Quantifying the Impact of Relativity and of Dispersion Interactions on

Jun 2, 2014 - We compared the mechanism of O2 dissociation catalyzed by Cu38, Ag38, and Au38 nanoparticles. Overall, our results indicate that O2 diss...
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Quantifying the Impact of Relativity and of Dispersion Interactions on the Activation of Molecular Oxygen Promoted by Noble Metal Nanoparticles Mohammed Benali Kanoun and Luigi Cavallo* KAUST Catalysis Center, Physical Sciences and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia S Supporting Information *

ABSTRACT: We compared the mechanism of O2 dissociation catalyzed by Cu38, Ag38, and Au38 nanoparticles. Overall, our results indicate that O2 dissociation is extremely easy on Cu38, with an almost negligible barrier for the O−O breaking step. It presents an energy barrier close to 20 kcal/mol on Ag38, which decreases to slightly more than 10 kcal/mol on Au38. This behavior is analyzed to quantify the impact of relativity and of dispersion interactions through a comparison of nonrelativistic, scalar-relativistic, and dispersioncorrected DFT methods. Nonrelativistic calculations show a clear trend down the triad, with larger in size nanoparticle (NP), weaker O2 adsorption energy, and higher O2 dissociation barrier, which is so high for Au38 to be in sharp contrast with the mild conditions used experimentally. Inclusion of relativity has no impact on the O2 adsorption energy, but it reduces the energy barrier for O2 dissociation on Au38 from 30.1 to 11.4 kcal/mol, making it even lower than that on Ag38 and consistent with the mild conditions used experimentally. Dispersion interactions have a remarkable role in improving the adsorption ability of O2 on the heavier Ag38 and especially Au38 NPs, contributing roughly 50% of the total adsorption energy, while they have much less impact on O2 adsorption on Cu38.

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experimentally and theoretically.16−23 It is found that the adsorption of these molecules on gold NPs strongly depends on the charge states and the size of the gold NP.8,20−28 Further, considering that molecular oxygen adsorption and dissociation on gold NPs is a fundamental step in the oxidation of basically any substrate, it is not surprising that a large number of theoretical studies have focused on this reaction.8,24−27 In this context, several studies suggested that the Au38 NP has special activity.24,25 Moving to the other noble metal NPs, the increased catalytic activity of NPs with confined sizes seems not limited to Au. For example, Ag and Cu NPs were found to have catalytic activity similar to that of Au NPs for the partial oxidation of hydrocarbons and for the oxidation of CO at low temperature.28 The remarkable catalytic properties of coinage NPs have spurred efforts to understand the mechanism of adsorption and reactivity of small molecules on them.18−,23,29−35 Previous studies shed light on the mechanism through which the shape and size of the NP, among other properties, influence the overall catalytic behavior.18−23,29−35 Nevertheless, although several theoretical studies have been performed to investigate oxygen activation on coinage metal NPs,36 with a special focus on gold NPs,24,25 no systematic comparison between the three metals, to highlight similarities and differences, has been performed. Relativity stabilizes the s and p orbitals of Au, while

INTRODUCTION Metal nanoparticles (NPs) generally exhibit different physicochemical behavior from the bulk material, which gives them an unusual behavior with useful applications across a diverse range of fields, including catalysis, photochemistry, and energy conversion.1−5 This diverse behavior has been of course related to their high surface-to-volume ratio, compared to flat surfaces of bulk materials, and to the large number of low-coordinated atoms at their surface.6−8 In this scenario, recent studies attribute the origin of the excellent catalytic performance of NPs to the fact that they actually have smaller dimensions than those previously reported in the literature.9−11 On the practical side, NPs can also be used in colloidal solution, which significantly improves the accessibility of the reacting molecules to the catalytic surface.12 Among the metals that have received more attention in the field certainly is gold. Despite that it had long been regarded as an inert metal,13 the pioneering work of Haruta demonstrated that it is active toward CO oxidation when in the form of NPs and dispersed on oxides.14 Since then, there has been intensive research work on Au-based catalysts due to its potential applications in technology.15 Some of the factors that predominantly govern the catalytic activity of these NP systems are, besides the aforementioned size, the particle shape, the charge state, and, when supported, the nature of the supporting material. Due to their particular ability to promote reactivity involving H2, O2, and CO, the adsorption process of these small molecules on gold clusters has been studied in detail © XXXX American Chemical Society

Received: April 20, 2014

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Table 1. Structural and Energy Data of the M38 NPsa

destabilizing the d orbitals, which perturbs the overall s−p−d hybridization and the d states, in turn influencing the bonding between the gold atoms and the adsorption of molecules that will undergo reactivity.20 For this reason, all the previous studies on O2 activation on Au NPs have used methods including relativity. Nevertheless, despite this recognized role, there is no study trying to quantify the impact of relativity in determining the behavior of gold NPs. This is at odds from the case of homogeneous catalysis, where it has been deconstructed how relativistic effects impact the behavior of gold catalysts.15,37 As for dispersion interactions, it is also clear that it will increase the adsorption ability of small molecules on any metal NP. However, to the best of our knowledge, no previous study included the dispersion correction term in the classic DFT electronic energy. In addition to offering the first systematic comparison of O2 dissociation on the three noble metal NPs, this paper intends to fill both the above gaps by analyzing dissociation of molecular oxygen on the Cu38, Ag38, and Au38 NPs through a comparison of all-electron nonrelativistic (NR) DFT calculations with results including scalar relativistic (SR) effects through the zeroth-order regular approximation (ZORA, see ref 38 and references therein), while dispersion interactions were included with a semiempirical van der Waals type correction term.

Cu38 NR SR D3 DD Exp. NR SR D3 DD NR SR D3 DD a

Ag38

Au38

M−M bond distance (Å) 2.551 3.005 3.114 2.518 2.911 2.885 2.486 2.894 2.868 2.475 2.855 2.843 2.533 2.889 2.88 radius of gyration (Å) 3.58 4.22 4.37 3.54 4.09 4.10 3.49 4.06 4.10 3.48 4.01 4.04 binding energy, per atom (kcal/mol) −56.7 −36.6 −34.1 −59.9 −40.9 −49.5 −66.8 −48.5 −60.9 −69.4 −49.9 −59.2

The experimental M−M bulk38−41 distance is also shown.

0.05 Å. The different average bond length is of course reflected in the radius of gyration of the NP, which follows the same trend (see again Table 1). In particular, at the SR level the Au and Ag NPs have the same size, which is roughly 17% larger than that of the Cu NP. Moving to the binding energy per atom of the M38 NPs, Eb, the data reported in Table 1 show that relativity has a remarkable role in keeping together the Au NP since roughly 30% of a total Eb, around 60 kcal/mol, can be ascribed to relativistic effects, a percentage that reduces to 10% and 5% in the Ag and Cu NPs. The role of dispersion interactions on Eb is instead quite constant, about 10 kcal/mol, corresponding to roughly 15−20% of the total Eb for all the metals. Overall, the trend in the calculated Eb in the absence of relativistic effects, Cu > Ag > Au, is not consistent with the trend in the melting point, Tm, of the pure metals, Cu: 1084.6 °C > Au: 1064.2 °C > Ag: 961.8 °C. At the SR level the correct trend is established; still the correlation between the Eb and the Tm, with an R2 parameter of 0.83, is not remarkable, and it is improved by dispersion interactions, with the R2 parameter increasing to 0.97 at the D3 level. Previous analysis indicated that coinage metal NPs can be described has having a core−shell structure, with the six core atoms (colored in red in Figure 1) positively charged and the 32 surface atoms negatively charged.23 Our analysis of the Hirshfeld charge distribution is in agreement with the previous findings at both the NR and SR levels. Further, it also indicates that this core−shell polarization is scarcely sensitive on relativity since the NR charge of the six core atoms along the triad, +0.013, +0.008, and +0.024e, is slightly greater at the SR level, +0.015, +0.014, and +0.035e. To understand thoroughly the impact of relativity on the electronic structure of the NPs, we calculated the total and the local density of states (DOS) of the naked M38 NPs. From the eigenvalues and eigenvectors solved at sufficient Γ k-points in the first Brillouin zone, the total DOS can be projected into its partial components (PDOS) with respect to different atoms. Figure 2 shows the calculated partial DOS for the M38 NPs at the NR and SR level (since geometries are scarcely affected by dispersion interactions, the D3 and DD DOS are not shown here as they are extremely similar to the SR DOS). From the local projected DOS displayed in Figure 2, there are two principle regions: the lowest energy band of the valence band

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RESULTS AND DISCUSSION Geometry and Electronic Structure of M38 NPs. The starting structure of coinage M38 NPs is modeled as a truncated octahedron with Oh symmetry, although no symmetry was enforced in the calculations. As shown in Figure 1, there are

Figure 1. Schematic representation of M38 nanoparticles. Red spheres indicate the six core atoms; blue spheres indicate atoms defining the (100) facets; and green spheres represent atoms at the center of the hexagons defining the (111) facets.

eight equivalent hexagonal fcc (111)-like facets and six equivalent square fcc (100)-like facets in M38 NPs. The average bond length between neighboring metals, predicted by the different computational approaches, is reported in Table 1 and compared with experimental bulk distances.39−41 As expected, inclusion of relativistic and dispersion energy terms reduces the average bond length, with the larger effect for the heavier Ag and Au metals, about 0.1 and 0.2 Å, deriving from relativistic effects. The SR average bond length values of Au38 are in good agreement with those achieved with a scalar relativistic variant of the linear combination of Gaussian-type orbital density functional (SR-LCGTO-DF) method, 2.86 Å,42 and by using a plane-wave method with relativistic pseudopotentials, 2.89 Å.43 On the other hand, dispersion interactions have a minor, still significant, influence on the average bond length, about 0.02− B

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extends in the −7 to −2 eV range, and it is mainly composed of d states; the next band occurs around the Fermi level mostly due to s states interacting with the d states. This s−d hybridization strengthens the bond between metal atoms. In addition, the DOS shows that in all the cases there is a gap located between the top of the d-band and the Fermi level. In all cases the NR and SR LDOS exhibit similar poor d-band character near the Fermi energy. In all the cases the bottom of the d-band is not significantly altered by relativity, while the top of the d-band is shifted toward the Fermi level. This effect is particularly relevant in Au38, with a broadening of the d-band of more than 3 eV and the top of the d-band arriving to −1 eV. Consequently, the center of the d-band is slightly right-shifted by about 0.5−0.9 eV when relativistic effects are included for Cu38 and Ag38, arriving to be right-shifted by 1.3 eV for Au38. Overall, the strong s−d hybridization and d−d interaction in Au leads to a clearly broader d-band at the SR level compared to the Cu and Ag NPs. Absorption of O 2 on M 38 NPs. We analyzed O 2 adsorption on the (100) facet since this is indicated as the preferred adsorption site in the literature.24,25,44,45 Also in this case we examined the impact of the different computational approaches on the energy and geometry of O2 absorption on the NP. The driving force for the binding is in the transfer of electron density from the NP to antibonding π orbitals of molecular oxygen, which weakens and elongates the O−O bond, facilitating its dissociation.24,25,44,45 We found a similar effect, with the larger adsorption energy corresponding to a longer O−O bond length as shown in Table 2. Focusing on Table 2. Energy and Geometry of Molecular O2 Adsorbed on M38 NPs, Obtained from NR, SR, D3, and DD Calculations Cu38 NR SR D3 DD

1.57 1.59 1.59 1.57

NR SR D3 DD

2.01 1.99 1.99 1.98 (kcal/mol) −39.1 −39.5 −42.7 −47.4

Eads NR SR D3 DD

Ag38 O−O (Å) 1.48 1.48 1.48 1.48 M−O (Å) 2.35 2.31 2.31 2.29 −14.9 −13.0 −20.6 −20.3

Au38 1.46 1.45 1.46 1.46 2.47 2.32 2.30 2.30 −8.7 −7.2 −18.3 −16.7

geometry, in all cases there is a remarkable elongation of the O−O bond from the initial value of 1.24 Å in the free state. After adsorption the O−O bond is 0.1 Å longer on Cu38 relative to Ag38 and Au38, with no impact of the various computational protocols used. Qualitatively similar results are obtained for the M−O bond length, although in the case of Au38 the M−O distance at the SR level is 0.15 Å shorter than at the NR level. The two dispersion correction terms we considered have basically no impact on both the O−O and M−O distances. Differently, the obtained O2 adsorption energy, Eads, exhibits noticeable differences depending on the metals considered and the computational protocol used. The overall trend is that the

Figure 2. Total and partial density of states of Cu38, Ag38, and Au38 NPs. The vertical dashed line denotes the Fermi level. The wine dotted line represents the total DOS of M38 NPs. Purple and orange lines represent PDOS of the M d and s states. The green arrow indicates the center of the d-band. C

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Figure 3. Reaction pathways for O2 dissociation on the Cu38, Ag38, and Au38 NPs.

quite close to that for Cu, is indeed remarkable. The SR value we calculated for Au is in excellent agreement with the value of 1.97 Å calculated with relativistic pseudopotentials in ref 26. In line with the results indicated in a previous section, dispersion interactions have basically no impact on the O−O bond length. The trend in the activation energy also indicates a remarkable role of relativity in determining the behavior of the Au NP. Indeed, the NR energy barrier for O−O dissociation for Cu, Ag, and Au is 3.5, 24.2, and 30.1 kcal/mol at the NR level, with a clear increasing trend down the triad, while at the SR level these barriers are 1.7, 19.1, and 11.4 kcal/mol. Dispersion interactions have a negligible impact on the overall energy barrier. In short, relativity reduces the energy barrier for O2 activation with all the metals, this effect being particularly remarkable for Au, making O2 dissociation on Au NPs an easy event under mild conditions.46,47 As for the other metals, O2 dissociation on Cu is almost barrierless, whereas on Ag it has a still reasonably low energy barrier, indicating that O 2 dissociation on Ag is also feasible under reasonably mild conditions. Interestingly, it is relativity that makes the O2 dissociation barrier lower for Au than for Ag NPs. As a final comment, the SR energy barrier for Au, 11.4 kcal/mol, compares excellently with the barriers of 10.8 and 9.9 kcal/ mol reported in refs 48 and 24. Considering that the NR and the SR geometries for Au are remarkably different, we decided to investigate if the low SR O2 dissociation energy barrier originates more from the different NR and SR geometries or from including relativity in the evaluation of the energy. To this end, we calculated the O2 dissociation energy barrier at the NR level through single-point energy calculations on the SR geometries, and for consistency, we calculated the same barrier at the SR level using the NR geometries. In the former case, the energy barrier amounts to 30.1 kcal/mol, while in the second case the barrier amounts to 14.8 kcal/mol. This result clearly indicates that the geometry has a minor impact on the energy barrier, which is instead profoundly influenced by relativity. Geometry and Energy of the O2 Dissociation Product. After dissociation, the two oxygen atoms are adsorbed in the most stable 3-fold hollow sites of the (111) facets for all NPs, as

O2 adsorption on the M38 NP becomes weaker moving down the triad. As expected, for Cu38 the calculated Eads value at the SR level is very close to that at the NR level, indicating nonsignificant relativistic effects. Conversely, for Ag38 and Au38 NPs, the nonrelativistic Eads values are larger than the relativistic ones. Comparison with literature data indicates that the SR Eads we calculated for Au38 is in good agreement with the value of 6.5 kcal/mol calculated by Illas with the revPBE functional.26 Dispersion correction obviously reinforces the binding, although this effect is minor in the case of Cu38, contributing roughly 10% to the Eads, while it accounts for about 30% and even 50% of Eads in the case of Ag38 and Au38. This result, together with the previously discussed cohesive Eb of the naked NP, highlights that inclusion of dispersion interactions is mandatory for the reliable modeling of heavy metal NPs. Hirshfeld charge analysis indicates that there is a transfer of electron density from the M38 NP to the coordinated O2, which at the SR level amounts to −0.50e, −0.52e, and −0.42e for Cu, Ag, and Au. Comparison between the amount of charge transfer between the NR and SR values indicates that relativity has an impact on this value, with the total charge on the O2 molecule at the NR level being −0.54e. The reduced charge transfer at the SR level can be associated with the more tightly bound s-electrons that are transferred less effectively to the electronegative O atoms. Activation Energy for O2 Dissociation. We move now to the oxygen dissociation mechanism on M38 NPs, according to the accepted mechanism proposed in the literature for Au38.24,25,43 The resulting energy profile is shown in Figure 3. Starting from the optimized geometry of molecular O2 absorbed on NP systems, the reaction pathway involves the breaking of the O−O bond. The value assumed by the O−O bond in the transition state is extremely dependent on the nature of the metal and the computational protocol used. Specifically, the O−O distance of 1.88, 2.43, and 2.46 Å at the NR level for Cu, Ag, and Au is reduced to 1.82, 2.28, and 1.96 at the SR level. While the trend at the NR level is of an increasing O−O distance, the amazingly shorter O−O distance in the case of Au relative to Ag at the SR level, and actually D

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stable than the separated species, which means that inclusion of entropic terms would make the O2 dissociated product thermodynamically unstable. Inclusion of relativistic effects lowers remarkably the energy barrier for O2 dissociation and stabilizes clearly the dissociation product, making it the thermodynamic sink. Dispersion interactions reinforce this behavior and render the adsorption product stable on a free energy scale. Comparison with the literature indicates that our SR energy barriers for Ag38 and Au38 are smaller than those of 24.0 and 48.8 kcal/mol corresponding to O2 dissociation on Ag(111) and Au(111) surfaces from bulk,49 but for Au it is in excellent agreement with the barriers of 10.8 and 9.9 kcal/mol reported for O2 dissociation on Au NPs.48,24 In a different instance, in the case of Ag38 and Au38 NPs, we found that the absorption energies calculated at NR and SR level using the revPBE functional are smaller than the energy barriers for dissociation. While it is known that the revPBE functional usually results in low adsorption energies compared to other functionals, such as the PW91 functional,25 still the calculated energy difference between absorption and dissociation is included within the error bar for chemisorption energies obtained for the revPBE functional by Hammer et al.50 On the other hand, inclusion of dispersion clearly stabilizes the adsorption product, making dissociation more competitive with desorption. To understand the details of O2 adsorption and dissociation, we evaluated the local density of states (LDOS) projected on the orbitals of the NP and O2 species along the reaction pathway (see Figure 5). For O2 activation on Cu38, the SR LDOS indicates strong overlap between d-states on the Cu38 NP and 2p orbitals on the O atoms (see Figure 5a). This overlap becomes larger in the dissociation product, as the top of the d-band on Cu38 broadens up to the Fermi level. This explains the strong O2 adsorption and the low energy barrier for its dissociation on Cu38. Moving to the interesting case of Au38, the NR LDOS of Figure 5b indicates scarce overlap between the very stable d-band on Au38, which lies well below the Fermi level, and the 2p orbitals on the O atoms. Only at the level of the dissociation products there is some limited overlap between the Au38 d-states and the O atom 2p orbitals near the Fermi level, indicative of weak bonding. This scenario is changed by relativity, which pushes the d-states on Au38 to higher energy, making the overlap with 2p orbitals on the O atoms much more effective, even at the O2 adsorption level (see Figure 5c). As the O2 dissociation proceeds, the LDOS clearly shows stronger mixing between the Au38 and O orbitals. This explains the improved interaction between O2 and the Au38 NP, together with the much lower O2 dissociation barrier and the stability of the dissociation product. For the sake of clarity, we do not discuss the NR LDOS plots for Cu since they are very similar to the SR LDOS and the NR and SR LDOS plots for Ag since they are intermediate between those for Cu and Au. We just mention here that in the case of Ag the limited relativistic effects are unable to push the d-states of Ag high enough in energy, thus preventing optimal overlap with the 2p orbital of oxygen. Finally, the contour plot for the SR electron density difference, Δρ, of O2 activation on the Au38 NP is reported in Figure 6. The electron density difference is calculated as Δρ = ρAu38/O2 − ρAu38 − ρO2, where ρAu38/O2, ρAu38, and ρO2 are the total electron density of the total Au38/O2 system and of the Au38 and O2 geometries rigidly separated in the geometry they

shown in Figure 4. The impact of relativistic effects and dispersion correction on the geometry of the dissociation

Figure 4. Representation of key structures along the reaction pathway for O2 dissociation on the Au38 NP at the SR level.

product shows almost the same trend as described in the previous section for O2 coordination. The average M−O bond distance goes from 1.97, 2.23, and 2.32 Å at the NR level to 1.93, 2.19, and 2.19 Å at the SR level. Consistently with previous structures, dispersion interaction has a minimal impact on geometries. Conversely, the impact of the computational protocol on the final energy of the O2 dissociated species relative to the O2 adsorbed species is remarkable. In fact, at the NR level the dissociation product is 38.8, 12.8, and 3.6 kcal/ mol below the adsorbed O2 species down the triad, indicative of an extremely strong Cu σ-bond that precipitates the O2 dissociated product 78.4 kcal/mol below the separated Cu38 and O2 moieties, versus a rather weak Au−O bond, with the separated Au38 and O2 moieties only 12.2 kcal/mol above the dissociation products. Further, at the NR level the preference for O2 dissociation versus O2 adsorption on Au38 is extremely low, 3.6 kcal/mol only, indicating that there even could be an equilibrium between molecular and dissociated oxygen on the Au38 NP. As already observed, at the NR level there is a trend in the triad, with the Ag behavior between that of Cu and Ag. At the SR level, instead, the dissociation product on Au38 lies 20.4 kcal/mol below the O2 adsorbed species, making dissociation of the adsorbed O2 more favorable for Au than for Ag. This trend is amplified by the Grimme-type dispersion term for Au. Interestingly, the dispersion term reduces the energy gain associated with dissociation for Cu and Ag. Discussion. As anticipated, the overall O2 dissociation profile is shown in Figure 3. The most favorable reaction pathway corresponds to Cu38, with a clearly downhill pathway characterized by very low energy barriers and scarcely affected by the computational protocol. The energy profiles for Ag38 show that the major correction comes from dispersion interactions, rather than relativity. The transition state for O2 dissociation is higher in energy than the separated Ag38 and O2 moieties, indicating that the most likely destiny of the O2 adsorbed species, also considering entropic effects that disfavor adsorption, is O2 desorption rather than dissociation. Nevertheless, the overall energy barrier for O2 dissociation remains reasonably low and accessible under relatively mild conditions. Dispersion interactions contribute to make dissociation favored over desorption. In all the cases the dissociation product is clearly more stable than the separated species, which indicates that there is a thermodynamic driving force to collapse the system into the O2 dissociation product. Finally, in the case of Au, relativity is fundamental for O2 dissociation. Indeed, in the absence of relativistic effects the energy barrier for O2 dissociation is remarkably high, actually unaccessible under mild conditions, and the dissociation product is scarcely more E

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have in the total Au38/O2 system. The contour plane contains the two O atoms, and it is orthogonal to the (100) Au coordination facet. Analysis of Figure 6a indicates that O2 adsorption results in a reduction of electron density along the O−O σ-bond, with a larger increase of density on the π orbitals on the O atoms, to enhance interaction with the Au38 NP, and with a total SR Hirshfeld charge transfer of 0.21e from the NP to each of the O atoms. The plot of Figure 6a indicates this charge transfer involves basically all the Au atoms of the NP. At the transition state for dissociation there is negligible accumulation of electron density on the incipient Au−O σbonds involving the Au atoms at the center of the nearby hexagonal (111) facets (see Figure 6b), and the total charge transfer of 0.26e from the NP to each of the O atoms is quite similar to the charge transfer in the O2 adsorption product, 0.21e. Finally, in the dissociation product the Au−O σ-bonds involving the Au atoms at the center of the nearby hexagonal (111) facets are clearly formed (see Figure 6c), and the bond is clearly polarized with 0.27e transferred from the NP to each of the O atoms. This indicates that the dissociation process is followed by an increase in the charge transferred from the NP to O molecule.

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CONCLUSIONS In this manuscript we compared the mechanism of O2 adsorption and dissociation on M38 coinage metals NPs, and we quantified the effect of relativity and dispersion interaction on structure and energy. As known in literature, relativistic effects push the d-states of the metals down the triad to higher energy, this effect being clearly negligible for the lighter Cu, and fundamental to rationalize the experimental behavior for the heavier congener, Au. Dispersion interactions are also expected to become more relevant down the triad although, to the best of our knowledge, no work on O2 dissociation on Au NPs included this energy term. In line with these expectations, our results quantify that relativity contributes to 5%, 9% and 25% of the cohesive energy of the Cu, Ag and Au NPs, while dispersion contributes 10%, 16% and 19% of the total cohesive energy down the triad. Good correlation between the cohesive energy of the NP and the experimental melting temperature of the bulk material requires not only the expected inclusion of relativistic effects, but also inclusion of dispersion effects. Differently, relativity has a minor role in determining the adsorption energy of O2 on the NP, less than 10% for all the metals, while it is dispersion interaction that has a remarkable stabilizing effect. While this is scarcely relevant for Cu38, 8% only of the total adsorption energy, it becomes fundamental for Ag, and especially Au, contributing 37% and 61% of the total adsorption energy, making O2 adsorption favored on a free energy scale. It is dispersion interaction that makes O2 adsorption on Au38 a clearly favored event. Moving to the O2 energy dissociation barrier, our results indicate this to be a substantially barrierless process for Cu38 and of moderate energy for Ag38, independently from the calculation protocol. Differently, for Au38 relativity reduces the O2 dissociation barrier from 30.1 kcal/mol to only 11.4 kcal/ mol making O2 dissociation an easy proc ess under mild conditions. The stability of the dissociate oxygen relative to the separated reactants indicates that relativity accounts for 35% of the total binding energy of Au38, while dispersion accounts 32% and 37% for Ag38 and Au38. As for the overall behavior when both relativity and dispersion are included, our results indicate that O2 dissociation

Figure 5. Projected density of states for oxygen dissociation on Cu38 at the SR level (a) and at the NR and SR level on Au38 (b and c). Purple and red areas represent the PDOS of the M d-states and O p-states. Along the lines, the first frame corresponds to the O2 adsorption intermediate, the second frame to the O−O breaking transition state, and the third frame to the O2 dissociation product.

Figure 6. Electron density difference maps for oxygen dissociation on the Au38 NP at the SR level. (a) O2 adsorption intermediate; (b) the transition state for O2 dissociation; (c) the O2 dissociation product.

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Notes

on Cu38 is extremely easily, with a strong adsorption energy, a negligible dissociation barrier, and a very stable dissociation product. O2 adsorption on Ag38 is equally favored, but its dissociation requires the overcome of a barrier of 18.3 kcal/ mol, before precipitating the system into the very stable oxidation product. This barrier is high enough to make O2 desorption clearly competitive with dissociation on a free energy scale. Concluding with Au38, the lower energy barrier for O2 dissociation makes it favored over O2 desorption also on a free energy scale

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Research reported in this publication was supported by the King Abdullah University of Science and Technology (KAUST).

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COMPUTATIONAL DETAILS All calculations were performed within density functional theory (DFT) as implemented in the software packages ADF51,52 and BAND.53,54 The generalized gradient approximation of the revised Perdew, Burke, and Ernzerhof (revPBE) formalism55 for electronic exchange and correlation was used. Basis sets formed by Slater-type atomic orbitals of valence triple ζ quality, with a polarization function (TZP basis set), were employed for all the atoms. To investigate the effect of relativity, we considered two cases: the first corresponding to a classical approach with no relativistic effect in the Hamiltonian or empirically fitted into the basis set, NR in the manuscript, and the other with scalar relativistic effects inserted in the Hamiltonian by employing the Zero Order Regular Approximation (ZORA),38 in connection with the ZORA tuned basis sets provided with the ADF package, SR in the manuscript. To include dispersion interactions, normally a deficiency of DFT, in addition to the SR calculations we employed the dispersion term DFT-D3 proposed by Grimme56 and the densitydependent dispersion correction57 scheme, D3 and DD in the manuscript. Geometry optimizations were considered converged when the maximum force on the atoms was lower than 5 × 10−4 Hartree/Å. Analytic second derivatives were calculated to characterize the transition states as first-order saddle points. The grid used for the numerical integration was controlled through the INTEGRATION keyword set to 5.0 for geometry optimizations and to 7.0 for frequency calculations. The criterion for the SCF convergence was set to the default value of 10−6 au. For all the NP-based systems, a singlet electronic state was considered. In case the SCF procedure was difficult to converge, a smearing parameter of 0.0015 au was used in the geometry optimization. Extrapolation of the energy to smearing zero was performed through single point energy calculations on the final geometry, by reducing the smearing parameter to 0.0005 au stepwise. The extrapolated energy was less than 1 kcal/mol lower than at smearing set to 0.0015 au. Adsorption energies (Eads) were calculated as Eads = ENP/O2 − (ENP − EO2), where ENP/O2 is the total energy of the complex; ENP is the energy of the relaxed NP; and EO2 is the energy of optimized O2 in the triplet state.

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ASSOCIATED CONTENT

S Supporting Information *

Cartesian coordinates of all the structures discussed in the manuscript. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. G

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The Journal of Physical Chemistry C

Article

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