Valorization of Methane for Ethylene Production Through Oxidative Coupling: An Application of Density Functional Theory and Data Analytics in Catalyst Design for Improved Methane Conversion ^†

Abstract

The combination of electronic and catalytic features, in conjunction with empirical investigation, provides enriched perspectives on the analysis of catalysts, thus propelling progress and design. This study employs computational methods to deduce electronic characteristics, including properties such as bandgap, Fermi energy, and magnetic moment, for known catalysts involved in the oxidative coupling of methane (OCM) reaction. Through the comparison of these attributes with existing experimental OCM data, the ability to forecast the effectiveness of catalysis and subsequent reaction results is achieved, spanning CH₄, C₂H₄, C₂H₆, and CO₂ production. Transition metals, including Pt, Rh, Ru, and Ir, turn out to be promising catalyst promoters of OCM reactions. This study identified 58 innovative blends of metallic oxides and 3480 new catalytic configurations specifically designed for methane conversion at a moderately low temperature of 700 °C, placing them as effective catalysts for the OCM reaction. These emerging catalysts are projected to result in a rise in methane conversion extending from ±38.5% to ±95%, presenting a significant increase from the upper limit methane conversion of 36% reported in previous investigations.

1. Introduction

The OCM reaction is exothermic in nature, with the initial step in the reaction involving the breaking of the C-H bond, which is energy intensive, beyond which the reaction progresses exothermally. The reaction is challenged with side reactions involving the partial oxidation of methane and the complete oxidation of methane, both of which give off the competing COx products from the reaction. The anticipation has been to design catalysts that will be selective towards the desired products and enhance methane activation, leading to the production of methyl radicals that are key to the forming of the desired products when they undergo coupling, which is more likely to happen at lower temperatures, typically in the range of 600–725 °C. However, the reaction usually takes place at high temperatures spanning 750 to 950 °C [1].

The main equation of the OCM reaction is provided below [2]:

2CH₄ + O₂ → C₂H₄ + 2H₂O (∆H = −280 kJ/mol)

(1)

DFT computations facilitate the examination of the connections among molecules undergoing reactions and the surfaces of catalysts, enabling the anticipation of reaction mechanisms and energies. This aids in devising catalysts that are not only more effective but also more selective for a range of chemical reactions. Particularly in assessing the electronic features of catalysts, the DFT approach functions as a tool for recognizing electronic characteristics pertinent to catalysis. Catalytic characteristics encompass variables employed to portray the efficacy and selectivity of catalysts within chemical reactions. DFT studies have been considered in the OCM reaction in relation to adsorption energy computations [3] and catalyst electronic structure calculations, including the density of states, d-band, p-band, band gap, and other electronic structure-related investigations [4]. It has also been applied in the study of the thermodynamics and kinetics of the OCM reaction, including micro-kinetics [3]. Bandgap has particularly been identified as an efficient descriptor of catalytic activity in the case of propene [5]. It is expected that it will have a similar impact in the case of ethylene production from the OCM reaction. Recently developed catalysts, such as Mn-Na-W-SiO₂, have shown substantial activity in driving the OCM reaction. In a comparative study, Fang et al. [6] identified the Mn/Na₂WO₄/SiO₂ catalyst as a standout performer, achieving an impressive 67% selectivity for C₂ (ethane and ethene) products, along with a 38% conversion of methane. Increasing methane conversion at low temperatures is key to increased C₂ yield.

The objective of this research is to derive insights by integrating data from high-throughput experiments and DFT to forecast the efficacy of catalysts in OCM, intending to diminish the generated COx while enhancing ethylene output. The research endeavors to suggest fresh catalyst formulations for effective OCM at temperatures below 700 °C, minimizing CO₂ production and augmenting CH₄ conversion, C₂H₄, and C₂H₆ yields. The recommended catalyst will possess the molecular structure M1_x-M2_yM3_zOn/Support.

2. Methodology

This study relies on a dataset comprising 12,708 data points that integrate details from high-throughput experimental (HTP) information sourced from the catalyst acquisition by data science (CADS) collection [7]. Complemented by forthcoming DFT computations in this analysis, the HTP OCM data amalgamate the electronic characteristics of the catalyst, the experimental conditions of the reaction, and the resulting outcomes of the reactions. The methods adopted for this study followed the following sequence:

• Primitive cells for the structure of catalyst constituent materials were sourced from databases such as the Materials Project repository. These cells were then enlarged into larger structures to improve the modeling of catalysts.
• Using the Quantum Espresso (QE) code, the crystal structures of the components of the catalysts were optimized to achieve the local minima electron state energy and atomic relaxed coordinates. This procedure prioritizes the optimization of total energy with respect to the positions of atoms within a unit cell. The kinetic energy cutoff for plane-wave calculations was decided using the open-source Materials Cloud QE input generator [8]. The relaxation of the unit cell and self-consistent field (SCF) calculations involved sampling the Brillouin zone using a K-points Monkhorst–Pack mesh grid.
• Calculations were performed using DFT to obtain the Fermi energy, bandgap, and magnetic moments for the catalyst components. Specifically, these include the catalyst promoter, active metal oxide, and support. The methodology utilizes plane-wave basis sets and pseudopotentials to estimate the electron exchange–correlation function.
• The subsequent analysis involved utilizing the computed results of the DFT-computed electronic characteristics in conjunction with the HTP OCM experimental data obtained from the CADS repository to find prognostic patterns between dataset features. The dataset consists of 34 features, encompassing 8 electronic properties computed through DFT for the catalyst promoter, active metal oxide, and the support, along with 26 attributes derived from the HTP experimental data. Additionally, regression evaluation was conducted on specific features of the dataset to examine the connections between the variables.

3. Results and Discussion

3.1. Catalyst Component Modeling and Calculations of Electronic Properties

With the help of crystal modeling applications, including Burai and Vesta, crystal structures containing atomic coordinates for the different catalyst components (the promoter, metal oxide, and support) were created. The sample crystal structure unit cell of an active metal oxide (MgWO₄) is shown in Figure 1. The catalyst properties, including Fermi energy, bandgap, and moment, were computed using DFT. For the nineteen transition metals used as promoters in the HTP data, the computational parameters, including the kinetic energy cut-off wavefunction and the kinetic energy cut-off charge density, were determined from the pseudopotentials used in the computations, which were restricted to the ultrasoft pseudopotentials, the projector-augmented wave functions and the norm-conserving pseudopotentials. Other computational parameters including the K-points, the convergence threshold for selfconsistency, the mixing factor for selfconsistency, and the convergence threshold on total energy and convergence threshold on forces, were provided by the Materials Cloud QE input generator. Given that the promoters are all metals, smearing was turned on using the cold and Gaussian options during the calculations. All of the promoter metals indicated substantial and varying Fermi energies but zero bandgaps, as is expected of metals. Iron (Fe) indicated full magnetic attributes with magnetic moments of 2 μB, while metals including Co, Ni, and Pd indicated para-magnetic properties. Figure 2 is a bar chart that illustrates the computed electronic properties of the catalyst promoter.

Similarly, the electronic properties of the catalyst active metal oxides (totaling thirteen) and the catalyst support materials (totaling thirteen) were computed in the same fashion as the catalyst promoter. However, given the non-metallic nature of the active metal oxides and catalyst supports, the “Fixed” occupation was used as appropriate in the case of materials with bandgaps and low electrical conductivity. As expected, all of the materials indicated substantial bandgaps except for FeMoO₄, which had a small bandgap of 0.221 and substantial magnetic moments of 2 μB owing to its ferromagnetic properties. As a means of control, the computed bandgaps for the different support materials and active metal oxides were compared with the bandgap from the literature to validate the calculations. Illustrations of the computed electronic properties are shown in Figure 3 and Figure 4.

The development of more effective catalyst promoters required the formulation of a prognostic model to evaluate the performance of a catalyst based on the impact of the enhancer. The dataset utilized for this objective originated from reactions involving M₁-Na₂WO₄/SiO₂ as the catalyst, carried out under specific conditions: a temperature of 700 °C, a total flow rate of 20 mol/s, a CH₄ flow rate of 11.3 mol/s, a resident time of 0.38 s, a CH₄/O₂ ratio of 2, and catalyst constituent mole percentages of 40, 40, and 20 for M1, M2, and M3, respectively. Using the ordinary least-squares (OLS) library, scikit learn, and numpy libraries in Python, a multilinear regression model was designed to predict CH₄ conversion. Electronic attributes, including the DFT computed Fermi energy, the magnetic moment, the number of electrons in the outermost D-orbital, the shell level of the outermost D-orbital, and the atomic number of the promoters in the dataset, made up the dataset features in the predictive model. The model summary is detailed in

Table 1. OLS model information for catalyst promoter-based CH₄ prediction.

Model	Method	R-Squared	Adj. R-Squared	F-Statistic	Prob (F-Statistic)	Log-Likelihood
OLS	Least squares	0.838	0.748	9.317	0.00231	−26.05

.

3.2. Catalyst-Promoter-Based CH₄ Conversion Prediction

From the model information in Table 1, the R-squared of 0.838 indicates that approximately 83.8% of the inconstancy in the dependent variable is described by the independent variables in the model. The adjusted R-squared of 0.748 means that, after adjusting for the number of predictors, about 74.8% of the variance in the dependent variable is described by the independent variables. Conversely, the F-statistic checks the overall significance of the model. In this case, a value of 9.317 suggests that the model in its entirety is statistically significant. The Prob (F-statistic) of 0.00231 is indicative of the summary p-value of the model parameters. Based on this value, at least one or more of the independent variables in the model are statistically significant in predicting the dependent variable. The log-likelihood, on the other hand, is usually negative, and a higher (less negative) log-likelihood indicates a better fit.

Using the catalyst-promoter-based CH₄ conversion predictive model, 4 novel promoters were identified, including Ir, Pt, Rh, and Ru. Figure 5 illustrates these predictions, comparing the predicted to real CH₄ conversion. The models were projected to identify the new promoters. The parity with an average absolute error of deviation (AAD) of 6.88 measured as the Euclidean distance between the plot point in Figure 6, compares the real and predicted CH₄ conversion for the M1-Na₂WO₄/SiO₂ catalyst promoted by varying transition metals. Equation (2) is the promoter-based CH₄ conversion predictive model.

CH_{4_Pred} = 0.9856 × E_F − 4.0414 × M_M1 + 1.1724 × D_N + 13.4029 × D_L − 0.6033 × Z_M1 − 35.8133

(2)

where:

• E_F = Fermi energy of M1; M_M1 = magnetic moment of M1
• D_N = number of electrons in the outmost D orbital of M1
• D_L = level of the electrons in the outmost D orbital of M1
• Z_M1 = atomic number of M1

Figure 5. Promoter-based CH4 conversion pred.

Figure 5. Promoter-based CH4 conversion pred.

Figure 6. Catalyst-promoter-based CH4 conversion parity plot.

Figure 6. Catalyst-promoter-based CH4 conversion parity plot.

Like the catalyst promoter, the predictive models for predicting new bimetallic oxides from the same dataset but including the atomic numbers of M1, M2, and M3, their Fermi energies and their D-orbital attributes, and their molar compositions were used to project the identification of new bimetallic oxides that will be efficacious in catalyzing the OCM reaction. The model summary is detailed in

Table 2. OLS model information for catalyst bimetallic oxide-based CH₄ prediction.

Model	Method	R-Squared	Adj. R-Squared	F-Statistic	Prob (F-Statistic)	Log-Likelihood
OLS	Least squares	0.792	0.428	2.177	0.231	−30.952

below.

The relatively high R-squared (0.792) suggests that the model elucidates a considerable portion of the variability in the dependent variable, while the lower adjusted R-squared (0.428) suggests that some of the variables in the model may not be adding much explanatory power and the model may be overfitting or including irrelevant variables. The F-statistic of 2.177 suggests the relative explanatory power of the model.

Figure 7 illustrates these predictions, comparing the predicted to real CH₄ conversion. Using the catalyst-active-oxide-based CH₄ conversion predictive model, 58 novel bimetallic oxides projecting CH₄ conversion of 38.5% and above were identified. The parity with an average absolute error of deviation (AAD) measured as the Euclidean distance (9.08) between the plot points in Figure 8 compares the real and predicted CH₄ conversion for the M2_xM3O_n bimetallic oxide in the Mn-M2_xM3O_n/SiO₂ catalyst promoted by Mn. The equation of the predictive model is detailed in Equation (3).

CH4_conv_Pred = −2.2956 + 195.6628 × M2_mol + 264.4932 × M3_mol − 0.0046 × E_{fM2 −} 6.2861 × E_fM3 + 0.231 × Z_M2 + 0.48 × Z_M3 − 14.5061 × D_N − 6.1545 × D_L + 14.6682 × E_BGav + 11.8994 × E_fav

(3)

where: E_F = average Fermi energy of the metal oxide compound

• E_fM2 and E_FM3 = average Fermi energy of M2 and M3, respectfully
• E_BGav = average bandgap energy of the metal oxide compound
• D_N = number of electrons in the outmost D orbital of the transition metal (M3)
• D_L = level of the electrons in the outmost D orbital of the transition metal (M3)
• Z_M2 and Z_M3 = atomic number of the M2 and M3, respectfully
• M2_mol = number of moles of M2 in the bimetallic oxide

Figure 7. Bimetallic oxide-based CH₄ conversion pred.

Figure 7. Bimetallic oxide-based CH₄ conversion pred.

Figure 8. Catalyst-bimetallic-oxide-based CH₄ conversion parity plot.

Figure 8. Catalyst-bimetallic-oxide-based CH₄ conversion parity plot.

It is assumed that the method of catalyst impregnation may not be total; hence, the catalyst support materials would contribute to the catalyst activity beyond their classical role of providing the required surface area. As is suggested in the literature, the bandgap of such materials would enhance the catalyst’s activity. As such, possible options for effective catalyst support material with large surface areas and wide band gaps would include mesoporous silica-based materials such as SBA-15 and MCM-41.

In total, based on the four proposed novel catalyst promoters, 58 bimetallic oxides, and the 15 possible catalyst support materials, a minimum of 3480 possible catalyst compositions have been identified.

4. Conclusions

The utilization of a combination of computational techniques (DFT) and advanced data analysis methods (ML) can function as a feasible approach to extract insights from catalytic reactions in the oxidative coupling of methane (OCM). DFT is employed for calculating the electronic properties of catalysts, while ML offers a diverse set of methodologies to model catalytic performance based on existing experimental data.

Effective catalyst promoters, namely Pt, Rh, Ru, and Ir, among four transition metals, have been suggested to enhance catalyst activity. The anticipated conversion of CH₄ utilizing the Na₂WO₄/SiO₂ catalyst, promoted using either of these transition metals, is expected to achieve a 17–27% conversion at 700 °C, with a total reactant flowrate of 20 mol/s, a CH₄ flow rate of 11.3 mols/s, a contact time of 0.38 s, and a CH₄/O₂ ratio of 2. This is in comparison with the known Mn-promoted Na₂WO₄/SiO₂ catalyst, which yields a maximum of 16% conversion under identical conditions.

Bimetallic oxides, akin to the established OCM catalyst’s active metal oxide (Na₂WO₄), incorporating alkali metals or alkaline earth metals, can be applicable in catalyzing OCM reactions. A bimetallic composition, especially with an elevated bandgap and Fermi energy, proves efficacious in catalyzing OCM, leading to enhanced CH₄ conversion. The study introduces 58 novel bimetallic oxides with catalytic activity, ensuring a minimum methane conversion of 38.5%.