Unraveling Thermodynamic Stability, Catalytic Activity and Electronic

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Unraveling Thermodynamic Stability, Catalytic Activity and Electronic Structure of [TMxMgyOz] Clusters at Realistic Conditions: A Hybrid DFT and ab initio Thermodynamics Study +/0/-

Shikha Saini, Pooja Basera, Ekta Arora, and Saswata Bhattacharya J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b01619 • Publication Date (Web): 07 Jun 2019 Downloaded from http://pubs.acs.org on June 8, 2019

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The Journal of Physical Chemistry

Unraveling Thermodynamic Stability, Catalytic Activity and Electronic Structure of [TMxMgy Oz ]+/0/ Clusters at Realistic Conditions: A Hybrid DFT and Ab initio Thermodynamics Study Shikha Saini⇤ , Pooja Basera, Ekta Arora, Saswata Bhattacharya⇤ Dept. of Physics, Indian Institute of Technology Delhi, New Delhi 110016 E-mail: [email protected][SS],[email protected][SB] Phone: +91-2659 1359. Fax: +91-2658 2037 Abstract Aiming towards catalytic applications, a large data set is generated on [TMx Mgy Oz ]+/0/ clusters (TM = Cr, Ni, Fe, Co, 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 pO2 . A thermodynamic phase diagram is drawn by minimizing Gibbs free energy of formation to identify the stable phases of neutral and charged [TMx Mgy Oz ]+/0/ clusters. From this analysis, we notice that neutral 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

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find that the nature of TM atoms towards controlling the activation barrier is less important. However, the TM gives rise to different structural motifs in the cluster, which may act as active centres for catalysis.

Introduction Transition metals (TMs) are well known for their efficient homogeneous and heterogeneous catalytic activity. 1,2 In heterogeneous catalysis, transition metal (TM) oxide nano-particles (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 the 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 TMx Mgy Oz (TM=Co, Ni, Fe, Cr and x+y  3) clusters) one central message; that catalytic reactivity of this type of bi-metallic 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 addressing this open question that out of four chosen TM atoms viz. Fe, Cr, Co, Ni, which one should be the best choice for catalysis and why? It’s interesting to understand the explicit role of TM despite one should aim for O-rich environment condition 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 being instrumental to 2


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influence the reactivity, stability and selectivity of metal oxide clusters. 21–23 In our former publication, 20 we have introduced TMx Mgy Oz clusters but not commented on anything on the thermodynamic stability of charged clusters. In view of this, it is more relevant to study the charged clusters to gain insights on how an excess or deficiency of charge density will influence its thermodynamic stability as well as catalytic properties. Note that in heterogeneous catalysis, TM nano-particles, at various charge states, exhibit significant variations as a function of size in their physico-chemical 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 active (functional) material. Therefore, one has to understand the functional properties of clusters in a technologically relevant atmosphere. However, the unambiguous 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 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 V2 O5 + and V4 O10 + clusters is in exact agreement to that occurring over Vanadia surfaces. 25 Similarly, the reaction mechanism of oxidation of methanol by Mox Oy + clusters is found in direct correspondence to reaction which occur over their bulk-surface counterpart. 26 Therefore, in last decades, there has been an increasing interest in understanding the physico-chemical properties of gas-phase clusters. 15,27–32 In this article, we have generated a large data set [TMx Mgy Oz ]+/0/ 3


(TM = Cr, Fe,


Co, Ni with x + y  5) (even bigger than the former publication 20 TMx Mgy Oz (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 rate determining 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-metals, 40–43 homonuclear 38,39,44–46 and heteronuclear 35,36,47–50 metal oxides) gas phase clusters have been reported. Among them noble metal based bi-metallic clusters (i.e. RhAl3 O4 + , RhAl2 O4 , PtAl2 O4 , AuV2 O6 + and AuTi3 O7,8 ) exhibit high activity for methane activation . 33,47,51–53 However, high cost and the limited availability limits their commercialization. Therefore, currently, researchers are extensively focused to find 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 until 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 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 centres 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 of the governing factors (including the role of TMs, electronic structures and the charged states) on the active centre to improve its reactivity for methane oxidation. Further, the aim of the study is to address the role of charged states on the thermodynamic stability of the clusters and their efficiency in reducing the activation barrier for the reaction kinetics for methane oxidation.

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Methodology We have generated a large data set of bi-metallic oxide [TMx Mgy Oz ]+/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 multi-stepped 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 upto 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 numeric atom centered basis set. The low energy structures obtained from the cGA are further optimized at higher level settings. In this step vdW-corrected (Tkatchenko-Scheffler scheme 57 ) PBE+vdW 58 exchange and correlation (✏xc ) 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 vdW-corrected-PBE0 60 hybrid ✏xc functional (PBE0+vdW), with “tight - tier 2” settings. It is reported that PBE+vdW highly overestimates stability of clusters containing larger concentration of O-atoms. 54 This results in a qualitatively wrong prediction of O2 adsorption for O-rich cases. Such behaviour 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 hybrid functional (PBE0) with tight numerical settings and tier 2 basis set to compute 5



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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 state-of-the-art many-body perturbation theory within the GW approximation. We have calculated Eg at the level of G0 W0 @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 PBE ✏xc functional as implemented in aims-chain feature for doing 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.

Results and Discussions Determination of the stable phases of [TMx Mgy Oz ]+/0/ clusters After generating the structures of all the low energy isomers [see Figure S1 in Supporting Information (SI)] of [TMx Mgy Oz ]+/0/

clusters (TM = Cr, Fe, Co, Ni with x + y 

5) using cascade genetic algorithm, we study the thermodynamic stability of gas-phase [TMx Mgy Oz ]+/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 , pO2 and doping 63 ) via the following equation: z [TM xMg y] q + O2 )* [TM xMg yO z] 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 [TMx Mgy Oz ]q structures as a 6


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function of T , pO2 , and chemical potential of electron (µe ). The most preferred composition at a given T , pO2 and µe , relevant for the experiments, will be the one that is having the minimum Gibbs free energy of formation at that experimental conditions. This is shown in the following equation: Gf (T, pO2 ) = F[TMx Mgy Oz ]q (T )

F[TMx Mgy ]0 (T )

(2)

z ⇥ µO (T, pO2 ) + q ⇥ µe Here, F[TMx Mgy Oz ]q (T ) and F[TMx Mgy ]0 (T ) are the Helmholtz free energies of the cluster+ligands [TMx Mgy Oz ]q and the pristine [TMx Mgy ]0 cluster respectively. The clusters are at their ground state configuration with respect to geometry and spin state. The term µO (T, pO2 ) is 1 the chemical potential of an oxygen atom (µO = µO2 ). The range of µe is taken from bulk 2 65 MgO. The free energy of each stoichiometry (cluster+ligands, pristine cluster) and the chemical potential of O2 was evaluated from the corresponding partition functions including translational, rotational, vibrational, electronic and configurational degree of freedom. The dependence of µO (T, pO2 ) on T and pO2 is calculated using the ideal (diatomic) gas 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 6= 0) of [TMx Mgy Oz ]+/0/ clusters is constructed to identify the lowest free 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 type of phase diagrams, the stable compositions at a given environmental condition of [TMx Mgy Oz ]q clusters can be determined. Here, on x-axis

µO is varied in accordance with the corresponding T and pO2 .

On y-axis µe is varied from valence band maximum to conduction band minimum of the bulk MgO. On z-axis the negative

Gf (T, pO2 ) values are plotted so that only the most stable

phases are visible from the top. In Figure 1 (a-d), the phase diagrams of [TM2 Mg2 Oz ]+/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. 7



close to HOMO level at -7.5 eV; implying p-type doping condition) neutral clusters are more stable, whereas at higher values of µe (i.e. close to LUMO level at 0 eV; implying n-type doping) anionic clusters get more stabilized. For example in case of TM = Cr, we see from

Figure 1: 2D view of 3D phase diagrams obtained for neutral and ionic [TM2 Mg2 Oz ]+/0/ clusters in the reactive atmosphere of O2 . Coloured regions show the most stable compositions in wide range of pressures and µe under thermodynamic equilibrium. In (TM2 Mg2 Oz )+/0/ clusters, TM = Cr (a), Fe (b), Co (c) and Ni (d). The top axis is representing the pressure of oxygen at T = 300 K. Figure 1a that at fixed T = 300 K for values µe suitable for p-type doping and at lower values of pO2 , (Cr2 Mg2 O8 )0 is the most stable phase, whereas, as we increase the pO2 , (Cr2 Mg2 O10 )0 is the most preferable phase in the phase diagram. However, if we set µe to the values suitable to n-type doping at lower pO2 , (Cr2 Mg2 O8 ) is the stable phase and on increasing the pO2 , (Cr2 Mg2 O10 ) is favourable at ambient pO2 and (Cr2 Mg2 O12 ) becomes stable configuration 8


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at higher pO2 . This trend of enhanced stability of neutral and anionic clusters respectively for lower and higher values of µe (i.e. at a given doping condition) with varying pO2 is also followed for other TMs (viz. Fe [Figure 1b], Co [Figure 1c], Ni [Figure 1d]). We have further noticed from these phase diagrams that at ambient environmental condition (i.e. T = 300 K, pO2 = 1 atm) non-stoichiometric O-rich clusters are the most stable phases in all the cases. Following this one 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) non-stoichiometric O-rich phases (with charge 0/ ) are more favourable at ambient conditions. After identification of all the stable (and / or meta-stable) configurations at a realistic environmental condition it’s 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 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 ionisation 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 is been assumed in many instances to act as one of the descriptors to correlate reactivity of a catalyst, 20,55,66–71 for TMs based MgO clusters (viz. TMx Mgy Oz ), 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 [TMx Mgy Oz ]+/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 Ni2 Mg2 O5 clusters as shown in Figure 2. The electronic charge density at each atom is also shown, whose relevance is 9



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

Figure 2: Electronic structures of Ni2 Mg2 O5 cluster (global minimum (a), meta-stables (b and c)). Coloured surface represents the hirshfeld charge density in the cluster. different cases for the C H bond activation on various configurations of Ni2 Mg2 O5 cluster. We have compared the Ea values for the GM structure with one of the meta-stable isomers (see Figure 3a and c). We see a smaller Ea is associated with the meta-stable isomer than the GM as a catalyst. Therefore, the meta-stable 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 meta-stable 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 active centre, it enhances its catalytic activity drastically. Let’s focus on the third isomer shown in Figure 2c and compare it with the structure as in Figure 2b. The catalytic behaviour of these two respective clusters is shown in Figure 3e and 3c. We see [Ref: Figure 3e and 3c] the former structure [i.e. Figure 2c] is having 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 into 10


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Figure 3: Minimum energy pathway of first C H bond activation of methane on GM of neutral (Ni2 Mg2 O5 )0 cluster (a), negatively charged (Ni2 Mg2 O5 ) (b), meta-stable structure of (Ni2 Mg2 O5 ) cluster in neutral state (c and e), and meta-stable structure of Ni2 Mg2 O5 cluster in negatively charge state (d and f). Reaction coordinate of 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 gap Eg of the clusters in all cases are shown in eV. Mg atoms than the nearby TM atoms (see Figure S3 and Figure 2 for Ni2 Mg2 O5 cluster). After C H bond activation, the H atom favours that O-atom site which is more negatively charged as compared to other O-atoms in the cluster (see Figure S2, S3 and S4 for details) and CH3 molecule gets adsorbed at 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 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 11



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equally distributed charge (⇡ -0.41e) due to the nature of the symmetry in the position of atoms. On the other hand, the meta-stable structures are somewhat asymmetric in nature. Thus, it has some O-atoms, where localized negative charge exists. This makes the site to act as an active centre. 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 reduces 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 the better activity for C H bond activation on Ni-based bi-metallic clusters than the cationic gold cluster (Au3 + ) reported by Lang. et al. (131.33 kJ/mol). 40 However, the activity of these clusters are 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 case of GM (see in Figure 3a and b), Ea for C H bond activation by a negatively charged cluster is obtained to be much lower (99.21 kJ/mol) than the neutral one (139.95 kJ/mol). The trend in Eg for the (Ni2 Mg2 O5 )

1

and (Ni2 Mg2 O5 )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 meta-stable clusters (see in the Figure 3d and f). On adsorbing one electron the clusters possess localized charge, which acts as active centre 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 is also having one active centre 12


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with localized charged density. Note that, it’s computationally very expensive to calculate Ea values of all the stable configurations of [TMx Mgy Oz ]+/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 G0 W0 @PBE0) of all the isomers relevant at a realistic experimental conditions.

Eg is a descriptor for catalytic activity

Figure 4: Eg (G0 W0 @PBE0) of all the charged and neutral [TMx Mgy Oz ]0/ clusters of the dataset 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..13. We have considered all the neutral and ionic (-ve) clusters of the dataset ([TMx Mgy Oz ]0/ ) to plot their Eg as shown in Figure 4(a-d). Here we see the Eg of negatively charged clusters (red points) are tending 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 13



trend but not any quantitative information of individual clusters to identify the Eg for neutral cluster and the same with one additional electron. This quantitative information is given in Table 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 are consistently having smaller Eg than its neutral counter part (except for only 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 trends of Eg for the choice of any specific TM atoms. This observation is inline to 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 TM atoms do not have much role to control the Eg , they give rise to different structural motifs in the TMx Mgy Oz 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 got adsorbed in atomic form. This is due to the presence of different no. of unpaired electrons in the outer shell of the TM atoms, giving rise to different types of structural features. This may play significant role in catalysis as active centres. It’s therefore important to understand these structural difference in TMx Mgy Oz clusters with various TM atoms.

Structural analysis: Radial distribution function of TMx Mgy Oz 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 TMx Mgy Oz 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 TMx Mgy Oz clusters viz. at atop site of metal atom, parallel site and cross bridge site. 72,73 Bond length of O2 moiety is 14


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highly dependent on the kind of adsorption at various mentioned sites. This is to be ⇡ 1.33 Å, 1.35 Å and 1.57 Å for 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 same for O2

1

(superoxo) and O2

2

(peroxo) are 1.36 Å, 1.6 Å

respectively. Thus, a superoxo moiety is formed when O2 is adsorbed at atop and parallel sites, whereas a peroxo moiety is formed at cross bridge site. The bond length of O2

1

(1.36

Å) is approximately equal to the bond length of O2 moieties at atop (1.33 Å) and parallel site (1.35 Å). And O2 moieties at cross site have the bond length comparable to the bond length of O2 2 . Oxygen ions O2

1

and O2

2

are the reactive species that enhance the reaction of

methane oxidation on bi-metallic oxide clusters as catalyst. 74

Figure 5: The radial distribution function for TMx Mgy Oz [TM = Cr (a), Fe (b), Co (c) and Ni (d) using all the data for all possible combination of x and y with x + y  5 and z=1..11] set of clusters. (e) visualization of different type of active moieties (cross bridge, parallel and atop) in the clusters. In Figure 5, the first order peaks (orange coloured) in all cases correspond to the O2 15



adsorption at atop and parallel sites. This first order peaks (orange coloured) are more intense (see Figure 5c and Figure 5d) for Co and Ni based bi-metallic clusters. However, in case of Cr and Fe based clusters, the second order peaks (blue coloured) represent the (TM-O) bond length where one dangling oxygen atom is bonded only to the TM atom. If we see the structures in SI (Figure S1), this TM-O case is totally absent in Co and Ni based bi-metallic clusters. Therefore, this blue coloured peaks are absent in Figure 5c and 5d. This signifies that in Cr and Fe based bi-metallic clusters, a dissociative adsorption of O2 is more favourable. On the other hand, in Co and Ni based bi-metallic clusters a molecular adsorption of O2 is favoured. Note that the latter is the prerequisite for methane oxidation reaction. Further, we have noticed another peak of very reduced intensity (maroon colour) next to orange coloured peak as in Figure 5c and 5d. This peak represents the bond length of O2 moieties bonded at cross-bridge site (bond length is same as TM-O bond). Note that O2 moieties bonded at cross-bridge site have more electronic interaction with metal atoms in clusters as compared to O2 moieties at atop site. Therefore, the bond length of cross-bridge O2 moiety is comparatively higher than atop moieties. However, with the increase of the no. of TM atoms in the clusters, dissociative adsorption of oxygen gets increased. This information should be very useful in the kinetic study to propose a reaction mechanism.

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 are determined by minimizing their Gibbs free energy of formation using ab initio atomistic thermodynamics method. A smaller C H bond activation barrier is noticed when the cluster possesses both a smaller fundamental gap alongwith an active centre for higher catalytic activity. The negatively charged clusters are in general more

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promising candidates for having smaller activation barrier with high stability. The role of TMs towards controlling the activation barrier is less. However, the nature of TMs determine the favourable type of O2 adsorption. Since Co and Ni based clusters favour molecular O2 adsorption, they are expected to have a better catalytic performance amongst various TMx Mgy Oz clusters.

Supporting Information (I) Global minimum (GM) structures of TMx Mgy Oz (z = 1..8) set of clusters. (II) Activation energy for the first C H bond activation of a methane molecule on the Ni-based bi-metallic clusters. (III) Fundamental gap (Eg ) of all the set of clusters [TMx Mgy Oz ]0/ at the level of G0 W0 @PBE0 with “really-tight” numerical settings.

Acknowledgement SS acknowledges CSIR, India, for the senior research fellowship [grant no. 09/086(1231)2015EMR-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 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.

References (1) Hill, C. L.; Prosser-McCartha, C. M. Homogeneous catalysis by transition metal oxygen anion clusters. Coord. Chem. Rev. 1995, 143, 407–455. (2) Aiken, J. D.; Finke, R. G. A review of modern transition-metal nanoclusters: Their

17



synthesis, characterization, and applications in catalysis. J. Mol. Catal. Chem. 1999, 145, 1–44. (3) Albonetti, S.; Cavani, F.; Trifiro, F. Key aspects of catalyst design for the selective oxidation of paraffins. Catal. Rev. 1996, 38, 413–438. (4) Albonetti, S.; Cavani, F.; Trifiro, F.; Venturoli, P.; Calestani, G.; Granados, M. L.; Fierro, J. G. A comparison of the reactivity of “nonequilibrated" and “equilibrated" V–P–O catalysts: structural evolution, surface characterization, and reactivity in the selective oxidation of n-butane andn-pentane. J. Catal. 1996, 160, 52–64. (5) Bañares, M. A. Supported metal oxide and other catalysts for ethane conversion: A review. Catal. Today 1999, 51, 319–348. (6) Hodnett, B. Vanadium-phosphorus oxide catalysts for the selective oxidation of C4 hydrocarbons to maleic anhydride. Catal. Rev. 1985, 27, 373–424. (7) Vining, W. C.; Goodrow, A.; Strunk, J.; Bell, A. T. An experimental and theoretical investigation of the structure and reactivity of bilayered VOx /TiOx /SiO2 catalysts for methanol oxidation. J. Catal. 2010, 270, 163–171. (8) Zhang, W.; Desikan, A.; Oyama, S. T. Effect of support in ethanol oxidation on molybdenum oxide. J. Phys. Chem. 1995, 99, 14468–14476. (9) Grasselli, R. K. Genesis of site isolation and phase cooperation in selective oxidation catalysis. Top. Catal. 2001, 15, 93–101. (10) Nikolov, V.; Klissurski, D.; Anastasov, A. Phthalic anhydride from o-xylene catalysis: science and engineering. Catal. Rev. 1991, 33, 319–374. (11) Heck, R. M. Catalytic abatement of nitrogen oxides–stationary applications. Catal. Today 1999, 53, 519–523.

18


Page 18 of 28

Page 19 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(12) Li, K.-T.; Huang, M.-Y.; Cheng, W.-D. Vanadium-based mixed-oxide catalysts for selective oxidation of hydrogen sulfide to sulfur. Ind. Eng. Chem. Res. 1996, 35, 621– 626. (13) Li, J.; Wu, X.-N.; Schlangen, M.; Zhou, S.; González-Navarrete, P.; Tang, S.; Schwarz, H. On the Role of the electronic structure of the heteronuclear oxide cluster [Ga2 Mg2 O5 ].+ in the thermal activation of methane and ethane: An unusual doping effect. Angew. Chem. Int. Ed. 2015, 54, 5074–5078. (14) Kwapien, K.; Paier, J.; Sauer, J.; Geske, M.; Zavyalova, U.; Horn, R.; Schwach, P.; Trunschke, A.; Schlögl, R. Sites for methane activation on Lithium-doped magnesium oxide surfaces. Angew. Chem. Int. Ed. 2014, 53, 8774–8778. (15) Li, J.; Zhou, S.; Zhang, J.; Schlangen, M.; Weiske, T.; Usharani, D.; Shaik, S.; Schwarz, H. Electronic origins of the variable efficiency of room-temperature methane activation by homo-and heteronuclear cluster oxide cations [XYO2 ]+ (X, Y= Al, Si, Mg): Competition between proton-coupled electron transfer and hydrogen-atom transfer. J. Am. Chem. Soc. 2016, 138, 7973–7981. (16) Zhao, Y.-X.; Wu, X.-N.; Ma, J.-B.; He, S.-G.; Ding, X.-L. Experimental and theoretical study of the reactions between vanadium- silicon heteronuclear oxide cluster anions with n-Butane. J. Phys. Chem. C 2010, 114, 12271–12279. (17) Baca, M.; Pigamo, A.; Dubois, J.; Millet, J. Propane oxidation on MoVTeNbO mixed oxide catalysts: study of the phase composition of active and selective catalysts. Top. Catal. 2003, 23, 39–46. (18) Burriesci, N.; Garbassi, F.; Petrera, M.; Petrini, G. Influence of the bulk and surface properties on the performance of iron–antimony catalysts. J. Chem. Soc., Faraday Trans. 1 1982, 78, 817–833.

19



(19) Soares, A. P. V.; Portela, M. F.; Kiennemann, A. Methanol selective oxidation to formaldehyde over iron-molybdate catalysts. Catal. Rev. 2005, 47, 125–174. (20) Saini, S.; Sarker, D.; Basera, P.; Levchenko, S. V.; Ghiringhelli, L. M.; Bhattacharya, S. Structure and electronic properties of transition-metal/Mg bimetallic clusters at realistic temperatures and oxygen partial pressures. J. Phys. Chem. C 2018, 122, 16788– 16794. (21) Schneider, W.-D.; Heyde, M.; Freund, H.-J. Charge control in model catalysis: The decisive role of the oxide–nanoparticle interface. Chem.: Eur. J. 2018, 24, 2317–2327. (22) Sterrer, M.; Heyde, M.; Novicki, M.; Nilius, N.; Risse, T.; Rust, H.-P.; Pacchioni, G.; Freund, H.-J. Identification of color centers on MgO (001) thin films with scanning tunneling microscopy. J. Phys. Chem. B 2006, 110, 46–49. (23) Yoon, B.; Häkkinen, H.; Landman, U.; Wörz, A. S.; Antonietti, J.-M.; Abbet, S.; Judai, K.; Heiz, U. Charging effects on bonding and catalyzed oxidation of CO on Au8 clusters on MgO. Science 2005, 307, 403–407. (24) Bhattacharya, S.; Levchenko, S. V.; Ghiringhelli, L. M.; Scheffler, M. Efficient ab initio schemes for finding thermodynamically stable and metastable atomic structures: Benchmark of cascade genetic algorithms. New J. Phys. 2014, 16, 123016. (25) Reilly, N. M.; Johnson, G. E.; Castleman, A. Model Systems in Catalysis; Springer, 2010; pp 293–317. (26) Fialko, E. F.; Kikhtenko, A. V.; Goncharov, V. B.; Zamaraev, K. I. Similarities between reactions of methanol with Mox Oy + in the gas phase and over real catalysts. J. Phys. Chem. B 1997, 101, 5772–5773. (27) Hinderling, C.; Feichtinger, D.; Plattner, D. A.; Chen, P. A combined gas-phase,

20


Page 20 of 28

Page 21 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


solution-phase, and computational study of C-H activation by cationic Iridium (III) complexes. J. Am. Chem. Soc. 1997, 119, 10793–10804. (28) Wallace, W. T.; Whetten, R. L. Coadsorption of CO and O2 on selected gold clusters: Evidence for efficient room-temperature CO2 generation. J. Am. Chem. Soc. 2002, 124, 7499–7505. (29) Socaciu, L. D.; Hagen, J.; Bernhardt, T. M.; Wöste, L.; Heiz, U.; Häkkinen, H.; Landman, U. Catalytic CO oxidation by free Au2 : Experiment and theory. J. Am. Chem. Soc. 2003, 125, 10437–10445. (30) Bernhardt, T. M.; Socaciu-Siebert, L. D.; Hagen, J.; Wöste, L. Size and composition dependence in CO oxidation reaction on small free gold, silver, and binary silver–gold cluster anions. Appl. Catal., A 2005, 291, 170–178. (31) Brönstrup, M.; Schröder, D.; Kretzschmar, I.; Schwarz, H.; Harvey, J. N. Platinum dioxide cation: Easy to generate experimentally but difficult to describe theoretically. J. Am. Chem. Soc. 2001, 123, 142–147. (32) Schwarz, H. Chemistry with methane: concepts rather than recipes. Angew. Chem. Int. Ed. 2011, 50, 10096–10115. (33) Zhao, Y.-X.; Li, Z.-Y.; Yang, Y.; He, S.-G. Methane activation by gas phase atomic clusters. Acc. Chem. Res 2018, 51, 2603–2610. (34) Schwarz, H.; Shaik, S.; Li, J. Electronic effects on room-temperature, gas-phase C–H Bond activations by cluster oxides and metal carbides: The methane challenge. J. Am. Chem. Soc. 2017, 139, 17201–17212. (35) Schwarz, H.; Gonzalez-Navarrete, P.; Li, J.; Schlangen, M.; Sun, X.; Weiske, T.; Zhou, S. Unexpected mechanistic variants in the thermal gas-phase activation of methane. Organometallics 2016, 36, 8–17. 21



Page 22 of 28

(36) Li, J.; Zhou, S.; Zhang, J.; Schlangen, M.; Usharani, D.; Shaik, S.; Schwarz, H. Mechanistic variants in gas-phase metal-oxide mediated activation of methane at ambient conditions. J. Am. Chem. Soc. 2016, 138, 11368–11377. (37) Ding, X.-L.; Wu, X.-N.; Zhao, Y.-X.; He, S.-G. C–H bond activation by oxygen-centered radicals over atomic clusters. Acc. Chem. Res. 2011, 45, 382–390. (38) Feyel, S.; Döbler, J.; Schröder, D.; Sauer, J.; Schwarz, H. Thermal activation of methane by tetranuclear [V4 O10 ]+ . Angew. Chem. Int. Ed. 2006, 45, 4681–4685. (39) Li, Z.-Y.; Zhao, Y.-X.; Wu, X.-N.; Ding, X.-L.; He, S.-G. Methane activation by yttrium-doped vanadium oxide cluster cations: Local charge effects. Chem. Eur. J. 2011, 17, 11728–11733. (40) Lang, S. M.; Bernhardt, T. M.; Chernyy, V.; Bakker, J. M.; Barnett, R. N.; Landman, U. Selective C-H bond cleavage in methane by small gold clusters. Angew. Chem. Int. Ed. 2017, 56, 13406–13410. (41) Lang, S. M.; Bernhardt, T. M.; Barnett, R. N.; Landman, U. Size-dependent binding energies of methane to small gold clusters. ChemPhysChem 2010, 11, 1570–1577. (42) Chen, Y.-M.; Armentrout, P. Activation of methane by gas-phase Rh+ . J. Phys. Chem. 1995, 99, 10775–10779. (43) Adlhart, C.; Uggerud, E. Reactions of platinum clusters Pt

n±

, n= 1–21, with CH4 : to

react or not to react. Chemical Communications 2006, 2581–2582. (44) Feyel, S.; Döbler, J.; Höckendorf, R.; Beyer, M. K.; Sauer, J.; Schwarz, H. Activation of methane by oligomeric (Al2 O3 )x + (x= 3, 4, 5): The role of oxygen-centered radicals in thermal hydrogen-atom abstraction. Angew. Chem. Int. Ed. 2008, 47, 1946–1950. (45) Schröder, D.; Roithová, J. Low-temperature activation of methane: It also works without a transition metal. Angew. Chem. Int. Ed. 2006, 45, 5705–5708. 22


Page 23 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(46) Zhao, Y.-X.; Wu, X.-N.; Wang, Z.-C.; He, S.-G.; Ding, X.-L. Hydrogen-atom abstraction from methane by stoichiometric early transition metal oxide cluster cations. Chem. Comm. 2010, 46, 1736–1738. (47) Li, Y.-K.; Yuan, Z.; Zhao, Y.-X.; Zhao, C.; Liu, Q.-Y.; Chen, H.; He, S.-G. Thermal methane conversion to syngas mediated by Rh1-doped aluminum oxide cluster cations RhAl3O4+. J. Am. Chem. Soc. 2016, 138, 12854–12860. (48) Wu, X.-N.; Li, J.; Schlangen, M.; Zhou, S.; González-Navarrete, P.; Schwarz, H. Striking doping effects on thermal methane activation mediated by the heteronuclear metal oxides [XAlO4 ].+ (X= V, Nb, and Ta). Chem. Eur. J. 2017, 23, 788–792. (49) Zhou, S.; Li, J.; Schlangen, M.; Schwarz, H. On the origin of the remarkably variable reactivities of [AlCeOx ]+ (x= 2–4) towards methane as a function of oxygen content. Angew. Chem. Int. Ed. 2017, 56, 413–416. (50) Li, J.; González-Navarrete, P.; Schlangen, M.; Schwarz, H. Activation of Methane and Carbon Dioxide Mediated by Transition-Metal Doped Magnesium Oxide Clusters [MMgO]+/0/ (M= Sc–Zn). Chem.: Eur. J. 2015, 21, 7780–7789. (51) Li, Y.-K.; Zhao, Y.-X.; He, S.-G. Selective Conversion of Methane by Rh1-Doped Aluminum Oxide Cluster Anions RhAl2 O4 : A Comparison with the Reactivity of PtAl2 O4 . J. Phys. Chem. A 2018, 122, 3950–3955. (52) Li, Z.-Y.; Li, H.-F.; Zhao, Y.-X.; He, S.-G. Gold (III) mediated activation and transformation of methane on Au1-doped vanadium oxide cluster cations AuV2 O6 + . J. Am. Chem. Soc. 2016, 138, 9437–9443. (53) Zhao, Y.-X.; Li, X.-N.; Yuan, Z.; Liu, Q.-Y.; Shi, Q.; He, S.-G. Methane activation by gold-doped titanium oxide cluster anions with closed-shell electronic structures. Chemical Science 2016, 7, 4730–4735.

23



(54) Bhattacharya, S.; Levchenko, S. V.; Ghiringhelli, L. M.; Scheffler, M. Stability and metastability of clusters in a reactive atmosphere: Theoretical evidence for unexpected stoichiometries of MgM Ox . Phys. Rev. Lett. 2013, 111, 135501. (55) Bhattacharya, S.; Sonin, B. H.; Jumonville, C. J.; Ghiringhelli, L. M.; Marom, N. Computational design of nanoclusters by property-based genetic algorithms: Tuning the electronic properties of (TiO2 )n clusters. Phys. Rev. B 2015, 91, 241115. (56) Blum, V.; Gehrke, R.; Hanke, F.; Havu, P.; Havu, V.; Ren, X.; Reuter, K.; Scheffler, M. Ab initio molecular simulations with numeric atom-centered orbitals. Comput. Phys. Commun. 2009, 180, 2175–2196. (57) Tkatchenko, A.; Scheffler, M. Accurate molecular van der Waals interactions from ground-state electron density and free-atom reference data. Phys. Rev. Lett. 2009, 102, 073005. (58) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865. (59) Lenthe, E. v.; Baerends, E.-J.; Snijders, J. G. Relativistic regular two-component Hamiltonians. J. Chem. Phys. 1993, 99, 4597–4610. (60) Perdew, J. P.; Ernzerhof, M.; Burke, K. Rationale for mixing exact exchange with density functional approximations. J. Chem. Phys. 1996, 105, 9982–9985. (61) Krukau, A. V.; Vydrov, O. A.; Izmaylov, A. F.; Scuseria, G. E. Influence of the exchange screening parameter on the performance of screened hybrid functionals. J. Chem. Phys. 2006, 125, 224106. (62) The concept of aiAT was earlier developed and successfully applied initially for bulk semiconductors, 75,76 and later applied to the study of oxide formation at the surface

24


Page 24 of 28

Page 25 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


of some transition metals and other materials. 77–80 Recently, we have extended this approach to clusters in a reactive atmosphere. 20,24,54,81,82 (63) By doping we mean fixing of chemical potential of the electron (µe ). (64) Beret, E. C.; Wijk, M. M.; Ghiringhelli, L. M. Reaction cycles and poisoning in catalysis by gold clusters: A thermodynamics approach. Int. J. Quantum Chem. 2014, 114, 57– 65. (65) The Valence Band Maximum (VBM) is the Fermi level of bulk MgO which is located at -7.5 eV as estimated from HSE06 functionals. 82 (66) Marom, N.; Kim, M.; Chelikowsky, J. R. Structure selection based on high vertical electron affinity for TiO2 clusters. Phys. Rev. Lett. 2012, 108, 106801. (67) Getsoian, A. â.; Zhai, Z.; Bell, A. T. Band-gap energy as a descriptor of catalytic activity for propene oxidation over mixed metal oxide catalysts. J. Am. Chem. Soc. 2014, 136, 13684–13697. (68) Khan, T. S.; Gupta, S.; Alam, M. I.; Haider, M. A. Reactivity descriptor for the retro Diels–Alder reaction of partially saturated 2-pyrones: DFT study on substituents and solvent effects. RSC Adv. 2016, 6, 101697–101706. (69) Mills, G.; Gordon, M. S.; Metiu, H. Oxygen adsorption on Au clusters and a rough Au (111) surface: The role of surface flatness, electron confinement, excess electrons, and band gap. J. Chem. Phys. 2003, 118, 4198–4205. (70) Grochala, W. The generalized maximum hardness principle revisited and applied to atoms and molecules. Phys. Chem. Chem. Phys. 2017, 19, 30964–30983. (71) Häkkinen, H.; Landman, U. Gold clusters (AuN , 2

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