrated in the previous section, methanol can be collected from the gas phase on certain oxide surfaces, lowering its free energy and increasing its effective activation barrier. Similarly, liquid water can act as a “collector” due to the favorable solvation free energy of methanol (−0.22 eV67 at 298 K), effectively lowering the ΔGa by up to this amount (depending on the solvation of the transition state, the correction could be smaller). This effect becomes evident when re-examining the experimental data presented earlier for single-site catalysts performed in aqueous conditions (Table S5, reaction type: aqueous). The only examples of continuous methane to methanol at temperatures below 400 K (and as low as 273 K) are those performed in liquid water. The lowest temperature reported for continuous methane to methanol in the gas phase is 483 K, but the corresponding conversion is one of the lowest published (0.001%).46 Unlike our workflow in section 2.3, we now do not extrapolate the experimental data (no temperature or solvation corrections) and instead apply a methanol solvation correction of −0.22 eV to the ΔGaDFT used in the model at 323 K (Figure 7, cyan curves). Comparing it to the unsolvated kinetic model at the same temperature (shown in blue) demonstrates the substantial improvement in the model yielded by including solvation. From examination of the dark blue sigmoid depicting the predicted selectivity in the absence of a solvation correction, it becomes evident that significant selectivities in the gas phase at 323 K are only observable at conversions below 0.001%. However, including a solvation correction of −0.22 eV (cyan curve) improves the selectivity by 4 orders of magnitude. Only 6901


Research Article

ACS Catalysis

unselective catalyst, blind to the identity of its substrate, is desirable. While it may sound counterintuitive, this idea is not new, having been highlighted in previous work by Labinger.9 The prospect of identifying catalysts able to activate methane as easily as methanol may be a challenge in itself, but the recent example of low-temperature methane activation over IrO2(110) at 88 K suggests that it may be a plausible strategy.6 Unfortunately, this study also exemplified several issues that will likely be problematic for highly reactive catalysts, namely, product removalthe products, CO and CO2, desorbed only above 400 Kand protection of the active site from potential poisonsoxygen binds strongly to the stoichiometric IrO2(110) surface and lowers its activity for methane activation. Still, highly reactive catalysts remain promising in their potential to bypass the scaling between radical methane and methanol activation barriers.

This trend, along with experimental sMMO data, is shown in Figure 8. The green point shows sMMO’s unoptimized, natural

4. CONSIDERING NONRADICAL METHANE ACTIVATION Up to now, our analysis and exploration of the selectivity− conversion limit applied only to catalysts that activate CH bonds via the radical pathway. Therefore, one might expect a potential strategy to be the exploration of materials that activate methane via the surface-stabilized pathway, which is more easily accessible in non-single-site catalysts. Although we note that the model is strictly applicable to only catalysts that activate via the radical pathway, we choose to reanalyze all data, including non-single-site catalysts, in the framework provided in section 2.2. Figure 9 shows the fitted ΔEa values and extrapolated selectivities of non-single-site catalysts from the literature (Table S5, single site: no) compared to those of single-site catalysts shown originally in Figure 5 (gray). Unfortunately, the data seem to suggest that non-single-site catalysts, such as MoO3 and VO2, tend to have higher effective ΔEaexp values than the single-site catalysts, i.e., worse performance on a selectivity−conversion basis. With the addition of non-single-site catalysts to the histogram, we see a significant number of catalysts with ΔEaexp values between 0.8 and 1.2 eV. The generally poorer performance of non-single-site catalysts may be because the higher density of active sites facilitates dehydrogenation of surface-bound intermediates, lowering the local methane to methanol selectivity. However, while it appears that no non-single-site catalysts in this data set show enhanced selectivity compared to single-site catalysts, they remain a possible avenue for further exploration as they are not

Figure 8. Selectivity−conversion limit as ΔGa approaches zero at 300 K shown along with the natural sMMO conversion98 (green) as well as optimized methanol selectivities and methane conversions from Methylosinus trichosporium104 (red).

conversion and selectivity. We see that the natural conversion of methane for sMMO is low enough to avoid an impending steep drop-off in selectivity.98 Additionally, the selectivity (moles of methanol produced per mole of methane consumed) of sMMO-expressing bacteria such as Methylosinus trichosporium (red data) tends to drop when these organisms are pushed to higher methane conversions.104 Further, sMMO has been experimentally shown to be strongly inhibited by concentrations of methanol above 6 mM,105,106 a concentration similar to the solubility of methane at 300 K and 1 atm (1 mM67). These findings support the idea that the active site of sMMO may actually be limited by the same selectivity− conversion trade-off as nonbiological catalysts. However, by restricting substrate diffusion to the active site, sMMO can achieve the methane conversions required for natural processes (1−2%) while maintaining high methanol selectivity. To engineer similar effects into a nonbiological catalyst, one could either decrease diffusion rates (for example, by using a highly porous surface) or increase CH activation rates as catalysts that activate methane with high enough rates will naturally become diffusion-limited. In other words, an

Figure 9. Including non-single-site catalysts. (a) Normalized histogram of ΔEaexp values fitted with the model and (b) extrapolated selectivities at 700 K including single-site (gray) and non-single-site (cyan) catalysts. 6902


Research Article

ACS Catalysis

Figure 10. Strategies for increasing methanol yields. (A) A collector material lowers the partial pressure of methanol. (B) Aqueous reaction conditions lower the free energy of methanol, increasing the effective methanol activation barrier compared to that of methane. (C) Limiting diffusion rates or increasing CH bond cleavage rates can lead to diffusion-limited catalysts able to activate methane and methanol at similar rates.

limited in theory by the catalyst-independent ΔGa that is characteristic of radical-like CH bond activation.

6. COMPUTATIONAL METHODS All analysis scripts, data sets, and much of the DFT generated data is available at https://github.com/alatimer/ Methane2MeOH. Our calculations were carried out using DFT107,108 with plane wave basis sets using Quantum Espresso software and analyzed using the Atomic Simulation Environment.109,110 BEEF-vdW34 was used for the exchange− correlation functional and to estimate error.111−113 Several calculations were verified using HSE06-D335,36 as noted. Details on convergence parameters and pseudopotentials using different sets of our calculations can be found in the SI section S9. Throughout the work, binding energies are defined such that an exothermic process corresponds to a negative adsorption energy. For instance, methanol binding energies are defined as

5. CONCLUSIONS Having demonstrated that a very simple kinetic model successfully describes the selectivity−conversion limit of a large library of experimental literature, we conclude that a truly continuous process for direct methane to methanol will ultimately be limited to achieving high methanol selectivities at very low methane conversions. We have suggested several potential strategies in section 3 for overcoming this intrinsic limitation, summarized in Figure 10. These include (1) a methanol “collector,” (2) aqueous reaction conditions, and (3) diffusion-limited systems. Bear in mind that these strategies are only meant to increase the methanol selectivity possible at a given methane conversion; we make no claims as to how to increase methane conversion. Finding a catalyst able to activate oxygen and methane and locally produce methanol is an important challenge in its own right but one that is beyond the scope of this work. Interestingly, we found in our analysis of sMMO and diffusion-limited systems (section 4.3), as has been noted previously,9 that the best catalyst for continuous methane to methanol may in fact be an unselective one. To achieve higher methanol yields than can be obtained by an unselective catalyst, it is imperative that we explore semicontinuous processes. One such process is that of using a “collector”, discussed in section 3.1. We propose that combining a collector material with a single-site catalyst can facilitate higher conversions while maintaining high selectivity, bridging the gap between continuous and stepwise processes. Using the simple model presented herein, we have successfully rationalized a representative library of experimental studies from the diverse fields of heterogeneous, homogeneous, biological, and gasphase methane to methanol catalysis. Our findings underscore the idea that continuous methane to methanol is generally limited, and we have provided a framework for understanding and evaluating new catalysts and processes.

E(CH3OH) = E(slab with adsorbed CH3OH) − E(bare slab) − E(CH3OH molecule)

Several zeolite, oxide, and metal calculations were previously performed in ref 19 but were recalculated to obtain vibrational frequencies, as noted in the SI. All calculations were spinpolarized. Climbing image nudged elastic band (CI-NEB) calculations114−117 were performed to determine the location of the transition state. The accuracy of these transition states was verified by finding an imaginary mode corresponding to the transition state reaction coordinate in a vibrational analysis. Occasionally, additional small imaginary modes were found, corresponding to rotations, and these were approximated to have frequencies with energies of 7 meV. Binding energies were calculated as the energy of the bound species minus the energy of the gas-phase references, such that negative binding energies correspond to favorable molecular adsorption. In the collector analysis, the gas-phase entropy of methanol was approximated to be 0.002 eV/K. Figures 3 and 6a were generated using VESTA visualization software;118 other figures were generated using Microsoft powerpoint and the Matplotlib plotting library.119 6903


Research Article

ACS Catalysis

■

Hydrogenation over Transition Metals. Phys. Chem. Chem. Phys. 2011, 13, 20760−20765. (5) Wang, C.-C.; Siao, S. S.; Jiang, J. C−H Bond Activation of Methane via σ−d Interaction on the IrO 2 (110) Surface: Density Functional Theory Study. J. Phys. Chem. C 2012, 116, 6367−6370. (6) Liang, Z.; Li, T.; Kim, M.; Asthagiri, A.; Weaver, J. F. LowTemperature Activation of Methane on the IrO 2 (110). Science (Washington, DC, U. S.) 2017, 356, 299−303. (7) Aljama, H.; Nørskov, J. K.; Abild-Pedersen, F. Theoretical Insights into Methane C−H Bond Activation on Alkaline Metal Oxides. J. Phys. Chem. C 2017, 121, 16440−16446. (8) Antony, A.; Asthagiri, A.; Weaver, J. F. Pathways and Kinetics of Methane and Ethane C−H Bond Cleavage on PdO(101). J. Chem. Phys. 2013, 139, 104702/1−104702/12. (9) Labinger, J. A. Selective Alkane Oxidation: Hot and Cold Approaches to a Hot Problem. J. Mol. Catal. A: Chem. 2004, 220, 27− 35. (10) Ravi, M.; Ranocchiari, M.; van Bokhoven, J. A. Die Direkte Katalytische Oxidation von Methan Zu Methanol - Eine Kritische Beurteilung. Angew. Chem. 2017, 129, 16684−16704. (11) Periana, R. A. Platinum Catalysts for the High-Yield Oxidation of Methane to a Methanol Derivative. Science (Washington, DC, U. S.) 1998, 280, 560−564. (12) Periana, R. A.; Taube, D. J.; Evitt, E. R.; Loffler, D. G.; Wentrcek, P. R.; Voss, G.; Masuda, T. A Mercury-Catalyzed, HighYield System for the Oxidation of Methane to Methanol. Science (Washington, DC, U. S.) 1993, 259, 340−343. (13) Durante, V. A.; Walker, D. W.; Gussow, S. M.; Lyons, J. E. Silicometallate Molecular Sieves and Their Use as Catalysts in Oxidation of Alkanes. U.S. Patent US4918249, 1990. (14) Woertink, J. S.; Smeets, P. J.; Groothaert, M. H.; Vance, M. A.; Sels, B. F.; Schoonheydt, R. A.; Solomon, E. I. A [Cu2O]2+ Core in Cu-ZSM-5, the Active Site in the Oxidation of Methane to Methanol. Proc. Natl. Acad. Sci. U. S. A. 2009, 106, 18908−18913. (15) Groothaert, M. H.; Smeets, P. J.; Sels, B. F.; Jacobs, P. A.; Schoonheydt, R. A. Selective Oxidation of Methane by the Bis(μOxo)Dicopper Core Stabilized on ZSM-5 and Mordenite Zeolites. J. Am. Chem. Soc. 2005, 127, 1394−1395. (16) Da Silva, J. C. S.; Pennifold, R. C. R.; Harvey, J. N.; Rocha, W. R. A Radical Rebound Mechanism for the Methane Oxidation Reaction Promoted by the Dicopper Center of a PMMO Enzyme: A Computational Perspective. Dalt. Trans. 2016, 45, 2492−2504. (17) Wulfers, M. J.; Teketel, S.; Ipek, B.; Lobo, R. F. Conversion of Methane to Methanol on Copper-Containing Small-Pore Zeolites and Zeotypes. Chem. Commun. 2015, 51, 4447−4450. (18) Kulkarni, A. R.; Zhao, Z.; Siahrostami, S.; Nørskov, J. K.; Studt, F. Cation-Exchanged Zeolites for the Selective Oxidation of Methane to Methanol. Catal. Sci. Technol. 2018, 8, 114−123. (19) Latimer, A. A.; Kulkarni, A. R.; Aljama, H.; Montoya, J. H.; Yoo, J. S.; Tsai, C.; Abild-Pedersen, F.; Studt, F.; Nørskov, J. K. Understanding Trends in C−H Bond Activation in Heterogeneous Catalysis. Nat. Mater. 2017, 16, 225−229. (20) House, J. E. Principles of Chemical Kinetics; Academic Press: Oxford, U.K., 2007; pp 47−53. (21) Sexton, A. W.; Kartheuser, B.; Batiot, C.; Zanthoff, H. W.; Hodnett, B. K. The Limiting Selectivity of Active Sites on Vanadium Oxide Catalysts Supported on Silica for Methane Oxidation to Formaldehyde. Catal. Today 1998, 40, 245−250. (22) Cant, N. W.; Lukey, C. A.; Nelson, P. F.; Tyler, R. J. The Rate Controlling Step in the Oxidative Coupling of Methane over a Lithium-Promoted Magnesium Oxide Catalyst. J. Chem. Soc., Chem. Commun. 1988, 12, 766−768. (23) Wei, J.; Iglesia, E. Isotopic and Kinetic Assessment of the Mechanism of Reactions of CH4 with CO2 or H2O to Form Synthesis Gas and Carbon on Nickel Catalysts. J. Catal. 2004, 224, 370−383. (24) German, E. D.; Sheintuch, M. Predicting CH4 Dissociation Kinetics on Metals: Trends, Sticking Coefficients, H Tunneling, and Kinetic Isotope Effect. J. Phys. Chem. C 2013, 117, 22811−22826.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acscatal.8b00220. Atomic coordinates for all calculated structures (ZIP) Equation 1 derivation, estimating the free energy contributions, the spread in ΔEa, different radical transition state energies, explicit temperature- and solvation-dependent models, the collector model, kinetics of collector heating, uncorrelated O* and CH3OH* binding energies, proper treatment to obtain dry alumina, computational methods, spread in ΔGa, temperature dependence of ΔGa, BEEF ensembles for RuO2, geometry comparisons for transition states, plots of selectivity vs conversion in both the aqueous and gas phase every 50 K, Langmuir isotherms on alumina for the collector model, thermodynamics of methanol removal from collector, transition state energies, vibrational frequencies, experimental data with references, and select bond dissociation energies (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Allegra A. Latimer: 0000-0003-3048-6593 Arvin Kakekhani: 0000-0002-8553-7776 Author Contributions §

A.A.L. and A.K contributed equally to this work.

Notes

The authors declare no competing financial interest. All data and analysis scripts used to generate this work are available at https://github.com/alatimer/Methane2MeOH.

■

ACKNOWLEDGMENTS Support from the U.S. Department of Energy Office of Basic Energy Science and Global Climate & Energy Project (GCEP) to the SUNCAT Center for Interface Science and Catalysis is gratefully acknowledged. A.R.K. acknowledges computing resources from the Carbon High-Performance Computing Cluster at Argonne National Laboratory under Proposal CNM-46405. The research of A.A.L. was conducted with Government support under and awarded by the DoD, Air Force Office of Scientific Research, National Defense Science and Engineering Graduate (NDSEG) Fellowship, 32 CFR 168a. We acknowledge Dr. Johannes Voss, Dr. Frank AbildPedersen, Dr. Samira Siahrostami, Michael J. Boyd, Cody J. Wrasman, and Colin F. Dickens for useful discussions, as well as Kilian Cavalotti and the Stanford Research Computing Center for HPC computing help and support.

■

REFERENCES

(1) U.S. Energy Information Administration. International Energy Statistics. https://www.eia.gov/beta/international/data/browser (accessed Dec 5, 2017). (2) Horn, R.; Schlögl, R. Methane Activation by Heterogeneous Catalysis. Catal. Lett. 2015, 145, 23−39. (3) Schwarz, H. Chemistry with Methane: Concepts Rather than Recipes. Angew. Chem., Int. Ed. 2011, 50, 10096−10115. (4) Wang, S.; Petzold, V.; Tripkovic, V.; Kleis, J.; Howalt, J. G.; Skúlason, E.; Fernández, E. M.; Hvolbæk, B.; Jones, G.; Toftelund, A.; et al. Universal Transition State Scaling Relations for (de)6904


Research Article

ACS Catalysis (25) Kumar, G.; Lau, S. L. J.; Krcha, M. D.; Janik, M. J. Correlation of Methane Activation and Oxide Catalyst Reducibility and Its Implications for Oxidative Coupling. ACS Catal. 2016, 6, 1812−1821. (26) Latimer, A. A.; Aljama, H.; Kakekhani, A.; Yoo, J. S.; Kulkarni, A.; Tsai, C.; Garcia-Melchor, M.; Abild-Pedersen, F.; Nørskov, J. K. Mechanistic Insights into Heterogeneous Methane Activation. Phys. Chem. Chem. Phys. 2017, 19, 3575−3581. (27) Krcha, M. D.; Mayernick, A. D.; Janik, M. J. Periodic Trends of Oxygen Vacancy Formation and C−H Bond Activation over Transition Metal-Doped CeO2 (111) Surfaces. J. Catal. 2012, 293, 103−115. (28) Chin, Y. H.; Buda, C.; Neurock, M.; Iglesia, E. Consequences of Metal-Oxide Interconversion for C-H Bond Activation during CH4 Reactions on Pd Catalysts. J. Am. Chem. Soc. 2013, 135, 15425− 15442. (29) Schlögl, R. Concepts in Selective Oxidation of Small Alkane Molecules, in Modern Heterogeneous Oxidation Catalysis: Design, Reactions and Characterization; Mizuno, N., Ed.; Wiley-VCH GmbH & Co. KGaA: Weinheim, Germany, 2009. (30) Thomas, J. M.; Raja, R.; Lewis, D. W. Single-Site Heterogeneous Catalysts. Angew. Chem., Int. Ed. 2005, 44, 6456− 6482. (31) Hammond, C.; Forde, M. M.; Ab Rahim, M. H.; Thetford, A.; He, Q.; Jenkins, R. L.; Dimitratos, N.; Lopez-Sanchez, J. A.; Dummer, N. F.; Murphy, D. M.; et al. Direct Catalytic Conversion of Methane to Methanol in an Aqueous Medium by Using Copper-Promoted FeZSM-5. Angew. Chem., Int. Ed. 2012, 51, 5129−5133. (32) Grundner, S.; Markovits, M. A. C.; Li, G.; Tromp, M.; Pidko, E. A.; Hensen, E. J. M.; Jentys, A.; Sanchez-Sanchez, M.; Lercher, J. A. Single-Site Trinuclear Copper Oxygen Clusters in Mordenite for Selective Conversion of Methane to Methanol. Nat. Commun. 2015, 6, 1−8. (33) Deshlahra, P.; Iglesia, E. Reactivity and Selectivity Descriptors for the Activation of C−H Bonds in Hydrocarbons and Oxygenates on Metal Oxides. J. Phys. Chem. C 2016, 120, 16741−16760. (34) Medford, A. J.; Wellendorff, J.; Vojvodic, A.; Studt, F.; AbildPedersen, F.; Jacobsen, K. W.; Bligaard, T.; Norskov, J. K. Assessing the Reliability of Calculated Catalytic Ammonia Synthesis Rates. Science (Washington, DC, U. S.) 2014, 345, 197−200. (35) Heyd, J.; Scuseria, G. E.; Ernzerhof, M. Hybrid Functionals Based on a Screened Coulomb Potential. J. Chem. Phys. 2003, 118, 8207−8215. (36) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. J. Chem. Phys. 2010, 132, 154104. (37) Parfenov, M. V.; Starokon, E. V.; Pirutko, L. V.; Panov, G. I. Quasicatalytic and Catalytic Oxidation of Methane to Methanol by Nitrous Oxide over FeZSM-5 Zeolite. J. Catal. 2014, 318, 14−21. (38) McCormick, R. L.; Alptekin, G. O. Comparison of Alumina-, Silica-, Titania-, and Zirconia-Supported FePO4 Catalysts for Selective Methane Oxidation. Catal. Today 2000, 55, 269−280. (39) Berndt, H.; Martin, A.; Brückner, A.; Schreier, E.; Müller, D.; Kosslick, H.; Wolf, G.-U.; Lücke, B. Structure and Catalytic Properties of VOx/MCM Materials for the Partial Oxidation of Methane to Formaldehyde. J. Catal. 2000, 191, 384−400. (40) Fornés, V.; López, C.; López, H. H.; Martínez, A. Catalytic Performance of Mesoporous VOx/SBA-15 Catalysts for the Partial Oxidation of Methane to Formaldehyde. Appl. Catal., A 2003, 249, 345−354. (41) Sugino, T.; Kido, A.; Azuma, N.; Ueno, A.; Udagawa, Y. Partial Oxidation of Methane on Silica-Supported Silicomolybdic Acid Catalysts in an Excess Amount of Water Vapor. J. Catal. 2000, 190, 118−127. (42) Dowden, D. A.; Geoffrey, T. W. Oxygenated Hydrocarbons Production. Patent GB1244001A, 1971. (43) Zhang, X.; He, D.; Zhang, Q.; Xu, B.; Zhu, Q. Comparative Studies on Direct Conversion of Methane to Methanol/Form-

aldehyde over La-Co-O and ZrO2 Supported Molybdenum Oxide Catalysts. Top. Catal. 2005, 32, 215−223. (44) Zhang, Q.; He, D.; Zhu, Q. Direct Partial Oxidation of Methane to Methanol: Reaction Zones and Role of Catalyst Location. J. Nat. Gas Chem. 2008, 17, 24−28. (45) Ipek, B.; Lobo, R. F. Catalytic Conversion of Methane to Methanol on Cu-SSZ-13 Using N2O as Oxidant. Chem. Commun. 2016, 52, 13401−13404. (46) Narsimhan, K.; Iyoki, K.; Dinh, K.; Román-Leshkov, Y. Catalytic Oxidation of Methane into Methanol over CopperExchanged Zeolites with Oxygen at Low Temperature. ACS Cent. Sci. 2016, 2, 424−429. (47) Raja, R.; Ratnasamy, P. Direct Conversion of Methane to Methanol. Appl. Catal., A 1997, 158, L7−L15. (48) Seki, Y.; Min, J. S.; Misono, M.; Mizuno, N. Reaction Mechanism of Oxidation of Methane with Hydrogen Peroxide Catalyzed by 11-Molybdo-1-Vanadophosphoric Acid Catalyst Precursor. J. Phys. Chem. B 2000, 104, 5940−5944. (49) Wang, Y.; Otsuka, K. Catalytic Oxidation of Methane to Methanol with H2-O2 Gas Mixture at Atmospheric Pressure. J. Catal. 1995, 155, 256−267. (50) Wang, Y.; Otsuka, K. Direct Conversion of Methane and Ethane to the Corresponding Alcohols Using Nitrous Oxide over Iron Phosphate Catalysts. J. Chem. Soc., Faraday Trans. 1995, 91, 3953− 3961. (51) Lyons, J. E.; Ellis, P. E.; Durante, V. A. Active Iron Oxo Centers for the Selective Catalytic Oxidation of Alkanes. In Structure−Activity and Selectivity Relationships in Heterogeneous Catalysis; Grasselli, R. K., Sleight, A. W., Eds.; Elsevier Science Publishers: Amsterdam, The Netherlands, 1991; pp 99−116. (52) Khan, M.; Somorjai, G. A. A Kinetic Study of Partial Oxidation of Methane with Nitrous Oxide on a Molybdena-Silica Catalyst. J. Catal. 1985, 91, 263−271. (53) Casey, P. S.; McAllister, T.; Foger, K. Selective Oxidation of Methane to Methanol at High Pressures. Ind. Eng. Chem. Res. 1994, 33, 1120−1125. (54) Chun, J. W.; Anthony, R. G. Partial Oxidation of Methane, Methanol, and Mixtures of Methane and Methanol, Methane and Ethane, and Methane, Carbon Dioxide, and Carbon Monoxide. Ind. Eng. Chem. Res. 1993, 32, 788−795. (55) Foulds, G. A.; Gray, B. F.; Miller, S. A.; Walker, G. S. Homogeneous Gas-Phase Oxidation of Methane Using Oxygen as Oxidant in an Annular Reactor. Ind. Eng. Chem. Res. 1993, 32, 780− 787. (56) Okolie, C.; Belhseine, Y. F.; Lyu, Y.; Yung, M. M.; Engelhard, M. H.; Kovarik, L.; Stavitski, E.; Sievers, C. Conversion of Methane into Methanol and Ethanol over Nickel Oxide on Ceria−Zirconia Catalysts in a Single Reactor. Angew. Chem., Int. Ed. 2017, 56, 13876− 13881. (57) Agarwal, N.; Freakley, S. J.; McVicker, R. U.; Althahban, S. M.; Dimitratos, N.; He, Q.; Morgan, D. J.; Jenkins, R. L.; Willock, D. J.; Taylor, S. H.; et al. Aqueous Au-Pd Colloids Catalyze Selective CH4 Oxidation to CH3OH with O2 under Mild Conditions. Science (Washington, DC, U. S.) 2017, 358, 223−227. (58) Wood, B.; Reimer, J. A.; Bell, A. T.; Janicke, M. T.; Ott, K. C. Methanol Formation on Fe/Al-MFI via the Oxidation of Methane by Nitrous Oxide. J. Catal. 2004, 225, 300−306. (59) Shan, J.; Li, M.; Allard, L. F.; Lee, S.; Flytzani-Stephanopoulos, M. Mild Oxidation of Methane to Methanol or Acetic Acid on Supported Isolated Rhodium Catalysts. Nature 2017, 551, 605−608. (60) Kwon, Y.; Kim, T. Y.; Kwon, G.; Yi, J.; Lee, H. Selective Activation of Methane on Single-Atom Catalyst of Rhodium Dispersed on Zirconia for Direct Conversion. J. Am. Chem. Soc. 2017, 139, 17694−17699. (61) Wang, Y.; Otsuka, K. Catalytic Oxidation of Methane to Methanol Initiated in a Gas Mixture of Hydrogen and Oxygen. J. Chem. Soc., Chem. Commun. 1994, 2209. (62) Wang, X.; Wang, Y.; Tang, Q.; Guo, Q.; Zhang, Q.; Wan, H. MCM-41-Supported Iron Phosphate Catalyst for Partial Oxidation of 6905


Research Article

ACS Catalysis Methane to Oxygenates with Oxygen and Nitrous Oxide. J. Catal. 2003, 217, 457−467. (63) Chen, S. Y.; Willcox, D. Effect of Vanadium Oxide Loading on the Selective Oxidation of Methane over Vanadium Oxide (V2O5)/ Silica. Ind. Eng. Chem. Res. 1993, 32, 584−587. (64) Michalkiewicz, B. Partial Oxidation of Methane to Formaldehyde and Methanol Using Molecular Oxygen over Fe-ZSM-5. Appl. Catal., A 2004, 277, 147−153. (65) Polnišer, R.; Š tolcová, M.; Hronec, M.; Mikula, M. Structure and Reactivity of Copper Iron Pyrophosphate Catalysts for Selective Oxidation of Methane to Formaldehyde and Methanol. Appl. Catal., A 2011, 400, 122−130. (66) Taylor, S. H.; Hargreaves, J. S. J.; Hutchings, G. J.; Joyner, R. W.; Lembacher, C. W. The Partial Oxidation of Methane to Methanol: An Approach to Catalyst Design. Catal. Today 1998, 42, 217−224. (67) Rizzo, R. C.; Aynechi, T.; Case, D. A.; Kuntz, I. D. Estimation of Absolute Free Energies of Hydration Using Continuum Methods: Accuracy of Partial Charge Models and Optimization of Nonpolar Contributions. J. Chem. Theory Comput. 2006, 2, 128−139. (68) Latimer, A. A. Interactive version of Figure 5. https://plot.ly/ ~alatimer/7 (accessed May 30, 2018). (69) Grundner, S.; Luo, W.; Sanchez-Sanchez, M.; Lercher, J. A. Synthesis of Single-Site Copper Catalysts for Methane Partial Oxidation. Chem. Commun. 2016, 52, 2553−2556. (70) Li, G.; Vassilev, P.; Sanchez-Sanchez, M.; Lercher, J. A.; Hensen, E. J. M.; Pidko, E. A. Stability and Reactivity of Copper OxoClusters in ZSM-5 Zeolite for Selective Methane Oxidation to Methanol. J. Catal. 2016, 338, 305−312. (71) Tsai, M.-L.; Hadt, R. G.; Vanelderen, P.; Sels, B. F.; Schoonheydt, R. A.; Solomon, E. I. [Cu 2 O] 2+ Active Site Formation in Cu−ZSM-5: Geometric and Electronic Structure Requirements for N 2 O Activation. J. Am. Chem. Soc. 2014, 136, 3522−3529. (72) Markovits, M. A. C.; Jentys, A.; Tromp, M.; Sanchez-Sanchez, M.; Lercher, J. A. Effect of Location and Distribution of Al Sites in ZSM-5 on the Formation of Cu-Oxo Clusters Active for Direct Conversion of Methane to Methanol. Top. Catal. 2016, 59, 1554− 1563. (73) Edwards, J. H.; Foster, N. R. The Potential for Methanol Production from Natural Gas by Direct Catalytic Partial Oxidation. Fuel Sci. Technol. Int. 1986, 4, 365−390. (74) Kulkarni, A. R.; Zhao, Z. J.; Siahrostami, S.; Nørskov, J. K.; Studt, F. Monocopper Active Site for Partial Methane Oxidation in Cu-Exchanged 8MR Zeolites. ACS Catal. 2016, 6, 6531−6536. (75) Zhao, Z.-J.; Kulkarni, A.; Vilella, L.; Nørskov, J. K.; Studt, F. Theoretical Insights into the Selective Oxidation of Methane to Methanol in Copper-Exchanged Mordenite. ACS Catal. 2016, 6, 3760−3766. (76) Tomkins, P.; Ranocchiari, M.; Van Bokhoven, J. A. Direct Conversion of Methane to Methanol under Mild Conditions over CuZeolites and Beyond. Acc. Chem. Res. 2017, 50, 418−425. (77) Ravi, M.; Ranocchiari, M.; van Bokhoven, J. A. The Direct Catalytic Oxidation of Methane to Methanol-A Critical Assessment. Angew. Chem., Int. Ed. 2017, 56, 16464−16483. (78) Ranea, V. A.; Carmichael, I.; Schneider, W. F. DFT Investigation of Intermediate Steps in the Hydrolysis of α-Al 2 O 3 (0001) †. J. Phys. Chem. C 2009, 113, 2149−2158. (79) Abild-Pedersen, F.; Greeley, J.; Studt, F.; Rossmeisl, J.; Munter, T. R.; Moses, P. G.; Skúlason, E.; Bligaard, T.; Nørskov, J. K. Scaling Properties of Adsorption Energies for Hydrogen-Containing Molecules on Transition-Metal Surfaces. Phys. Rev. Lett. 2007, 99, 016105. (80) Kakekhani, A.; Roling, L.; Kulkarni, A.; Latimer, A. A.; Abroshan, H.; Schumann, J.; Aljama, H.; Siahrostami, S.; Ismail-Beigi, S.; Abild-Pedersen, F.; Nørskov, J. K. Nature of Lone-Pair−Surface Bonds and Their Scaling Relations. Inorg. Chem. 2018, 57, 7222. (81) Chrétien, S.; Metiu, H. Acid−Base Interaction and Its Role in Alkane Dissociative Chemisorption on Oxide Surfaces. J. Phys. Chem. C 2014, 118, 27336−27342.

(82) Schneider, W. F. Qualitative Differences in the Adsorption Chemistry of Acidic (CO2, SOx) and Amphiphilic (NOx) Species on the Alkaline Earth Oxides. J. Phys. Chem. B 2004, 108, 273−282. (83) Schneider, W. F.; Hass, K. C.; Miletic, M.; Gland, J. L. Dramatic Cooperative Effects in Adsorption of NOx on MgO(001). J. Phys. Chem. B 2002, 106, 7405−7413. (84) Castelli, I. E.; Man, I. C.; Soriga, S. G.; Parvulescu, V.; Halck, N. B.; Rossmeisl, J. Role of the Band Gap for the Interaction Energy of Coadsorbed Fragments. J. Phys. Chem. C 2017, 121, 18608−18614. (85) Campbell, C. T.; Sellers, J. R. V. Enthalpies and Entropies of Adsorption on Well-Defined Oxide Surfaces: Experimental Measurements. Chem. Rev. 2013, 113, 4106−4135. (86) Carrasco, J.; Klimeš, J.; Michaelides, A. The Role of van Der Waals Forces in Water Adsorption on Metals. J. Chem. Phys. 2013, 138, 024708. (87) Hu, X. L.; Carrasco, J.; Klimeš, J.; Michaelides, A. Trends in Water Monomer Adsorption and Dissociation on Flat Insulating Surfaces. Phys. Chem. Chem. Phys. 2011, 13, 12447−12453. (88) Fernández-Torre, D.; Kośmider, K.; Carrasco, J.; GandugliaPirovano, M. V.; Pérez, R. Insight into the Adsorption of Water on the Clean CeO 2(111) Surface with van Der Waals and Hybrid Density Functionals. J. Phys. Chem. C 2012, 116, 13584−13593. (89) Kebede, G. G.; Spångberg, D.; Mitev, P. D.; Broqvist, P.; Hermansson, K. Comparing van Der Waals DFT Methods for Water on NaCl(001) and MgO(001). J. Chem. Phys. 2017, 146, 064703. (90) Wagner, C.; Fournier, N.; Ruiz, V. G.; Li, C.; Müllen, K.; Rohlfing, M.; Tkatchenko, A.; Temirov, R.; Tautz, F. S. NonAdditivity of Molecule-Surface van der Waals Potentials from Force Measurements. Nat. Commun. 2014, 5, 1−8. (91) Ruiz, V. G.; Liu, W.; Zojer, E.; Scheffler, M.; Tkatchenko, A. Density-Functional Theory with Screened van der Waals Interactions for the Modeling of Hybrid Inorganic-Organic Systems. Phys. Rev. Lett. 2012, 108, 2−6. (92) Tkatchenko, A.; Scheffler, M. Accurate Molecular van Der Waals Interactions from Ground-State Electron Density and FreeAtom Reference Data. Phys. Rev. Lett. 2009, 102, 6−9. (93) Grimme, S. Semiempirical GGA-Type Density Functional Constructed with a Long-Range Dispersion Correction. J. Comput. Chem. 2006, 27, 1787−1799. (94) Elam, J. W.; Nelson, C. E.; Cameron, M. A.; Tolbert, M. A.; George, S. M. Adsorption of H2O on a Single-Crystal α-Al2O3 (0001) Surface. J. Phys. Chem. B 1998, 102, 7008−7015. (95) Wang, X.-G.; Chaka, A.; Scheffler, M. Effect of the Environment on A-Al2O3(0001) Surface Structures. Phys. Rev. Lett. 2000, 84, 3650−3653. (96) Rosenzweig, A. C.; Frederick, C. A.; Lippard, S. J.; Nordlund, P. Crystal Structure of a Bacterial Non-Haem Iron Hydroxylase Thatcatalyses the Biological Oxidation of Methane. Nature 1993, 366, 537−543. (97) Lipscomb, J. D. Biochemistry of the Soluble Methane Monooxygenase. Annu. Rev. Microbiol. 1994, 48, 371−399. (98) Colby, J.; Stirling, D. I.; Dalton, H. The Soluble Methane Mono-Oxygenase of Methylococcus Capsulatus (Bath). Its Ability to Oxygenate n-Alkanes, n-Alkenes, Ethers, and Alicyclic, Aromatic and Heterocyclic Compounds. Biochem. J. 1977, 165, 395−402. (99) Baik, M. H.; Newcomb, M.; Friesner, R. A.; Lippard, S. J. Mechanistic Studies on the Hydroxylation of Methane by Methane Monooxygenase. Chem. Rev. 2003, 103, 2385−2419. (100) Zheng, H.; Lipscomb, J. D. Regulation of Methane Monooxygenase Catalysis Based on Size Exclusion and Quantum Tunneling. Biochemistry 2006, 45, 1685−1692. (101) Ambundo, E. A.; Friesner, R. A.; Lippard, S. J. Reactions of Methane Monooxygenase Intermediate Q with Derivatized Methanes. J. Am. Chem. Soc. 2002, 124, 8770−8771. (102) Brazeau, B. J.; Lipscomb, J. D. Thermodynamic and Kinetic Evidence for a Two-Step Reaction between Methane Monooxygenase Compound Q and Substrates. Int. Congr. Ser. 2002, 1233, 229−233. (103) Mai, B. K.; Kim, Y. Substrate-Dependent H/D Kinetic Isotope Effects and the Role of the Di(μ-Oxo)Diiron(IV) Core in Soluble 6906


Research Article

ACS Catalysis Methane Monooxygenase: A Theoretical Study. Chem. - Eur. J. 2014, 20, 6532−6541. (104) Mountfort, D. O.; Pybus, V.; Wilson, R. Metal Ion-Mediated Accumulation of Alcohols during Alkane Oxidation by Whole Cells of Methylosinus Trichosporium. Enzyme Microb. Technol. 1990, 12, 343−348. (105) Furuto, T. Semicontinuous Methanol Biosynthesis by Methylosinus Trichosporium OB3b. J. Mol. Catal. A: Chem. 1999, 144, 257−261. (106) Hwang, I. Y.; Lee, S. H.; Choi, Y. S.; Park, S. J.; Na, J. G.; Chang, I. S.; Kim, C.; Kim, H. C.; Kim, Y. H.; Lee, J. W.; et al. J. Microbiol. Biotechnol. 2014, 24, 1597−1605. (107) Hohenberg, P.; Kohn, W. Inhomogeneous Electron Gas. Phys. Rev. 1964, 136, B864−B871. (108) Kohn, W.; Sham, L. J. Self-Consistent Equations Including Exchange & Correlation Effects. Phys. Rev. 1965, 140, A1133−A1138. (109) Giannozzi, P.; Baroni, S.; Bonini, N.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Chiarotti, G. L.; Cococcioni, M.; Dabo, I.; et al. Quantum ESPRESSO: A Modular and Open-Source Software Project for Quantum Simulations of Materials. J. Phys.: Condens. Matter 2009, 21, 395502−395521. (110) Hjorth Larsen, A.; Jørgen Mortensen, J.; Blomqvist, J.; Castelli, I. E.; Christensen, R.; Dułak, M.; Friis, J.; Groves, M. N.; Hammer, B.; Hargus, C.; et al. The Atomic Simulation Environmenta Python Library for Working with Atoms. J. Phys.: Condens. Matter 2017, 29, 273002. (111) Laasonen, K.; Pasquarello, A.; Car, R.; Lee, C.; Vanderbilt, D. Car-Parrinello Molecular Dynamics with Vanderbilt Ultrasoft Pseudopotentials. Phys. Rev. B: Condens. Matter Mater. Phys. 1993, 47, 10142−10153. (112) Laasonen, K.; Car, R.; Lee, C.; Vanderbilt, D. Implementation of Ultrasoft Pseudopotentials in Ab Initio Molecular Dynamics. Phys. Rev. B: Condens. Matter Mater. Phys. 1991, 43, 6796−6799. (113) Vanderbilt, D. Soft Self-Consistent Pseudopotentials in a Generalized Eigenvalue Formalism. Phys. Rev. B: Condens. Matter Mater. Phys. 1990, 41, 7892. (114) Mills, G.; Jónsson, H.; Schenter, G. K. Reversible Work Transition State Theory: Application to Dissociative Adsorption of Hydrogen. Surf. Sci. 1995, 324, 305−337. (115) Mills, G.; Jonsson, H. Quantum and Thermal Effect in H2 Dissociative Adsorption: Evaluation of Free Energy Barriers in Multidimensional Quantum Systems. Phys. Rev. Lett. 1994, 72, 1124−1127. (116) Henkelman, G.; Uberuaga, B. P.; Jónsson, H. A Climbing Image Nudged Elastic Band Method for Finding Saddle Points and Minimum Energy Paths A Climbing Image Nudged Elastic Band Method for Finding Saddle Points and Minimum Energy Paths. J. Chem. Phys. 2000, 113, 9901−9904. (117) Henkelman, G.; Jónsson, H. Improved Tangent Estimate in the Nudged Elastic Band Method for Finding Minimum Energy Paths and Saddle Points. J. Chem. Phys. 2000, 113, 9978−9985. (118) Momma, K.; Izumi, F. VESTA 3 for Three-Dimensional Visualization of Crystal, Volumetric and Morphology Data. J. Appl. Crystallogr. 2011, 44, 1272−1276. (119) Hunter, J. D. Matplotlib: A 2D Graphics Environment. Comput. Sci. Eng. 2007, 9, 90−95.

6907


Direct Methane to Methanol - ACS Publications - American Chemical

Recommend Documents