Article pubs.acs.org/IECR
Impact of Support Interactions for Single-Atom Molybdenum Catalysts on Amorphous Silica Christopher S. Ewing,†,‡,§ Abhishek Bagusetty,†,§,∥ Evan G. Patriarca,† Daniel S. Lambrecht,§,⊥ Götz Veser,†,‡ and J. Karl Johnson*,†,§ †
Department of Chemical and Petroleum Engineering, ‡Mascaro Center for Sustainable Innovation, ∥Computational Modeling and Simulation, and ⊥Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, United States § Pittsburgh Quantum Institute, Pittsburgh, Pennsylvania 15260, United States S Supporting Information *
ABSTRACT: Amorphous silica is a commonly used catalyst support, yet there are relatively few experimental or computational studies on catalyst−support interactions for this material. This is largely due to the inherent difficulty in modeling and experimentally characterizing amorphous silica. We used a recently developed surface model for amorphous silica surfaces to study the support effects on single-atom molybdenum catalysts. We found that the local structure of the silica support in the vicinity of the Mo site has a profound effect on the energetics and kinetics of metallacycle rotation, which is related to ethene metathesis. We have compared site energies, reaction energies, and reaction barriers computed from simple cluster models with results from surface models. The cluster models show a clear relationship between Si−Si distances and the site energies and reaction energies. In contrast, the surface model shows no correlation between Si−Si distances and energetics. The reaction barriers clearly increase with increasing Si−Si distances in the cluster model, whereas there is only a qualitative trend in the surface model. Analysis of the surface results indicates that the reaction energetics are affected by neighboring hydroxyl groups and Si atoms in the surface that are not accounted for in the cluster models. We therefore conclude that the simple trends relating support atom geometries to reaction energetics observed in the cluster models are artifacts of the model.
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INTRODUCTION Atomically dispersed metal catalysts supported on amorphous surfaces (silica and silica−alumina) are promising catalytic materials for a number of hydrocarbon reactions.1−3 Although many of these catalysts have been studied for decades,1−11 the combination of amorphous support structure and single metal atom catalytic site has severely limited the information attainable via experiments because of the diversity of catalyst sites and the inherent difficulty of characterizing single-atom sites.12−15 Furthermore, first-principles calculations of catalyst materials on highly accurate models of amorphous surfaces have been very difficult until recently.16,17 Developing atomistic explanations of catalyst−support interactions in these materials will allow for catalyst optimization and may inform the development of new, superior catalysts. The primary challenge associated with modeling single-atom catalysts on amorphous supports is the difficulty of obtaining an accurate, atomically resolved description of the active site. Unfortunately, isolated metal centers on amorphous supports cannot be accurately described using a single atomistic model structure because the local atomic structure varies significantly across amorphous surfaces.16 As a result, individual single-atom sites on amorphous silica and other amorphous supports can differ dramatically in electronic structure, and hence stability © 2016 American Chemical Society
and reactivity. It is therefore important for models of such systems to accurately capture the physical and chemical distribution of active sites, because the reactivity of singleatom catalysts is likely dominated by a few sites exhibiting the highest activity.1,2 Ab initio-based cluster models have allowed for tremendous advances in the understanding of isolated metal center catalysts.1,2,4−6,13,18 Recently, Goldsmith et al. developed a novel algorithmic approach for modeling isolated metal sites on amorphous supports, which accounts for surface structure heterogeneities.1,19 This formalism was used to calculate the lowest energy Mo/SiO2 cluster model structure for a given rotational activation energy, corresponding to the formation of an off-pathway intermediate in the ethene metathesis reaction. Using this approach, Goldsmith et al. calculated the average reactivity, and revealed clear correlations relating both reaction energy (enthalpy of the rotation) and Si−Si distance to the rotational activation energy. Due to the size of the cluster model used, however, this method neglects the effects of local Received: Revised: Accepted: Published: 12350
September 13, 2016 November 3, 2016 November 7, 2016 November 7, 2016 DOI: 10.1021/acs.iecr.6b03558 Ind. Eng. Chem. Res. 2016, 55, 12350−12357
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Figure 1. Bridged Mo/SiO2 metallacycle cluster model in the (a) trigonal bipyramidal and (b) square pyramidal geometries, and nonbridged cluster model in the (c) trigonal bipyramidal and (d) square pyramidal geometries. Atoms within the dashed region are denoted “moiety”, and atoms within the solid blue line are denoted “anchoring”. The anchoring atoms are meant to represent the atoms in the amorphous support. Atom colors are red for oxygen, yellow for silicon, pink for molybdenum, teal for carbon, white for hydrogen, and light blue for fluorine.
silanol groups per nm2, respectively, for a total of 15 silica surfaces. Generating isolated metal center sites. In a recent theoretical study, it was determined that MoO2 sites on amorphous silica are almost exclusively anchored to two silanol groups.18 Thus, we identified sites on amorphous silica that could potentially host MoO2 moieties by first determining which silanols were within range to form a Si−O−Mo−O−Si structure. Based on the results of preliminary studies, we considered silanol pairs with Si−Si and O−O distances of less than 6.8 and 4.5 Å, respectively. We found that distances larger than these resulted in very high energies and/or unrealistic ending structures. Every silanol pair was considered as a potential site for the Mo moiety, based on the Si−Si and O−O cutoff distances. The details of site generation are explained in the Results and Discussion. Density functional theory calculations. All atomistic calculations performed in this work used the CP2K code, which employs a Quickstep20 implementation of the DFT method using plane waves with pseudopotentials and localized basis sets. We used the Perdue−Burke−Ernzerhof generalized gradient functional21 and GTH pseudopotentials22,23 in conjunction with short-range double-ζ basis sets with polarization functions (SR-DZVP).24 Van der Waals interactions were described using the DFT-D2 method,25 which has been shown to accurately describe MoO2.26 All surface slabs were relaxed using CP2K treated as periodic in all directions with at least 20 Å of vacuum between periodic images in the z dimension to mitigate interactions between the periodic images of the surface slabs. The vacuum spacing for the silica surfaces has been validated previously.17 Validation of the plane wave energy cutoff, plane wave energy relative cutoff, and basis sets can be found in the Supporting Information. (Figures S1, S2, and S3, respectively.)
structure beyond the impact of the immediate anchoring Si atoms on site energetics. Our hypothesis is that the local environment of these anchoring Si atoms plays an important role in the energetics of the reactions. We test this hypothesis by comparing energetics related to ethene metathesis on isolated Mo centers using cluster models and realistic surface models of amorphous silica surfaces using density functional theory (DFT) calculations. Rather than study the actual metathesis reaction, we follow the work of Goldsmith et al.,1 who studied a metallacycle rotation of the Mo active site from a trigonal bipyramidal to a square pyramidal structure (see Figure 1). This rotation corresponds to the formation of a kinetically trapped off-pathway intermediate; the square pyramidal structure is kinetically inactive for ethene metathesis. We have computed site energies, the reaction (rotation) energies (i.e., the difference between the energies of the square pyramidal and trigonal bipyramidal structures), and the reaction (rotation) barriers for both cluster and surface models of catalytic Mo centers on amorphous silica. Our results indicate that while clear structure-energy trends can readily be identified for the cluster models, explicit inclusion of the support material reveals a very complex structure−energy relationship. In particular, we are unable to identify relationships between site, reaction, or activation energies and Si−Si distances. In general, the complex interplay between energies and surface structure is a result of the wide variation of hydrogen bonding interactions, silanol types, bond lengths, and bond angles, on amorphous supports which cannot be captured without explicit treatment of the surface. Our results caution against the use of simplified cluster models for amorphous catalyst systems.
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METHOD Model amorphous silica surfaces. We used periodic amorphous silica surface structures constructed from a model developed by Ewing et al.16 to study single-atom Mo/SiO2 catalysts. These model surface structures are based on firstprinciples simulations and have been found to accurately predict the hydroxyl density and distribution of hydroxyl groups as a function of pretreatment temperature without any adjustable parameters.16 Five distinct model surfaces were generated, and the hydroxyl density of each system was adjusted using an algorithm to mimic a range of silica pretreatment temperatures Tpre, as seen in Figure 4 of Ewing et al.16 The unit cell dimensions are 23.7 Å × 18.3 Å × ∼12 Å (slab thickness, not counting vacuum) and contain between 250 and 270 atoms. In this work, we use three different silica surface structures from each of the five distinct model surfaces, corresponding to Tpre values of 210, 340, and 540 °C, corresponding approximately to densities of 4, 3.2, and 2.3
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RESULTS AND DISCUSSION Generating low-energy isolated metal center sites. To sample a wide distribution of surface sites, it is necessary to generate Mo sites at a large number of surface locations. The use of annealing for the generation of each surface site is therefore not practical. We, hence, limited our utilization of DFT in generating Mo sites to local relaxation. It is extremely important that the initial geometry for local relaxation is sufficiently accurate so that the system is not optimized to an incorrect local energy minimum. Generating the correct initial conditions for amorphous structures is nontrivial because the energy landscape is disordered and, hence, often difficult to predict. 12351
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Figure 2. (a) Relative site energy as a function of Si−Si distance for Mo/SiO2 cluster models, referenced to the lowest cluster energy. (b) Reaction energies as functions of Si−Si distance for Mo/SiO2 cluster models.
Figure 3. (a) Siloxane and O−Mo−O bond angles and (b) siloxane bond lengths vs Si−Si distance for the bridged cluster model. The two sets of symbols in (b) refer to the two different Si−O bond lengths in the cluster for the Si−O−Mo linkers (see Figure 1a).
We developed a transferable protocol for generating lowenergy Mo/SiO2 sites based on atom positions taken from cluster models, to which we adsorb an intermediate structure for ethene metathesis. First, we employed two Mo/SiO2 cluster models developed by Goldsmith et al.,1 shown in Figure 1, to represent Mo moieties bound to bridged and nonbridged sites. A six-membered Mo/SiO2 ring cluster represents bridged sites (Figure 1a), and a minimal (i.e., no specific structural assumptions beyond what is observed by EXAFS) Mo/SiO2 cluster model (Figure 1c) is used to represent nonbridged sites.1 Both cluster models are terminated with basis set deficient fluorine atoms, which mimic the size and electronegativity of oxygen atoms in an extended silica network, as shown by Peters and co-workers.1,2 We denote the Si atoms and their nearest neighbors as “anchoring” atoms (i.e., representing the amorphous support) and the remaining Mo site atoms as “moiety” atoms (shown explicitly, for cluster models, in Figure 1). To sample a distribution of potential Mo sites, we mapped atom coordinates for cluster models having a range of Si−Si distances, obtained via optimization. This was accomplished by holding the Si−Si distance fixed at a desired value and allowing all other atoms to relax. This procedure resulted in cluster models representative of a wide range of surface site geometries, from which the positions of Mo moiety atoms relative to anchoring atoms can be extracted. After identifying silanol pairs on the silica surface models, we generated potential Mo binding sites based on the atomic positions of the corresponding cluster models (i.e., bridged or nonbridged and having similar Si−Si distance). First, hydrogen
was removed from the anchoring silanol groups. Then, the distance between silanol group O atom positions was reduced to that of the corresponding cluster model. Using the anchoring O atoms and the Si−Si midpoint as a reference, the moiety atoms were then placed on the surface model with the same relative positions as those of the corresponding cluster model. As a result, the initial structures for geometry optimization are relatively close to a local minimum. Efficient relaxation of the initial structure was carried out by first relaxing the moiety, the Si atoms to which it was bound, and first nearest-neighbors, while fixing the remaining atoms. Finally, the entire system was fully relaxed to a local minimum. To test the reliability of this approach, we performed energy minimum searches for two of the Mo sites using ab initio molecular dynamics simulations. Each system was annealed at 750 K for 6 ps while holding all atoms fixed except for the moiety and anchoring atoms. After every 1 ps of simulation, a snapshot of the system geometry was taken and relaxed following the same procedure used for site generation (i.e., local atom relaxation followed by full system relaxation). In both cases, annealed structures had energies either higher than, or within, 0.1 eV of structures obtained using our approach, confirming the effectiveness of our method (see Figure S4 in the Supporting Information). Cluster model site energies are correlated with Si−Si distance. Using the approach described above, we generated model systems representing two different off-pathway intermediates in ethene metathesis: the trigonal bipyramidal and square pyramidal geometries. During ethene metathesis, Mo/ SiO2 sites can deactivate via metallacycle rotation from the 12352
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Figure 4. (a) O−Mo−O bond angle and (b) Si−O bond lengths as functions of the Si−Si distance for the nonbridged cluster model. The two different symbol types in (b) represent the two distinct Si−O bond lengths in the cluster (see Figure 1c).
Figure 5. (a) Relative site energy as a function of Si−Si distance for Mo sites on full silica surface models. (b) Reaction energy as a function of Si−Si distance for Mo sites on full silica surface models. In both figures, all Si−Si distances of less than 3.5 Å correspond exclusively to bridged sites, whereas Si−Si distances greater than 3.5 Å are for nonbridged sites.
bridged and nonbridged clusters, indicating that the site and reaction energetics can also be correlated in terms of the O− Mo−O bond angles. Likewise, the Si−O−Si bond angles for the bridged clusters correlate well with the Si−Si bond lengths, as expected (Figure 3a). The Si−O bond lengths for bridged and nonbridged clusters also correlate well with the Si−Si distance, as can be seen from Figures 3b and 4b, respectively. Energetics of Mo sites on periodic surface models. We generated Mo sites on amorphous silica surfaces (modeled as periodic structures with large unit cells) in order to examine the effects of the extended silica network not accounted for by cluster models. When heated, neighboring silanol groups condense (dehydroxylate) to form water and a siloxane bridge.15,27,28 Both the number of silanol groups and the local structure of the silica surface change with the extent of dehydroxylation.15,16,27,28 It is thus likely that the properties of Mo sites may differ on silica surfaces that have been treated at different temperatures and hence have undergone different degrees of dehydroxylation. We therefore generated sites at all possible anchoring locations on 15 different surface structures, which represent three average silica pretreatment temperatures (5 surfaces per temperature) of approximately 210, 340, and 540 °C. For cluster models with a constant number of atoms, the relative energetics of different sites (site energies) can be calculated as the difference in system energies.1 For sites on a surface, however, this definition does not sufficeeven for different sites on the same surfacebecause the Mo moiety replaces atoms on the surface (OH groups). To compare site
trigonal bipyramidal geometry to the square pyramidal geometry, which is inactive for metathesis.5,6 Figure 2a shows the site energy as a function of Si−Si distance for both bridged and nonbridged cluster models. The site energy is defined by the total energy of the cluster referenced to the cluster having the lowest energy. Both cluster models show that the site energy is clearly correlated to the Si−Si distance; that is, the site energy is, within statistical noise, a unique function of the Si−Si distance for each type of cluster. Reaction (rotation) energies as a function of Si−Si distance calculated for both bridged and nonbridged clusters in this study are shown in Figure 2b. The energy profiles of bridged and nonbridged clusters show similar features, giving an increase in energy with increasing Si−Si distance at the smallest distances, after which the reaction energy reaches a maximum and then decreases with increasing Si−Si distance. In the next section we compare and contrast the behavior observed for these cluster models with site energies and reaction energies on periodic surface models. We note that the site and reaction energies reported in Figure 2 span a larger range than for essentially the same cluster models studied by Goldsmith et al.1 This is because we have studied a larger range of Si−Si distances in this work, to explore whether the trends remain consistent, even for what might be considered unphysically large Si−Si distances. In addition to correlations of the site and reaction energies with Si−Si distances, we have also found strong correlations in the O−Mo−O bond angles for bridged (Figure 3a) and nonbridged (Figure 4a) clusters. The O−Mo−O bond angles increase monotonically with Si−Si bond lengths for both the 12353
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pretreatment temperature. All possible sites on a given surface were randomly populated in a given trial, and 1000 trials were attempted for each surface to improve statistics (further details are given in the Supporting Information). Silica pretreatment temperatures of 200, 400, and 600 °C had 33, 28, and 15% bridged sites, respectively. The decrease in the fraction of bridged sites with increasing pretreatment temperature is a logical consequence of dehydroxylation of bridged Si−Si groups having a lower free energy than nonbridged groups, on average. We deduce from Figure 5b that surfaces with lower pretreatment temperatures will have a larger fraction of catalytic sites that have an endothermic, i.e., thermodynamically unfavorable, reaction energy. Recall that the reaction we are exploring here is the rotation of the Mo active site from a trigonal bipyramidal to a square pyramidal structure, with the latter structure being catalytically inactive toward ethane metathesis. Hence, our calculations predict that amorphous silica surfaces with lower pretreatment temperatures may be more catalytically active due to a smaller fraction of energetically favorable deactivation channels. Reaction barriers on periodic surfaces and clusters. We have computed reaction barriers for the rotation of the metallacycle moiety on the model surfaces by selecting a number of sites from the reactions plotted in Figure 5b, both for bridged and nonbridged Mo sites. The climbing-image nudged elastic band method29 was used to locate the transition states connecting the reactants and products for the systems chosen. As an example, snapshots of the reactant state (initial state), transition state, and product (final state) computed from this procedure are shown in Figure 7, along with the relative energies of each of the images. The reaction barriers for a total of 44 reactions sampled from the five different model surfaces are plotted in Figure 8. The reaction barriers for nonbridged cluster models from Goldsmith et al.1 are also plotted in Figure 8 for comparison. The cluster models show that the rotation barrier generally increases with Si−Si distance. This same general trend can be seen in the nonbridged sites on the surfaces, although the barriers can vary by more than a factor of 2 at different sites having essentially the same Si−Si distance, making the trend more difficult to recognize in the surface models. Thus, the cluster model is useful for predicting general trends, but it fails to capture the diversity of sites on a surface model. Our analysis of other simple variables, such as O−Mo− O bond angles, also failed to identify clear correlations for our calculated reaction barriers, in contrast to the trends observed for the cluster models shown in Figures 3 and 4. This indicates that the barriers are dependent upon the details of the local structure at each site, such as the configuration of neighboring atoms, which cannot be captured by a simplified cluster model lacking the full connectivity of the amorphous surface. Visualization of the reaction pathway images shows that neighboring hydroxyl groups may form hydrogen bonds with the metallacycle as it rotates. In addition, we have noted relaxation (movement) of Si atoms in the surface that are nextnearest neighbors to the anchoring Si atoms to the metallacycle moiety. These atoms are not accounted for in any way in the cluster models considered in this work, and therefore, it is not surprising that the details of the reaction energetics are not accurately captured by these simple models.
energies similar to the approach used for the cluster models, we calculated site energy as follows: Esite = EMo/SiO2 − ESiO2 − OH
(1)
where EMo/SiO2 denotes the energy of the Mo/SiO2 system, with all atoms relaxed. ESiO2−OH denotes the silica surface, minus the two anchoring OH groups, fixed in the relaxed geometry of the bare silica surface (with all OH groups). By calculating the reference silica surface system without the anchoring OH groups, both moiety−silica interactions and moiety deformation are explicitly accounted for, and silica network deformation is estimated. The site and reaction energies computed from our surface models are shown in Figure 5. Comparison of Figure 5 with Figure 2 demonstrates several key differences between the site and reaction energies on amorphous surfaces and cluster models. The most striking difference is that the surface models do not show any relationship between the site energies and the Si−Si distances. Likewise, reaction energies are not correlated with Si−Si distances. The clear trends observed in the cluster models appear to be artifacts of those models. Another difference between the cluster and surface models is the more narrow range of Si−Si distances appearing in the surface models compared with the clusters, which can be attributed to the structural constraints of the amorphous solid matrix. The surface models contain bridged and nonbridged catalyst binding sites, analogous to the cluster models shown in Figure 1. Examples of bridged and nonbridged sites on the surface models are shown in Figure 6. The bridged sites have
Figure 6. Examples of (a) nonbridged and (b) bridged metallacycle moieties on amorphous silica surfaces. The color scheme is the same as in Figure 1. The anchoring Si atoms and bridging O atom are emphasized. Both metallacycles are in the square pyramidal structures.
Si−Si distances between about 2.8 and 3.3 Å in Figure 5, and the nonbridged sites have Si−Si distances between about 3.9 and 6.2 Å. In contrast, cluster models having about the same range of site energies have Si−Si distances between 2.1 and 3.6 Å for bridges sites and 2.6 to 7.3 Å for nonbridged sites (Figure 2a). Note that the bridged and nonbridged Si−Si distances overlap for the cluster models but not for the surface model. This may indicate that the nonbridged cluster model allows Si− Si distances that are unphysically small compared with real amorphous surfaces. From Figure 5a it is clear that the bridged and nonbridged sites have similar site energies; however, bridged sites on average have significantly higher reaction energies than nonbridged sites (Figure 5b). We modeled one site on the surface at a time in our calculations presented in Figure 5. We used a simple Monte Carlo approach to simulate the formation of multiple Mo/SiO2 sites on the surfaces, up to full coverage, in order to estimate the ratio of bridged to nonbridged sites as a function of silica
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CONCLUSIONS Our results indicate that small cluster models consisting only of the Mo sites and the anchoring Si tetrahedron are likely 12354
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Figure 7. Reactant (a), transition (b), and product (c) states of a metallacycle rotation reaction on an arbitrary amorphous surface site. The atom colors are the same as in Figure 1. (d) The computed reaction pathway energetics for this site, relative to the reactant state. The reaction barrier is 0.72 eV, and the reaction energy is −0.29 eV. The reaction coordinate is the root-mean-square displacement of the atoms in the metallacycle moiety. The line is a guide to the eye.
inadequate for accurately describing the reaction energies and barriers. Silica surfaces exhibit a wide range of atomic surface structures, which are not represented by the low-energy cluster models and which broaden the range of site energies and reaction energies to the point where statistically significant correlations are lost. The disordered structure of amorphous silica can also result in Mo sites being close enough to neighboring hydroxyl groups on the surface to affect the site energetics. Furthermore, we have observed rotation-induced relaxation of Si atoms in the surface that are farther away from the Mo moiety than can be accounted for by the simple cluster models considered in this work. Thus, we caution against relying on simple cluster models, such as silsesquioxanes30 and alumino-silsesquioxanes,31 to represent the rich complexity of amorphous silica and aluminosilicates, respectively. It is not immediately clear whether 2-dimensional random networks of SiO232 can provide much more realistic models of amorphous silica than the cluster models examined here. Addressing this question is beyond the scope of this work. We developed a transferable approach for generating realistic geometries for isolated metal atom sites on amorphous surfaces based on constrained cluster calculations. This approach facilitates the computationally efficient generation of a large number of atomic sites, which is essential to reveal the full richness of these complex, amorphous surfaces. Our approach could be applied to the development of atomistic models of other isolated metal center catalysts on amorphous surfaces.
Figure 8. Barriers for rotation of the metallacycle of the Mo active site from a trigonal bipyramidal to a square pyramidal configuration as a function of Si−Si distance for the nonbridged cluster model (line), generated from the sequential quadratic programming algorithm of Goldsmith et al.,1 and for model amorphous surfaces (points). The different symbol types correspond to each of the five different model amorphous silica surfaces. Si−Si distances for the symbols of less than 3.5 Å correspond to bridged sites, whereas Si−Si distances greater than 3.5 Å are for nonbridged sites. All surfaces have silanol concentrations corresponding to a pretreatment temperature of 210 °C.
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(10) Bell, A. T. Single iron sites for catalytic, nonoxidative conversion of methane. Sci. China: Chem. 2014, 57 (7), 923−923. (11) Guo, X. G.; Fang, G. Z.; Li, G.; Ma, H.; Fan, H. J.; Yu, L.; Ma, C.; Wu, X.; Deng, D. H.; Wei, M. M.; Tan, D. L.; Si, R.; Zhang, S.; Li, J. Q.; Sun, L. T.; Tang, Z. C.; Pan, X. L.; Bao, X. H. Direct, nonoxidative conversion of methane to ethylene, aromatics, and hydrogen. Science 2014, 344 (6184), 616−619. (12) Rozanska, X.; Delbecq, F.; Sautet, P. Reconstruction and stability of beta-cristobalite 001, 101, and 111 surfaces during dehydroxylation. Phys. Chem. Chem. Phys. 2010, 12 (45), 14930− 14940. (13) Tielens, F.; Gervais, C.; Lambert, J. F.; Mauri, F.; Costa, D. Ab initio study of the hydroxylated surface of amorphous silica: A representative model. Chem. Mater. 2008, 20 (10), 3336−3344. (14) Ugliengo, P.; Sodupe, M.; Musso, F.; Bush, I. J.; Orlando, R.; Dovesi, R. Realistic models of hydroxylated amorphous silica surfaces and MCM-41 mesoporous material simulated by large-scale periodic B3LYP calculations. Adv. Mater. 2008, 20 (23), 4579−4583. (15) Zhuravlev, L. T. The surface chemistry of amorphous silica. Zhuravlev model. Colloids Surf., A 2000, 173 (1−3), 1−38. (16) Ewing, C. S.; Bhavsar, S.; Veser, G.; McCarthy, J. J.; Johnson, J. K. Accurate amorphous silica surface models from first-principles thermodynamics of surface dehydroxylation. Langmuir 2014, 30 (18), 5133−5141. (17) Ewing, C. S.; Hartmann, M. J.; Martin, K. R.; Musto, A. M.; Padinjarekutt, S. J.; Weiss, E. M.; Veser, G.; McCarthy, J. J.; Johnson, J. K.; Lambrecht, D. S. Structural and electronic properties of Pt13 nanoclusters on amorphous silica supports. J. Phys. Chem. C 2015, 119 (5), 2503−2512. (18) Guesmi, N.; Grybos, R.; Handzlik, J.; Tielens, F. Characterization of molybdenum monomeric oxide species supported on hydroxylated silica: a DFT study. Phys. Chem. Chem. Phys. 2014, 16 (34), 18253−18260. (19) Goldsmith, B. R.; Fong, A.; Peters, B., Chapter 9 Understanding reactivity with reduced potential energy landscapes: Recent advances and new directions. In Reaction Rate Constant Computations: Theories and Applications; The Royal Society of Chemistry: 2013; pp 213−232. (20) VandeVondele, J.; Krack, M.; Mohamed, F.; Parrinello, M.; Chassaing, T.; Hutter, J. Quickstep: fast and accurate density functional calculations using a mixed Gaussian and plane waves approach. Comput. Phys. Commun. 2005, 167 (2), 103−128. (21) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77 (18), 3865− 3868. (22) Goedecker, S.; Teter, M.; Hutter, J. Separable dual-space gaussian pseudopotentials. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54 (3), 1703−1710. (23) Krack, M. Pseudopotentials for H to Kr optimized for gradientcorrected exchange-correlation functionals. Theor. Chem. Acc. 2005, 114 (1−3), 145−152. (24) VandeVondele, J.; Hutter, J., Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases. J. Chem. Phys.2007, 127 (11), 11410510.1063/1.2770708 (25) Grimme, S. Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J. Comput. Chem. 2006, 27 (15), 1787−1799. (26) Ding, H.; Ray, K. G.; Ozolins, V.; Asta, M., Structural and vibrational properties of alpha-MoO3 from van der Waals corrected density functional theory calculations. Phys. Rev. B: Condens. Matter Mater. Phys.2012, 85 (1), 10.1103/PhysRevB.85.012104 (27) Zhuravlev, L. T. Structurally bound water and surface characterization of amorphous silica. Pure Appl. Chem. 1989, 61 (11), 1969−1976. (28) Zhuravlev, L. T. Surface characterization of amorphous silica - a review of work from the former USSR. Colloids Surf., A 1993, 74 (1), 71−90. (29) Henkelman, G.; Uberuaga, B. P.; Jónsson, H. A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J. Chem. Phys. 2000, 113 (22), 9901−9904.
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.6b03558. Site generation procedure, simulation details, annealing results, and Monte Carlo simulation details (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
J. Karl Johnson: 0000-0002-3608-8003 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This contribution was identified by Session Chair Baron Peters (U. C. Santa Barbara) as the Best Presentation in the session CATL: Amorphous Catalytic Materials of the 2016 ACS Spring National Meeting in San Diego, CA. We thank Bryan Goldsmith for many helpful discussions and for sharing the cluster model data reported in Figure 8. This work was supported by the Department of Education GAANN program (P200A100087) and the Mascaro Center for Sustainable Innovation at the University of Pittsburgh. C.S.E. acknowledges a graduate fellowship from the Pittsburgh Quantum Institute (PQI). Calculations were performed using the Extreme Science and Engineering Discovery Environment (XSEDE, TGDMR110091), which is supported by National Science Foundation grant number ACI-1053575, and the Center for Simulation and Modeling at the University of Pittsburgh.
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DOI: 10.1021/acs.iecr.6b03558 Ind. Eng. Chem. Res. 2016, 55, 12350−12357
