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Charge and Geometrical Effects on the Catalytic NO Reduction by Rh and Rh Clusters 2

6-

6+

Héctor Isaí Francisco-Rodríguez, Virineya Bertin, Jorge R. Soto, and Miguel Castro J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b08172 • Publication Date (Web): 26 Sep 2016 Downloaded from http://pubs.acs.org on October 1, 2016

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The Journal of Physical Chemistry 1

Charge and Geometrical Effects on the Catalytic N2O Reduction by Rh6- and Rh6+ Clusters Héctor Francisco1, Virineya Bertin1*, Jorge R. Soto2, and Miguel Castro3* 1

Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, Col. Vicentina, México, D. F. 09340, México. 2 Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México (UNAM), CP 04510, México, D. F, México. 3 Departamento de Física y Química Teórica, DEPg. Facultad de Química, UNAM, Del. Coyoacán, México D.F., 04510, México

ABSTRACT: The catalytic conversion of nitrous oxide (N2O) is of crucial environmental relevance, because this chemical compound is a greenhouse gas with an important contribution to climate change, even larger than CO2, depleting the ozone layer. Recently, reduction of N2O catalyzed by rhodium subnanoclusters has been the subject of intensive research, both experimental and theoretical, finding dependencies of reaction rate on the size and geometry and electronic structure of the cluster. In this work, the catalytic reduction mechanism of N2O by Rh6– and Rh6+ ionic clusters have been studied by means of density functional theory calculations within the zero-order-regular approximation (ZORA), which explicitly include relativistic effects. The N2O + Rh6– and N2O + Rh6+ reaction pathways were approached starting from a comprehensive search of different stable adsorption modes; transition states were determined as well. We have obtained that the Rh6– anions present the lowest activation barriers without spin selectivity. The N2O reduction pathway on the Rh6– anion resulted more favorable that the simple desorption channel; whereas on Rh6+ both channels are in competition, as it was experimentally observed. The N2O reduction on Rh6– and Rh6+ is sensitive to the charge; it seems to be independent of geometry.

Corresponding author: Phone: 52-55-56-22-37-83

Fax: 52-55-56-16-20-10

E-mail: [email protected]

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Introduction The nitrous oxide, N2O, molecule is a very dangerous pollutant because it promotes the destruction of the ozone layer, the protector of life on the earth, that prevents the entry of excessive UV radiation. Indeed, in the stratosphere it is the main anthropogenic threat for ozone depletion. In this regard, extensive experimental and theoretical studies have been performed to achieve N2O reduction. Theoretical studies on the mechanism involved in catalytic reactions of a metal with N2O are important for the identification of the electronic and energetic parameters that make the rupture of nitrous oxide feasible. For instance, some authors have considered the electronic effects, charge transfer from the metal towards the nitrous oxide molecule, as an appropriate mechanism for the N2O bond rupture1,2. Specifically, the N2O reduction by CO on Rh carbonyl and hydroxide systems was addressed 3. The authors propose that the [Rh(CO)4]– anion is the active complex able to reduce N2O in the presence of [Rh4(CO)11]2– with the release of CO2 and N2 from the radical species. The reaction is a catalytic cycle with an electron transfer from [Rh(CO)4]– to the nitrous oxide giving N2O– which is trapped by [Rh4(CO)11]2– to form [Rh4(CO)11(N2O)3]–. The last complex evolves releasing CO2 and N2O. It should be marked that in heterogeneous catalysis involving metal-oxide interfaces, it is recognized that the activity of a catalyst is much determined by its ability to transfer charge to and from surface reaction intermediates 4. Charge transfer effects will be studied in this work for the N2O reduction by ionized Rh6 clusters. Alkali metals were employed for the control of N2O in kinetic studies,5 the authors use NaOH and conclude that one Na atom is potentially capable of reducing many N2O molecules in combustion systems. However, this reaction is not easy to produce, because there are other competitive reactions. It gave rise to large discrepancy between experimental and theoretical results.5 There are processes as Raprenox (cyanuric acid injection) to reduce the NOx´s but they produce significant N2O molecules. Chemisorption and oxidation reactions of small molecules, N2O among them, employing small clusters of anionic Ni, Pd and Pt, not including Rh particles, were addressed experimentally by Hintz et al.6 It was found that the reactions depend on the cluster composition. The reactions over Pdn– are faster and more efficient than the reactions on other metals. The small Pd5– ion appears to be the most active. The efficiency of the clusters varies with size. For example, Pt6– presents anomalous low reactivity with many molecules, including N2O. In general, the reaction proceeds through a fast sequential addition of oxygen atoms on the cluster, forming N2 in the gas phase. That is, the O atoms bond to the anions yielding Pd3O3–, Pd4O4–, Pd5O4–, Pd6O4–, Pd7O5–, and Pd8O6–. Some clusters suffer fragmentation during


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the reactions. The Ptn– and Nin– anions also add oxygen sequentially thus increasing the N2O flow. Molecular N2O was not adsorbed on bare cluster anions. Small Cun– clusters were also used to reduce N2O through the CO catalytic oxidation process.7 CunO– ions are formed in N2O breaking. The most efficient reaction between Cu5–Cu16, was the one corresponding to n=7. Harding et al.8 who studied the reaction of Rhn± with N2O, using resonance mass spectrometry, found significant reactions for the small charged clusters, with a better activity than bigger systems, such as crystal surfaces. They also found evidence of the reaction rate dependence on the size, and geometrical and electronic structures. Furthermore, they found multiple isomers, several of them degenerate, probably formed in particle collisions. In the N2O reaction, the authors observed a sequential addition of O atoms on the nanoparticles, as was established for other metals (Cu, Pd, and Pt). For negatively charged small clusters, they detected a decay process by charge transfer effects during the reaction. For neutral Rhn particles, we have identified, however, degenerate ground and excited states with different geometries and spin multiplicities.9 We also studied the importance of excited states of neutral Pd, Pt, and Au atoms in the N2O capture and activation.10-12 There are few studies on N2O reduction using nanoparticles. For example, Hamilton et al.13 by means of infrared multiple photon dissociation spectroscopy, IR-MPD, have studied the infrared induced reactivity on the surface of isolated Rh6+ particles. In this way, it was observed that the N2O molecule experiments adsorption and further dissociation producing N2 and a partially oxidized rhodium clusters. Moreover, the combination of far-infrared multiple dissociation spectroscopy, FIR- MPD, with density functional theory calculations allow the determination of the structure of small rhodium clusters, as it was demonstrated for the specific case of Rh8+. 14 A theoretical study on N2O reaction with Rh1 to Rh6 neutral clusters performed using the VASP code, by Rodríguez-Kessler et al., shows that bridged and some top sites are active for NO reduction.15 The adsorption energy increases with cluster size. For small particles, dissociation occurs with small barriers. In Rh5 and Rh6 the process is barrier-less, but the fragments bind strongly to the cluster, stopping the reaction. The magnetic moments are related to the cluster activity to disassociate N2O.15 Martinez et al.16 addressed the role of ammonia in the activity of ionized Fe supported on zeolites to reduce N2O, using DFT calculations. They obtained that the activation barriers are in agreement with the experimental results and conclude that ammonia favors oxide reduction. By monitoring the oxidation state at the surface of rhodium nanoparticles during CO oxidation, using in situ ambient pressure X-ray photoelectron spectroscopy, Grass et al. 17 showed that the oxidation



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of the catalyst surface is fundamental for its activation and that the oxidized layer formation is dependent on the particle size. Reaction rates and oxide formation increase as the size of the particle decreases. More recently, Yamada et al.18 also have found that both, N2O reduction and CO oxidation on Rhn (n= 10–30) oxide particles are more efficient than on pure bare Rhn. The CO and N2O species were mixed with gas containing Rhn. As quoted, sequential addition of oxygen to Rhn yields the RhnOm-1 + N2O → RhnOm + N2 reaction; where CO extracts O atoms from the clusters: RhnOm + CO → RhnOm-1 + CO2.18 Larger clusters present higher rate constants for the studied reactions and are consistent with theoretical and experimental studies. By means of the ZORA/PBE method, we have studied the reduction of N2O on neutral Rh5 and Rh6 clusters.19, 20 It was found that a square pyramid, in a sextet, defines the ground state (GS) of Rh5. This state, jointly with the degenerate quartet and octet, are active for the N2O reaction. The breaking of the N-O bond is achieved for N2O on Rh5 for geometrical approaches that maximize the overlap and electron transfer of the frontier orbitals. In the case of Rh5, the 4d orbital energies fall in between those of HOMO and LUMO of N2O. For neutral Rh6, there are many degenerate states, of different geometries (octahedral and triangular prism) and multiplicities (1 and 7), which are active to reduce N2O.20 In this work, a detailed study was performed on the catalytic reduction of N2O by Rh6– and Rh6+ clusters. To provide reliable structures, relativistic and Jahn-Teller effects were considered as well as different spin multiplicities that the cluster can have due to the inclusion of a transition metal such as rhodium. All possible local minima and transition states were searched to determine the most favorable reaction pathways for the two low-lying cluster geometries. Population analyses were carried out to qualitatively understand charge transfers in the relevant stages of the reduction process. We expect that the results obtained will provide insight into the effects of charge and geometry on the reduction of N2O by Rh6– and Rh6+ ions.

1. Computational details The calculations were carried out using the Amsterdam Density Functional software (ADF 2013).21 For scalar relativistic effects the Zero-Order Regular Approximation (ZORA) was used,22-24 not including spin-orbit coupling. Relativistic effects are essential to properly describe transition metals reactions; therefore, their inclusion is needed as was done here for the Rh atoms. The 1s to 3d orbitals of Rh were considered in a frozen core. This approximation is compatible with ZORA,22 so the valence space configuration is 4s24p65s14d8. Slater type orbitals were used and expanded in a triple zeta basis set


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with two polarization functions (TZ2P). However, all electrons were included for the O and N atoms. The estimation of total energies was carried out using the Generalized Gradient Approximation (GGA). The exchange-correlation was taken into account with the PBE functional, which is free of empirical parameters.25 We have validated this method in previous works, obtaining good results for the interaction of Rh5 and Rh6 with N2O19, 20 and for other transition metals. The ground state and low-lying excited states geometries and spin multiplicities of the Rh6─ and Rh6+ ions, were determined using the geometries previously identified for the neutral Rh6 particle as inputs.20 We have obtained that structures around octahedral and triangular prism forms define the ground states of Rh6─ and Rh6+, at the PBE/ZORA level of theory. During the relaxation procedure, Jahn-Teller (JT) symmetry breakings were considered by means of all possible subgroups of the Oh and D3h point symmetry groups. This procedure was performed for all studied multiplicities of the Rh6+ and Rh6

–

ionic clusters. In this way, the determined lowest

energy Rh6±1 structures were used to study the Rh6±1–N2O interactions. Several approaches of N2O on the surface of Rh6─ and Rh6+ were attempted in order to determine the local minima. For the identified Rh6––N2O and Rh6+–N2O low-lying states, a vibrational analysis was performed, under the harmonic approximation, to confirm if they are true minima on the potential energy surface. Adsorption energies, Eads, of N2O on Rh6– and Rh6+, were estimated according to the equation: Eads = Eb (Rh6± – N2O) - [Eb(Rh6±) + Eb(N2O)]

(1)

Here, Eb(Rh6±–N2O) is the binding energy of Rh6±–N2O; Eb(Rh6±) and Eb(N2O) are the GS binding energies of Rh6+, Rh6─ and nitrous oxide species. For a complete reaction pathway analysis, additional geometry optimization was performed to search for saddle points, which represent transition states (TS). Both, eigenvector-following and specification of reaction coordinates for TS search (TSRC) techniques were used. For all TSs, it was confirmed that they had only one imaginary frequency. The N2O bond lengths and vibrational frequencies were previously determined by our group.20 The computed frequency, 2276.0 cm-1, is in good accord with the experimental one 2224.2 cm-1. 26 Likewise, the estimated bond lengths, d(NN) = 1.137 Å and d(NO) = 1.192 Å, are in reasonable agreement with the experimental results, d(NN) = 1.128 Å and d(NO) = 1.184 Å.26 The short N–N and N–O distances reflect the particular stability of the nitrous oxide molecule. Note also that the population analysis indicate that both terminal N and O atoms have partial negative charges, with the latter being



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the biggest.20 This is quite important for N2O reduction, since in the earlier steps of this process the O atom and the N terminal site, need to be activated.

2. Results and Discussion 2.1 Low-lying states of Rh6+ and Rh6– Similarly to the neutral cluster Rh6,20 it was found that the low-lying states of the Rh6+ and Rh6– ions present geometries that are near to the regular octahedron and triangular prism, for the first six multiplicities. For smaller clusters, Chen et al.27 have also obtained that the neutral and ionic clusters present similar GS geometries, by employing the ZORA approach, in the ADF code.

Table 1. Multiplicity (M), Jahn-Teller (JT) symmetry, binding energy (Eb), relative Eb (ΔEb), Rh–Rh distance (d), and vibrational frequencies (ν) for the lowest energy states of Rh6+. Geometry

2

JT Symmetry D3d

Eb (kcal/mol) -509.14

∆Eb (kcal/mol) 6.87

d (Å) 2.46, 2.54

ν (cm-1) 215.6

4

C2h

-508.43

7.58

2.46, 2.50, 2.53, 2.58

234.9

6

D2h

-511.78

4.23

2.47, 2.55

220.7

8

D4h

-516.01

0.00

2.49, 2.55

232.2

10

Oh

-512.80

3.21

2.55

233.4

12

Non Aufbau

2

D3h

-507.55

8.46

2.35, 2.45

261.2

4

C2v

-511.35

4.66

2.36, 2.44, 2.47

408.6

6

C2v

-512.82

3.19

2.38, 2.44, 2.48

258.9

8

C2v

-509.41

6.60

2.39, 2.43, 2.53

255.6

10

D3h

-506.44

9.57

2.40, 2.49

263.2

12

Non Aufbau

M

Rh6+

Rh6+

Multiplicities, JT symmetries, binding energies, relative energies, bond lengths, and vibrational frequencies of highest IR absorption intensity for the Rh6+ and Rh6─ ions are reported in Tables 1 and 2.


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Most of the obtained structures are slightly distorted, which depends on the spin multiplicity, due to the Jahn-Teller effect. The binding energies of the Rh6– clusters are larger than those of the cations. The average values of the Rh-Rh bond distances in the low-lying octahedrons, 2.54, 2.52, and 2.51 Å, for the neutral, cation, and anion, respectively, are larger than those in the prisms, 2.42, 2.43, and 2.44 Å, in the same order; values for the neutrals are from Reference 20. Note also that in the octahedrons, the anions present the shortest metal–metal distances, which is consistent with their having the largest Eb. Therefore, electron attachment produces more compact and stable geometries for Rh6– clusters. The lowest energy state of Rh6+ is an octet of octahedral geometry, whereas the M = 10 and 6 states were located at 3.21 and 4.23 kcal/mol above. That is, electron detachment from the septet GS of neutral Rh620 yields an increase for the magnetic moment, number of unpaired electrons, of Rh6+. However, the low-lying state of the prism, a sextet lying at 3.19 kcal/mol, shows a smaller total spin, than its neutral counterpart. Other spin states lie at higher energies; see Table 1. An interesting question we can ask is: which of the two isomers, octahedron (high spin) or prism (low spin), is more feasible for N2O reduction? This issue will be addressed in the following sections. On experimental grounds, the existence of two different structural isomers for the low-lying states of Rh6+ was proposed.28, 29 Both are able to react with NO with different reaction rates. The relative population of the forms depends on the experimental conditions, being one more active than the other.The two calculated lowest energy states, M = 8 (D4h) and M = 10 (Oh), are quasi-degenerated, since they are separated by 3.21 kcal/mol (0.14 eV); as seen in Table 1, they have similar vibrational frequencies of highest IR intensity. The same is true for the prism, where the sextet and quartet differ by only 1.47 kcal/mol (0.06 eV), which means the difference lies within the computational error of the method used. The octet (M=8) of the Rh6+ ion corresponds to an apical octahedron with a slightly distorted apex of 3.7 Å; the central square presents bond lengths of 2.49 Å and the length to the apices is 2.55 Å. The low-lying state of the prism, a sextet, has two isosceles triangular faces with two bond lengths of 2.44 Å and a larger one of 2.48 Å, separated by parallel edges of 2.38 Å. The frequencies presenting highest IR absorption intensities fall over a narrow range, within the 215 – 235 cm–1 for octahedral, and 255 – 264 cm–1 for prism. The exception is the quartet of the prism, showing the highest IR intensity peak at 408.6 cm─1. This result implies that the cationic clusters share an important feature in their IR spectra for most cases, regardless of their spin multiplicity for each geometry. Electron addition to the GS of neutral Rh6º, a septet of octahedral geometry, gives enhancement for the magnetic moment of Rh6–, as high spin state, M=12, was found for the GS of this ion (Table 2).



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Note that in the Rh6– octahedral isomers, the M= 6 and 8 states (obtained from the neutral through the ΔM = ± 1 rule), are clearly located at higher energies: 11.77 and 8.12 kcal/mol, respectively. However, the GS of Rh6─ (M = 12) is degenerate in energy with two high spin-states, M = 8 and 10, of the prism. Indeed, these states, both of low-symmetry, differ negligibly (less than 2 kcal/mol) from the GS, see Table 2. These isomers have rectangular faces with sides of 2.44 and 2.47 Å for M = 8 and 2.38 and 2.56 Å for M=10, respectively. Triangular bases are scalene triangles with sides of 2.42 and 2.44 Å. The vibrational frequencies of highest IR absorption for Rh6+ and Rh6– are close to the calculated values for neutral Rh6°,20 (see Tables 1 and 2). The exceptions are for the anionic prism with M = 10 and, as mentioned above, the cationic prism with M = 4. In the first case, the IR spectrum has active modes at 232 and 266 cm-1; however, the largest intensity peak appears at a low frequency of 141 cm-1.

Table 2. Multiplicity (M), Jahn-Teller (JT) symmetry, binding energy (Eb), relative Eb (ΔEb), average Rh–Rh distance (d) and vibrational frequencies (ν) for the low-lying states of Rh6–.

2

JT Symmetry D3d

Eb (kcal/mol) -681.09

∆Eb (kcal/mol) 9.03

D (Å) 2.50, 2.51

ν (cm-1) 231.7

4

D2h

-677.25

12.87

2.49, 2.52, 2.53

221.1

6

D2h

-678.35

11.77

2.52, 2.52

243.1

8

D4h

-682.00

8.12

2.52, 2.55

241.7

10

Non Aufbau

12

Oh

-690.12

0.00

2.51

238.6

2

D3h

-682.53

7.59

2.39, 2.44

261.4

4

C2

-683.99

6.13

2.36, 2.37, 2.44, 2.45

260.0

6

C2v

-686.48

3.64

2.35, 2.43, 2.45

216.0

8 10

C2 C2

-688.23 -688.55

1.89 1.57

2.34, 2.42, 2.44, 2.47 2.38, 2.41, 2.43, 2.56

210.8 141.0

12

Non Aufbau

M Geometry

Rh6─

Rh6─

An octahedron with M=10 was found as the GS for Rh6+ by Torres et al30 using the PBE method and a corrected pseudopotential. In our study, Table 1, the M = 8 and 10 states are very near in energy,


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complicating the assignment for the GS of the Rh6+ ion. For the anion, their calculated GS is a triangular prism with M = 8, whereas the octahedron lies at higher energy, ΔEb = 3.46 kcal/mol (0.15 eV). This order differs from that of the present work, and reveals the sensitivity of these small particles to selected computational details: PBE, ZORA, pseudopotentials, orbital basis sets, but especially the Jahn-Teller effect considered. The average bond distances obtained by Torres et al.24 for Rh6° (2.59 Å), Rh6+ (2.64 Å), and Rh6– (2.50 Å) are close to each other and they show also more compact structures for the anion. However, we found that such bond lengths are in a broad range, due to the asymmetries produced by the JT effect. Moreover, they indicate that in the triangular prism, Rh6°, Rh6+ and Rh6– have similar average bond distances (2.50 Å), which are shorter than that of the neutral octahedral GS; whereas we found that they are in a range from 2.34 to 2.56 Å; see Tables 1 and 2. Harding et al. 31 performed another electronic and geometrical study of Rh6° and Rh6+. They reported an octahedron for the GS of Rh6+, where the M = 8 and 10 states are degenerate. In a lower spin state, a sextet, the triangular prism was located at 6.45 kcal/mol over the octahedral GS. This structure also presents degeneration for the quartet, octet, and dectet states. Furthermore, they conclude that these two structural isomers, octahedron and triangular prism, are roughly iso-energetic. In a subsequent study, Harding et al. 32 made comparisons between far-infrared spectroscopy results with theoretical predictions for Rh6+ to Rh12+ structures. For the ground state of Rh6+, they only report a distorted octahedral geometry, which is in excellent agreement with the experimental spectrum; for instance, there is one principal rather broad band at 225 cm–1, which is very close to their calculated value of 235 cm–1. 32 The trigonal prism previously reported as a roughly isoenergetic state with the octahedral one,

31

is now

reported as a saddle point using the hybrid PBE1 functional with a SDD (Stuttgart/Dresden) basis set.32 However, in more recent work the trigonal prism structure is reconsidered with the TPSSh functional; finding that its GS is about 0.2 eV higher than the octahedral GS.33 On the other hand, in the theoretical analysis performed in reference 33, the PBE functional was discarded due to poor agreement obtained with the experimental vibrational spectrum. In contrast, we calculated higher IR active modes, by the PBE/ZORA method, for the bare octahedral Rh6+ cluster with M = 8 and 10. Our obtained frequencies, 232 and 233 cm-1, are similar to those found in reference 32 with the PBE1/SSD method and in turn agree well with experiment (225 cm-1).



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Table 3. Relative adsorption energies (kcal/mol) for the octahedron Rh6+ + N2O minima of multiplicities M.

Local minimum geometries M

2

6.87

-----

-14.00

-14.43

---

-63.56

-42.93

4

7.58

-0.87

-13.77

-----

-----

-64.88

-43.72

6

4.23

-3.47

-14.91

-----

-----

-63.29

-42.17

8

0.00

-7.15

-18.71

-13.91

-----

-58.97

-37.09

10

3.21

-4.80

-17.26

-----

-0.92

-55.65

-35.39

Since the FIR-MPD spectrum32 shows two IR active modes, we believe that the experimental results seem to be more compatible with our predicted octahedral JT distorted (D4h) dectet for the Rh6+ ion. 2.2 The Rh6+ and Rh6– ions interacting with N2O

In order to model the reduction of N2O produced by the positively and negatively charged Rh6 cluster, the Rh6+–N2O and Rh6––N2O systems were studied and will be discussed in the next sections. 2.2.1 The interaction of Rh6+ ion with nitrous oxide, N2O, molecule. The local minima for the Rh6+ + N2O interactions are shown in Tables 3 and 4 for octahedron and prism, respectively. For the studied multiplicities of the Rh6+–N2O system, some local minima were determined where the adsorbed N2O molecule is O-bound or N-bound on atop configurations (see the 3rd and 4th columns in Table 3 and 4). The first process is physisorption with adsorption energies lower than 10 kcal/mol. The second one is chemisorption as the Eb of N2O lies between -21.35 kcal/mol (= 13.77 - 7.58 kcal/mol) for the octahedral with M = 4, and -18.51 kcal/mol for the prism with M = 10. The low-lying M = 8 octahedral state is close to the upper limit (-18.71 kcal/mol), see Table 3. Hamilton


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et al.33 using FIR-MPD spectroscopy studied this kind of binding experimentally and theoretically, using the TPSSh functional. They found Eb of 0.68 and 0.77 eV for Rh6+ octahedral with multiplicities of 8 and 10, respectively. However, using the PBE method they found 0.83 eV for the octet, which compares well with our result of 18.71 kcal/mol (0.81 eV). Furthermore, the bridge formation (5th column of Table 3) was identified as a local minimum between two transition structures; for the octet and dectet spin states of the Rh6+ octahedral clusters.33 For the octet we have identified a bridge local minimum, lying at +4.8 kcal/mol (0.21 eV) from the atop one (-13.91 kcal/mol in Table 3). However, for M=10 we did not find a local minimum for the bridge adsorption mode. Instead, the structure in the 6th column (N2O in front of and bisecting a face with the O atom nearest to a Rh atom) was found as the local minimum. The resulting energy, 0.92 kcal/mol, is only 4.13 kcal/mol lower than the N2O desorption energy (3.21 kcal/mol) and corresponds to physisorption. For other multiplicities, we did not find a non-dissociative arrangement forming a bridge structure, except for a doublet (M = 2). Table 4. Relative adsorption energies (kcal/mol) for the prism Rh6+ + N2O minima of multiplicities M. Local minimum geometries M

2

8.46

-1.04

-12.17

1.77

-65.22

-64.09

-21.81

-43.81

4

4.66

-3.03

-14.82

----

-63.91

-64.41

-23.38

-43.43

6

3.19

-4.91

-16.34

----

-56.94

-58.49

-26.57

-36.3

8

6.60

-1.27

-12.53

1.76

-49.56

-51.25

-24.03

-30.26

10

9.57

2.07

-8.94

7.95

-37.69

-39.57

-18.82

-20.3

There is also a possible bridge configuration for the prism (5th column in Table 4) that is stable for M = 2, 8 and 10. These minima correspond to physisorption and can favor the reduction of N2O. Table 3 also shows a dissociated N2 + O stable arrangement with the lowest energy state for all M values on



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Page 12 of 27 12

the Rh6+ surface (7th column) which by adding an energy input can release N2 molecules. The additional energies necessary for N2 desorption are 20.26 kcal/mol (0.88 eV) for the dectet and 21.88 kcal/mol (0.95 eV) for the octet. These PBE/ZORA results for N2 desorption are above those found using the TPPSh method,33 0.44 and 0.71 eV, respectively. For the prism (Table 4) there are two stable dissociated, almost degenerated, N2 + O formations with the lowest energy for all spin-states (6th and 7th columns), which by adding energy can release N2 molecules. The average additional energies, necessary for N2 desorption (9th column), are in the range of 19.27 kcal/mol (0.84 eV) for the dectet up to 22.19 kcal/mol (0.96 eV) for the sextet. The bridge conformation of N2O on the surface of the triangular prism Rh6+ ion emerges as an active intermediate that can produce the dissociation of N2O. The doublet, octet and dectet states favor the existence of this intermediate and thus the reduction. Though the doublet is not a lowestenergy state, oxide-supported clusters could reduce the total spin of the prism Rh6+ cluster. These results indicate the spin state selectivity on the reduction process catalyzed by cationic Rh6 clusters. 2.2.2 Interaction of the Rh6– anion with N2O. Table 5 shows the five local minima identified for the adsorption of N2O on the octahedral Rh6– anion (columns 3 – 7). Markedly, as seen in the 3rd and 6th columns, two new minima emerge for this negatively charged particle; such states were not found for the studied Rh6+ octahedral clusters. However, no local minima with activated N2O were located for the searched configurations, presumably due to the repulsion effects between the oxygen atom (sharing a partial negative charge) and the atomic sites of the Rh6– ion. We believe that due to such charge distribution, the O-bound atop structure does not appear as a local minimum. Instead, we have found that the pathways starting with the O atom near to the cluster lead mainly to dissociation. Note that all the local minima either bridged or centered, are chemisorptions in the N-bound atop configurations. Some of these chemisorptions (columns 6 and 7) could lead to poisoning of the catalyst due to the large energy requirement to activate the oxygen atom in the absence of suitable transition structures. It will be seen at section 2.4.3 that the atop formation (column 5) is the precursor for the N2O reduction reaction. The other local minima configurations have low probability of occurrence in the first stage of the reaction because they require additional rearrangements on the cluster surface. In the pathways where the N2O molecule is dissociated, energies of 18.48 and 24.34 kcal/mol for M = 12 and 8, respectively will be required to desorb the N2 product. A larger value, 33 kcal/mol, is needed for the other spin states.


Page 13 of 27

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Table 5. Relative adsorption energies (kcal/mol) for the octahedron Rh6- + N2O minima of multiplicities M. Local minimum geometries M

2

9.03

---

-16.78

-24.53

-30.93

-36.31

-98.80

-65.88

4

12.87

---

-15.32

-23.55

---

-35.32

-98.23

-63.46

6

11.77

-7.69

-18.04

-24.86

-31.51

-36.60

-99.43

-67.74

8

8.12

-10.45

-17.18

-26.61

-34.2

-35.37

-95.91

-71.57

0.00 2

-7.72

-16.78

-25.30

-25.29

-31.4

-80.87

-62.39

1

Table 6. Relative adsorption energies (kcal/mol) for the prism Rh6- + N2O minima of multiplicities M. Local minimum geometries M

2

7.59

-12.60

-13.28

-21.40

-26.31

-17.42

-91.86 -91.87

-46.35

-65.47

4

6.13

-13.09

-12.73

-22.38

-29.54

-18.87

-94.54 -94.86

-49.18

-66.62

6

3.64

-14.15

-16.77

-23.97

-31.75

-21.13

-94.18 -96.84

-35.36

-69.26

8

1.89

-13.83

-19.11

-23.69

-33.17

-23.78

-89.30 -93.02

-40.74

-66.36

10

1.65

-17.09

-17.09

-22.55

-32.57

-21.57

-85.01 -82.73

-37.43

-61.00

Lastly, in Table 6 it can be observed that for the prism isomer there are also five local minima for the adsorption of N2O on the Rh6– particle (columns 3 – 7), all belonging to chemisorptions regimes. The seventh column stands out for having an N2O activated mode. That is, for this arrangement the oxygen–



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Page 14 of 27 14

metal repulsion is avoided, producing the attachment of nitrous oxide throughout its terminal atoms. The structural flexibility of the prism (of lower symmetry) should be marked to promote (even if it is negatively charged) the N2O activated stage, which can be a crucial precursor for the breaking of N2O. Via this local minimum, the reduction of nitrous oxide could be feasible for all the addressed multiplicities. N-bound chemisorptions in bridge and atop fashions are candidates for the first stage (columns 3-5), where the later dominates. The difference between the relative energies of this structure and that of the N2O activated stage is very small, indicating a switching between them. It should be pointed out that the horse shaped minimum (column 6) establishes a channel that could contribute to the poisoning of the catalyst. Finally, the dissociation can be any of the columns 8 and 9, which are quasi-degenerated in energy. The N2 desorption to atop (column 11) can be achieved with an additional energy of 21.73 kcal/mol for M =10. Larger energies, around 27 kcal/mol, are required for the other multiplicities. Notably, all the total spin-states studied here for the anionic trigonal prism promotes the formation of an N2O activated intermediate. Thus, they could be good candidates to dissociate the nitrous oxide molecule. We will see in Sect. 2.4.4 that the reaction pathway does not necessarily constrained to pass through these local minima and an almost spontaneous reaction can be achieved from the atop configuration. 2.3 Charge transfer effects. In this section the Hirshfeld population analysis (HPA) is presented for Rh6+–N2O and Rh6––N2O, with selected multiplicities that can show the different reaction stages. 2.3.1 Hirshfeld population analysis for Rh6+ + N2O. The charges for the Rh6+ + N2O octahedral and prism systems are reported in Table 7. M = 8 and 10 were the multiplicities considered for the octahedron and M = 8 for the prism. The total transferred charges on the N2O molecule are given in the last column. The total charges on the N2O molecule for atop adsorptions (rows 2, 3, 7 and 8) are near to +0.16e for the O-bound mode and slightly lower, +0.11e (octahedral) or +0.14e (prism), for the N-bound modes. From this stage, the polarities of the adsorbed N2O reactive have a similar pattern, Nδ–Nδ+Oδ–, as that of the free N2O molecule, before their dissociation. For instance, the bridge configuration for the octahedron (row 9) and prism present the N(0.12)N(+0.05)O(-0.14) polarities. As expected, there is negative charge transfer, from the octahedral and prism Rh6+ particles into the N2O moiety, in the bridged structures. Such charge goes into anti-bonding molecular orbitals of N2O, producing the weakening of the N–O bond. This is a key electronic feature of the Rh6+ catalyst, as it promotes the N2O reduction. Specifically, in the octahedral bridge modes (row 6) the charge on Rh1, on which the O site is bonded, reaches a value of about +0.22e; a similar value was


Page 15 of 27

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found for the bridge of the prism (row 14), showing that electrons on N2O come mainly from this atomic site. Moreover, in the bridged octahedral complex of the 9th row, the two Rh8 and Rh9 atoms, on which the Nterminal atom is adsorbed, present charges of about +0.23e. Thus, the bridged modes present both activated N and O atoms, where the O sites have significant negative charges, of about -0.14e, independently of geometry. These findings suggest that oxygen activation on the cluster surface, as it is done on Rh6+, is crucial for the N2O breaking. The total transferred charge on the dissociated molecule is lower than that arranged in bridge. However, the Hirshfeld charge of O increases considerably being around -0.20e, coming mainly from the Rh atoms in the neighborhood. The transferred charge on the N2 molecule is lower than +0.07e for both octahedron and prism. Table 7. Hirshfeld charges per atom of the Rh6+ + N2O complex. Local Minimum Rh(1)

Rh(2)

Rh(3)

Rh(4)

Rh(5)

Rh(6)

N(7)

N(8)

O(9)

N 2O

8

0.08

0.15

0.14

0.16

0.16

0.16

0.01

0.22

─0.07

0.16

10

0.10

0.17

0.16

0.16

0.12

0.13

0.01

0.22

─0.07

0.16

8

0.09

0.16

0.14

0.15

0.17

0.17

─0.06

0.22

─0.04

0.12

10

0.08

0.16

0.13

0.17

0.17

0.18

─0.06

0.22

─0.04

0.11

8

0.22

0.16

0.19

0.18

0.20

0.20

─0.09

0.07

─0.14

─0.15

10*

---

---

---

---

---

---

---

---

---

---

8*

---

---

---

---

---

---

---

---

---

---

10

0.21

0.18

0.19

0.23

0.23

0.17

─0.12

0.05

─0.14

─0.21

8

0.23

0.19

0.16

0.22

0.13

0.18

0.02

0.06

─0.19

─0.11

10

0.21

0.21

0.15

0.21

0.13

0.19

0.07

0.03

─0.20

─0.10

8

0.15

0.16

0.15

0.09

0.14

0.15

0.02

0.22

─0.07

0.17

Geometry



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Page 16 of 27 16

8

0.16

0.16

0.15

0.08

0.16

0.15

─0.06

0.23

─0.03

0.14

8

0.22

0.20

0.16

0.16

0.25

0.21

─0.12

0.05

─0.13

─0.20

8

0.19

0.17

0.19

0.19

0.24

0.13

0.02

0.06

─0.19

-0.11

*Do not converge

Table 8. Hirshfeld charges per atom of the Rh6– + N2O complex. Local Minimum M

Rh(1)

Rh(2)

Rh(3)

Rh(4)

Rh(5)

Rh(6)

N(7)

N(8)

O(9)

12

─0.10

─0.15

─0.14

─0.15

─0.12

─0.16

─0.10

+0.13

─0.21

12

0.00

─0.12

─0.15

─0.12

─0.14

─0.01

─0.22

+0.03

─0.27

─0.46

12

─0.13

─0.10

─0.10

+0.02

─0.05

─0.08

─0.05

─0.12

─0.39

─0.56

10

─0.08

─0.15

─0.17

─0.15

─0.16

─0.14

─0.09

+0.14

─0.20

─0.15

10

─0.13

─0.12

─0.12

─0.13

0.00

─0.01

─0.23

+0.02

─0.28

─0.49

Geometry


N2O

─0.18

Page 17 of 27

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10

─0.02

─0.03

─0.13

─0.18

─0.03

─0.12

─0.19

─0.07

─0.23

─0.49

10

─0.10

─0.14

─0.11

─0.12

+0.07

─0.06

─0.05

─0.13

─0.36

─0.54

2.3.2 Hirshfeld population analysis for Rh6– + N2O The atomic charges for the octahedral and prism Rh6– + N2O pathways are reported in Table 8. The M = 12 and 10 multiplicities were selected for the octahedral and triangular prism structures, respectively. For these anions, the total transferred charges for the atop adsorption modes (rows 2 and 5) are -0.18e and -0.15e for octahedron and prism, respectively. The Rh6– to N2O charge transfer becomes more negative, 0.49e, for the bridge mode, only found for prism. Such movement of charge is necessary in order to activate the N2O reduction process, as was seen for the cationic case. The charge distribution in this mode, N(-0.19e)N(-0.07e)O(-0.23e), is consistent with the N2O breaking, as the transfer electrons occupying N2O antibonding orbitals weaken the bonding of the molecule. The horse octahedral configuration (3rd row) is also characterized by a large charge transfer (-0.46e), producing a considerable increase in the polarity of the N2O molecule: Nt(-0.22)N(+0.03)O (-0.27e). This charge mainly comes from the Rh1 and Rh6 atoms, which are directly linked to the N2O moiety, and to a lesser degree from the next neighbors, Rh2 and Rh4. The N2O breaking has a less probability of occurrence through the horse pathway, because in this coordination mode, the oxygen atom is located far away from the Rh6– particle and, quite importantly, the complex has reached a considerable stable state. Note that the total transferred charge, 0.56e and -0.54e, in the dissociated molecule (4th and 8th rows) is more negative than in the horse and bridge, for both octahedron and prism. Such charge, as in the cationic systems, mainly resides in the O atom, in this case being -0.38e and -0.37e for the octahedron and prism, respectively; the transferred charge mainly comes from the Rh atom linked to it. Besides, the final charge in the N2 molecule is lower than -0.18e for both octahedron and prism. From the previous analysis we can conclude that a negative charge transfer towards the N2O molecule in necessary to weaken the N-O bond, independently of the geometry and charge of Rh6. However, this process only occurs in the cation for some spin multiplicities, while in the anion occurs only for the prism. This does not mean that the reaction cannot be activated for the complexes where a



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Page 18 of 27 18

stable bridged structure was not found. In the next section, we will discuss the role of the transition structures in the reaction pathway of the N2O reduction process catalyzed by the clusters under study. 2.4. The reaction pathways for the catalytic reduction of N2O by Rh6+ and Rh6– clusters 2.4.1 Reaction pathway Rh6+ + N2O  (Rh6O)+ + N2 In order to compare our results with the experiments, the complete Rh6+ + N2O  (Rh6O)+ + N2 reaction pathway was studied, at the PBE/ZORA level of theory. The schematic energy profile diagram for the octahedral (OCT) and prism (PRI) reaction pathways is shown in Figure 1. Only the lowest energy states, M = 8 and 10, for both considered geometries are presented in this figure; the results for all multiplicities are shown in Figs. S1 and S2 of Supporting Information (SI). These diagrams include the local minima results from Tables 3 and 4 corresponding to the more favorable reaction pathway. As discussed above, the reaction was found as possible only for the M = 2, 8 and 10 states; no intermediates appear for M = 4 and 6 for both geometries. For these spin multiplicities similar energy barriers were obtained through the transition structure TS1‡ with activation energies of 12.47, 13.68, and 13.97 kcal/mol for M = 2, 8, and 10, respectively for the octahedron and 13.75, 16.18, and 15.95 kcal/mol for the same multiplicities in the case of the prism. Starting the reaction (stage #2 in Fig. 1) by means of the N–bond, N2O is adsorbed on atop mode on the Rh6+ cluster with the stabilization energies shown in Table 3 and 4. In the stage #3 the N2O molecule is rotated towards the nearest Rh atom arriving to the activated complex TS1‡. Note that in these high spin channels, TS1‡ is a frustrated bridge, because formation of the O–Rh bond is not completely achieved. Afterwards, for the M = 8 channel (see Fig. 1), in a bent geometry the NNO molecule is bridged in a parallel manner to a Rh–Rh bond (stage #4) for octahedron. Instead, for prism the molecule is bridged with O bonded to an Rh atom and the N at the end forming a bridge between two Rh atoms in the opposite bond of the cluster. This stage is close to the transition structure TS2‡, with energies that are at most 0.1 and 3.65 kcal/mol above for octahedron and prism, respectively. In contrast, for the M =10 pathway, the reaction can proceed from TS1‡ directly to dissociation (stage #6 in Fig. 1). Afterwards, the N–O bond cleavage and the consequent Rh–O bond formation spontaneously take place, leading to the global minima for the dissociative adsorption of the N2O reactive (stage #6). Finally, a N2 molecule is released with an additional energy input, leaving (Rh6O)+ and N2 as products.


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Figure 1. Energy profile diagram for the (Rh6)+ + N2O  (Rh6O)+ + N2 reaction, including reactants, local minima intermediates, transition structures and products. Labels: octahedral (OCT) and prism (PRI).



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Page 20 of 27 20

The Rh6+ + N2O reaction is exothermic and the energies can be computed from the data in Tables 3 and 4. The released energies are equal to 49.56, 40.26, and 38.39 kcal/mol (or 2.15, 1.75, and 1.66 eV) for the M = 2, 8 and 10, respectively for the octahedron. In reference 33 the reaction pathways for M = 8 and 10 were calculated using the TPSSh, PBE0 and PBE levels of theory for this cluster geometry; the last one was chosen only for comparison. An energy profile diagram was also reported for the Rh6+ + N2O reaction, at the TPSSh level of theory.33 Using the PBE/ZORA method, our calculated binding energy (0.81 eV) for the M = 8 route (stage #2) compares well with their reported value, 0.83 eV, using PBE, as we mentioned in section 2.2.2. Also, our predicted activation energy (0.59 eV), is in good agreement with the value reported by them (0.51 eV) using the same method.33 For M=10 our activation barrier is only 0.09 eV below the one reported in 33 using TPSSh, while the Rh6+–N2O binding energy is 0.12 eV above. Note that our estimated released energies, 1.75 and 1.66 eV, are relatively close to those obtained through the use of the TPSSh hybrid functional (1.48 eV for M =8 and 10).33 For this case, our prediction agrees with those of reference 33 but with a transition state (TS1‡) just below 3 kcal/mol. Our results show that the inclusion of an accurate (ZORA) relativistic approach and the consideration of clusters with JT distortions permits good predictions of activation energies and IR spectrums, using the same functional for both. These two physical effects (relativistic and Jahn-Teller) turn out to be fundamental in understanding the mechanism under which Rh6+ catalyzes the reduction reaction on N2O. In Tables S1 and S2 of SI are included the evolution of the N-N, N-O, Rh-O, and Rh-N bond lengths and Hirshfeld charges through the different reaction stages for both octahedron and prism Rh6+-N2O pathways. The charges of the Rh(N) and Rh(O) atoms and the bond distances in the stages #3-6 (Fig. 1) reveal the leading role of the catalyst Rh6+ in the reduction of N2O. The bridge formation is characterized by three main events for octahedron: a) TS1‡ (stage #3), with notorious changes in the Rh-Rh-N (84.6°) and N-N-O (154.9°) angles with respect to the isolated configuration; b) the bridge (stage #4), with RhRh-N (82.1°) and N-N-O (120.5°) angles and; c) the transition structure TS2‡ (stage #5), presenting smaller Rh-Rh-N (81.8 °) and N-N-O (118.3°) angles. For the prism: a) TS1‡ (stage #3), with notorious changes in the Rh-Rh-N (84.6°) and N-N-O (154.9°) angles with respect to the isolated configuration; b) the bridge (stage #4), with Rh-Rh-N (82.1°) and N-N-O (120.5°) angles and; c) the transition structure TS2‡ (stage #5), presenting smaller Rh-Rh-N (81.8 °) and N-N-O (118.3°) angles. Comparing the results obtained for both cluster morphologies, the two reactions are very similar, however the prism geometry can equilibrate an arrangement with N2O bridged obliquely and not necessarily parallel to a Rh-Rh bond. This additional degree of freedom leads to a gradual transition to


Page 21 of 27

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the dissociation process, while in octahedral this step proceeds spontaneously. Thus, two low-lying structures of Rh6+, octahedron and prism in selected spin states (M = 2, 8, and 10), are able to produce dissociation of the N2O molecule. As far as we know, this is the first time that N2O breaking is studied on the surface of the trigonal prism of Rh6+. 2.4.2 Reaction pathway Rh6- + N2O  (Rh6O)- + N2 The schematic energy profile diagram for the Rh6– + N2O  (Rh6O)– + N2 reaction pathway, for each spin multiplicity, including the related local minima data from Tables 5 and 6 and calculated transition states, is reported in Fig. 2. Only the lowest energy states, M = 12 and 10, for octahedron and prism are presented in the figure; the complete results for all spin states are shown in Figs. S3 and S4. As seen in the energy profile diagrams, all pathways present similar energy barriers through the transition structure TS‡ with activation energies from 4.79 (for M = 4) to 6.94 kcal/mol (for M =12) for octahedron and from 5.93 (for M = 8) to 8.96 kcal/mol (for M =10) for prism. The kinetic of the reaction for the dissociation channel starts from the N-bound atop adsorption of the N2O molecule on the Rh6– particle (stage #2 in Fig. 2), with the stabilization energies shown in Tables 5 and 6. The N2O structure on the octahedral cluster is characterized by slightly lengthened bond distances (by 0.01 – 0.03 Å) and smaller N-N-O angle (155.9°) than in the free molecule while for the prism is almost the same as in the bare case (stage #1). In stage #3 the N2O molecule is rotated towards the nearest Rh atom arriving to the activated complex TS1‡ which is a frustrated bridge. In this configuration the Rh-Rh-N (85.2°) and N-N-O (142.2°) angles for octahedron and the same angles with values of 98.1°, 139° for prism show a trend to form the bridge and a greater structure bending, compared to stage #2. Afterwards, the N2O dissociation proceeds spontaneously, leading to the global minima (stage #4). Finally, a N2 molecule is released with an additional energy input, leaving (Rh6O)– and N2 as products. The thermodynamically preferable M12OCT (Fig. 2) reaction pathway needs the lowest energy (18.48 kcal/mol) to liberate the N2 molecule. Even more, the activation energies for the octahedral Rh6– anion, < 7 kcal/mol, are smaller than those (12 – 14 kcal/mol) for the octahedral Rh6+ cation, signifying an increase of the catalytic performance for Rh6–, from the energetic point of view. Moreover, activation energies which are  2 kcal/mol smaller than those of trigonal prism Rh6– were found for the octahedron. An important point to remark for this reaction is that, unlike the cation, the reduction channel is more favorable than the simple desorption channel. The atop minimum requires 25.3 kcal/mol to desorption for M12OCT, which is far above the activation barrier calculated.



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Page 22 of 27 22

Figure 2. Energy profile diagram corresponding to the (Rh6)– + N2O  (Rh6O)– + N2 reaction, including reactants, local minima intermediates, transition structures and products. Labels: octahedral (OCT) and prism (PRI).


Page 23 of 27

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In Tables S3 and S4 of SI are included the evolution of the bond lengths and Hirshfeld charges through the different reaction stages for both octahedron and prism Rh6- clusters.

Conclusions Relativistic DFT-ZORA calculations by means of the PBE functional were performed in this work to understand the reaction mechanism involved in the reduction of the N2O molecule by the Rh6–1 and Rh6+1 catalyst particles, in the two low-lying symmetries: octahedral (Oh) and triangular prism (D3h). The role of spin multiplicity, relativistic approach, charge (+1, -1), and Jahn-Teller effect was addressed. The isolated Rh6+1,-1 clusters suffer Jahn-Teller distortions for most of the considered multiplicities. The asymmetries induced by this effect are more important in the (low-symmetry) prism clusters because they are more flexible. However, competence in total energy with the octahedral particles is maintained. An exhaustive search for local minima was performed for all adsorbed approaches of N2O on the Rh6+ and Rh6– clusters in order to have a better characterization of the reaction pathways for different cases. By confirming previous experimental and theoretical results, it was determined that the cationic octahedral Rh6+ cluster favors the reduction of the N2O molecule, which depends on the multiplicity. Activation barriers in the (12 – 14 kcal/mol) range are needed to activate the oxygen and nitrogen atoms and proceed to the N2O dissociation. A better compatibility with experiment was found for M =10. In fact, we obtained an activation energy,  14 kcal/mol, which is barely 6 kcal/mol below the N2O desorption energy, indicating dissociation versus desorption competition, as it is experimentally observed. For the cationic prisms with M = 2, 8 and 10 a similar process can lead to the reduction and desorption of N2 with activation energies in a slightly higher energy range (14-16 kcal/mol). The N2O reduction on the octahedral and prism Rh6– anions was also studied for different multiplicities and pathways. Remarkably, the results show that the activation energies, 5 - 7 kcal/mol for Rh6– (octahedron) and 6 - 9 kcal/mol for Rh6– (prism), are smaller than those found for the cations and do not present spin multiplicity selectivity. Therefore, these results suggest clearly that negatively charged Rh6– particles could be better catalysts than Rh6+ cations, allowing spontaneous dissociation on their surface. The reduction process was more favorable on the anionic Rh6 cluster than in simple molecular desorption, while on the cationic one both channels are in competition. These results provide insight on the role of charge in the improvement for the catalytic performance of small rhodium particles.



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We found that using an adequate relativistic approach and considering possible Jahn-Teller distortions, the reduction mechanism of N2O on Rh6+ and Rh6– could be properly described. The N2O reduction process seems to be independent on the geometry of the Rh particles, but it is quite sensitive on the chosen charge. Positively charged particles allow the attractive interaction between an Rh atom of the cluster with the oxygen atom of the N2O molecule. In this way, the N2O molecule is bridged through its terminal atoms on the surface of Rh6+, weakening the NNO bonding. A frustrated bridge occurs on Rh6– (N2O), which, having more available electrons for donation, produces lower activation energies for the N2O reduction. We expect that this work will motivate future experimental research on negatively charged rhodium clusters as catalysts for the N2O molecule reduction. ASSOCIATED CONTENT Supporting Information. Energy profile diagrams for the reaction (Rh6)+1,-1 (octahedral, prism) + N2O  (Rh6O)+1,-1 + N2 for all multiplicities and Tables of the evolution of the bond lengths and Hirshfeld charges of the complex Rh6+1,-1(octahedral, prism) + N2O in the different reaction stages. This material is available free of charge via the Internet at http://pubs.acs.org. ACKNOWLEDGEMENTS H. Francisco acknowledges the CONACYT México scholarship for master degree funding (Reg. 370238). Very valuable discussions on this research with Dr. Enrique Poulain are strongly appreciated. V. Bertin deeply acknowledges the financial resources provided by UAM for access to the software used in the present work. M. Castro acknowledges financial support provided by DGAPA-UNAM, under Project PAPIIT IN-212315, and from Facultad de Química, under the PAIP–FQ program. Miguel Castro and Jorge R. Soto are thankful to the Dirección General de Cómputo y de Tecnologías de la Información (DGTIC-UNAM) for providing supercomputing resources on the Miztli supercomputer; Projects SC161-IG-65 and SC16-1-IR-23.

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