Unraveling Thermodynamic Stability, Catalytic Activity, andElectronic Structure of [TMxMgyOz]

+/0/− Clusters at RealisticConditions: A Hybrid DFT and ab Initio Thermodynamics StudyShikha Saini,* Pooja Basera, Ekta Arora, and Saswata Bhattacharya*

Department of Physics, Indian Institute of Technology Delhi, New Delhi 110016, India

*S Supporting Information

ABSTRACT: Aiming toward catalytic applications, a largedata set is generated on [TMxMgyOz]

+/0/− clusters (TM = Cr,Fe, Co, Ni, x + y ≤ 5) using a massively parallel cascadegenetic algorithm (cGA) approach at the hybrid densityfunctional level of theory. The low-energy isomers are furtheranalyzed via ab initio atomistic thermodynamics to estimatetheir free energy of formation at a realistic temperature T andpartial pressure of oxygen pO2

. A thermodynamic phase

diagram is drawn by minimizing Gibbs free energy offormation to identify the stable phases of neutral and charged[TMxMgyOz]

+/0/− clusters. From this analysis, we notice thatneutral and negatively charged clusters are stable in the wide range of (T, pO2

). The negatively charged clusters are more

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

■ INTRODUCTION

Transition metals (TMs) are well-known for their efficienthomogeneous and heterogeneous catalytic activity.1,2 Inheterogeneous catalysis, transition metal (TM) oxide nano-particles (typically clusters consisting of a well-defined numberof atoms) comprise a large family of catalysts that are used forselective oxidation of various hydrocarbons.3−12 From veryrecent studies, it has been revealed that the reactivity andselectivity of homogeneous metal oxides can be enhanceddrastically upon doping and/or mixing with other metalatoms.13−16 The most active and selective TM oxidessometimes involve mixtures of multiple metal oxides,17−19

the performance of which is typically quite different from thatof the component oxides. The catalytic activity in mixed oxidesystems can be explored by the stoichiometry, size, andstructure of the catalyst. These bi-metallic oxide clusterspossess intriguing electronic properties to enhance thechemical reactivity of the composite systems. For example, inour previous study,20 we have conveyed (and validated byforming a huge data set of TMxMgyOz (TM = Cr, Fe, Co, Niand x + y ≤ 3) clusters) one central message: that catalyticreactivity of this type of bimetallic oxide system is expected tobe correlated more strongly with oxygen-rich environmentthan the choice of any specific TM atoms. The latter is,however, conventionally believed to play the lead role incatalysis. The present work, therefore, originates by addressingthis open question: out of four chosen TM atoms, viz., Cr, Fe,Co, and Ni, which one should be the best choice for catalysis

and why? It is interesting to understand the explicit role of TMdespite that one should aim for O-rich environment conditionsfor synthesis of these catalysts.A charge transfer from support to the cluster can have a

significant influence on the performance of the cluster. This iswhy charged defects are always instrumental in influencing thereactivity, stability, and selectivity of metal oxide clusters.21−23

In our former publication,20 we have introduced TMxMgyOzclusters but not commented on anything about thethermodynamic stability of charged clusters. In view of this,it is more relevant to study the charged clusters to gain insightinto how an excess or deficiency of charge density willinfluence its thermodynamic stability as well as catalyticproperties. Note that in heterogeneous catalysis TM nano-particles, at various charge states, exhibit significant variationsas a function of size in their physicochemical nature andelectronic properties. In the presence of a realistic reactiveatmosphere (i.e., temperature (T), pressure (p), and doping),clusters change their stoichiometry by adsorbing the ligands(usually oxygen) from the environment, under certainconditions.24 This new composition (with specific activesites) may work as an active (functional) material. Therefore,one has to understand the functional properties of clusters in atechnologically relevant atmosphere. However, the unambig-

Received: February 19, 2019Revised: May 21, 2019Published: June 7, 2019

Article

pubs.acs.org/JPCCCite This: J. Phys. Chem. C 2019, 123, 15495−15502

© 2019 American Chemical Society 15495 DOI: 10.1021/acs.jpcc.9b01619J. Phys. Chem. C 2019, 123, 15495−15502

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uous identification of active sites, detailed insight of elementarysteps of the reaction process, the selectivity, and the stability ofintermediate products are sometimes a daunting task due tothe complexity involved in catalytic processes.Theory and computation have played an important role in

understanding and predicting chemical reactivity of variousTM-oxide catalysts at the nanoscale. Gas-phase metal clustershave been considered to be versatile model systems to explorethe basic principles of catalytic reaction mechanisms at amolecular level. Previous reports have identified a directcorrelation between the products yielded in gas-phase clustercalculations and condensed-phase catalytic reactions.25,26 Forinstance, oxidation of ethylene by V2O5

+ and V4O10+ clusters is

in exact agreement with that occurring over Vanadia surfaces.25

Similarly, the reaction mechanism of oxidation of methanol byMoxOy

+ clusters is found in direct correspondence to reactionswhich occur over their bulk-surface counterpart.26 Therefore,in the last decades, there has been an increasing interest inunderstanding the physicochemical properties of gas-phaseclusters.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 aswell as charged clusters to analyze their thermodynamicstability. Following this, we have explicitly calculated theactivation barrier of bi-metallic clusters to abstract the first C−H bond from the methane. This step is considered to be a rate-determining step for a catalyst to convert methane intovaluable chemical products.33−41 Numerous interesting studiesfor C−H bond activation of methane at room temperature byvarious (noble metals40−43 and homonuclear38,39,44−46 andheteronuclear35,36,47−50 metal oxides) gas-phase clusters havebeen reported. Among them, noble-metal-based bi-metallicclusters (i.e., RhAl3O4

+, RhAl2O4−, PtAl2O4

−, AuV2O6+, and

AuTi3O7,8− ) exhibit high activity for methane activa-

tion.33,47,51−53 However, their high cost and the limitedavailability limit their commercialization. Therefore, currently,researchers are extensively focused on finding the mostpromising substitutes based on non-noble active transitionmetals with high activity, low cost, and formidable abundance.From the literature, to the best of our knowledge, there are notmany reports on this topic to date. We find only Li et al. havestudied the activation of methane on transition-metal-dopedmagnesium oxide clusters.50 In view of this, we aim to addressthe activity of non-noble metal (Cr, Fe, Co, and Ni) basedMgO clusters. By analyzing the barrier height of the first C−Hbond activation of methane on different cluster configurations,we have established a direct correlation of the fundamental gapwith the activation barrier of a catalyst. Here, in addition tothat, we have addressed the presence of active centers in thesebi-metallic oxide clusters to facilitate the first C−H bonddissociation in the context of methane activation. Moreover,we have explicitly provided the information on the governingfactors (including the role of TMs, electronic structures, andthe charged states) of the active center to improve its reactivityfor methane oxidation. Further, the aim of the study is toaddress the role of charged states in the thermodynamicstability of the clusters and their efficiency in reducing theactivation barrier for the reaction kinetics for methaneoxidation.

■ 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 valueof z (no. of oxygen atoms) from zero to the saturation value,where no more oxygen atom can be absorbed by the cluster. Asa first step, we have used a massively parallel cascade geneticalgorithm (cGA) to thoroughly scan the potential energysurface (PES) to determine all possible low-energy structures(including the global minimum). The term “cascade” means amultistepped algorithm where successive steps employ higherlevel of theory and each of the next level takes informationobtained at its immediate lower level. Typically, a cGAalgorithm starts with classical force field and goes up toDensity Functional Theory (DFT) with hybrid functionals[see ref.24,54,55 for details of this cGA implementation, accuracyand validation].All the DFT calculations are carried out using FHI-aims

code,56 which is an all-electron calculation using the numericatom centered basis set. The low energy structures obtainedfrom the cGA are further optimized at higher level settings. Inthis step, the vdW-corrected (Tkatchenko−Schefflerscheme57) PBE+vdW58 exchange and correlation (εxc) func-tional is used. The atomic forces are converged up to 10−5 eV/Å using “tight” settings with “tier 2” basis set as implementedin FHI-aims code. The atomic zero-order regular approx-imation (ZORA) is considered for the scalar relativisticcorrection.56,59 Finally, the total single-point energy iscalculated on top of this optimized structure using the vdW-corrected-PBE060 hybrid εxc functional (PBE0+vdW), with“tight-tier 2” settings. It is reported that PBE+vdW highlyoverestimates the stability of clusters containing a largerconcentration of O atoms.54 This results in a qualitativelywrong prediction of O2 adsorption for O-rich cases. Suchbehavior is not confirmed by hybrid functionals [e.g HSE06,61

PBE0] as employed in our calculations. The difference inenergetics of PBE0 and HSE06 is always within 0.04 eV.20 Thespin states of the clusters are also different as found by PBEand PBE0/HSE06. In view of this, we have used a hybridfunctional (PBE0) with tight numerical settings and tier 2 basisset 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 theorywithin the GW approximation. We have calculated Eg at thelevel of G0W0@PBE0 with “really tight” numerical settings andtier 4 basis set.56 To determine the structure of the transitionstate (TS) and to find the minimum energy path for first C−Hbond activation of methane on bi-metallic clusters, we haveused FHI-aims code using the PBE εxc functional asimplemented in aims-chain feature for the nudged elasticband method (NEB) calculations. We have analyzed thevibrational frequencies of TS to confirm the one imaginaryfrequency in the direction of the reaction coordinate.

■ RESULTS AND DISCUSSIONS

Determinat ion of the Stab le Phases of[TMxMgyOz]

+/0/− Clusters. After generating the structures ofall the low energy isomers [see Figure S1 in SupportingInformation (SI)] of [TMxMgyOz]

+/0/− clusters (TM = Cr, Fe,Co, Ni with x + y ≤ 5) using the cascade genetic algorithm, westudy the thermodynamic stabi l i ty of gas-phase

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[TMxMgyOz]+/0/− clusters in an oxygen atmosphere using the

ab initio atomistic thermodynamics (aiAT) approach.62 Herewe assume when a bi-metallic cluster is exposed in a reactiveatmosphere of gas-phase O2 it will react with the atmospheredepending on environmental conditions (viz. T, pO2

, and

doping63) via the following equation

F[ ] + [ ]zTM Mg

2O TM Mg Ox y

qx y z

q2 (1)

q is the electric charge of the cluster. Here, we have used “+”for cationic clusters with charge +1, “0” for neutral, and “−” forthe anionic clusters with charge −1. Since the ligand O2 is aneutral species, the charge q remains the same during thereaction.64 Using aiAT, we determine the Gibbs free energy offormation of all the [TMxMgyOz]

q structures as a function ofT, pO2

, and chemical potential of electrons (μe). The most

preferred composition at a given T, pO2, and μe, relevant for the

experiments, will be the one with the minimum Gibbs freeenergy of formation at the experimental conditions. This isshown in the following equation:

μ μ

Δ = −

− × + ×

[ ] [ ]G T p F T F T

z T p q

( , ) ( ) ( )

( , )

f O TM Mg O TM Mg

O O e

x y zq

x y20

2 (2)

Here, [ ]F T( )TM Mg Ox y zq and [ ]F T( )TM Mgx y

0 are the Helmholtz free

energies of the cluster + ligands [ ]TM Mg Ox y zq and the pristine

[ ]TM Mgx y0 cluster, respectively. The clusters are at their

ground-state configuration with respect to geometry and spinstate. The term μ T p( , )O O2

is the chemical potential of an

oxygen atom (μ μ=O12 O2

). The range of μe is taken from bulk

MgO.65 The free energy of each stoichiometry (cluster +ligands, pristine cluster) and the chemical potential of O2 haveevaluated from the corresponding partition functions includingtranslational, rotational, vibrational, electronic, and configura-tional degrees of freedom. The dependence of μ T p( , )O O2

on

T and pO2is calculated using the ideal (diatomic) gas

approximation with the same DFT functional as for theclusters. The details of this methodology can be found in ref24. Following this, a three-dimensional (3D) phase diagram forall possible combinations of x + y ≤ 5 (y ≠ 0) of[TMxMgyOz]

+/0/− clusters is constructed to identify the lowestfree energy composition and structure at a specific T, pO2

, and

μe condition (see Figure 1 where one specific case for x = 2, y= 2 is shown). From these types of phase diagrams, the stablecompositions at a given environmental condition of[TMxMgyOz]

q clusters can be determined. Here, on the x-axis ΔμO is varied in accordance with the corresponding T andpO2

. On the y-axis, μe is varied from the valence band maximum

to the conduction band minimum of the bulk MgO. On the z-axis the negative ΔG T p( , )f O2

values are plotted so that only

the most stable phases are visible from the top. In Figure 1(a−d), the phase diagrams of [TM2Mg2Oz]

+/0/− clusters are shownas one of the representative cases for four different TMs, viz.,Cr, Fe, Co, and Ni, respectively. From Figure 1(a−d), it can beinferred that at lower values of μe (i.e., close to the HOMOlevel at −7.5 eV; implying p-type doping conditions) neutralclusters are more stable, whereas at higher values of μe (i.e.,

close to LUMO level at 0 eV; implying n-type doping) anionicclusters are more stabilized. For example, in the case of TM =Cr, we see from Figure 1a that at fixed T = 300 K for values μesuitable for p-type doping and at lower values of pO2

,

(Cr2Mg2O8)0 is the most stable phase, whereas as we increase

the pO2, (Cr2Mg2O10)

0 is the most preferable phase in the

phase diagram. However, if we set μe to the values suitable ton-type doping at lower pO2

, (Cr2Mg2O8)− is the stable phase,

and on increasing the pO2, (Cr2Mg2O10)

− is favorable at

ambient pO2, and (Cr2Mg2O12)

− becomes a stable config-

uration at higher pO2. This trend of enhanced stability of

neutral and anionic clusters, respectively, for lower and highervalues of μe (i.e., at a given doping condition) with varying pO2

is also followed for other TMs (viz. Fe [Figure 1b], Co [Figure1c], and Ni [Figure 1d]). We have further noticed from thesephase diagrams that at ambient environmental conditions (i.e.,T = 300 K, pO2

= 1 atm) nonstoichiometric O-rich clusters are

the most stable phases in all the cases. Following thisrepresentative case (with x = 2 and y = 2), we have verifiedall possible combinations of x and y by limiting x + y ≤ 5 to seethe trends at other sizes. We have found that the observedtrend in thermodynamic stability holds at other values of x, y aswell and are in line to this representative case of x = 2 and y =2: i.e., (i) positively charged clusters are not stable throughoutthe 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 nowimportant to understand their catalytic properties fromelectronic structure analysis.

Correlation of Fundamental Gap (Eg) vs C−H BondActivation Barrier (Ea) of a Catalyst. A catalyst is expected

Figure 1. 2D view of 3D phase diagrams obtained for neutral andionic [TM2Mg2Oz]

+/0/− clusters in the reactive atmosphere of O2.Colored regions show the most stable compositions in a wide range ofpressures and μe 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.

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to be more effective, if it can accept or donate electrons moreeasily.55,66 Therefore, if a particular cluster has simultaneouslyhigh electron affinity (EA) and low ionization potential (IP), itis expected to act as a good catalyst. This means the clustershould have a low fundamental gap (Eg), which is simply thedifference between IP and EA. Over the past, Eg has beenassumed in many instances to act as one of the descriptors tocorrelate reactivity of a catalyst,20,55,66−71 and for TM-basedMgO clusters (viz., TMxMgyOz), we, presumably for the firsttime, 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 bondactivation 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

density at each atom is also shown, whose relevance isdiscussed later. The structure in Figure 2a is the globalminimum (GM) isomer, whereas the other two are low energyisomers lying within 2 eV from the GM. These three structuresare used to estimate the C−H bond activation energy. InFigure 3, we have shown six different cases for the C−H bondactivation on various configurations of the Ni2Mg2O5 cluster.We have compared the Ea values for the GM structure withone of the metastable isomers (see Figure 3a and c). We seethat a smaller Ea is associated with the metastable isomer thanthe GM as a catalyst. Therefore, the metastable isomer shouldbe a better catalyst than the GM structure, and this observationis inline to the Eg values of the respective clusters. The Eg ofthe metastable structure is indeed lower than the Eg of the GMstructure. This clear correlation between Eg and Ea holds formost of the cases with a few exceptions, where they do notfollow exactly the same trend. For example, if some structuralfeature of a specific catalyst starts working as an active center, itenhances its catalytic activity drastically. Let us focus on thethird isomer shown in Figure 2c and compare it with thestructure as in Figure 2b. The catalytic behavior of these tworespective clusters is shown in Figure 3e and 3c. We see[Figure 3e and 3c] the former structure [i.e., Figure 2c] has asmaller Eg but not Ea than the latter structure as shown inFigure 2b.The reason can easily be understood from identifying the

active site present in the structure shown in Figure 2b byanalyzing its hirshfeld charge distribution, but before this let usnote a few important points. We find that the methanemolecule gets adsorbed to the Mg atom site (see Figure S2).This is due to the presence of more positive charge density inMg atoms than the nearby TM atoms (see Figure S3 andFigure 2 for the Ni2Mg2O5 cluster). After C−H bond

activation, the H atom favors the O atom site which is morenegatively charged as compared to other O atoms in the cluster(see Figures S2, S3, and S4 for details), and the CH3 moleculegets adsorbed at the Mg site. Note that the C−H bondactivation energy depends on the charge density of the Oatom, where the H atom tends to make a bond afterdissociating from CH4. For example, at the most negativelycharged O site the Ea is lower (82.44 kJ/mol) than that on theother less negatively charged O site (115.68 kJ/mol) (seeFigure S4). Therefore, in Figure 3, for the GM structure, all theO atoms have an approximately equally distributed charge(≈−0.41e) due to the nature of the symmetry in the positionof atoms. On the other hand, the metastable structures aresomewhat asymmetric in nature. Thus, it has some O atoms,where localized negative charge exists. This makes the site ableto act as an active center. In Figure 2b and 2c, such cases areshown. Note that in Figure 2b one O atom with charge density≈−0.63e is present to act as an active site, whereas in Figure2c, two such localized orbitals are noticed, both with charge(≈−0.50e). The latter structure is less active than the formeras two O sites effectively reduce the overall activity as in theformer structure with one active O site (Figure 2b). Therefore,both the metastable structures are having smaller Ea and Egthan the GM structure, but the former one is supposed to bemore effective with a reduced Ea than the latter one despitehaving a smaller gap than the former. We have obtained betteractivity for C−H bond activation on Ni-based bi-metallic

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

Figure 3. Minimum energy pathway of the first C−H bond activationof methane on GM of the neutral (Ni2Mg2O5)

0 cluster (a), negativelycharged (Ni2Mg2O5)

− (b), metastable structure of the (Ni2Mg2O5)cluster in the neutral state (c and e), and the metastable structure ofthe Ni2Mg2O5 cluster in negatively charged state (d and f). Reactioncoordinates of the initial (R), final (P), transition state (TS), andintermediates are shown. Activation barriers (Ea) for all cases are alsoindicated in the respective graphs in kJ/mol. The fundamental gaps Egof the clusters in all cases are shown in eV.

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clusters than the cationic gold cluster (Au3+) reported by Lang

et al. (131.33 kJ/mol).40 However, the activity of these clustersis slightly less as compared to the noble-metal-based bi-metallicoxide clusters.33,52

From the phase diagram (as in Figure 1), the most stablephases are either neutral clusters (under p-typed dopedcondition) or negatively charged clusters (under n-typedoped condition). Therefore, we have also shown theactivation energy to break the C−H bond by negativelycharged clusters. In fact, we have noticed that the chargedclusters are more effective in doing the same. In the case ofGM (see in Figure 3a and b), Ea for C−H bond activation by anegatively charged cluster is found to be much lower (99.21kJ/mol) than the neutral one (139.95 kJ/mol). The trends inEg for the (Ni2Mg2O5)

−1 and (Ni2Mg2O5)0 are also in

agreement with the respective Ea values. Further, we havealso noticed a remarkable reduction in C−H bond activationbarrier Ea by negatively charged metastable clusters (see inFigure 3d and f). On adsorbing one electron, the clusterspossess localized charge, which acts as an active center toreduce the C−H bond activation barrier. Therefore, thisanalysis concludes that a smaller value of Eg is usuallyassociated with a lowered C−H bond activation barrier Ea. Thelatter gets further reduced if the structure also has one activecenter with localized charged density. Note that it iscomputationally very expensive to calculate Ea values of allthe stable configurations of [TMxMgyOz]

+/0/− clusters tounderstand their catalytic activity. However, a very goodqualitative description can be drawn for the same, fromcomparing the respective Eg values (estimated with G0W0@PBE0) of all the isomers relevant at realistic experimentalconditions.Eg is a Descriptor for Catalytic Activity. We have

considered all the neutral and ionic (-ve) clusters of the dataset ([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 neutralclusters (black points). However, it should be mentioned herethat there are some scattered red points showing larger Eg. Wehave manually checked those data points (clusters) and foundthat the corresponding Eg of the neutral cluster is even higher.Note that this figure gives only overall qualitative trend but notany quantitative information on individual clusters to identifythe Eg for neutral cluster and the same with one additionalelectron. This quantitative information is given in Tables S1,S2, S3 and S4, where for all the data set points the Eg values ofboth neutral and negatively charged clusters are given. Fromthis data set, it can be clearly seen that the negatively chargedclusters consistently have smaller Eg than its neutral counter-part (except for only a few cases). Therefore, for sure thenegatively charged clusters are expected to be a better catalystthan 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 choiceof any specific TM atoms. This observation is in line with ourformer publication,20 where we have shown that highercatalytic reactivity is correlated more strongly with the oxygencontent in the cluster than with any specific TM type.However, despite that TM atoms do not have much role tocontrol the Eg, they give rise to different structural motifs in theTMxMgyOz clusters with respective TM components [seeFigure S1 in SI]. For some TMs, the structures containmolecular O2, whereas in some other cases, this O2 getsdissociated and is adsorbed in atomic form. This is due to thepresence of different numbers of unpaired electrons in theouter shell of the TM atoms, giving rise to different types ofstructural features. This may play a significant role in catalysisas active centers. It is therefore important to understand thesestructural differences in TMxMgyOz clusters with various TMatoms.

Structural Analysis: Radial Distribution Function ofTMxMgyOz Clusters. In order to present a quantitativeunderstanding of the structural motifs, in Figure 5(a−d), wehave shown the radial distribution function (RDF) for variousTMxMgyOz clusters with four different TM atoms (viz., Cr, Fe,Co, and Ni and z = [1−13]). Note that, in general, there arethree types of molecular O2 adsorption in O-rich bi-metallicTMxMgyOz clusters, viz., at the atop site of the metal atom,parallel site, and cross-bridge site.72,73 The bond length of theO2 moiety is highly dependent on the kind of adsorption atvarious mentioned sites. This is ≈1.33, 1.35, and 1.57 Å for theatop, parallel, and cross-bridge site, respectively (see Figure5e). It should be mentioned here that the calculated bondlength for isolated molecular oxygen O2 is 1.22 Å, whereas thesame for O2

−1 (superoxo) and O2−2 (peroxo) are 1.36 and 1.6 Å,

respectively. Thus, a superoxo moiety is formed when O2 isadsorbed at the atop and parallel sites, whereas a peroxomoiety is formed at the cross-bridge site. The bond length ofO2

−1 (1.36 Å) is approximately equal to the bond length of O2moieties at atop (1.33 Å) and parallel sites (1.35 Å), and O2moieties at the cross site have the bond length comparable tothe bond length of O2

−2. Oxygen ions O2−1 and O2

−2 are thereactive species that enhance the reaction of methane oxidationon bi-metallic oxide clusters as catalyst.74

In Figure 5, the first-order peaks (orange colored) in allcases correspond to the O2 adsorption at atop and parallelsites. The first-order peaks (orange colored) are more intense(see Figure 5c and Figure 5d) for Co- and Ni-based bi-metallicclusters. 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.

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second-order peaks (blue colored) represent the (TM−O)bond length, where one dangling oxygen atom is bonded onlyto 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 bi-metallic clusters. Therefore, the blue colored peaks are absentin Figure 5c and 5d. This signifies that in Cr- and Fe-based bi-metallic clusters a dissociative adsorption of O2 is morefavorable. On the other hand, in Co- and Ni-based bi-metallicclusters a molecular adsorption of O2 is favored. Note that thelatter is the prerequisite for methane oxidation reaction.Further, we have noticed another peak of very reducedintensity (maroon color) next to the orange colored peak as inFigure 5c and 5d. This peak represents the bond length of O2moieties bonded at the cross-bridge site (bond length is thesame as the TM−O bond). Note that O2 moieties bonded atthe cross-bridge site have more electronic interaction withmetal atoms in clusters as compared to O2 moieties at the atopsite. Therefore, the bond length of the cross-bridge O2 moietyis comparatively higher than atop moieties. However, with theincrease of the number of TM atoms in the clusters,dissociative adsorption of oxygen is increased. This informa-tion should be very useful in the kinetic study to propose areaction mechanism.

■ CONCLUSIONIn summary, we have presented a robust methodology to studythe catalytic activity of small TM-based bi-metallic oxideclusters. As a first step we have used a massively parallelcascade genetic algorithm to determine all the low energyisomers. The thermodynamic stability of such structures isdetermined by minimizing their Gibbs free energy of formationusing an ab initio atomistic thermodynamics method. A smallerC−H bond activation barrier is noticed when the clusterpossesses both a smaller fundamental gap along with an active

center for higher catalytic activity. The negatively chargedclusters are in general more promising candidates for havingsmaller activation barrier with high stability. The role of TMstoward controlling the activation barrier is less. However, thenature of TMs determines the favorable type of O2 adsorption.Since Co- and Ni-based clusters favor molecular O2adsorption, they are expected to have a better catalyticperformance among various TMxMgyOz clusters.

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.jpcc.9b01619.

(I) Global minimum (GM) structures of TMxMgyOz (z= 1.8) set of clusters. (II) Activation energy for the firstC−H bond activation of a methane molecule on the Ni-based bi-metallic clusters. (III) Fundamental gap (Eg) ofall the sets of clusters [TMxMgyOz]

0/− at the level ofG0W0@PBE0 with “really tight” numerical settings(PDF)

■ AUTHOR INFORMATIONCorresponding Authors*E-mail: shikha.saini@physics.iitd.ac.in.*E-mail: saswata@physics.iitd.ac.in. Phone: +91-2659 1359.Fax: +91-2658 2037.ORCIDSaswata Bhattacharya: 0000-0002-4145-4899NotesThe authors declare no competing financial interest.

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

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