Photodissociation of Cerium Oxide Nanocluster ... - ACS Publications

Apr 1, 2016 - S. T. Akin,. †. S. G. Ard,. †. B. E. Dye,. †,‡. H. F. Schaefer,. †,‡ and M. A. Duncan*,†. †. Department of Chemistry, Un...
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Photodissociation of Cerium Oxide Nanocluster Cations S. T. Akin,† S. G. Ard,† B. E. Dye,†,‡ H. F. Schaefer,†,‡ and M. A. Duncan*,† †

Department of Chemistry, University of Georgia, Athens, Georgia 30602, United States Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, United States



S Supporting Information *

ABSTRACT: Cerium oxide cluster cations, CexOy+, are produced via laser vaporization in a pulsed nozzle source and detected with time-of-flight mass spectrometry. The mass spectrum displays a strongly preferred oxide stoichiometry for each cluster with a specific number of metal atoms x, with x ≤ y. Specifically, the most prominent clusters correspond to the formula CeO(CeO2)n+. The cluster cations are mass selected and photodissociated with a Nd:YAG laser at either 532 or 355 nm. The prominent clusters dissociate to produce smaller species also having a similar CeO(CeO2)n+ formula, always with apparent leaving groups of (CeO2). The production of CeO(CeO2)n+ from the dissociation of many cluster sizes establishes the relative stability of these clusters. Furthermore, the consistent loss of neutral CeO2 shows that the smallest neutral clusters adopt the same oxidation state (IV) as the most common form of bulk cerium oxide. Clusters with higher oxygen content than the CeO(CeO2)n+ masses are present with much lower abundance. These species dissociate by the loss of O2, leaving surviving clusters with the CeO(CeO2)n+ formula. Density functional theory calculations on these clusters suggest structures composed of stable CeO(CeO2)n+ cores with excess oxygen bound to the surface as a superoxide unit (O2−).



INTRODUCTION Cerium oxide has many industrial applications, both as an active catalyst and as a catalyst support.1,2 Consequently, this material is widely studied in solid form, as thin-layers, and as nanoparticles.3−15 Small gas phase clusters of cerium oxide have also been studied. Several groups have examined the sizespecific reactions of cationic or anionic clusters.16−26 Asmis and co-workers studied the structures of these species using infrared laser photodissociation spectroscopy.27 Computational studies have also investigated these systems, primarily using density functional theory (DFT).27−32 In the present study, we examine the photodissociation and mass spectrometry of cerium oxide clusters to probe the stable stoichiometries produced in the small clusters. Much of the previous work on small cerium oxide clusters focused on their reactivity. Ding and co-workers produced gas phase cluster cations of cerium oxide and examined their reactivity toward CH4, C2H4, and C2H6.17−19 They found that small stoichiometric cluster cations (CemO2m+) were particularly reactive, while nonstoichiometric and larger clusters (m ≥ 7) were less so. Several other groups investigated reactions of these cluster ions with CO, CO2, and water.20−26 In the only spectroscopy study, Asmis and co-workers were able to study the structures of small cluster cations by employing infrared photodissociation spectroscopy and rare gas tagging, complemented by DFT computational work.27 Several structural assignments were made based on good agreement between observed and predicted spectra. To our knowledge, cerium oxide clusters have not been investigated with either collisional © XXXX American Chemical Society

or photodissociation methods to probe their preferred stoichiometries or relative stabilities, although Mafuné and co-workers used a thermal heating experiment for this purpose.24 Mass spectrometry methods have been employed extensively for small metal oxide clusters using a variety of production methods and ionization schemes.33−44 In some cases threshold ionization methods have been employed to probe abundant neutral clusters.36,37 However, mass-selected photodissociation methods have been shown to be less sensitive to preparation conditions and more sensitive to intrinsic cluster stability patterns.33,34,38−44 These experiments have documented the occurrence of specific oxide stoichiometries for virtually every system studied, in both the tendencies for cluster formation, and especially in the repeated occurrence of certain preferred fragments. In some cases, the stoichiometries observed correspond to a common oxidation state of the metal, but in other cases, the small oxide species form entirely new combining ratios. In the case of vanadium oxide clusters, the clusters with new combining ratios were stable enough to be isolated with ligand coatings in macroscopic amounts.45 Although many transition metal oxides39−42,44 and some main group systems38,43 have been investigated, the only lanthanide system studied to date was lanthanum oxide.42 Computational methods have been applied extensively to small oxide Received: February 27, 2016 Revised: March 29, 2016

A

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The Journal of Physical Chemistry A clusters,20,27,29,30,45−48 but these methods have difficulty predicting stability trends over different cluster sizes. In the present study, we employ mass-selected photodissociation measurements to the small gas phase cluster cations of cerium oxide to investigate their stability patterns. We also investigate the stable species identified with quantum chemistry calculations.



EXPERIMENTAL SECTION Cerium oxide cluster cations were produced by laser vaporization in a pulsed nozzle source,49 and investigated with photodissociation in a reflectron time-of-flight (RTOF) mass spectrometer.50 The second harmonic (532 nm) of a Nd:YAG (Continuum Surelite) is employed to vaporize metal from a translating and rotating cerium rod. A mixture of helium seeded with 5−15% oxygen is pulsed through the sample rod holder with a General Valve (200 psig backing pressure, 0.5 mm orifice) allowing cluster ions to grow directly from the laser plasma. The resulting molecular beam expands in a source chamber and is then skimmed into a differentially pumped mass spectrometer chamber. Here, pulsed voltages accelerate the ions into the RTOF instrument and pulsed deflection plates are used to size-select the ions of interest. Photodissociation employs a second Nd:YAG laser (Quanta Ray INDI) operating at either 532 or 355 nm (30−60 mJ/cm2), timed such that it intersects the ions at their turning point in the reflectron field. The resulting fragment ions as well as the remaining parent ions are then reaccelerated and mass analyzed in the second flight tube section, followed by detection with an electron multiplier tube and digital oscilloscope (LeCroy 9310A). Computational studies were performed with the ORCA package51 using the zeroth-order regular relativistic approximation Hamiltonian (ZORA)52 and a relativistically recontracted version of Ahlrichs’ triple-ζ valence basis set having one additional polarization function (TZVP).53 TZVP was treated with a segmented all electron relativistically contracted (SARC) basis set for Ce and O.54,55 Resolution of the identity (RI) Coulomb fitting approximation was used for the pure functionals and split resolution of the identity in combination with a chain of spheres (RIJCOSX) approximation was used for the for the Hartree−Fock exchange term of the hybrid functionals and MP2.56,57 Ahlrichs’ Coulomb fitting basis for the TZVP basis (TZV/J) was used as the auxiliary basis set for the functionals and (TZV/C) was used for MP2. Geometry optimizations were performed on all structures using default ORCA parameters, except TightSCF, and confirmed with a frequency analysis. Thermal and entropic corrections to the zero point vibrational energy (ZPVE) were taken at 298 K. The doublet ground state multiplicity of all cations was confirmed by running the same computations on the quartet state. Benchmarking of CeO2 was conducted using several DFT functionals (BP86, B2PLYP, mPW2PLYP, PBE, and PBE0) as well as ab initio methods MP2, CCSD, and CCSD(T). BP86 was used to study all other cluster sizes.

Figure 1. Mass spectra of cerium oxide cluster cations produced by laser vaporization of a cerium metal sample in an expansion containing 5% oxygen in helium. The x,y labels refer to the Ce x O y + stoichiometries.

but with the same main stoichiometries present. Clusters formed from oxygen-rich expansions (e.g., 15%) primarily formed smaller clusters (x < 7) but with larger intensities for the stoichiometries with more oxygen. Under such oxygen-rich conditions, metal−oxygen collisions are more likely than metal−metal collisions, which could limit the growth of larger metal aggregates. In the spectrum shown here, measured with a lower (5%) oxygen concentration, clusters are present containing up to 11 cerium atoms with a varying number of oxygen atoms. As seen before with other metal oxide clusters, certain specific stoichiometries are observed for each metal increment. In the present data, the most prominent peak for each metal increment in the medium-to-small CexOy+ clusters corresponds to y = 2x − 1; i.e., the clusters follow the formula CeO(CeO2)n+. Additional mass peaks are seen with lower intensities corresponding to one additional or one less oxygen. In the larger clusters, the pattern changes slightly, so that there are two comparable oxide peaks for each metal increment. These doublet features correspond to Ce(CeO2)n+ and CeO(CeO2)n+ masses for n = 5−9. The intensities in this mass spectrum are somewhat different from those reported by Mafuné and co-workers, in which a larger range of higher oxides were detected and the y = 2x + 1 species were more intense. This variation with two different cluster sources, probably arising from slightly different gas pressure/laser conditions, highlights the difficulty in assigning cluster stabilities on the basis of mass spectral intensities. To investigate the relative stabilities of these clusters more directly, we employ mass-selected photodissociation experiments at either 532 or 355 nm. The results of these experiments are shown in Table 1 and Figures 2−4. These photodissociation mass spectra are collected via a difference technique, (photodissociation laser on−photodissociation laser off), leading to negative peaks corresponding to depletion of the parent ion and positive peaks corresponding to fragment ions produced from the dissociation. We find that either wavelength produces fragmentation, although both require relatively high laser fluence (30−60 mJ/cm2) for efficient dissociation. This is consistent with multiphoton photodissociation, as we have seen for other metal oxide systems.38−44 The requirement of multiphoton excitation for dissociation is understandable because of the strong bonds expected for metal oxides (see computed bond energies below).



RESULTS AND DISCUSSION The mass spectrum of cerium oxide cluster cations produced with an expansion gas mixture of 5% oxygen in helium is shown in Figure 1. To obtain this mass spectrum, the ions that grow directly in the laser plasma are sampled into the mass spectrometer without any form of post ionization. Other gas mixtures produce spectra extending to lower or higher masses, B

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The Journal of Physical Chemistry A Table 1. Stoichiometries of Cerium Oxide Cluster Photofragments (CexOy+ = x, y) Observed with Photodissociation at 355 nma

a

parent cation cluster

fragment ions

2,3 2,4 2,5 2,6 2,7 3,4 3,5 3,6 3,7 3,8 4,6 4,7 4,8 4,9 5,9 6,10 6,11 9,17 11,21

1,1 2,3; 1,1 2,3 2,4; 2,3 2,3 none observed 2,3 3,5; 3,4; 2,4; 2,3 3,5; 2,3 3,6; 3,5; 3,4 3,4 3,5; 2,3 4,7; 4,6 4,7 4,7; 3,5 5,8 5,9; 4,7 8,15; 7,13; 6,11 10,19; 9,17; 8,15

Figure 3. Multiphoton photodissociation mass spectra of Ce6O11+, Ce9O17+, and Ce11O21+ cation clusters at 355 nm. The negative peak indicates the loss of the parent ion, and the positive peaks indicate its photofragments. Each of these clusters eliminates one or two CeO2 units as photofragments.

The stoichiometries indicated in bold were most prominent.

Figure 4. Multiphoton photodissociation mass spectra of Ce2O5+, Ce3O7+, and Ce4O9+ cation clusters at 355 nm. The Ce2O5+ and Ce2O3+ mass peaks are doubled because of the cerium isotopes, which can only be resolved at low mass under certain focusing conditions. The negative peak indicates the loss of the parent ion, and the positive peaks indicate its photofragments. Each of these oxygen-rich clusters eliminates O2 as its main photofragment.

Figure 2. Multiphoton photodissociation mass spectra of Ce3O5+, Ce4O7+, and Ce5O9+ cation clusters at 355 nm. The negative peak indicates the loss of the parent ion, and the positive peaks indicate its photofragments. Each of these clusters eliminates CeO2 as its main photofragment.

Table 1 summarizes the photofragmentation results for all cluster sizes studied, (CexOy+ = x, y), with the most intense fragment ion for each indicated in bold. Figures 2 and 3 show the photodissociation mass spectra for selected prominent cluster masses following the CeO(CeO2)n+ formula. The signal levels and mass selection are somewhat marginal for the larger clusters shown in Figure 3 because of the low intensities in these higher masses and the limited resolution of our mass gate. Small amounts of adjacent clusters differing by one oxygen leak through the mass gate in these cases. As shown, all the clusters in Figures 2 and 3 dissociate by the apparent loss of neutral

Fragmentation at both 532 and 355 nm produces the same fragments. However, 355 nm excitation produces fragmentation more efficiently, perhaps due to the larger energy delivered per photon (80.5 vs 53.7 kcal/mol) or to a larger cross section for absorption at this wavelength. Therefore, the data shown in the figures here were generated at 355 nm. The band gap for bulk CeO2 is about 3.1 eV, and that for nanoparticles in the 1 nm size range is about 4.4 eV.58,59 Thus, it makes sense that the 355 nm (3.49 eV) photons would be absorbed more efficiently. C

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The Journal of Physical Chemistry A CeO2, producing cations which also follow the CeO(CeO2)n+ formula. We do not detect the neutral leaving groups and therefore cannot distinguish between the loss of intact CeO2 units versus atomic or molecular pieces that add up to this. However, we see no evidence for intermediate fragment ions, and therefore conclude that the loss is most likely an intact CeO2 unit. Less intense fragments corresponding to the loss of two CeO2 units are also evident. We also cannot determine definitively whether this additional loss is sequential or concerted, but it appears to be sequential on the basis of laser power variations. Figure 4 shows the fragmentation of selected clusters with higher oxygen content (y ≥ 2x). As indicated here and in Table 1, these oxygen-rich species tend to eliminate two oxygen atoms, presumably in the form of the O2 molecule. This channel is especially efficient for those clusters of the form CeO(CeO 2 ) n (O 2 ) +, which can dissociate to form the corresponding CeO(CeO2)n+ cluster preceding it. As noted above, we are unable to distinguish between the loss of two oxygen atoms versus O2. However, the loss of O2 is more likely because it is energetically lower. We also see this decrement for clusters having only one “excess” oxygen that produce Ce(CeO2)n+ rather than the usual CeO(CeO2)n+ cluster fragment. Only a couple of systems show evidence for the loss of a single oxygen atom, and these are minor fragmentation channels. Overall, the fragmentation of the oxygen-rich clusters also supports the stability of the CeO(CeO2)n+ species. In the only other data relevant to this, Mafuné and coworkers investigated the thermal decomposition of cerium oxide clusters. However, in those experiments the clusters were not mass selected, but rather the whole cluster distribution was heated in a tube attached to the cluster source, and the emergence of more prominent cluster ions was observed. The work of Mafuné detected relatively intense signals for CeO(CeO2)n+ and (CeO2)n+ clusters. The former species agree with the present experiments, but we see no evidence for the latter (CeO2)n+ clusters in the present work. These data suggest strongly that the cerium in these clusters has the usual +4 oxidation state that it does in bulk CeO2 and other compounds. The CeO(CeO2)n+ formula that describes all the most abundant ion masses corresponds as closely as possible to this, with the missing oxygen apparently necessary to accommodate the charge on the cluster. All of the most prominent photofragments correspond to elimination of CeO2 units. There is no evidence in any of the mass increments detected for formulas corresponding to the less-common Ce2O3. We saw a similar effect in the case of lanthanum oxide, where the +3 oxidation state was prominent in the clusters. In both of these systems, the most common oxidation state of the metal in its compounds or most stable solid form carries through to the clusters. This is in contrast to our previous studies of transition metal systems such as vanadium or iron, where less common oxidation states were favored for the small clusters.39−41 In minor mass channels, where some clusters form with additional oxygen beyond the CeO(CeO2)n+ masses, the fragmentation corresponds to the loss of oxygen. These combined observations suggest that there are relatively stable clusters with the CeO(CeO2)n+ formula and that the oxygen-rich masses just beyond this correspond to these same stable clusters with excess oxygen molecules adsorbed on their surface. To investigate the possible structures for these systems, we carried out computational studies using density functional

theory on several of the small clusters seen here. In deciding between the many possible methods that might be useful for this, we did benchmarking studies on the CeO2 molecule. This species has been isolated in a neon matrix and studied with infrared spectroscopy, resulting in vibrational frequencies for the a1 and b2 stretching modes that should be very close to gas phase values.60 These computational studies employed the DFT functionals BP86, B3P86, TPSS, B2PLYP, mPW2PLYP, PBE, and PBE0, as well as selected ab initio methods [MP2, CCSD, and CCSD(T)]. Additionally D ∞h, C 2v , and C s geometries were compared between the functionals and ab initio methods. The full details of these benchmarking studies are presented in the Supporting Information for this paper. The Cs structures optimized to form their corresponding C2v structures in all cases except for that with the B2PLYP functional. The D∞h structures were found to be second order saddle points in all cases except for the MP2 studies, where a slight bending (0.06°) of the O−Ce−O angle removed one imaginary frequency. All functionals except B2PLYP predict that the zero point vibrational energy (ZPVE) of the linear structure of CeO2 lies 2−5 kcal/mol higher in energy than the bent structure. Surprisingly, MP2 predicts this energy difference to be much greater at 21.9 kcal/mol. CCSD and CCSD(T) are nearly identical, also predicting large energy differences of 18.7 and 18.6 kcal/mol, respectively. A large range of O−Ce−O bond angles were found for the nonlinear structures. BP86, B3P86, PBE, PBE0, and TPSS all found values close to 130°; B2PLYP and mPW2PLYP found values close to 138°; MP2, CCSD, and CCSD(T) systematically increased the bond angle (109−114°) as the correlation level increased. It is difficult to evaluate the error in the CCSD and CCSD(T) calculations because of the multireference character of CeO2 (T1 diagnostic was between 0.031 and 0.036). Because its a1 and b2 frequencies are within 2 cm−1 of the experimental frequencies, BP86 was chosen to investigate all other larger clusters and their isomers. The structures resulting for the selected clusters studied are presented in Figure 5. Additional details on these computations are presented in the Supporting Information. Some of the clusters examined here were investigated previously by Asmis and co-workers using DFT/B3LYP methods, with comparable basis sets.27 In that work, the IR spectra for different isomers at each of several cluster sizes were compared to experimentally

Figure 5. Lowest energy structures calculated for the Ce2O3+, Ce3O5+, Ce4O7+, Ce2O5+, Ce3O7+, and Ce4O9+ cations. Relative energies for each isomer are shown in kcal/mol. D

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we can also derive O2 binding energies for each of these clusters. As shown in Table 3, these values are in the range of

measured spectra. We therefore compare the structures determined here to those found in this previous work. All of the clusters having formulas of the form CeO(CeO2)n+ are found to have cage-like structures with most of the oxygen atoms involved in the cage framework, bound to two metal atoms. Another motif for oxygen in some structures is a terminal configuration, i.e., CeO, attached to a cage framework. As shown in Figure 5, several isomers lying close together in energy were identified for each cluster size. Asmis and co-workers found most of these same isomers, but the relative energies in their work vary somewhat from those found here.27 Referring to Figure 5, the relative energies of isomers a and b for the Ce2O3+ ion (0.0 and +7.7 kcal/mol) were reversed in the work of Asmis and co-workers (+1.7 and 0.0 kcal/mol). In their work, the isomer indicated here as b was found to be lower in energy and to match the IR spectrum measured. In particular, the spectrum had a clear band at higher frequency for the terminal oxygen stretch. Likewise for the Ce3O5+ cluster, our energy order of a, b = 0.0, + 5.6 compares to that of Asmis of +0.2, 0.0. Again, the IR spectrum detected agreed better with that for isomer b. For Ce4O7+, we found four isomers at low energy, whose relative energies were a, b, c, d = 0.0, +0.4, +7.2, and +16.7 kcal/mol, whereas Asmis and coworkers had values of +4.5, +1.7, 0.0, + 4.5 kcal/mol for these same structures. In each of these cases, the energy differences between isomers are small compared to the total binding energies, and so it is not too surprising that the BP86 and B3LYP methods with different basis sets would produce slightly different relative energies. Both methods find the same isomeric structures at each cluster size. However, on the basis of the comparison with the IR spectra, it appears that the B3LYP method of Asmis does a better job identifying the most stable structures than our BP86 method. Using our computed energies for CeO(CeO2)n+ clusters differing by one CeO2 unit, it is also possible to derive effective binding energies for each cluster with respect to the loss of CeO2, as seen in the photodissociation. This is done by taking the energy of the larger cluster compared to that of the smaller cluster plus a separate CeO2. As shown in Table 2, these numbers are in the 80−90 kcal/mol range. Considering this, it is not surprising that the photodissociation required multiple photon absorption conditions.

Table 3. Calculated Bond Lengths (Å) and Bond Energies (kcal/mol) for Clusters with Superoxide O2 Ligands

bond energy

3,5/a → 2,3/a 3,5/b → 2,3/b 4,7/a → 3,5/a 4,7/b → 3,5/a 4,7/c → 3,5/b 4,7/d → 3,5/b

88.5 89.5 84.8 84.5 83.2 73.7

Ce−O2 bond length

O−O bond length

Ce−O2 bond energy

2,5/a 2,5/b 3,7/a 3,7/b 4,9/a 4,9/b 4,9/c 4,9/d

2.32/2.32 2.34/2.35 2.36/2.36 2.34/2.37 2.36/2.37 2.34/2.37 2.35/2.36 2.36/2.37

1.32 1.32 1.32 1.32 1.32 1.32 1.32 1.32

27.3 16.4 21.0 20.8 19.9 25.6 17.9 16.6

16−28 kcal/mol. These computed binding energies are somewhat higher than the estimates for the 3,7 and 4,9 cations (10 kcal/mol) derived from thermal decomposition experiments.24 In either case, these binding energies suggest that single photon absorption at either 532 or 355 nm would be energetic enough to eliminate O2 from these clusters, consistent with their greater observed photodissociation efficiency. Another aspect of the clusters with excess oxygen concerns the structure of the adsorbed O2 units. As shown in Table 3, the O−O bond distances for each of these molecules is computed to be about 1.32 Å. According to well-established ideas about the activation of O2,61,62 this indicates that these units have superoxide character, corresponding to negatively charged O2− molecules. This indicates that the core units identified above as stable clusters donate charge to adsorbed oxygen, in turn becoming more positive in the process. This kind of charge transfer makes sense because it allows the odd cerium atom in the CeO(CeO2)n+ formula to become oxidized and closer to its ideal +4 oxidation state. We saw evidence previously for superoxide O2 units like this in the infrared spectra of uranium oxide species (UO4+, UO6+).63 Zhou and co-workers saw similar behavior in the IR spectra of Ni(O2)n+ complexes.64 It may be possible in future computational work to analyze the distributions of charge on these systems to further explore this charge transfer interaction or to investigate the adsorption of different ligands on the surfaces of these clusters.



Table 2. Calculated Bond Energies for the Process CeO(CeO2)n+ → CeO(CeO2)n‑1+ + CeO2 in kcal/mol cluster/isomer

cluster/isomer

CONCLUSIONS Cerium oxide cluster cations, CexOy+ were formed by laser ablation in a supersonic expansion and investigated with mass spectrometry, laser photodissociation, and density functional theory calculations. Mass spectrometry and photodissociation experiments show that cation clusters with the stoichiometry (x = 2y − 1), i.e., CeO(CeO2)n+, are formed preferentially. Neutral CeO2 was found to be the most common neutral eliminated by photodissociation, consistent with the most common oxidation state of bulk cerium oxide (IV). Calculations show that most of the prominent clusters have cage structures, with all oxygens bound in the framework to two or more metal centers. Some species have an additional terminal oxygen bound to a single metal. Clusters with excess oxygen exhibit the same cage structures, but with an additional O2 molecule bound to the surface. According to calculations, the external surface-bound oxygen molecules have superoxide (O2−) character, presumably obtained via charge transfer from the core cluster framework.

Figure 5 also shows the computed structures from our work for clusters with “excess” oxygens, i.e., those with compositions of CeO(CeO2)n(O2)+, which were found to eliminate O2 efficiently via photodissociation. These clusters were not investigated by Asmis and co-workers.27 They also are found to have core structures resembling the cages seen for corresponding CeO(CeO2)n+ clusters, but with an additional external O2 attached. Using the energies computed for the corresponding CeO(CeO2)n+ and CeO(CeO2)n(O2)+ isomers, E

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Infrared spectroscopy or further computational studies on these larger clusters would be useful to probe the nascent oxygen activation chemistry in these systems.



ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b02052. Full details of the DFT computations done, including the structures and energetics for each of the clusters considered (PDF)



AUTHOR INFORMATION

Corresponding Author

*(M.A.D.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS We gratefully acknowledge the generous support for this work from the Air Force Office of Scientific Research through grant no. FA9550-15-1-0088 (MAD) and from the National Science Foundation through grant no. CHE-1361178 (HFS).



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