Theoretical Study on the Reaction Mechanism of N2O with H2

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Theoretical Study on the Reaction Mechanism of NO with H Catalyzed by the Rh Cluster 2

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Hue Minh Thi Nguyen, and Ngoc Thu Thi Pham J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp505663c • Publication Date (Web): 12 Nov 2014 Downloaded from http://pubs.acs.org on November 20, 2014

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The Journal of Physical Chemistry

Theoretical Study on the Reaction Mechanism of N2O with H2 Catalyzed by the Rh5 Cluster Hue Minh Thi Nguyen* and Ngoc Thu Thi Pham Faculty of Chemistry and Center for Computational Science, Hanoi National University of Education, Hanoi, Vietnam Abstract: The efficiency and selectivity of rhodium clusters in the conversion of NOx into N2 has been proved. DFT calculations were carried out to probe the mechanisms of the reaction of N2O with H2 on a Rh5 cluster. The reaction can form three products including P1 (N2 + H2O); P2 (NO + NH2); P3 (OH + N2H) via six different pathways. The pathway involving the product P1 is the most energetically favored because its energy barrier amounts only to 15 kcal/mol, significantly lower than that of 42 kcal/mol in gas phase without catalyst. This study contributes to the understanding of the reaction mechanisms of N2O with H2 on a rhodium surface, which is essential to limit N2O emissions in transportation. Keywords: Conversion of NOx, catalyst, rhodium clusters, potential energy surface (PES), reaction mechanisms, DFT calculations. I. INTRODUCTION Nitrogen oxides are among the most important gaseous pollutants emitted by automobile and stationary industries and they participate in cyclization reactions leading to ozone destruction.1,2 The reduction of NOx by H2 which can be catalyzed by many transition metals has been the subject of several studies due to its relevance in the improvement of the air quality.3-7 The core nature of heterogeneous catalytic processes is believed to be related to an increase of the surface area and

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Corresponding author; email address: [email protected] Telephone number: +84-944566456 ACS Paragon Plus Environment


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maximization of the number of active sites in structures of transition metals.8,9 Thus, intensive attempt has been devoted to the investigation of fascinating properties of small metal clusters which are employed as tractable model systems for practical catalysts.10,11 Specially, rhodium clusters play an important role in heterogeneous catalysis, used in reactions related to hydrogenation and dehydrogenation of alcohols,12 as well as in the reduction of harmful gases.13 The dissociation of NOx by rhodium is crucial in the conversion of the automobile’s three-way catalyst. In an attempt to understand the underlying process, we carried out a theoretical study using quantum chemical methods on the molecular mechanism of the N2O + H2 reaction with the presence of Rh5 rhodium cluster as a catalyst. Let us first summarize the previous results on this process. The adsorption and decomposition of N2O on surfaces of rhodium clusters have attracted special attention of the surface scientists.14-21 Orita and coworkers22 performed DFT calculations to study the adsorption and decomposition of N2O on Rh (100). The interaction of N2O with Rh (110) was investigated by Kokalj.23 The Fourier transform ion cyclotron resonance mass spectrometry was employed to observe reactions of nitrous oxide dispersed rhodium clusters, RhnN2O+ with n = 5, 6.24 These experiments showed that when interaction with small rhodium clusters, nitrous oxide can be decomposed. Hamilton25 carried out experimental studies on the gas phase reactivity of N2O on small rhodium clusters, in going from four to eight atoms, and proposed a mechanism of decomposition reaction of N2O on the Rh6+ cluster. Calculated DFT results revealed that the Rh-N and Rh-O bonds on surfaces of Rh (100) and Rh (110) are weaker than those on rhodium clusters, thus indicating that N2O decomposition may take place more easily upon appearance of rhodium catalysts. Formation of products N2 + H2O from reaction N2O + H2 requires high temperature range from 1700 to 3000o K, which was reviewed by Henrici.26 Lemos27 used Monte Carlo simulations to study and control the N2O + H2 reaction on Ir (110). Decomposition of N2O which was performed by Kalimeri,28 under steam electrolysis in a Pd|SrCe0.95Yb0.05O3-a|Ag proton with solid electrolyte membrane reactor (SEMR) also required high temperature up to ~550ºK. These studies

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suggested the mechanism of N2O and H2 catalyzed and uncatalyzed reaction including a dissociation of N2O to form a N2 molecule and an O atom, and then yield of H2O. Despite many experimental and theoretical studies on the nitrous oxide and hydrogen reduction, and adsorption reaction on the different rhodium surfaces, relatively little is sufficiently known about the elementary steps between N2O and H2 with the presence of rhodium clusters.Therefore, a description of a detailed mechanism at the molecular level deserves a special attention. We set out to carry out a DFT study, and present here the results, on the reaction mechanism between N2O and H2 on the Rh5 cluster, which would be a contribution to the understanding of N2O and H2 reaction mechanisms in heterogeneous catalytic chemistry. II. COMPUTATIONAL METHODS Geometrical parameters of the equilibrium structures including the reactants, intermediates, transition structures and products were fully optimized using density functional theory (DFT) with the pure BP86 functional. The performance of this functional in describing the structures and energetics of transition metals, was widely tested and reported in previous papers.29-31 The 6311++G(d,p) basis set was chosen to describe the N, O and H atoms, and the LANL2DZ basis set was considered for rhodium atom. For each structure located, a vibrational analysis was carried out in order to verify whether it is a minimum or a transition structure on the potential energy surface (PES), and to obtain the zero-point energy (ZPE). To verify the identity of each transition structure, intrinsic reaction coordinate (IRC) calculations were carried out to confirm its connection with a couple of minima. To probe the electron distribution, the natural population atomic (NPA) charges were computed using the natural bond orbital (NBO) analysis at the same level.32-33 All electronic structure calculations were carried out using the Gaussian 09 suite of programs.35 In this work, we explored mainly the high spin state, namely the sextet state for the Rh5N2O-H2 systems. III. RESULTS AND DISCUSSION A. Molecular mechanism of the gas phase N2O + H2 reaction.



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As presented above, experimental results indicated that the reduction of N2O by H2 forming the products N2 + H2O meets a great challenge in part due to the relatively high reaction temperature. There is no theoretical investigation reported explaining the mechanism of this gas phase reduction. The potential energy surface constructed to map out the N2O + H2 reaction is shown in Figure 1, in which the symbol TSx/y (TSR/1, TS1/2, TS4/P, etc…) is used to denote the transition state connecting the isomers ISx (IS1, IS2, etc...) or reactants RA (N2O + H2) and ISy or products P (N2 + H2O). Thus, TS3/4 is a transition state connecting both IS3 and IS4 isomers. Figure 2 shows selected optimized geometries of IS, TS involved in the N2O + H2 reaction. Table 1 presents relative energies ∆E (kcal/mol) of intermediates and transition states in the N2O + H2 reaction. Table S1 of the Supplementary Information (SI) lists the Cartesian coordinates, vibrational frequencies, single point energies and ZPE of the species considered in the gas phase reaction. Production of N2 and H2O may occur following three different pathways. The two first pathways start by the attack of H2 molecule to N1 and O atoms (TSR/1) or N2 and O atoms (TSR/3) of N2O molecule, with the former overcoming a barrier of 42 kcal/mol, and the latter requiring an energy of 74.5 kcal/mol. The next step in these pathways involves an out-of-plane O-H1 rotation via TS1/2 (14 kcal/mol) or TS3/4 (22 kcal/mol). Finally, the H atom migrates from N1 atom to O atom via TS2/P with an energy of 18 kcal/mol, or from N2 atom to O atom via TS4/P with an energy of 7 kcal/mol, releasing N2 and H2O molecules. The last pathway to P (N2 + H2O) occurs via TSR/5 (99 kcal/mol) describing an attack of H2 molecule into both N1 and N2 atoms of N2O, yielding IS5 (13 kcal/mol). Then, IS5 experiences an out-of-plane N1-H rotation leading to a more stable isomer IS6 (8 kcal/mol) via TS5/6 with a high rotation energy of 29 kcal/mol. From IS6, a N1-to-O H migration via TS6/4 (50 kcal/mol) to IS4 or a N2-to-O H migration via TS6/2 (50 kcal/mol) to IS2 is available. Transformation from IS2 or IS4 to P has already been discussed. Thus, at investigated condition (0º K, 1 atm), of the three pathways, the pathway related to the attack of H2 atom to N1 and O atoms of N2O molecules is the most energetically preferred, and the barrier of the ratelimiting step is equal to 42 kcal/mol. Such an energy barrier is relatively high. Therefore, we are


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examining as to whether a Rh cluster could play an important role in lowering energy barrier of reaction. We will chiefly focus on the elucidation of reaction mechanism using the Rh5 cluster as a catalyst. The reason we choose this cluster is that it is relatively stable in square pyramid structure of sextet configuration and insignificantly small HOMO-LUMO gap (0.056 eV) compared to this in other Rhn clusters (n=2-13). The high active barrier of 42 kcal/mol in the gas phase reaction of N2O with H2 proves the difficulty of reaction to take place without catalyst, and is thus in line with experiment of N2O + H2 reaction required to be carried out at hardship temperature range. B. Reaction mechanism of N2O with H2 catalyzed by the Rh5 cluster. According to previous studies, 36-37 the Rh5 cluster has two low energy isomers, namely, a square pyramid and a trigonal bipyramid structure. The ground state of the former is a sextet, which is more stable than the latter in a spin quartet configuration by ~9 kcal/mol. As a result, trigonal bipyramid structure was not considered further in the following sections. The low energy Rh5 cluster with a sextet state was used to account as the beginning reactant together with N2O and H2. Optimized geometries of species of the main channel are illustrated in Figures 3a, 3b, 3c, 4a, 4b and Figure S1 of SI describes optimized geometries of other species. The important reaction channel of N2O + H2 potential energy surface is simplified and shown in the Figures 5, 6, and the detailed scheme of PES including other product channels are shown in Figures S2, S3, S4. Again, let us mention that the symbols ISx/1, ISy/2, ISz/3 and TSx/1, TSy/2, TSz/3 stand for xth, yth, zth intermediate and transition structures of products P1, P2, P3, respectively. Relative energies ∆E (kcal/mol) predicted at theoretical level for species of the N2O + H2 + Rh5 reaction is summarized in Table 2. Table S2 (ESI) lists Cartesian coordinates of the species considered, Table S3 their vibrational frequencies and Table S4 single point energies (a.u), zero point energy ZPE (kcal/mol) for species of the N2O + H2 catalyzed reaction. Tables S2, S3, S4 are available in the SI. Experimental study on reaction kinetics between nitrous oxide and molecular hydrogen found the existence of small molecules such as N2, H2O, OH, NO….26,38 Thus, we suggest that the reaction can form three products including P1 (N2+H2O), P2 (NO+NH2), P3 (OH + N2H). The ACS Paragon Plus Environment


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formation of P1, which is the most stable and friendly product with environment may occur via four pathways I, II, III, IV, while two pathways V and VI involve the products of P2 and P3. 1. Formation of main product P1 (N2 + H2O) The calculation shows that the yield of P1 experiences three steps. The first step of the reaction is the adsorption of N2O on the surface of the Rh5 cluster. Secondly, the decomposition of N2O gives an O atom plus a N2 molecule. Finally, the O atom interacts with the H2 molecule dispersed on different Rh atoms of cluster to release H2O molecule. The addition of N2O molecule to the Rh2 atom of cluster is the first step of reaction. A natural population atomic (NPA) charges analysis points out that the charge of N2O group in IS1/1 is -0.1 electron (N1, -0.1; N2, 0.4; O, -0.3). These values reveal that electron in 4d obitals of rhodium atoms is transferred to the П* antibonding obitals of N2O group, leading to thus the weakening of N1-N2, N2-O bonds. This result is confirmed by the N1-N2, N2-O bond lengths analysis in IS1/1 with the values of 1.152 and 1.204 Å, respectively, being longer than those of N1N2 (1.143 Å) and N2-O (1.193 Å) bond lengths in isolated N2O molecule. The adsorption of N2O molecule on the Rh2 atom of Rh5 cluster via the N1 atom is consistent with previous study by Hamilton.25 As displayed in Figure 5, formation of IS1/1 (Rh5-N2O) is a significant exothermicity of -21 kcal/mol, which may facilitate formation of intermediate IS2/1 via transition state TS1/1 with an energy obstruction of only 6 kcal/mol. The unique negative frequency of -88i cm-1 in TS1/1 corresponds to appearance of the Rh5-O bond with the predicted distance to be 3.276 Å. In IS2/1, the charge of N2O group shows an obvious change with the value of -0.4 electron (N1, -0.2, N2, 0.2; O, -0.4), implying that the N1-N2 (1.220 Å), N2-O (1.328 Å) bonds are activated, the Rh5-O distance is equal to 2.076 Å. Formation of a more stable minimum IS2/1 releases an energy of -7 kcal/mol. The next step relates to a decomposition of N2O to release N2 molecule. IS3/1 can be generated via TS2/1 with a modest energy of only 4 kcal/mol. Compared to IS2/1, the Rh5-O (1.745 Å), N1-N2 (1.126 Å) bond lengths in IS3/1 markedly decrease, the Rh2-N1 distance increases to 1.974 Å due to the produce of N1-N2 strong triple bond. TS2/1 has a unique negative frequency of -538i cm-1 being ACS Paragon Plus Environment

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similar to the cleavage of the N2-O bond. The rupture of the N2-O bond is an energetic favor with an overall exothermic energy of -34 kcal/mol, which is large enough to compensate energy for the desorption of the N2 molecule from the surface of cluster and form IS4/1. In the final step, from IS4/1, the reaction may take place in four channels. The pathway initiated by the adsorption of H2 molecule on the Rh2 atom of IS4/1 is called the pathway I. IS4/1 can lead to a more stable compound IS9/1. A NPA charge analysis in IS9/1 shows that all five Rh atoms lose electron for the O atom, as they possess the positive charge (Rh1, 0.1; Rh2, 0.3; Rh3, 0.1; Rh4, 0.0 and Rh5, 0.2). It means that the adsorption of the H2 molecule on the Rh2 atom is the weakest and on the Rh4 atom is the strongest. Therefore, we explore three pathways II, III, IV involving the addition of H2 molecule on Rh3, Rh4, Rh5 atoms to find out the most energetically favored pathway. For the pathway I, IS4/1 adsorbs the H2 molecule to produce IS5/1. This process releases an energy of 12 kcal/mol. Because of their small size, both H1 and H2 atoms of H2 molecule are adsorbed on Rh2 atom with the calculated distances of 1.710 and 1.739 Å, respectively. The H1-H2 bond length in IS5/1 amounts to 0.888 Å, a bit longer than that in isolated H1-H2 bond (0.752 Å). IS5/1 can follow two ways to form IS6/1. First, IS5/1 may directly lead to IS6/1 via TS3/1 with an energy barrier of 17 kcal/mol. The unique negative frequency of -1004i cm-1 in TS3/1 corresponds to the breaking of H1-H2 bond (0.969 Å) and formation of O-H1 bond (1.539 Å). The O-H1 bond length in IS6/1 is shortened sharply to 0.976 Å, resulting in a lengthened Rh5-O bond of 1.931 Å. Second, the H1-H2 bond in IS5/1 breaks to produce IS8/1 via TS5/1, which requires an energy of only 1 kcal/mol, then the H1 atom migrates from Rh2 to O atom (TS6/1), over a obstruction of 16 kcal/mol to lead to IS6/1. The Rh2-H1, Rh2-H2 bond lengths in IS8/1 are calculated to be 1.547 and 1.595 Å, respectively. In Figure 6, IS8/1 lies bit higher than TS5/1 due to the spatial effect between H1 and H2 atoms dispersed on the Rh2 atom of cluster. In the next stage, the H2 atom in IS6/1 moves to OH1 group via TS4/1 characterized by unique negative frequency of -221i cm-1 to form IS7/1. This process is easy characterized by a low barrier of only 5 kcal/mol with released energy of -6 ACS Paragon Plus Environment


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kcal/mol. The broken distances Rh2-H2 and O-H2 bond in TS4/1 are predicted to be 1.650 and 1.640 Å, respectively. The Rh5-O bond length changes sharply from 1.931 Å in IS6/1, 2.091 Å in TS4/1 to 2.352 Å in IS7/1 as a result of the formation of H2O molecule adsorbed on the Rh5 atom of cluster. Finally, the H2O molecule in IS7/1 is free from the surface of cluster with the endothermicity of 14 kcal/mol. The Rh5 cluster comes back the initial state for the next catalytic cycle. For the pathway II, overcoming a energy barrier of only 7 kcal/mol, IS4/1 can be converted to the lower lying isomer IS9/1 via TS7/1. The O atom in IS9/1 binds both Rh2 and Rh5 atoms to form three-membered ring. The H2 molecule is adsorbed on the Rh5 atom in IS9/1 to produce isomer IS10/1 with exergonic energy of -9 kcal/mol. Similarly to the pathway I, formation of O-H1 bond can undergo two different ways. From IS10/1, the first way requires a relatively high obstruction of 24 kcal/mol to overcome TS8/1, generating IS11/1. The O atom in IS11/1 still binds both Rh2 and Rh5 atoms but the distances Rh2-O (2.211 Å), Rh5-O (2.122 Å) increase markedly in comparison with those in structures IS10/1 and TS8/1.Then, through a 1,3-H transfer, intermediate IS11/1 leads to intermediate IS12/1 via TS9/1 with a low obstruction of 3 kcal/mol. The only negative frequency of -758i cm-1 in TS9/1 relates to the breaking of Rh5-H2 bond (1.795 Å) and the formation of O-H2 bond (1.531 Å). In the Figure 6, the structure IS12/1 (-32 kcal/mol) with the H2O molecule adsorbed on Rh2 atom lies little lower than the structure IS7/1 (-31 kcal/mol) from which the H2O molecule is adsorbed on the Rh5 atom. Another way to go to P1 originates from minimum IS10/1 by a H1-H2 bond cleavage described by the transition state TS10/1 (-13 kcal/mol) with the unique negative frequency of -420i cm-1. Similarly to the pathway I, the process of the H1-H2 bond rupture is far from difficult. In isomer IS13/1, the H2 atom binds to both Rh3 and Rh5 to produce a three-membered ring with the lengths of binding predicted to be 1.768 and 1.673 Å, respectively; the Rh5-H1 bond length is only equal to 1.576 Å. The distances of O atom with Rh2 and Rh5 atoms change insignificantly in IS10/1, TS10/1 and IS13/1. Isomer IS13/1 has to overcome the TS11/1 (7.9 kcal/mol) which shows a 1,2 H


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movement generating intermediate IS14/1 (-24 kcal/mol). Then, two options are available to yield P1: a cleavage of Rh3-H2 bond to break the three-membered ring via TS12/1 (-19 kcal/mol) to give IS15/1 (-19 kcal/mol) or Rh2-O bond rupture via TS13/1 (-23 kcal/mol) to lead to the lowest lying IS16/1 (-36 kcal/mol) of potential energy surface. The first part proceeds from IS15/1 via TS9/1 (17 kcal/mol) to IS12/1 (-32 kcal/mol) which involves a migration of H2 atom from Rh5 to O atom to form the H2O molecule adsorbed on the Rh2 atom. The yield of IS16/1 in the second part generating 12 kcal/mol may facilitate the formation of IS7/1 (-32 kcal/mol) via TS4/1 with a required energy of 15 kcal/mol. In comparison with the first part, the second is energetically preferred. The pathway III involves the adsorption of the H2 molecule on the Rh4 atom to lead to IS17/1. After adsorbed on cluster, the H1-H2 bond is significantly weakened and reaches the bond length of 0.899 Å. As a consequence, the H1-H2 bond cleavage via TS14/1 to form IS18/1 takes place easily by a tiny barrier of only about 0.5 kcal/mol. While the H1 atom in IS18/1 is dispersed on the Rh4 atom, the H2 atom binds to both Rh4 and Rh5 atoms via a three-membered ring with the distances of 1.612 and 2.020 Å, respectively. Transformation from IS18/1 to IS20/1 undergoes two transition states TS15/1, TS16/1 and an intermediate IS19/1. These processes involve the migration of H1 atom from Rh4 atom to Rh3 atom. In general, the barriers to transfer the H1 atom are low by the values of 4.6 kcal/mol and 6.4 kcal/mol for TS15/1 and TS16/1, respectively. Then, by a Rh3-toO H1 atom migration, IS20/1 can produce IS21/1 via TS17/1. The transition state TS17/1 has only one negative frequency of -1186i cm-1 corresponding to appearance of O-H1 bond (1.432 Å) and breaking of Rh3-H1 bond (1.777 Å). The ∠ORh3H1 bond angle strongly decreases from 160º in IS20/1 to 19.5º in TS17/1. Compared to the energy barrier of the attract H1 on the O atom in pathways I (17.1; 15.6 kcal/mol), II (23.6; 22.0 kcal/mol), IV (18.1 kcal/mol), the energy obstruction of 11 kcal/mol in the pathway III shows an energetic favor. Formation IS21/1 is an exothermicity of -12 kcal/mol, supporting the next processes to occur. The Rh2-O-Rh5 three membered ring in IS21/1 (-31 kcal/mol) can lead to lower lying structure IS16/1 (-36 kcal/mol) via TS18/1. The processes involving the change from IS16/1 to P1 are discussed in the pathway II.



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From the Figure 6, we find that the yield of O-H2 bond in the pathway III is the reaction ratelimiting step with an energy barrier of 15 kcal/mol. The pathway IV starts by the adsorption of the H2 molecule on the Rh3 atom in IS9/1 to lead to IS22/1. Similarly to the previous pathways, the H1-H2 bond rupture in TS19/1 requires a small energy of 2 kcal/mol to yield IS23/1. Then, over an obstruction of 18 kcal/mol, the H1 atom moves from Rh3 atom to O atom to form IS24/1 with a released energy of 9 kcal/mol. The breaking of Rh2-O-Rh5 three membered ring via TS21/1 needs the energy of only 3 kcal/mol to generate more stable isomer IS25/1 (-31 kcal/mol). The Rh2 atom in IS25/1 binds to the OH1 group with the distance of 1.954 Å while the Rh3 atom binds to the H2 atom with the bond length of 1.560 Å. TS22/1 has the only imaginary frequency of -429i cm-1 describing a Rh3-to-O H2 atom migration to produce the H2O molecule adsorbed on the Rh2 atom of IS12/1. The energy of this process to overcome is 15 kcal/mol. In brief, formation of the product P1 including N2 and H2O can proceed via three steps with four pathways. Energy barriers in these pathways are relatively low, which prove the important role of the Rh5 cluster catalyst in the reduction of N2O by H2. Specially, the pathway III relating to the adsorption of H2 molecule on the Rh4 least positive charge atom shows an energetic preference with the highest energy barrier of only 15 kcal/mol. 2. Formation of minor products P2 (NO + NH2) and P3 (OH + N2H) For P2 (NO + NH2) - the pathway V, production of P2 is classified into two steps. Firstly, the N2O molecule decomposes into a NO molecule and N atom dispersed on cluster. The second step is the interaction of the H2 molecule to the last N atom giving rise to NH2 radical. In the formative step, after adsorbed on cluster, the N1-N2 bond in N2O of IS2/1 is weakened. However, the breaking of N1-N2 bond to form IS1/2 via TS1/2 still meets a difficulty due to a relatively high energy barrier of 48 kcal/mol as illustrated in Figure S2 of SI. The unique imaginary frequency of -94i cm-1 in TS1/2 is similar to the breaking vibration mode of the N1-N2 bond. The NO molecule formed in IS1/2 binds to the Rh5 atom of cluster via the O atom with the ACS Paragon Plus Environment

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bond length of 2.018 Å, the N2-O, Rh2-N distances are equal to 1.183 and 1.662 Å, respectively. IS1/2 can transfer to IS2/2 due to the desorption of the NO molecule from the cluster surface. The spin state of IS2/2 will rearrange by dint of the doublet state of the NO molecule. Geometry optimizations of compound IS2/2 with the spin multiplicity of 3, 5, 7, 9 are converged to stable minima. The spin state of 5 lies lower than those of 3, 7 and 9 by 2, 9 and 20 kcal/mol, respectively. Thus, the spin multiplicity of 5 in compound IS2/2 is employed for the following calculations by dint of its relatively stable structure. The processes of the formation IS1/2 and IS2/2 induces an endothermicity of 44 and 12 kcal/mol, respectively. Over a barrier of 8 kcal/mol, IS2/2 (29 kcal/mol) leads to more stable isomer IS3/2 (11 kcal/mol) which describes the N atom binding to both Rh2 and Rh5 atoms of cluster. Thus, the first step in the pathway V ending at IS3/2 reveals an energetic disadvantage to produce P2. The last step is related to the interaction of H2 molecule to the N atom to free NH2 radical. A NPA charges analysis of intermediate IS3/2 shows that the Rh5 atom has the most negative charge -0.02 electrons while Rh1, Rh2, Rh3, Rh4 atoms have small but positive charges. This result indicates that the adsorption of H2 molecule on Rh5 is the most favorable. As displayed in Figure S3 of SI, when the H2 molecule adsorbs on the cluster via Rh5 atom, IS3/2 can generate IS4/2 liberating 8 kcal/mol. After that, the H1-H2 bond breaks to produce IS5/2 via TS3/2 with an energy obstruction of only about 2 kcal/mol. The H1 atom in IS7/2 is dispersed on the Rh5 atom whereas the H2 atom gives a three-membered ring with Rh3 and Rh5 atoms. The next process involves a Rh5-to-N H1 migration via TS4/2 with a barrier of 19 kcal/mol to yield IS6/2. In comparison with the pathway II, the cleavage of Rh3-H2 bond of the Rh5-Rh3-H2 threemembered ring via TS5/2 (-2 kcal/mol) to lead to IS7/2 (-5 kcal/mol) and the formation of N-H2 bond via TS6/2 (10 kcal/mol) to produce IS8/2 (-18 kcal/mol) require less energy. The NH2 radical formed binds to the Rh5 cluster in a bidentate fashion. The lengths of both N-H1 and N-H2 bond in IS8/2 are 1.027 Å, shorter than those in isolated N-H bond (1.04 Å) of NH2 species. The shortened distances relate to the doublet of NH2 radical. The negative charge of -0.2 of NH2 group in IS8/2



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

shows that electron is transferred from 4d orbitals of Rh atoms in the cluster to both binding MOs which have an unpaired electron and antibonding MOs of NH2 group. However, we suggest that the electron transfer to the former is dominant because of a more energetic priority. Release of NH2 radical from the surface of cluster is greatly endothermic with an reaction enegy of 61 kcal/mol. For P3 (OH + N2H) - the pathway VI, the addition of H2 molecule to IS2/1 leads to isomer IS1/3 (-36 kcal/mol). TS1/3 (-19 kcal/mol) is the transition state for a simultaneous H1-H2 bond rupture (0.959 Å) and a O-H1 yield (1.382 Å), connecting minima IS1/3 and IS2/3 with a required energy of 17 kcal/mol. Due to the formed O-H1 bond, the Rh5-O bond is broken and the N2-O bond length increases markedly from 1.291 Å in TS1/3 to 1.427 Å in IS2/3. The structure IS3/3 (-19 kcal/mol) is formed from isomer IS2/3 (-23 kcal/mol) by a simple bond cleavage without a TS. The doublet state of OH radical makes the spin multiplicity of IS3/3 change. Structure optimization of IS3/3 with spin state of 5, 7, 9 and 11 converges to minima. Moreover, the structures with spin states 7, 9 and 11 are less stable than that of multiplicity 5 by 7, 9 and 27 kcal/mol, respectively. As a result, the structure with multiplicity 5 is used for the next calculations. Isomer IS3/3 has to overcome the TS2/3 (26 kcal/mol) which illustrates a 1,3-H movement yielding intermediate IS4/3 (9 kcal/mol), or undergoes a 1,4-H migration yielding IS5/3 (10 kcal/mol) via TS3/3 (16 kcal/mol). The distances to break the Rh5-H bond in both TS2/3 and TS3/3 amount to 2.403 and 2.010 Å, respectively. As shown in Figure S4 of SI, the move of H atom from Rh5 atom to N1 or N2 atom requires much energy to take place but the 1,4-H migration is more energetically preferred. The N2H group binds to the Rh2 atom of cluster via N1 atom (IS5/3) or forms a three-membered ring (IS4/3). The processes of the release of N2H radical from the Rh5 cluster continues to be significantly endothermic by at least 45 kcal/mol. IV. CONCLUSIONS The mechanism of reaction between N2O and H2 in the gas phase and on the surface of Rh5 cluster has been studied by method of DFT calculations. The results computed on the sextet potential energy surface have shown that the reaction catalyzed by the Rh5 cluster can form three ACS Paragon Plus Environment

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products P1 (N2 + H2O), P2 (NO + NH2) and P3 (OH + N2H) via six channels. For the formation of P1, the predicted energy barrier is about 15 kcal/mol, being much lower than that of 42 kcal/mol in the uncatalyzed reaction. Moreover, the exothermicity of about -61 kcal/mol in this reaction may facilitate the easy catalytic reaction. Meanwhile, formation of P2 and P3 has to overcome relatively high barriers and are disfavored by large endothermicity of 54 and 55 kcal/mol, respectively. These calculated results confirm again that the contribution of products P2 (NO + NH2) and P3 (OH + N2H) is much less important than that of P1 (N2 + H2O) in the N2O + H2 reaction. Our calculations also point out that the Rh5 cluster turns out to be a potential catalyst for the reduction of N2O by H2 into N2 and H2O. This work could thus help us with a deeper understanding of mechanisms occurring on the different rhodium surface.

Supporting Information Available: Cartesian coordinates, vibrational frequencies, single point energies and zero-point vibrational energies (ZPE) of reactants, intermediates, transition states and products considered in the gas phase and catalyzed reactions, optimized geometries of some species and energy profiles for the minor channels of the reaction. This material is available free of charge via the internet at http://pubs.acs.org. Acknowledgements HMTN thanks the Vietnamese Ministry of Education and Training for support under the project B2012-17-28.



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References (1) Chen, P.; Cabrito, I.; Moura, J. J. G.; Moura, I.; Solomon, E. I. Reduction of Nitrous Oxide to Dinitrogen by a Mixed Valent Tricopper-Disulfido Cluster.J.Am. Chem. Soc. 2002, 124, 1049710505. (2) Loffreda, D.; Delbecq, F.; Simon, D.; Sautet, J. Molecular Adsorption of NO on a Pd4 Cluster: A Density Functional Theory (DFT) Study. J. Chem. Phys.2001, 115, 8101-8108. (3) Taylor, K. C. A Study of NO + CO Reaction over Various Supported Catalysts in the Presence of O2 and H2O. Catal. Rev. Sci. Eng. 1993, 35, 457-468.. (4) Houghton, J. T.; Ding. Y.; Griggs. D. J.; Noguer. M.; van der Linden. P. J.; Dai. X.; Maskell. K.; Johnson. C. A. In climate change 2001 : The scientific basis; Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA. 2001, 881-890. (5) Shelef, M.; Graham, G. W. Why Rhodium in Automotive Three-Way Catalysts? Catal. Rev. Sci. Eng. 1994, 36, 433-439. (6) Nieuwenhuys, B. E. The Surface Science Approach toward Understanding Automotive Exhaust Conversion Catalysis at the Automic Level. Adv. Catal. 2000, 44, 259-267. (7) Araya, P.; Gracia, F.; Cortes, J.; Wolf, E. E. FTIR Study of the Reduction Reaction NO by CO over Rh/SiO2 Catalysts with Different Crystallite Size Appl. Catal. B. Environ. 2002, 38, 77-87. (8) DeLouise, L. A.; Winograd, N. Adsorption and Desorption of NO From the Rh (111) and Rh (331) Surfaces. Surf. Sci. 1985, 159, 199-208. (9) Qiu, G.; Wang, M.; Wang, G.; Diao, X.; Zhao, D.; Du, Z.; Li, Y. Structure and Electronic Properties of Pdn Clusters and their Interactions with Single S Atom Studied by Density-Functional Theory. J. Mol. Stru. 2008, 861, 131-136. (10) Armentrout, P. B. Reactions and Thermochemistry of Small Transition Metal Cluster Ions. Annu. ReV. Phys. Chem. 2001, 52, 423-461. (11) Knickelbein, M. B. Reactions of Transition Metal Clusters with Small Molecules. Annu. ReV. Phys. Chem. 1999, 50, 79-115.


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(12) Hickman, D. A.; Schmidt, L. D. A Mercury-Catalyzed, High-Yield System for the Oxidation of Methane to Methanol. Science 1993, 259, 340-343. (13) Zhdanov, V. P.; Kasemo, B. Mechanism and kinetics of the NO-CO reaction on Rh. Surf. Sci. Rep. 1997, 29, 31-37. (14) Teffo, J. L.; Chedin, A. Internuclear Potential and Equilibrium Structure of the Nitrous Oxide Molecule from Rovibrational Data J. Mol. Spectrosc. 1989, 135, 389-400. (15) Zeigarnik, A. V. Adsorption and Reactions of N2O on Transition Metal Surfaces. Kinet. Catal. 2003, 44, 233-246. (16) Schmatlock, V.; Jirka, I.; Kruse, N. Nitric Oxide Decomposition on Small Rhodium Clusters, Rhn+/-.J. Chem. Phys. 1994, 100, 8471-8477. (17) Burch, R.; Breen, J. P.; Meunier, F. C. A Review of the Selective Reduction of NOx with Hydrocarbons under Lean-burn Conditions with Non-zeolitic Oxide and Platinum Group Metal Catalysts.Appl. Catal. B. 2002, 39, 283-288. (18) Taylor, K. C.; Schlatter, J. C. Selective Reduction of Nitric Oxide over Noble Metals. J. Catal. 1980, 63, 53-58. (19) Loffreda, D.; Simon, D.; Sautet, P. Structure Sensitivity for NO Dissociation on Palladium and Rhodium Surfaces. J. Catal. 2003, 213, 211-218. (20) Inderwildi, O. R.; Lebiedz, D.; Deutschmann, O.; Warnatz, J. Influence of Initial Oxygen Coverage and Magnetic Moment on the NO Decomposition on Rhodium (111) J. Chem. Phys. 2005, 122, 154702. (21) Loffreda, D.; Delbecq, F.; Simon, D.; Sautet, P. Breaking the NO Bond on Rh, Pd, and Pd3Mn Alloy (100) Surfaces: A Quantum Chemical Comparison of Reaction Paths. J. Chem. Phys. 2001, 115, 8101-8108. (22) Hideo, O.; Toshitaka, K.; Tatsuo, M.; Anton, K. DFT Calculations of Adsorption and Decomposition of N2O on Rh(100). J. Phys. Chem. C, 2010, 114 , pp 21444–21449. (23) Anton, K; Tatsuo, M. A Density Functional Theory Study of the Interaction of N2O with



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Rh(110). J. Chem. Phys. 2005, 122, 034708. (24) Parry, I. S.; Kartouzian, A.; Hamilton, S. M.; Balaj, O. P.; Beyer, M. K.; Mackenzie, S. R. Collisional Activation of N2O Decomposition and CO Oxidation Reactions on Isolated Rhodium Clusters. J. Phys. Chem A. 2013, 117, 8855-8863. (25) Hamilton, S. M.; Hopkins, W. S.; Harding, D. J.; Tiffany R.; Walsh, T. R.; Haertelt, M.; Kerpal, C.; Gruene, P.; Meijer, G.; Fielicke, A.; Mackenzie, S. R. Infrared-Induced Reactivity of N2O on Small Gas-Phase Rhodium Clusters J. Phys. Chem. A. 2011, 115, 2489–2497. (26) Henrici, H.; Hunt, M.; Bauer, S. H. Kinetics of the Nitrous Oxide - Hydrogen Reaction. J. Chem. Phys. 1969, 50, 1333-1341. (27) Lemos, M. C.; Gálvez, F. E. Study and Control of the N2O + H2 Reaction on Ir(110) by Monte Carlo Simulations. Cyb. Phys. 2012, 1, 169–178. (28) Kalimeri, K.; Pekridis, G.; Kaklidis, N.; Iliopoulou, E. F.; Athanasiou, C.; Marnellous, G. E. Electrocatalytic

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of

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Oxide

Using

Steam

Electrolysis

in

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Pd|SrCe0.95Yb0.05O3-a|Ag Proton Conducting Solid Electrolyte Membrane Reactor (SEMR) OREPOC, Thessaloniki‐Greece. 2007, 95-98. (29) Mineva, T.; Russo, N.; Freund, H. J. CO Interaction with Small Rhodium Clusters from Density Functional Theory: Spectroscopic Properties and Bonding Analysis. J. Phys. Chem. A. 2001, 105, 10723-10730. (30) Furche, F.; Rappoport, D. Density Functional Methods for Excited States: Equilibrium Structure and Electronic Spectra. Theo. Com. Chem. 2005, 16, 93–128. (31) Schneider, N.; Finger, M.; Haferkemper, C.; Stéphane, B. L.; Hofmann, P.; Gade, L. H. Multiple Reaction Pathways in Rhodium Catalyzed Hydrosilylations of Ketones. Chemistry. 2009, 15, 11515-11529. (32) Reed, A. E.; Weinstock, R. B.; Weinhold, F. Natural Population Analysis. J. Chem. Phys. 1985, 83, 735-745. (33) Reed, A. E.; Weinhold, F. Natural Localized Molecular Orbitals. J. Chem. Phys. 1985, 83,


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1736-1745. (34) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Intermolecular Interactions from a Natural Bond Orbital, Donor-Acceptor Viewpoint. Chem. Rev. 1988, 88, 899-910. (35) Frisch, M. J.; Trucks, G.. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, Revision A.1; Gaussian, Inc., Wallingford CT, 2009. (36) Mora, M. A.; Mora-Ramírez, M. A.; Rubio-Arroyo, M. F. Structural and Electronic Study of Neutral, Positive, and Negative Small Rhodium Clusters [Rhn, Rhn+ and Rhn-]. Int. J. Quantum Chem. 2010, 110, 2541–2547. (37) Chien, C. H.; Barojas, E. B.; Pederson, M. R. Magnetic and Electronic Properties of Rhodium Clusters. Phys. Rev. 1998, 58, 2916-2203. (38) Hinshelwood, C. N. The Kinetics of the Interaction of Nitrous Oxide and Hydrogen. Proc. R. Soc. London, Ser. A. 1924, 106, 292-298.



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Page 18 of 29

Table 1: Theoretical predication of related energies ∆E (kcal/mol) for intermediates, transition states, and products of the N2O + H2 gas phase reaction calculated at BP86/6-311++g(d,p) level. Species

∆E

Species

(kcal/mol)

Species

∆E (kcal/mol)

∆E (kcal/mol)

RA (N2O + H2)

0.0

IS6

7.7

TS4/P

23.3

IS1

9.9

TSR/1

42.1

TSR/5

98.7

IS2

3.3

TS1/2

13.9

TS5/6

41.9

IS3

21.4

TS2/P

21.4

TS6/4

49.6

IS4

16.6

TSR/3

74.5

TS6/2

50.6

IS5

13.2

TS3/4

22.0

P (N2+H2O)

Table 2: Theoretical predication of related energies ∆E (kcal/mol) for intermediates, transition states, and products of the N2O + H2 reaction catalyzed by the Rh5 cluster. Species

∆E

Species

(kcal/mol)

Species

∆E (kcal/mol)

∆E (kcal/mol)

Rh5+N2O

0.0

TS12/1

-18.9

IS3/2+NO

10.8

IS1/1

-20.6

IS15/1

-18.8

IS3/2+H2

0.0

TS1/1

-14.2

TS13/1

-22.7

IS4/2

-7.9

IS2/1

-27.2

IS16/1

-35.9

TS3/2

-5.9

TS2/1

-23.7

IS17/1

-18.9

IS5/2

-6.7

IS3/1

-61.3

TS14/1

-18.4

TS4/2

12.7

IS4/1

-43.4

IS18/1

-19.8

IS6/2

-8.1

IS4/1+H2

0.0

TS15/1

-15.2

TS5/2

-2.4

IS5/1

-12.3

IS19/1

-24.7

IS7/2

-4.6

TS3/1

4.8

TS16/1

-18.3

TS6/2

9.8

IS6/1

-25.8

IS20/1

-18.7

IS8/2

-18.4

TS4/1

-21.0

TS17/1

-7.8

Rh5 + NH2

42.8

IS7/1

-31.5

IS21/1

-30.8

Rh5 +N2O+H2

0.0

TS5/1

-11.1

TS18/1

-29.6

IS1/1

-20.6

IS8/1

-10.6

IS22/1

-16.4

TS1/1

-14.2

TS6/1

5.1

TS19/1

-14.7

IS2/1

-27.2

TS7/1+H2

7.4

IS23/1

-15.5

IS1/3

-36.3

IS9/1+H2

-5.9

TS20/1

2.6

TS1/3

-18.6

IS10/1

-14.5

IS24/1

-24.0

IS2/3

-23.2


Page 19 of 29

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TS8/1

9.1

TS21/1

-20.7

IS3/3

-18.6

IS11/1

-20.6

IS25/1

-31.2

TS2/3

25.6

TS9/1

-17.2

TS22/1

-16.4

IS4/3

9.0

IS12/1

-31.6

Rh5 + H2O

-17.5

TS3/3

16.1

TS10/1

-12.8

TS1/2

20.5

IS5/3

10.1

IS13/1

-14.2

IS1/2

16.9

Rh5 + P3

55.2

TS11/1

7.9

IS2/2+NO

29.0

IS14/1

-24.3

TS2/2+NO

37.1



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Figure 1. Potential energy surface of N2O + H2 reaction calculated by using the BP86/6-311++G(d,p) level.


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IS1

IS2

IS3

IS4

IS5

IS6

TSR/1

TS1/2

TS2/P

TSR/3

TS3/4

TS4/P

TSR/5

TS5/6

TS6/4

TS6/2

Figure 2: Optimized geometries of the intermediates and transition states of the N2O + H2 reaction forming N2 and H2O in the gas phase.



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

Rh5(6)

N2O

H2

Page 22 of 29

IS1/1(6)

IS2/1(6)

IS3/1(6)

IS4/1(6)

IS5/1(6)

IS6/1(6)

IS7/1(6)

IS8/1(6)

IS9/1(6)

IS10/1(6)

(a)


Page 23 of 29

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


IS11/1(6)

IS14/1(6)

IS17/1(6)

IS20/1(6)

IS12/1(6)

IS15/1(6)

IS18/1(6)

IS21/1(6)

(b)


IS13/1(6)

IS16/1(6)

IS19/1(6)

IS22/1(6)


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

IS23/1(6)

IS24/1(6)

Page 24 of 29

IS25/1(6)

(c)

Figure 3. Optimized geometries of the reactants and intermediates of the N2O + H2 reaction catalyzed by the Rh5 cluster to form P1. Values in parenthesis are multiplicities.


Page 25 of 29

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TS1/1(6)

TS2/1(6)

TS3/1(6)

TS4/1(6)

TS5/1(6)

TS6/1(6)

TS7/1(6)

TS8/1(6)

TS9/1(6)

TS10/1(6)

TS11/1(6)

TS12/1(6)

TS13/1(6)

TS14/1(6)

TS15/1(6)



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

Page 26 of 29

(a)

TS16/1(6)

TS17/1(6)

TS18/1(6)

TS19/1(6)

TS20/1(6)

TS21/1(6)

TS22/1(6)

(b)

Figure 4. Optimized geometries of transition states of the N2O + H2 reaction catalyzed by the Rh5 cluster to form P1. Values in parenthesis are multiplicities.


Page 27 of 29

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Figure 5. Energy profile for the adsorption and dissociation of N2O molecule on the Rh5 cluster to form P1 (N2 + H2O).



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

Figure 6. Potential energy surface for the interaction of H2 with IS4/1 to form H2O of P1 (N2 + H2O).


Page 28 of 29

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Table of content graphic The reaction of N2O with H2 catalyzed by the Rh5 cluster


Theoretical Study on the Reaction Mechanism of N2O with H2

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