Unraveling Thermodynamic Stability, Catalytic Activity, and Electronic

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Article Cite This: J. Phys. Chem. C 2019, 123, 15495−15502

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Unraveling Thermodynamic Stability, Catalytic Activity, and Electronic Structure of [TMxMgyOz]+/0/− Clusters at Realistic Conditions: A Hybrid DFT and ab Initio Thermodynamics Study Shikha Saini,* Pooja Basera, Ekta Arora, and Saswata Bhattacharya* Department of Physics, Indian Institute of Technology Delhi, New Delhi 110016, India

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S Supporting Information *

ABSTRACT: Aiming toward catalytic applications, a large data set is generated on [TMxMgyOz]+/0/− clusters (TM = Cr, Fe, Co, Ni, x + y ≤ 5) using a massively parallel cascade genetic algorithm (cGA) approach at the hybrid density functional level of theory. The low-energy isomers are further analyzed via ab initio atomistic thermodynamics to estimate their free energy of formation at a realistic temperature T and partial pressure of oxygen pO . A thermodynamic phase 2

diagram is drawn by minimizing Gibbs free energy of formation to identify the stable phases of neutral and charged [TMxMgyOz]+/0/− clusters. From this analysis, we notice that neutral and negatively charged clusters are stable in the wide range of (T, pO ). The negatively charged clusters are more 2

effective as a catalyst to lower the C−H bond activation barrier for oxidation of methane. We find that the nature of TM atoms toward controlling the activation barrier is less important. However, the TM gives rise to different structural motifs in the cluster, which may act as active centers for catalysis.

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INTRODUCTION Transition metals (TMs) are well-known for their efficient homogeneous and heterogeneous catalytic activity.1,2 In heterogeneous catalysis, transition metal (TM) oxide nanoparticles (typically clusters consisting of a well-defined number of atoms) comprise a large family of catalysts that are used for selective oxidation of various hydrocarbons.3−12 From very recent studies, it has been revealed that the reactivity and selectivity of homogeneous metal oxides can be enhanced drastically upon doping and/or mixing with other metal atoms.13−16 The most active and selective TM oxides sometimes involve mixtures of multiple metal oxides,17−19 the performance of which is typically quite different from that of the component oxides. The catalytic activity in mixed oxide systems can be explored by the stoichiometry, size, and structure of the catalyst. These bi-metallic oxide clusters possess intriguing electronic properties to enhance the chemical reactivity of the composite systems. For example, in our previous study,20 we have conveyed (and validated by forming a huge data set of TMxMgyOz (TM = Cr, Fe, Co, Ni and x + y ≤ 3) clusters) one central message: that catalytic reactivity of this type of bimetallic oxide system is expected to be correlated more strongly with oxygen-rich environment than the choice of any specific TM atoms. The latter is, however, conventionally believed to play the lead role in catalysis. The present work, therefore, originates by addressing this open question: out of four chosen TM atoms, viz., Cr, Fe, Co, and Ni, which one should be the best choice for catalysis © 2019 American Chemical Society

and why? It is interesting to understand the explicit role of TM despite that one should aim for O-rich environment conditions for synthesis of these catalysts. A charge transfer from support to the cluster can have a significant influence on the performance of the cluster. This is why charged defects are always instrumental in influencing the reactivity, stability, and selectivity of metal oxide clusters.21−23 In our former publication,20 we have introduced TMxMgyOz clusters but not commented on anything about the thermodynamic stability of charged clusters. In view of this, it is more relevant to study the charged clusters to gain insight into how an excess or deficiency of charge density will influence its thermodynamic stability as well as catalytic properties. Note that in heterogeneous catalysis TM nanoparticles, at various charge states, exhibit significant variations as a function of size in their physicochemical nature and electronic properties. In the presence of a realistic reactive atmosphere (i.e., temperature (T), pressure (p), and doping), clusters change their stoichiometry by adsorbing the ligands (usually oxygen) from the environment, under certain conditions.24 This new composition (with specific active sites) may work as an active (functional) material. Therefore, one has to understand the functional properties of clusters in a technologically relevant atmosphere. However, the unambigReceived: February 19, 2019 Revised: May 21, 2019 Published: June 7, 2019 15495

DOI: 10.1021/acs.jpcc.9b01619 J. Phys. Chem. C 2019, 123, 15495−15502

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uous identification of active sites, detailed insight of elementary steps of the reaction process, the selectivity, and the stability of intermediate products are sometimes a daunting task due to the complexity involved in catalytic processes. Theory and computation have played an important role in understanding and predicting chemical reactivity of various TM-oxide catalysts at the nanoscale. Gas-phase metal clusters have been considered to be versatile model systems to explore the basic principles of catalytic reaction mechanisms at a molecular level. Previous reports have identified a direct correlation between the products yielded in gas-phase cluster calculations and condensed-phase catalytic reactions.25,26 For instance, oxidation of ethylene by V2O+5 and V4O+10 clusters is in exact agreement with that occurring over Vanadia surfaces.25 Similarly, the reaction mechanism of oxidation of methanol by MoxOy+ clusters is found in direct correspondence to reactions which occur over their bulk-surface counterpart.26 Therefore, in the last decades, there has been an increasing interest in understanding the physicochemical properties of gas-phase clusters.15,27−32 In this article, we have generated a large data set [TMxMgyOz]+/0/− (TM = Cr, Fe, Co, Ni with x + y ≤ 5) (even bigger than the former publication20 TMxMgyOz (TM = Cr, Fe, Co, Ni with x + y ≤ 3)) consisting of all the neutral as well as charged clusters to analyze their thermodynamic stability. Following this, we have explicitly calculated the activation barrier of bi-metallic clusters to abstract the first C− H bond from the methane. This step is considered to be a ratedetermining step for a catalyst to convert methane into valuable chemical products.33−41 Numerous interesting studies for C−H bond activation of methane at room temperature by various (noble metals40−43 and homonuclear38,39,44−46 and heteronuclear35,36,47−50 metal oxides) gas-phase clusters have been reported. Among them, noble-metal-based bi-metallic clusters (i.e., RhAl3O+4 , RhAl2O−4 , PtAl2O−4 , AuV2O+6 , and − AuTi 3 O 7,8 ) exhibit high activity for methane activa33,47,51−53 However, their high cost and the limited tion. availability limit their commercialization. Therefore, currently, researchers are extensively focused on finding the most promising substitutes based on non-noble active transition metals with high activity, low cost, and formidable abundance. From the literature, to the best of our knowledge, there are not many reports on this topic to date. We find only Li et al. have studied the activation of methane on transition-metal-doped magnesium oxide clusters.50 In view of this, we aim to address the activity of non-noble metal (Cr, Fe, Co, and Ni) based MgO clusters. By analyzing the barrier height of the first C−H bond activation of methane on different cluster configurations, we have established a direct correlation of the fundamental gap with the activation barrier of a catalyst. Here, in addition to that, we have addressed the presence of active centers in these bi-metallic oxide clusters to facilitate the first C−H bond dissociation in the context of methane activation. Moreover, we have explicitly provided the information on the governing factors (including the role of TMs, electronic structures, and the charged states) of the active center to improve its reactivity for methane oxidation. Further, the aim of the study is to address the role of charged states in the thermodynamic stability of the clusters and their efficiency in reducing the activation barrier for the reaction kinetics for methane oxidation.

Article

METHODOLOGY

We have generated a large data set of bi-metallic oxide [TMxMgyOz]+/0/− clusters (TM = Cr, Fe, Co, Ni with x + y ≤ 5) at different charge states (+, 0, -). We have varied the value of z (no. of oxygen atoms) from zero to the saturation value, where no more oxygen atom can be absorbed by the cluster. As a first step, we have used a massively parallel cascade genetic algorithm (cGA) to thoroughly scan the potential energy surface (PES) to determine all possible low-energy structures (including the global minimum). The term “cascade” means a multistepped algorithm where successive steps employ higher level of theory and each of the next level takes information obtained at its immediate lower level. Typically, a cGA algorithm starts with classical force field and goes up to Density Functional Theory (DFT) with hybrid functionals [see ref.24,54,55 for details of this cGA implementation, accuracy and validation]. All the DFT calculations are carried out using FHI-aims code,56 which is an all-electron calculation using the numeric atom centered basis set. The low energy structures obtained from the cGA are further optimized at higher level settings. In this step, the vdW-corrected (Tkatchenko−Scheffler scheme57) PBE+vdW58 exchange and correlation (εxc) functional is used. The atomic forces are converged up to 10−5 eV/ Å using “tight” settings with “tier 2” basis set as implemented in FHI-aims code. The atomic zero-order regular approximation (ZORA) is considered for the scalar relativistic correction.56,59 Finally, the total single-point energy is calculated on top of this optimized structure using the vdWcorrected-PBE060 hybrid εxc functional (PBE0+vdW), with “tight-tier 2” settings. It is reported that PBE+vdW highly overestimates the stability of clusters containing a larger concentration of O atoms.54 This results in a qualitatively wrong prediction of O2 adsorption for O-rich cases. Such behavior is not confirmed by hybrid functionals [e.g HSE06,61 PBE0] as employed in our calculations. The difference in energetics of PBE0 and HSE06 is always within 0.04 eV.20 The spin states of the clusters are also different as found by PBE and PBE0/HSE06. In view of this, we have used a hybrid functional (PBE0) with tight numerical settings and tier 2 basis set to compute the formation energies of various configurations [see details in the next section]. To examine the fundamental gap (Eg) of all the clusters, we have used the state-of-the-art many-body perturbation theory within the GW approximation. We have calculated Eg at the level of G0W0@PBE0 with “really tight” numerical settings and tier 4 basis set.56 To determine the structure of the transition state (TS) and to find the minimum energy path for first C−H bond activation of methane on bi-metallic clusters, we have used FHI-aims code using the PBE εxc functional as implemented in aims-chain feature for the nudged elastic band method (NEB) calculations. We have analyzed the vibrational frequencies of TS to confirm the one imaginary frequency in the direction of the reaction coordinate.

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RESULTS AND DISCUSSIONS Determination of the Stable Phases of [TMxMgyOz]+/0/− Clusters. After generating the structures of all the low energy isomers [see Figure S1 in Supporting Information (SI)] of [TMxMgyOz]+/0/− clusters (TM = Cr, Fe, Co, Ni with x + y ≤ 5) using the cascade genetic algorithm, we study the thermodynamic stability of gas-phase 15496

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The Journal of Physical Chemistry C [TMxMgyOz]+/0/− clusters in an oxygen atmosphere using the ab initio atomistic thermodynamics (aiAT) approach.62 Here we assume when a bi-metallic cluster is exposed in a reactive atmosphere of gas-phase O2 it will react with the atmosphere depending on environmental conditions (viz. T, pO , and 2

doping63) via the following equation z [TMxMg y]q + O2 F [TMxMg yOz ]q 2

(1)

q is the electric charge of the cluster. Here, we have used “+” for cationic clusters with charge +1, “0” for neutral, and “−” for the anionic clusters with charge −1. Since the ligand O2 is a neutral species, the charge q remains the same during the reaction.64 Using aiAT, we determine the Gibbs free energy of formation of all the [TMxMgyOz]q structures as a function of T, pO , and chemical potential of electrons (μe). The most 2 preferred composition at a given T, pO , and μe, relevant for the 2

experiments, will be the one with the minimum Gibbs free energy of formation at the experimental conditions. This is shown in the following equation: Figure 1. 2D view of 3D phase diagrams obtained for neutral and ionic [TM2Mg2Oz]+/0/− clusters in the reactive atmosphere of O2. Colored regions show the most stable compositions in a wide range of pressures and μ e under thermodynamic equilibrium. In [TM2Mg2Oz]+/0/− clusters, TM = Cr (a), Fe (b), Co (c), and Ni (d). The top axis represents the pressure of oxygen at T = 300 K.

ΔGf (T , pO ) = F[TMxMg Oz ]q(T ) − F[TMxMg ]0(T ) y

2

y

− z × μO(T , pO ) + q × μe

(2)

2

Here, F[TMxMg Oz ]q(T ) and F[TMxMg ]0(T ) are the Helmholtz free y

y

energies of the cluster + ligands [TMxMg yOz ]q and the pristine

close to LUMO level at 0 eV; implying n-type doping) anionic clusters are more stabilized. For example, in the case of TM = Cr, we see from Figure 1a that at fixed T = 300 K for values μe suitable for p-type doping and at lower values of pO ,

[TMxMg y]0 cluster, respectively. The clusters are at their

ground-state configuration with respect to geometry and spin state. The term μO(T , pO ) is the chemical potential of an

2

2

(Cr2Mg2O8)0 is the most stable phase, whereas as we increase the pO , (Cr2Mg2O10)0 is the most preferable phase in the

1

oxygen atom ( μO = 2 μO ). The range of μe is taken from bulk 2 MgO.65 The free energy of each stoichiometry (cluster + ligands, pristine cluster) and the chemical potential of O2 have evaluated from the corresponding partition functions including translational, rotational, vibrational, electronic, and configurational degrees of freedom. The dependence of μO(T , pO ) on 2 T and pO is calculated using the ideal (diatomic) gas

2

phase diagram. However, if we set μe to the values suitable to n-type doping at lower pO , (Cr2Mg2O8)− is the stable phase, 2 and on increasing the pO , (Cr2Mg2O10)− is favorable at 2

ambient pO , and (Cr2Mg2O12)− becomes a stable config2 uration at higher pO . This trend of enhanced stability of

2

2

approximation with the same DFT functional as for the clusters. The details of this methodology can be found in ref 24. Following this, a three-dimensional (3D) phase diagram for all possible combinations of x + y ≤ 5 (y ≠ 0) of [TMxMgyOz]+/0/− clusters is constructed to identify the lowest free energy composition and structure at a specific T, pO , and

neutral and anionic clusters, respectively, for lower and higher values of μe (i.e., at a given doping condition) with varying pO 2

is also followed for other TMs (viz. Fe [Figure 1b], Co [Figure 1c], and Ni [Figure 1d]). We have further noticed from these phase diagrams that at ambient environmental conditions (i.e., T = 300 K, pO = 1 atm) nonstoichiometric O-rich clusters are

2

μe condition (see Figure 1 where one specific case for x = 2, y = 2 is shown). From these types of phase diagrams, the stable compositions at a given environmental condition of [TMxMgyOz]q clusters can be determined. Here, on the xaxis ΔμO is varied in accordance with the corresponding T and pO . On the y-axis, μe is varied from the valence band maximum

2

the most stable phases in all the cases. Following this representative case (with x = 2 and y = 2), we have verified all possible combinations of x and y by limiting x + y ≤ 5 to see the trends at other sizes. We have found that the observed trend in thermodynamic stability holds at other values of x, y as well and are in line to this representative case of x = 2 and y = 2: i.e., (i) positively charged clusters are not stable throughout the phase diagram and (ii) nonstoichiometric O-rich phases (with charge 0/−) are more favorable at ambient conditions. After identification of all the stable (and/or metastable) configurations at a realistic environmental condition, it is now important to understand their catalytic properties from electronic structure analysis. Correlation of Fundamental Gap (Eg) vs C−H Bond Activation Barrier (Ea) of a Catalyst. A catalyst is expected

2

to the conduction band minimum of the bulk MgO. On the zaxis the negative ΔGf (T , pO ) values are plotted so that only 2

the most stable phases are visible from the top. In Figure 1(a− d), the phase diagrams of [TM2Mg2Oz]+/0/− clusters are shown as one of the representative cases for four different TMs, viz., Cr, Fe, Co, and Ni, respectively. From Figure 1(a−d), it can be inferred that at lower values of μe (i.e., close to the HOMO level at −7.5 eV; implying p-type doping conditions) neutral clusters are more stable, whereas at higher values of μe (i.e., 15497

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The Journal of Physical Chemistry C to be more effective, if it can accept or donate electrons more easily.55,66 Therefore, if a particular cluster has simultaneously high electron affinity (EA) and low ionization potential (IP), it is expected to act as a good catalyst. This means the cluster should have a low fundamental gap (Eg), which is simply the difference between IP and EA. Over the past, Eg has been assumed in many instances to act as one of the descriptors to correlate reactivity of a catalyst,20,55,66−71 and for TM-based MgO clusters (viz., TMxMgyOz), we, presumably for the first time, study the correlation of Eg with the catalytic activity. We, therefore, first try to investigate how a smaller Eg of [TMxMgyOz]+/0/− clusters is correlated with the C−H bond activation barrier (Ea) for oxidation of methane. To do that, we have taken three different isomers of Ni2Mg2O5 clusters as shown in Figure 2. The electronic charge

Figure 3. Minimum energy pathway of the first C−H bond activation of methane on GM of the neutral (Ni2Mg2O5)0 cluster (a), negatively charged (Ni2Mg2O5)− (b), metastable structure of the (Ni2Mg2O5) cluster in the neutral state (c and e), and the metastable structure of the Ni2Mg2O5 cluster in negatively charged state (d and f). Reaction coordinates of the initial (R), final (P), transition state (TS), and intermediates are shown. Activation barriers (Ea) for all cases are also indicated in the respective graphs in kJ/mol. The fundamental gaps Eg of the clusters in all cases are shown in eV.

Figure 2. Electronic structures of Ni2Mg2O5 cluster (global minimum (a), metastables (b and c)). Colored surface represents the hirshfeld charge density in the cluster.

density at each atom is also shown, whose relevance is discussed later. The structure in Figure 2a is the global minimum (GM) isomer, whereas the other two are low energy isomers lying within 2 eV from the GM. These three structures are used to estimate the C−H bond activation energy. In Figure 3, we have shown six different cases for the C−H bond activation on various configurations of the Ni2Mg2O5 cluster. We have compared the Ea values for the GM structure with one of the metastable isomers (see Figure 3a and c). We see that a smaller Ea is associated with the metastable isomer than the GM as a catalyst. Therefore, the metastable isomer should be a better catalyst than the GM structure, and this observation is inline to the Eg values of the respective clusters. The Eg of the metastable structure is indeed lower than the Eg of the GM structure. This clear correlation between Eg and Ea holds for most of the cases with a few exceptions, where they do not follow exactly the same trend. For example, if some structural feature of a specific catalyst starts working as an active center, it enhances its catalytic activity drastically. Let us focus on the third isomer shown in Figure 2c and compare it with the structure as in Figure 2b. The catalytic behavior of these two respective clusters is shown in Figure 3e and 3c. We see [Figure 3e and 3c] the former structure [i.e., Figure 2c] has a smaller Eg but not Ea than the latter structure as shown in Figure 2b. The reason can easily be understood from identifying the active site present in the structure shown in Figure 2b by analyzing its hirshfeld charge distribution, but before this let us note a few important points. We find that the methane molecule gets adsorbed to the Mg atom site (see Figure S2). This is due to the presence of more positive charge density in Mg atoms than the nearby TM atoms (see Figure S3 and Figure 2 for the Ni2Mg2O5 cluster). After C−H bond

activation, the H atom favors the O atom site which is more negatively charged as compared to other O atoms in the cluster (see Figures S2, S3, and S4 for details), and the CH3 molecule gets adsorbed at the Mg site. Note that the C−H bond activation energy depends on the charge density of the O atom, where the H atom tends to make a bond after dissociating from CH4. For example, at the most negatively charged O site the Ea is lower (82.44 kJ/mol) than that on the other less negatively charged O site (115.68 kJ/mol) (see Figure S4). Therefore, in Figure 3, for the GM structure, all the O atoms have an approximately equally distributed charge (≈−0.41e) due to the nature of the symmetry in the position of atoms. On the other hand, the metastable structures are somewhat asymmetric in nature. Thus, it has some O atoms, where localized negative charge exists. This makes the site able to act as an active center. In Figure 2b and 2c, such cases are shown. Note that in Figure 2b one O atom with charge density ≈−0.63e is present to act as an active site, whereas in Figure 2c, two such localized orbitals are noticed, both with charge (≈−0.50e). The latter structure is less active than the former as two O sites effectively reduce the overall activity as in the former structure with one active O site (Figure 2b). Therefore, both the metastable structures are having smaller Ea and Eg than the GM structure, but the former one is supposed to be more effective with a reduced Ea than the latter one despite having a smaller gap than the former. We have obtained better activity for C−H bond activation on Ni-based bi-metallic 15498

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The Journal of Physical Chemistry C clusters than the cationic gold cluster (Au+3 ) reported by Lang et al. (131.33 kJ/mol).40 However, the activity of these clusters is slightly less as compared to the noble-metal-based bi-metallic oxide clusters.33,52 From the phase diagram (as in Figure 1), the most stable phases are either neutral clusters (under p-typed doped condition) or negatively charged clusters (under n-type doped condition). Therefore, we have also shown the activation energy to break the C−H bond by negatively charged clusters. In fact, we have noticed that the charged clusters are more effective in doing the same. In the case of GM (see in Figure 3a and b), Ea for C−H bond activation by a negatively charged cluster is found to be much lower (99.21 kJ/mol) than the neutral one (139.95 kJ/mol). The trends in Eg for the (Ni2Mg2O5)−1 and (Ni2Mg2O5)0 are also in agreement with the respective Ea values. Further, we have also noticed a remarkable reduction in C−H bond activation barrier Ea by negatively charged metastable clusters (see in Figure 3d and f). On adsorbing one electron, the clusters possess localized charge, which acts as an active center to reduce the C−H bond activation barrier. Therefore, this analysis concludes that a smaller value of Eg is usually associated with a lowered C−H bond activation barrier Ea. The latter gets further reduced if the structure also has one active center with localized charged density. Note that it is computationally very expensive to calculate Ea values of all the stable configurations of [TMxMgyOz]+/0/− clusters to understand their catalytic activity. However, a very good qualitative description can be drawn for the same, from comparing the respective Eg values (estimated with G0W0@ PBE0) of all the isomers relevant at realistic experimental conditions. Eg is a Descriptor for Catalytic Activity. We have considered all the neutral and ionic (-ve) clusters of the data set ([TMxMgyOz]0/−) to plot their Eg as shown in Figure 4(a− d). Here we see the Eg values of negatively charged clusters

(red points) tend to have smaller values than that of neutral clusters (black points). However, it should be mentioned here that there are some scattered red points showing larger Eg. We have manually checked those data points (clusters) and found that the corresponding Eg of the neutral cluster is even higher. Note that this figure gives only overall qualitative trend but not any quantitative information on individual clusters to identify the Eg for neutral cluster and the same with one additional electron. This quantitative information is given in Tables S1, S2, S3 and S4, where for all the data set points the Eg values of both neutral and negatively charged clusters are given. From this data set, it can be clearly seen that the negatively charged clusters consistently have smaller Eg than its neutral counterpart (except for only a few cases). Therefore, for sure the negatively charged clusters are expected to be a better catalyst than the neutral clusters. In addition to this, note that these data points are distributed in such a way that there is no specific trend of Eg for the choice of any specific TM atoms. This observation is in line with our former publication,20 where we have shown that higher catalytic reactivity is correlated more strongly with the oxygen content in the cluster than with any specific TM type. However, despite that TM atoms do not have much role to control the Eg, they give rise to different structural motifs in the TMxMgyOz clusters with respective TM components [see Figure S1 in SI]. For some TMs, the structures contain molecular O2, whereas in some other cases, this O2 gets dissociated and is adsorbed in atomic form. This is due to the presence of different numbers of unpaired electrons in the outer shell of the TM atoms, giving rise to different types of structural features. This may play a significant role in catalysis as active centers. It is therefore important to understand these structural differences in TMxMgyOz clusters with various TM atoms. Structural Analysis: Radial Distribution Function of TMxMgyOz Clusters. In order to present a quantitative understanding of the structural motifs, in Figure 5(a−d), we have shown the radial distribution function (RDF) for various TMxMgyOz clusters with four different TM atoms (viz., Cr, Fe, Co, and Ni and z = [1−13]). Note that, in general, there are three types of molecular O2 adsorption in O-rich bi-metallic TMxMgyOz clusters, viz., at the atop site of the metal atom, parallel site, and cross-bridge site.72,73 The bond length of the O2 moiety is highly dependent on the kind of adsorption at various mentioned sites. This is ≈1.33, 1.35, and 1.57 Å for the atop, parallel, and cross-bridge site, respectively (see Figure 5e). It should be mentioned here that the calculated bond length for isolated molecular oxygen O2 is 1.22 Å, whereas the −2 same for O−1 2 (superoxo) and O2 (peroxo) are 1.36 and 1.6 Å, respectively. Thus, a superoxo moiety is formed when O2 is adsorbed at the atop and parallel sites, whereas a peroxo moiety is formed at the cross-bridge site. The bond length of O−1 2 (1.36 Å) is approximately equal to the bond length of O2 moieties at atop (1.33 Å) and parallel sites (1.35 Å), and O2 moieties at the cross site have the bond length comparable to −1 −2 the bond length of O−2 2 . Oxygen ions O2 and O2 are the reactive species that enhance the reaction of methane oxidation on bi-metallic oxide clusters as catalyst.74 In Figure 5, the first-order peaks (orange colored) in all cases correspond to the O2 adsorption at atop and parallel sites. The first-order peaks (orange colored) are more intense (see Figure 5c and Figure 5d) for Co- and Ni-based bi-metallic clusters. However, in the case of Cr- and Fe-based clusters, the

Figure 4. Eg (G0W0@PBE0) of all the charged and neutral [TMxMgyOz]0/− clusters of the data set are shown for TM = Cr (a), Fe (b), Co (c), and Ni (d) as a function of the oxygen content (z), which is varied from 1 to 13. 15499

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center for higher catalytic activity. The negatively charged clusters are in general more promising candidates for having smaller activation barrier with high stability. The role of TMs toward controlling the activation barrier is less. However, the nature of TMs determines the favorable type of O2 adsorption. Since Co- and Ni-based clusters favor molecular O 2 adsorption, they are expected to have a better catalytic performance among various TMxMgyOz clusters.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.9b01619.

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Figure 5. Radial distribution function for the TMxMgyOz [TM = Cr (a), Fe (b), Co (c), and Ni (d) using all the data for all possible combinations of x and y with x + y ≤ 5 and z = 1−11] set of clusters. (e) Visualization of different types of active moieties (cross bridge, parallel, and atop) in the clusters.

(I) Global minimum (GM) structures of TMxMgyOz (z = 1.8) set of clusters. (II) Activation energy for the first C−H bond activation of a methane molecule on the Nibased bi-metallic clusters. (III) Fundamental gap (Eg) of all the sets of clusters [TMxMgyOz]0/− at the level of G0W0@PBE0 with “really tight” numerical settings (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Phone: +91-2659 1359. Fax: +91-2658 2037. ORCID

Saswata Bhattacharya: 0000-0002-4145-4899

second-order peaks (blue colored) represent the (TM−O) bond length, where one dangling oxygen atom is bonded only to the TM atom. If we see the structures in the SI (Figure S1), this TM−O case is totally absent in Co- and Ni-based bimetallic clusters. Therefore, the blue colored peaks are absent in Figure 5c and 5d. This signifies that in Cr- and Fe-based bimetallic clusters a dissociative adsorption of O2 is more favorable. On the other hand, in Co- and Ni-based bi-metallic clusters a molecular adsorption of O2 is favored. Note that the latter is the prerequisite for methane oxidation reaction. Further, we have noticed another peak of very reduced intensity (maroon color) next to the orange colored peak as in Figure 5c and 5d. This peak represents the bond length of O2 moieties bonded at the cross-bridge site (bond length is the same as the TM−O bond). Note that O2 moieties bonded at the cross-bridge site have more electronic interaction with metal atoms in clusters as compared to O2 moieties at the atop site. Therefore, the bond length of the cross-bridge O2 moiety is comparatively higher than atop moieties. However, with the increase of the number of TM atoms in the clusters, dissociative adsorption of oxygen is increased. This information should be very useful in the kinetic study to propose a reaction mechanism.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS SS acknowledges CSIR, India, for the senior research fellowship [grant no. 09/086(1231)2015-EMR-I]. PB acknowledges UGC, India, for the senior research fellowship [grant no. 20/12/2015 (ii) EU-V]. SB and EA acknowledge the financial support from the YSS-SERB research grant, DST, India (grant no. YSS/2015/001209). SB thanks Luca Ghiringhelli and Sergey Levchenko for helpful discussions. We acknowledge the High Performance Computing (HPC) facility of IIT Delhi for computational resources.

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CONCLUSION In summary, we have presented a robust methodology to study the catalytic activity of small TM-based bi-metallic oxide clusters. As a first step we have used a massively parallel cascade genetic algorithm to determine all the low energy isomers. The thermodynamic stability of such structures is determined by minimizing their Gibbs free energy of formation using an ab initio atomistic thermodynamics method. A smaller C−H bond activation barrier is noticed when the cluster possesses both a smaller fundamental gap along with an active 15500

DOI: 10.1021/acs.jpcc.9b01619 J. Phys. Chem. C 2019, 123, 15495−15502

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