Theoretical Study on the Catalytic Reduction Mechanism of NO by CO

Article pubs.acs.org/JPCA

Theoretical Study on the Catalytic Reduction Mechanism of NO by CO on Tetrahedral Rh4 Subnanocluster Hua-Qing Yang,† Hong-Quan Fu,† Ben-Fang Su,† Bo Xiang,† Qian-Qian Xu,‡ and Chang-Wei Hu*,‡ †

College of Chemical Engineering and ‡Key Laboratory of Green Chemistry and Technology, Ministry of Education, College of Chemistry, Sichuan University, Chengdu, Sichuan 610065, People’s Republic of China S Supporting Information *

ABSTRACT: The catalytic mechanism of 2NO + 2CO → N2 + 2CO2 on Rh4 cluster has been systematically investigated on the ground and first excited states at the B3LYP/6-311+G(2d),SDD level. For the overall reaction of 2NO + 2CO → N2 + 2CO2, the main reaction pathways take place on the facet site rather than the edge site of the Rh4 cluster. The turnover frequency (TOF) determining transition states are characteristic of the second N−O bond cleavage with rate constant k4 = 1.403 × 1011 exp (−181 203/RT) and the N−N bond formation for the intermediate N2O formation with rate constant k2 = 3.762 × 1012 exp (−207 817/RT). The TOF-determining intermediates of 3NbRh4NO and 3NbRh4Ob(NO) are associated with the nitrogen-atom molecular complex, which is in agreement with the experimental observation of surface nitrogen. On the facet site of Rh4 cluster, the formation of CO2 stems solely from the recombination of CO and O atom, while N2 originates partly from the recombination of two N atoms and partly from the decomposition of N2O. For the N−O bond cleavage or the synchronous N−O bond cleavage and C−O bond formation, the neutral Rh4 cluster exhibits better catalytic performance than the cationic Rh4+ cluster. Alternatively, for N−N bond formation, the cationic Rh4+ cluster possesses better catalytic performance than the neutral Rh4 cluster. precovered Rh(100) surface.15 Cortes et al. did not consider the beta nitrogen step in the reduction mechanisms of NO by CO on rhodium surfaces and supported the existence of surface nitrogen.16,17 Zaera et al. studied the deposition of atomic nitrogen on Rh(111) surface via effusive collimated beams and found evidence for a N2O intermediate in the catalytic reduction of NO to N2 on Rh(111) surfaces.18−21 It was also shown that the two nitrogen atoms of N2 come from different sources. Anderson et al. and Ford et al. revealed the high activity of Rhn± (n < 30) cluster toward the dissociation of the NO molecule using Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry.22,23 These authors found that the cationic clusters react significantly faster than the anions and proposed that the nitric oxide decomposition process seems to be defined by a simple multistage mechanism. It is obvious that the mechanism of CO2 formation is in debate, whether through the reaction between CO and NO or through recombination of CO and O atom, the latter being originated from the NO decomposition.12−15 Following this experimental work, by means of density functional theory calculations, Ghosh et al. studied the binding of NO to the small rhodium clusters including 1−5 atoms.24 It was revealed that the NO bonds more strongly to Rh clusters than it does to Rh(100) or Rh(111) surface, indicating that the rhodium clusters may be good catalysts for NO reduction.

1. INTRODUCTION Catalytic conversion of the oxides of nitrogen and carbon monoxide, as atmospheric pollutants and greenhouse gases, into nitrogen and carbon dioxide is of great practical importance with respect to automotive exhaust gas catalysis both environmentally and economically.1,2 Such a catalytic conversion is accomplished in car exhaust using three-way catalysts (TWC) composed of Rh, Pd, and Pt,3−5 in which Rh is the component responsible for the removal of NOx.6,7 Recently, the catalytic activity of various types of Rh nanostructures has received a lot of attention.8−11 From the theoretical side, small clusters, besides being more computationally tractable, better reflect the surface defects present in catalytic materials than do perfect extended surfaces.1 Thus, understanding the catalytic reduction mechanism of NO by CO on the Rh-based nanoparticles at the molecular level is of great importance in designing suitable catalysts. Experimentally, previous studies suggested that the mechanism of the CO and NO reaction on Rh(111) surface includes reversible adsorption of CO and NO, subsequent irreversible dissociation of NO to N and O atoms, recombination of N atoms to produce N2, and recombination of CO and O atom to form CO2.12,13 Belton et al. revealed that the disproportionation between adsorbed NO and N atoms via an N2O intermediate (NO + N → N2 + O) was the second N2 formation channel.14 However, Brandt et al. suggested a direct reaction channel for CO2 formation between CO and NO, which may follow the Eley−Rideal kinetics, using a molecular beam of gas-phase-oriented NO molecules incident on a CO© XXXX American Chemical Society

Received: August 8, 2015 Revised: October 24, 2015

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DOI: 10.1021/acs.jpca.5b07713 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A Harding et al. investigated the reaction of NO with two Rh6+ isomers having a square bipyramid structure and trigonal prism structure, respectively. They found three favorable reaction paths, two of them starting with the trigonal prism, and the third was associated with the square bipyramid structure.25 Torres et al. studied the consecutive adsorption of two NO molecules on Rh6+ cluster and confirmed the dissociative adsorption of NO on Rh6+.26 Xie et al. investigated the NO adsorption and decomposition reaction mechanism on Rh7+ cluster.27 They suggested that the reaction can proceed via three steps: NO adsorption, NO decomposition to N and O atoms, and N-atom reaction with another adsorbed NO and then reduction to N2 molecule.27 Later, Xie et al. studied the catalytic reduction mechanism of NO by CO on Rh7+ cluster. They suggested that the reaction proceeds via three steps.28 First, NO and CO are adsorbed on the Rh7+ cluster; then the adsorbed NO decomposes to N and O atoms. The O atom reacts with the adsorbed CO, leading to formation of a CO2 molecule. Second, another NO is adsorbed and decomposes to N and O atoms; then the two N atoms couple with each other to yield a N2 molecule. Finally, the second CO can be oxidized to CO2 molecule. Therein, the second adsorbed NO generating N and O atoms in the second step is the rate-limiting step of the whole catalytic cycle. Romo-Á vila et al. theoretically analyzed the stability and dissociation behavior of NO molecules adsorbed on a small nonmagnetic Rhn0,± cluster (n = 3, 4, 6, and 13).29 They found that dissociation of the N−O bond is more easily obtained on square facets than on triangular atomic environments and that the energy barriers to break the N−O bond depend on the charge state of the systems.29 These theoretical studies supported that the mechanism of CO2 formation is in accord with recombination of CO and O atom, the latter being originated from NO decomposition.12−14,28,29 Zeinalipour-Yazdi et al. performed a systematic study of the adsorption of CO on a Rh4 cluster.30 Their model demonstrated that a critical parameter that determines the converage-dependent energetics of the adsorption of CO at low converage is the polarization of metal−metal π bonds during the effective charge transfer, which enhances the adsorption of CO vertical to the metal−metal bond. Lately, we investigated the catalytic reaction mechanism of NO and CO on the Rh atom and Rh4+ cluster.31,32 On the Rh atom, the key reaction step is associated with NO deoxygenation to generate N2O, in which self-deoxygenation of the NO reaction pathway is kinetically more preferable than that in the presence of CO.31 On the cationic Rh4+ clusters, at low temperatures (300−760 K), the turnover frequency (TOF)-determining transition state (TDTS) is the simultaneous C−O bond formation and N−O bond cleavage, whereas at high temperatures (760−900 K), the TDTS is applied to the N−O bond cleavage.32 However, we have taken into account the edge site of the Rh4+ cluster but not the facet site of the Rh4+ cluster.32 Despite these numerous studies, further work is required to explore the intrinsic reaction mechanism or how NO reduction by CO gets catalyzed on the neutral Rh4 cluster at the molecular level. Three review articles mentioned that there are also a number of concomitant channels yielding N2O, NCO, and CN in the catalytic conversion of 2NO + 2CO → N2 + 2CO2, which complicates a comprehensive understanding.3,33,34 Therefore, of particular interest in this study is probing the complete reaction mechanism of NO and CO catalyzed by Rh4

cluster along with the relevant side reactions, as exemplified by the reactions 2NO + 2CO → N2 + 2CO2

(1)

NO + 2CO → NCO + CO2

(2)

NO + 3CO → CN + 2CO2

(3)

The goals of the present study are as follows: (a) to provide reliable structures and vibration frequencies of the reactants, intermediates (IMs), transition states (TSs), and products as well as their chemically accurate energetics, (b) to elucidate the determining transition state (TDTS) and the determining intermediate (TDI) of the turnover frequency (TOF), (c) to obtain a better understanding of the preference of reaction pathway at different temperature range, (d) to gain a deep insight into the cooperativeness of multi-Rh on the catalytic reduction of NO with CO, and (e) to shed light on the charge effect of cluster on the catalytic reduction of NO with CO.

2. COMPUTATIONAL DETAILS All calculations were carried out with the Gaussian 09 program package.35 Full geometry optimizations were run to locate all stationary points and transition states (TSs) on the ground and first excited states using the B3LYP36,37 functional method with the 6-311+G(2d) basis set for carbon, nitrogen, and oxygen,38,39 and the Stuttgart/Dresden (SDD) basis set and the corresponding effective core potential (ECP) for rhodium,40 namely, B3LYP/6-311+G(2d),SDD. Meanwhile, the stability of the wave function of the auxiliary Kohn−Sham determinant in density function theory (DFT) was tested.41,42 If instability is found, the wave function is reoptimized with appropriate reduction in constraints and the stability tests and reoptimizations are repeated until a stable wave function is found.41,42 Computed ⟨S2⟩ values suggested that only small spin contamination is included in the calculations. Systematic frequency calculations were performed to characterize stationary points obtained and to take corrections of zero-point energy (ZPE) into account. For the reaction pathway analysis, we ensured that every transition structure has only one imaginary frequency, and the connections between transition states and corresponding intermediates were verified by means of intrinsic reaction coordinate (IRC) calculations.43,44 The dominant occupancies of natural bond orbitals and dominant stabilization energies E(2) between donors and acceptors for some species have been analyzed with the help of natural bond orbital (NBO) analysis.45,46 Unless otherwise mentioned, the Gibbs free energy of formation (ΔG) is relative to the initial ground state reactants including ZPE correction obtained at the B3LYP/6-311+G(2d),SDD level in the gas phase under room temperature and atmospheric pressure (298.15 K and 1 atm). The turnover frequency (TOF) of the catalytic cycle determines the efficiency of the catalyst. On the basis of transition state theory,47,48 TOF can be calculated by eqs i and ii,49−51 in which δE (the energetic span52) is defined as the energy difference between the summit and the trough of the catalytic cycle. GTDTS and GTDI are the Gibbs free energies of the TOF-determining transition state (TDTS) and the TOFdetermining intermediate (TDI), and ΔGr is the global free energy of the whole cycle TOF = B

kBT −δE / RT e h

(i) DOI: 10.1021/acs.jpca.5b07713 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A ⎛ if TDTS appears after ⎞⎟ ⎜ GTDTS − GTDI TDI ⎜ ⎟ δE = ⎜ ⎟ if TDTS appears ⎟ ⎜⎜GTDTS − GTDI + ΔGr ⎟ ⎝ ⎠ before TDI

addition, the ground tetrahedronal Rh4 cluster can isomerize to the ground square one, with an energy barrier of 73.2 kJ mol−1, as shown in Figure S1b of the SI. Such energy barrier traps the Rh4 cluster in the tetrahedronal structure rather than in the square structure. Therefore, the tetrahedronal Rh4 cluster is preferred in the present study. Unless otherwise mentioned, the Rh4 cluster is referred to the tetrahedronal structure in the present study. In this work, we will mainly discuss the following six reactions

(ii)

where kB is Boltzmann’s constant, T is the absolute temperature, and h is Plank’s constant. The rate constants (k) have been evaluated according to conventional transition state theory k(T) (TST), based on Winger’s formulation as follows48 k(T ) =

kBT hc

0

‡

e−ΔG / kBT

(iii)

where kB is Boltzmann’s constant, T is the absolute temperature, h is Plank’s constant, c0 is the standard concentration (1 mol dm−3), and ΔG‡ is the activation Gibbs free energy barrier.

3. RESULTS AND DISCUSSION The same method B3LYP/6-311+G(2d),SDD was successfully used to perform the geometric structure optimization in the reaction mechanisms of methane catalyzed by the neutral RhO,53 the cationic RhO+,54 the Rh/γ-Al2O3 model catalyst,55 and in the reduction mechanism of NO by CO catalyzed by Rh atom.31,32 Moreover, for some experimentally available species (Rh, ORh, O2Rh, CRh, and C2Rh), the ion energetics (IEs) are calculated and then compared with the experimental data. These calculated gas-phase IEs are listed in Table 1.

Rh(4F) → Rh+(3D) CRh(2∑) → CRh+(1∑) ORh(4∑) → ORh+(3Π) O2Rh(2A′) → O2Rh+(1A′) C2Rh(4∑) → C2Rh+(3∑)

calculated IE (kJ mol−1)

experimental IE (kJ mol−1)

refs

751.8 748.6

719.7 887.7 ± 96.5

56 56

878.5

823.7 ± 41.5

57

943.7

964.9

58

823.4

781.5 ± 38.6

59

(4)

Rh4 + N2O → Rh4Ob + N2

(5)

Rh4Ob + CO → Rh4 + CO2

(6)

Rh4 + NO + CO → Rh4Nb + CO2

(7)

Rh4Nb + NO → Rh4Ob + N2

(8)

Rh4Nb + NO → Rh4 + N2O

(9)

Besides the aforementioned six reactions, the following two side reactions will also be discussed to generalize the overall catalytic reduction mechanism of NO by CO on the Rh4 cluster Rh4Nb + CO → Rh4 + NCO

(10)

Rh4 + NCO → RhOb + CN

(11)

Achieving the main reaction in eq 1 of 2NO + 2CO → N2 + 2CO2, there are two kinds of catalytic cycles. One is made up of reactions 4, 5, and 2 × reaction 6 through N−O bond cleavage in the absence of CO; another is composed of reactions 7, 8, and 6 or reactions 7, 9, 5, and 6 through N−O bond cleavage in the presence of CO. It is obvious that the main difference between the two catalytic cycles originates from reactions 4, 5, 7, 8, and 9, which are mainly associated with the formation of N2. Accomplishing the side reaction in eq 2 of NO + 2CO → NCO + CO2, there is a unique reaction pathway, which is composed of reactions 7 and 10. Acquiring the side reaction in eq 3 of NO + 3CO → CN + 2CO2, there is a unique reaction pathway, which comprises reactions 7, 10, 11, and 6. The ΔGr values of reactions 1, 2, and 3 are calculated to be −696.4, −114.1, and −74.5 kJ mol−1, respectively. It is indicated that all three reactions are thermodynamically favorable. Therefore, we will discuss the kinetics of the above three reactions, the competition of the catalytic cycles, and the selectivity of main and side reactions infra. Since spin crossing is often involved in the transition-metalcontaining reactions,64 particular attention was devoted to the possible occurrence of a two-state reactivity phenomenon. Thus, the potential energy profiles for the ground and first excited states of rhodium-containing reactions are investigated. The superscript prefixes 3, 4, 5, 6, and 7 will be used to indicate the triplet, quartet, quintet, sextet, and septet states, respectively. 3.1. 2NO + 2CO → N2 + 2CO2 Through N−O Bond Cleavage in the Absence of CO. This overall reaction is divided into three sequent reactions of eqs 4, 5, and 2 × 6. Thus, it is necessary to investigate the above three reactions, both thermodynamically and kinetically. This reaction can be divided into two kinds of reaction pathways, through N−O bond cleavage in the absence and presence of another NO molecule, denoted as “RP-1NO” and “RP-2NO”, respectively.

Table 1. Calculated Gas-Phase Ion Energetics (IE) at the B3LYP/6-311+G(2d),SDD Level for Some Typical Species species

Rh4 + 2NO → Rh4Ob + N2O

As shown in Table 1, the gas-phase IEs of these species (Rh, CRh, ORh, O2Rh, and C2Rh) are in good agreement with the experimental data.56−59 It is indicated that the present method and basis sets should be appropriate for the present system (Rh4 + NO + CO). According to previous studies,16,60,61 the Rh4 cluster has two low-energy isomers, namely, tetrahedron and square, having previously been reported. Since both thermal fluctuation and magnetostructural effects play critical roles on the structures of the isomers at the temperature range,62,63 both the tetrahedral and the square Rh4 clusters with quintet, septet, and nonet were taken into account at the temperature range of 300−900 K. The curves of the relative Gibbs free energies of Rh4 clusters dependent on the temperatures are plotted in Supporting Information (SI) Figure S1a. As seen in Figure S1a of the SI, the lowest energy structure of Rh4 is the septet tetrahedron at a temperature range of 300−900 K. Furthermore, the ground state of the square Rh4 cluster is the septet state, which locates 48.5 kJ mol−1 above the septet tetrahedronal Rh4 cluster. In C


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Figure 1. continued

D


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Figure 1. Geometric structures of the reactants, intermediates, TSs, and products, and the schematic energy diagrams for the reaction of Rh4 + 2NO → Rh4Ob + N2O calculated at the B3LYP/6-311+G(2d),SDD level. Bond lengths are reported in Angstroms and bonds angles in degrees. Relative energies (kJ mol−1) for the corresponding species relative to 7Rh4 + 2NO are shown: (a, b, c, and d) Rh4 + 2NO → NbRh4Ob(NO) reaction stage for RP-1NO-2Rh, RP-1NO-3Rh, RP-2NO-2Rh, and RP-2NO-3Rh, respectively; (e) NbRh4Ob(NO) → Rh4Ob + N2O reaction stage.

2NO → Rh4Ob + N2O is calculated to be exergonic by 173.6 kJ mol−1 on its minimal energy reaction pathway (MERP). It is shown that this reaction is thermodynamically preferable. Then we will discuss its kinetics from potential energy surfaces (PESs). As shown in Figure 1a for the reaction pathway RP-1NO2Rh, when one NO molecule is initially adsorbed on the top Rh atom and the edge of two Rh atoms on the Rh4 cluster, there are three kinds of configurations: one top Rh4NO through N end, one bridge b-Rh4NO through N end, and one bridge−bridge bb-Rh4NO through N and O ends with stabilization energies of 147.0, 126.1, and 126.6 kJ mol−1 on the ground sextet state, respectively. Among these three configurations, the top 6Rh4NO is the most thermodynamically preferable. In 6Rh4NO, the Mülliken spin densities of −Rh4 and −NO moieties are 5.11 and −0.11, respectively, indicating unpaired electrons mainly on the −Rh4 moiety. From NBO

Besides, N−O bond cleavage takes place on two kinds of active sites, the edge of two Rh atoms and the triangular facet of three Rh atoms in tetrahedral Rh4 cluster, denoted as “2Rh” and “3Rh”, respectively. Then there are four reaction pathways, RP1NO-2Rh, RP-1NO-3Rh, RP-2NO-2Rh, and RP-2NO-3Rh. These reaction pathways include the following steps: (1) NO adsorption, (2) NO decomposition to N and O atoms, (3) reaction of the N atom with the second adsorbed NO to form a N2O molecule, (4) N2O molecule decomposition into N2 molecule and O atom, and (5) recombination of CO and O atom to form CO2. 3.1.1. Rh4 + 2NO → Rh4Ob + N2O. The geometric structures and the schematic energy diagrams for reaction 4 Rh4 + 2NO → Rh4Ob + N2O are depicted in Figure 1a−e. As indicated in Figure 1a, the septet state Rh4 cluster is the ground state. The quintet state Rh4 cluster, which is the first excited state, lies 36.1 kJ mol−1 above the ground septet state. The reaction of Rh4 + E


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The Journal of Physical Chemistry A analysis, in 6Rh4NO the occupancies of the Rh−NO bond orbital is 2.65 e. It is indicated that there is a complete single bond of Rh−NO in 6Rh4NO. Thus, the formation of the chemical bond in Rh−NO makes the 6Rh4NO complex thermodynamically favorable. Then on the edge of two Rh atom, N−O bond scission takes place to form a top-top configuration NRh4O via a four-membered ring TS1a-1. Because the sextet TS1a-1 lies above the quartet one, the sextet−quartet spin crossing should take place once. Thereby, the MERP should go forward via the minimum energy crossing point (MECP) between 6Rh4NO and 4Rh4NO. Afterward, when the second NO molecule is adsorbed on the top Rh atom in the Rh4 cluster, a molecular complex NRh4O(NO) is formed. The triplet NRh4O(NO) locates 20.3 kJ mol−1 below the quintet one. Therefore, the MERP should start at the septet state and end on the triplet one, with an exergonic value of 132.1 kJ mol−1. From NRh4O(NO), the [1,2] shifts of the topO and the top-N successively proceed via TS1a-2 and TS1a-3, respectively, to produce a more stable bridge−bridge NbRh4Ob(NO). As depicted in Figure 1b for the reaction pathway RP-1NO3Rh, when one NO molecule is initially adsorbed on the triangular facet of three Rh atoms in the Rh4 cluster, there are two kinds of configurations: one facet-top ft-Rh4NO through the N end and one facet-bridge fb-Rh4NO through N and O ends with stabilization energies of 131.5, and 98.7 kJ mol−1 on their MERPs, respectively. Among the five molecular complexes (Rh4NO, b-Rh4NO, bb-Rh4NO, ft-Rh4NO, and fb-Rh4NO), the top 6Rh4NO is the most thermodynamically preferable. The top Rh4NO can isomerize to the facet-bridge fb-Rh4NO. Next, from fb-Rh4NO, N−O bond cleavage takes place via five-center TS1b-1 to form an ortho bridge-O and bridge-N intermediate o-N b Rh 4 O b . Then from o-N b Rh 4 O b the [1,2]-O shift successively takes place twice via three-membered ring TS1b2 and TS1b-3 to yield a more stable bridge-O and bridge-N intermediate NbRh4Ob. Finally, when the second NO molecule is adsorbed on the top Rh atom in the Rh4 cluster, a more stable bridge−bridge molecular complex NbRh4Ob(NO) is generated. As shown in Figure 1c for the reaction pathway RP-2NO2Rh, when two NO molecules are initially adsorbed on the respective top Rh atom in the Rh4 cluster simultaneously, a toptop configuration molecular complex Rh4(NO)2 is generated through the N end. The quintet 5Rh4(NO)2 deposits 26.7 kJ mol−1 below the triplet 3Rh4(NO)2. In 5Rh4(NO)2, the Mülliken spin densities of −Rh4 and two −NO moieties are 2.98, −0.06, and 1.02, respectively, indicating three unpaired electrons on the −Rh4 moiety and one unpaired electron on the −NO moiety. The occupancies of two Rh−NO bond orbitals are 4.53 and 5.78 e from NBO analysis. It is indicated that there are approximately one double bond of Rh−NO and one triplet bond of Rh−NO in 5Rh4(NO)2. Therefore, formation of the chemical bond in Rh−NO makes the 5Rh4(NO)2 complex thermodynamically preferable. Next, one N−O bond cleavage occurs on the edge of two Rh atoms via a four-membered ring TS1c-1 to form NRh4O(NO). Since the quintet TS1c-1 stands above the triplet one, the triplet−quintet spin crossing should take place once. Accordingly, the MERP should proceed via MECP between 5Rh4(NO)2 and 3Rh4(NO)2. As mentioned earlier, NRh4O(NO) can convert into a more stable bridge− bridge NbRh4Ob(NO) through the [1,2] shifts of the top-O and top-N via TS1a-2 and TS1a-3, respectively.

As depicted in Figure 1d for the reaction pathway RP-2NO3Rh, when two NO molecules are initially adsorbed on Rh4 cluster there are two kinds of molecular complexes: one top-top configuration Rh4(NO)2 and one top-facet-bridge configuration fb-Rh4(NO)2 with stabilization energies of 281.7 and 226.5 kJ mol−1 on their MERPs, respectively. The top-top Rh4(NO)2 can isomerize to the top-facet-bridge configuration fbRh4(NO)2. Next, from fb-Rh4NO, the N−O bond cleavage occurs via five-center TS1d-1 to form an ortho bridge-O and bridge-N intermediate o-NbRh4Ob(NO). Then from oNbRh4Ob(NO), the [1,2]-N shift successively takes place twice via three-membered ring TS1d-2 and TS1a-3 to produce a more meta bridge-O and bridge-N intermediate NbRh4Ob(NO). In 3NbRh4Ob(NO), the Mülliken spin densities of the −Rh4, −Nb, −Ob, and −NO moieties are 1.43, 0.25, 0.28, and 0.04, respectively, indicating unpaired electrons mainly on the −Rh4 moiety. From NBO analysis, the occupancies of the Rh−NO bond orbitals are 1.96 e, indicating one single bond of Rh−NO in 3NbRh4Ob(NO). Therefore, formation of the chemical bond in Rh−NO makes the 3NbRh4Ob(NO) complex thermodynamically stable. In view of Figure 1a−d, for the NbRh4Ob(NO) formation, there are four reaction pathways (RP-1NO-2Rh, RP-1NO3Rh, RP-2NO-2Rh, and RP-2NO-3Rh). First, for the reaction pathway RP-1NO-2Rh, the MERP should include the highest energy barrier (HEB) of 185.7 kJ mol−1 at the 4Rh4NO → 4 TS1a-1 reaction step, with the energy height of the highest point (EHHP) of 93.1 kJ mol−1 at 4TS1a-1. Second, for the reaction pathway RP-1NO-3Rh, the MERP should involve the HEB of 144.6 kJ mol−1 at the 4o-NbRh4Ob → 4TS1b-2 reaction step, with the energy height of the EHHP of 30.8 kJ mol−1 at 4 TS1b-1. Comparing with RP-1NO-2Rh, RP-1NO-3Rh exhibits better catalytic performance in view of the energy barrier for N−O bond cleavage. Third, for the reaction pathway RP-2NO-2Rh, the MERP should include the HEB of 195.7 kJ mol−1 at the 3Rh4(NO)2 → 3TS1c-1 reaction step, with the energy height of the EHHP of 0.0 kJ mol−1 at the entrance. Last, for the reaction pathway RP-2NO-3Rh, the MERP should involve the HEB of 137.9 kJ mol−1 at the 3o-NbRh4Ob(NO) → 3 TS 1d-2 reaction step, with the energy height of the EHHP of 0.0 kJ mol−1 at the entrance. Comparing with RP-2NO-2Rh, RP-2NO-3Rh possesses better catalytic performance, considering the energy barrier for the N−O bond cleavage. One can see that the N−O bond cleavage occurs more easily on the triangular facet site than on the edge site of the Rh4 cluster. As shown in Figure 1e, there are two reaction pathways from NbRh4Ob(NO) to Rh4Ob + N2O and (O)2Rh4(N)2 formation. One is N−N bond formation via a four-membered ring TS1e-1 to yield a molecular complex ObRh4N2O. Another is the N−O bond rupture of the second NO molecule via a four-membered ring TS1f-1 to form (O)2Rh4(N)2. These two reaction pathways are competitive. The triplet 3TS1e-1 locates 26.7 kJ mol−1 below the triplet 3TS1f-1, and the triplet 3ObRh4N2O deposits 88.1 kJ mol−1 below the triplet 3(O)2Rh4(N)2 on their MERPs. Therefore, the reaction pathway of the N−N bond formation is more favorable than that of the N−O bond scission, both thermodynamically and kinetically. Last, the ObRh4N2O set the N2O molecule free, leaving Rh4Ob behind. This result is in agreement with the experimental result, where a N2O intermediate was observed in the catalytic reduction of NO to N2 on Rh(111) surfaces.18−21 F


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Figure 2. Geometric structures of the reactants, intermediates, TSs, and products, and schematic energy diagrams for the reaction of Rh4 + N2O → Rh4Ob + N2 calculated at the B3LYP/6-311+G(2d),SDD level. Bond lengths are reported in Angstroms and bonds angles in degrees. Relative energies (kJ mol−1) for the corresponding species relative to 7Rh4 + N2O are shown.

Figure 3. Geometric structures of the reactants, intermediates, TSs, and products, and schematic energy diagrams for the reaction of Rh4Ob + CO → Rh4 + CO2 calculated at the B3LYP/6-311+G(2d),SDD level. Bond lengths are reported in Angstroms and bonds angles in degrees. Relative energies (kJ mol−1) for the corresponding species relative to 7Rh4Ob + CO are shown.

respectively. It is difficult to distinguish which reaction pathway is the most kinetically favorable, because of their same HEB and EHHP for RP-2NO-2Rh and RP-2NO-3Rh. Therefore, it is necessary to evaluate their TOFs using the energetic span model. For the reaction of Rh4 + 2NO → Rh4Ob + N2O, the MERP should start at the septet state and end on the septet one, conserving the spin multiplicity.

In view of Figure 1a−e, for N2O formation there are four reaction pathways (RP-1NO-2Rh, RP-1NO-3Rh, RP-2NO2Rh, and RP-2NO-3Rh). The four reaction pathways include the same HEB of 197.7 kJ mol−1 at the 3NbRh4Ob(NO) → 3 TS1e-1 reaction step. They differ from the EHHPs, which are 93.1 kJ mol−1 at 4TS1a-1, 30.8 kJ mol−1 at 4TS1b-1, 0.0 kJ mol−1 at the entrance and 0.0 kJ mol−1 at the entrance for RP1NO-2Rh, RP-1NO-3Rh, RP-2NO-2Rh, and RP-2NO-3Rh, G


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Figure 4. Geometric structures of the reactants, intermediates, TSs, and products, and schematic energy diagrams for the reaction of Rh4 + NO + CO → Rh4Nb + CO2 calculated at the B3LYP/6-311+G(2d),SDD level. Bond lengths are reported in Angstroms and bonds angles in degrees. Relative energies (kJ mol−1) for the corresponding species relative to 7Rh4 + NO + CO are shown: (a) N−O bond cleavage on the facet site of Rh4 cluster; (b) N−O bond cleavage on the edge site of Rh4 cluster.

3.1.2. Rh4 + N2O → Rh4Ob + N2. The geometric structures and schematic energy diagrams for reaction 5 Rh4 + N2O → Rh4Ob + N2 are depicted in Figure 2. As shown in Figure 2, reaction of Rh4 + N2O → Rh4Ob + N2 is calculated to be exergonic by 191.6 kJ mol−1 on its MERP. Thereby, this

reaction is thermodynamically preferable. At the beginning, when one N2O molecule is adsorbed on the Rh4 cluster, two configurations are obtained, (μ-1,3-O,N)-Rh4ON2 and (μ-1,2N,N)-Rh4N2O with stabilization energies of 7.5 and −11.0 kJ mol−1 on their MERPs, respectively. It is indicated that the H


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The Journal of Physical Chemistry A septet 7Rh4ON2 is more thermodynamically stable than the septet 7Rh4N2O. Next, from Rh4ON2, N−O bond cleavage and Rh−O bond formation proceed via a five-membered ring TS2-1 to generate a molecular complex ORh4N2. Then ORh4N2 releases the free N2 molecule, leaving Rh4O behind. Finally, from the top Rh4O, the [1,2]-O shift occurs via a threemembered ring TS2-2 to yield a more stable bridge Rh4Ob. As depicted in Figure 2, the quintet TS2-1 locates 1.8 kJ mol−1 slightly below the septet one. Accordingly, the MERP should go ahead via two MECPs of 7Rh4ON2−5Rh4ON2 and 5 ORh4N2−7ORh4N2. Besides, the quintet TS2-2 stands 46.0 kJ mol−1 below the septet one. Then the MERP should proceed via two MECPs of 7Rh4O−5Rh4O and 5Rh4Ob−7Rh4Ob. As a result, for the reaction of Rh4 + N2O → Rh4Ob + N2, the MERP should start at the septet state and terminate on the septet one, conserving the spin multiplicity, with the HEB of 11.8 kJ mol−1 at the 5Rh4ON2 → 5TS2-1 reaction step and the EHHP of 16.4 kJ mol−1 at 5TS2-1. 3.1.3. Rh4Ob + CO → Rh4 + CO2. The geometric structures and schematic energy diagrams for reaction 6 Rh4Ob + CO → Rh4 + CO2 are depicted in Figure 3. As shown in Figure 3, reaction of Rh4Ob + CO → Rh4 + CO2 is calculated to be exergonic by 165.6 kJ mol−1 on its MERP. Therefore, this reaction is thermodynamically favorable. First, one CO molecule is adsorbed on Rh4Ob through the C end to form a molecular complex ObRh4CO. Then [1,2]-O shift takes place via a three-membered ring TS3-1 to produce a top ObRh4CO. After that [1,3]-O migration occurs via a four-membered ring TS3-2 to yield a molecular complex Rh4CO2. Last, Rh4CO2 set the CO2 molecule free, making the Rh4 cluster reduced and completing the catalytic cycle. As indicated in Figure 3, the MERP should go forward via two MECPs of 7ORh4CO−5ORh4CO and 5Rh4CO2−7Rh4CO2. Hence, the MERP should begin on the septet state and end on the septet one, conserving the spin multiplicity, with the HEB of 109.8 kJ mol−1 at the 5ORh4CO → 5TS3-2 reaction step and the EHHP of 17.3 kJ mol−1 at 5TS3-2. In the gross reaction in eq 1 2NO + 2CO → N2 + 2CO2, first, for RP-1NO-2Rh, the TDI and TDTS are 6Rh4NO and 4 TS1a-1, respectively, using TOF analysis. Second, for RP1NO-3Rh, the TDI and TDTS are 3NbRh4Ob(NO) and 4TS1e1, respectively. Last, for both RP-2NO-2Rh and RP-2NO-3Rh, the TDI and TDTS are 5Rh4(NO)2 and 3TS1e-1, respectively. The TDIs, 6Rh4NO, 3NbRh4Ob(NO), and 5Rh4(NO)2 are associated with the NO molecularly adsorbed on the Rh4 or NbRh4Ob cluster. Both 4TS1a-1 and 3TS1e-1 represent the N− O bond cleavage step and N−N bond formation, respectively. Then the rate constants of 6Rh4NO → 4TS1a-1 (k1), 3 NbRh4Ob(NO) → 3TS1e-1 (k2), and 5Rh4(NO)2 → 3TS1e-1 (k3) are characteristic of the rate constants of RP-1NO-2Rh (k1), RP-1NO-3Rh (k2), RP-2NO-2Rh (k3), and RP-2NO3Rh (k3), respectively, for the gross reaction in eq 1 2NO + 2CO → N2 + 2CO2. Over the 300−900 K temperature range, the rate constants k1, k2, and k3 can be adapted by the following expression (in s−1) k1 = 3.593 × 1012 exp(− 238 400/RT )

(iv)

k 2 = 3.762 × 1012 exp(− 207 817/RT )

(v)

k 3 = 2.257 × 1010 exp( − 235 500/RT )

(vi)

Over the 300−900 K temperature range, the rate constant k1 is 1−2 magnitude orders greater than the rate constant k3. Therefore, RP-1NO-2Rh (k1) is kinetically more favorable than RP-2NO-2Rh (k3). Moreover, the rate constant k2 is seven to four magnitude orders greater than the rate constant k3. Therefore, RP-1NO-3Rh (k2) is kinetically more favorable than RP-2NO-2Rh (k3). These results indicate that the N−O bond cleavage in the absence of another NO molecule is kinetically more preferable than that in the presence of another NO molecule. In other words, the presence of the second NO molecule in some degree hampers the first N−O bond cleavage, which originates from the oxidizability of NO. Furthermore, the rate constant k2 is five to one magnitude orders greater than the rate constant k1. Thus, RP-1NO-3Rh (k2) is kinetically more favorable than RP-1NO-2Rh (k1). It is indicated that the first N−O bond cleavage on the facet site is kinetically more favorable than that on the edge site. It is obvious that the rate constant k2 is the greatest among these k1−k3 rate constants. Therefore, RP-1NO-3Rh is the kinetically most favorable. 3.2. 2NO + 2CO → N2 + 2CO2 Through N−O Bond Cleavage in the Presence of CO. This overall reaction is divided into three sequent reactions (reactions 7, 8, and 6). Because reaction 6 has been discussed earlier, it is necessary to investigate reactions 7 and 8, both thermodynamically and kinetically. This overall reaction can be divided into three reaction pathways consisting of N−O bond cleavage on the triangular facet of three Rh atoms in the Rh4 cluster before C− O bond formation, N−O bond cleavage on the edge of two Rh atoms in the Rh4 cluster before C−O bond formation, and simultaneous N−O bond cleavage on the top Rh atom in the Rh4 cluster and C−O bond formation, denoted as “RP-CO3Rh”, “RP-CO-2Rh”, and “RP-CO-1Rh”, respectively. These three reaction pathways mainly involve the following steps: (1) NO and CO coadsorption, (2) NO decomposition to N and O atoms (PR-CO-3Rh and RP-CO-2Rh) or recombination of CO and NO to form CO2 molecule and N atom (RP-CO1Rh), (3) reaction of the N atom with the second adsorbed NO to form N2 molecule and O atom, and (4) recombination of the O atom and CO to again form CO2. 3.2.1. Rh4 + NO + CO → Rh4Nb + CO2. The geometric structures and schematic energy diagrams for reaction 7 Rh4 + NO + CO → Rh4Nb + CO2 are depicted in Figure 4a and 4b. As shown in Figure 4a and 4b, reaction 7 is calculated to be exergonic by 276.3 kJ mol−1 on its MERP. Thus, this reaction is thermodynamically preferable. At the beginning, when both NO and CO molecules are adsorbed on the Rh4 cluster, a top-top molecular complex ONRh4CO is formed, with a stabilization of 248.2 kJ mol−1 on its MERP. In 6ONRh4CO, the Mülliken spin densities of −Rh4, −CO, and −NO moieties are 5.09, 0.04, and −0.08, respectively, indicating five unpaired electrons on the −Rh4 moiety. By NBO analysis, the occupancies of Rh−C and Rh−N bond orbitals are 1.96 and 4.73 e. It is indicated that there are approximately one single bond of Rh−C and one double bond of Rh−N in 6ONRh4CO. Thereby, the chemical bonds both in Rh−NO and in Rh−CO make the 6ONRh4CO complex thermodynamically favorable. From ONRh4CO, there are three reaction pathways (PR-CO-3Rh, RP-CO-2Rh, and RP-CO1Rh) for the formation of Rh4Nb + CO2. As shown in Figure 4a, first, for the reaction pathway PR-CO-3Rh, the top-top molecular complex ONRh4CO can isomerize to facet-bridgetop molecular complex fb-ONRh 4 CO. Next, from fbONRh4CO, the N−O bond cleavage takes place on the I


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Figure 5. Geometric structures of the reactants, intermediates, TSs, and products, and schematic energy diagrams for the reaction of Rh4Nb + NO → Rh4 + N2O calculated at the B3LYP/6-311+G(2d),SDD level. Bond lengths are reported in Angstroms and bonds angles in degrees. Relative energies (kJ mol−1) for the corresponding species plus CO2 relative to 7Rh4 + 2NO + CO are shown: (a) N−O bond cleavage on the facet site of Rh4 cluster; (b) N−O bond cleavage on the edge site of Rh4 cluster. J


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The Journal of Physical Chemistry A triangular facet in the Rh4 cluster via a five-center TS4a-1 to form an ortho bridge-N and bridge-O molecular complex oNbRh4Ob(CO). Then from o-NbRh4Ob(CO), [1,2]-O shift occurs via a three-membered ring TS4a-2 to generate a bridgeN and top-N molecular complex NbRh4O(CO). After that from NbRh4O(CO) C−O bond formation takes place via a fourmembered ring TS4a-3 to produce a molecular complex NbRh4(CO2). Last, NbRh4(CO2) releases the CO2 molecule free, leaving a bridge Rh4Nb behind. As depicted in Figure 4b, second, for the reaction pathway RP-CO-2Rh, from ONRh4CO, the N−O bond ruptures to form a top-top NRh4OCO via a four-membered ring TS4b-1. Then C−O bond formation takes place via a four-membered ring TS4b-2 with a [1,3]-O shift to yield a molecular complex NRh4CO2. Alternatively, for the reaction pathway RP-CO-1Rh, from ONRh4CO, the C−O bond forms via a five-membered ring TS4c-1, to produce a five-membered ring intermediate Rh4NCO2. Next, the N−O bond breaks to form the molecular complex NRh4CO2 via a five-membered ring TS4c-2. After that NRh4CO2 releases the CO2 molecule free, keeping a top Rh4N behind. From the top Rh4N, a [1,2]-N migrates to form a bridge Rh4Nb via a three-membered ring TS4b-3. The bridge 4 Rh4Nb deposits at −276.3 kJ mol−1 in a deep well. It is indicated that the bridge 4Rh4Nb is thermodynamically favored. This bridge Rh4Nb is in agreement with the experimental result, which supports the existence of surface nitrogen.16,17 As indicated in Figure 4a, for the reaction pathway RP-CO3Rh, the MERP should advance via one MECP between 6 ONRh4CO and 4ONRh4CO with the HEB of 123.3 kJ at the 4 NbRh4O(CO) → 4TS4a-3 reaction step associated with C−O bond formation and the EHHP of 0.0 kJ mol−1 at the entrance. As shown in Figure 4b, for the reaction pathway RP-CO-2Rh, the MERP should proceed via one MECP between 6NRh4OCO and 4NRh4OCO with the HEB of 183.3 kJ at the 6ONRh4CO → 6TS4b-1 reaction step with N−O bond cleavage and the EHHP of 3.0 kJ mol−1 at 4TS4b-2 representing C−O bond formation. Alternatively, for the reaction pathway RP-CO-1Rh, the MERP should go ahead via one MECP between 6 ONRh4CO and 4ONRh4CO, with the HEB of 199.0 kJ at the 4ONRh4CO → 4TS4c-1 reaction step associated with N−O bond cleavage and C−O bond formation and the EHHP of 0.0 kJ mol−1 at the entrance. One can see that the reaction pathway RP-CO-3Rh is the most kinetically favorable one among the three reaction pathways, because of its lowest HEB and lowest EHHP. Overall, the MERP should begin on the septet state and be terminated on the quartet one. 3.2.2. Rh4Nb + NO → Rh4Ob + N2. The geometric structures and schematic energy diagrams for reaction 8 Rh4Nb + NO → Rh4Ob + N2 and for reaction 9 Rh4Nb + NO → Rh4 + N2O are depicted in Figure 5a and 5b, respectively. It is obvious that reaction 8 is equal to reaction 9 plus reaction 5, denoted as the reaction pathways “RP-N2” and “RP-N2O”, respectively. As shown in Figure 5a, reaction 8 is calculated to be exergonic by 84.7 kJ mol−1 on its MERP. Hence, this reaction is thermodynamically favorable. As shown in Figure 5a, when the NO molecule is adsorbed on Rh4Nb, a molecular complex NbRh4NO is formed through N-end, with a stabilization energy of 146.0 kJ mol−1 on its MERP. In 3NbRh4NO, the Mülliken spin densities of −Rh4, −Nb, and −NO moieties are 2.27, −0.08, and −0.18, respectively, indicating three unpaired electrons mainly on the −Rh4 moiety. From NBO analysis, the occupancies of the

Rh−NO bond orbital are 1.99 e. It is indicated that there is one complete single bond of Rh−NO in 3NbRh4NO. Accordingly, formation of a single bond in Rh−NO makes the 3NbRh4NO complex thermodynamically stable. Then NbRh4NO can isomerize to a facet-bridge molecular complex fb-NbRh4NO. After that from fb-NbRh4NO N−O bond cleavage takes place via a five-center TS5a-1 to form a bridge-N intermediate (Nb)2Rh4Ob. Next, from (Nb)2Rh4Ob, N−N bond formation occurs via a five-center TS5a-2 to yield a molecular complex N2Rh4Ob. Finally, N2Rh4Ob sets N2 free, leaving Rh4Ob behind. For the reaction pathway RP-N2, the MERP should include the HEB of 99.8 kJ mol−1 at the 5(Nb)2Rh4Ob → 5TS5a-2 reaction step and the EHHP of −231.7 kJ mol−1 at 3TS5a-1. As shown in Figure 5b, from NbRh4NO there are two reaction pathways to form NRh4NO and (N)b(N)Rh4O. One is the [1,2]-N shift via a three-membered ring TS5b-1 to form a top NRh4NO, and another is the N−O bond cleavage via a four-membered ring TS5c-1 to form a top-top (N)b(N)Rh4O. On their MERPs, 3TS5c-1 lies 95.9 kJ mol−1 above 3TS5b-1 and 3(N)b(N)Rh4O deposits 12.3 kJ mol−1 above 3NRh4NO. It is indicated that the reaction pathway of the [1,2]-N shift is more preferable than that of the N−O bond cleavage, both thermodynamically and kinetically. After that from NRh4NO there are also two reaction pathways to generate Rh4N2O and (N)2Rh4O. One is N−N bond formation via a four-membered ring TS5b-2 with the [1,3]-N shift to form a molecular complex Rh4N2O, and another is the N−O bond scission via a fourmembered ring TS5c-2 to form a top-top (N)2Rh4O. On their MERPs, 3TS5c-2 locates 119.8 kJ mol−1 above 3TS5b-2 and 3 (N)2Rh4O lies 207.6 kJ mol−1 above 7Rh4N2O. It is indicated that the reaction pathway of N−N bond formation is more preferable than that of the N−O bond cleavage, both thermodynamically and kinetically. In other words, the reaction pathway of N−N bond formation is predominate, compared with that of N−O bond cleavage. Finally, Rh4N2O set a N2O molecule free, keeping Rh4 behind, without any energy requirement at the exit. Combining reaction 9 with reaction 5, for the reaction pathway RP-N2O the MERP should include the HEB of 130.3 kJ mol−1 at the 3NbRh4NO → 3TS5b-1 reaction step and the EHHP of −191.4 kJ mol−1 at 3TS5b-2. Comparing with RP-N2O, RP-N2 is more kinetically favorable, because of its lower HEB (99.8 vs 130.3 kJ mol−1) and lower EHHP (−231.7 vs −191.4 kJ mol−1). This result is in accordance to the experimental observation, where a N2O intermediate was found in the catalytic reduction of NO to N2 on Rh(111) surfaces.18−21 As mentioned earlier, for the reaction of Rh4 + NO + CO → Rh4Nb + CO2 there are three reaction pathways, RP-CO-3Rh, RP-CO-2Rh, and RP-CO-1Rh. For the reaction of Rh4Nb + NO → Rh4Ob + N2, there are two reaction pathways, RP-N2 and RP-N2O. Furthermore, for reaction 6 Rh4Ob + CO → Rh4 + CO2 there is a unique reaction pathway. Making these two kinds of reaction pathways combine together, there are six reaction pathways, denoted as “RP-CO-3Rh-N2”, “RP-CO3Rh-N2O”, “RP-CO-2Rh-N2”, “RP-CO-2Rh-N2O”, “RP-CO1Rh-N2”, and “RP-CO-1Rh-N2O” for the gross eq 1 2NO + 2CO → N2 + 2CO2. Using TOF analysis, first, for RP-CO3Rh-N2, TDI and TDTS are 3NbRh4NO and 4TS5a-1, respectively. Second, for RP-CO-3Rh-N2O, TDI and TDTS are 3NbRh4NO and 4TS5b-2, respectively. Third, for both RPCO-2Rh-N2 and RP-CO-2Rh-N2O the TDI and TDTS are 6 ONRh4CO and 4TS4b-2, respectively. Fourth, for RP-CO1Rh-N2, the TDI and TDTS are 6ONRh4CO and 4TS4c-2, K


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42%), the comparative minor k7 is preferred for the characteristic rate constant of the catalytic cycle. As depicted Figure 5a and 5b, from Rh4Nb + NO, the formation Rh4Ob + N2 is kinetically more favorable than that of Rh4 + N2O. One can see that RP-CO-1Rh-N2 (k7) is kinetically more favorable than RP-CO-1Rh-N2O (k7). Because k4 is greater than k5, RPCO-3Rh-N2 (k4) is kinetically more favorable than RP-CO3Rh-N2O (k5), that is, N2 formation would rather proceed through recombination of two N atoms on the facet site which originate from decomposition of NO than N2O intermediate which stems from recombination of the N atom and NO molecule on the edge site. Furthermore, because k4 is greater than k6, RP-CO-3Rh-N2 (k4) is kinetically more favorable than RP-CO-2Rh-N2 (k6). It is indicated that the first N−O bond cleavage on the facet site is kinetically more favorable than that on the edge site. The rate constant k4 is the greatest among these k4−k7 rate constants. It is indicated that RP-CO-3Rh-N2 is the kinetically most favorable. On the basis of the above results, there are two main reaction pathways RP-1NO-3Rh (k2) and RP-CO-3Rh-N2 (k4) on the facet site of the Rh4 cluster, while there are two main reaction pathways RP-1NO-2Rh (k1) and RP-CO-1Rh-N2 (k7) on the edge site. The branch ratios of k2/(k2 + k4), k4/(k2 + k4), k1/(k1 + k7), and k7/(k1 + k7) as a function of temperature are depicted in Figure 6.

respectively. Last, for RP-CO-1Rh-N2O, the TDIs are 6 ONRh4CO and 3NbRh4NO with the degrees of TOF control (42% and 58%), respectively, while the TDTSs are 4TS4c-2 and 4 TS5b-2 with the degrees of TOF control (42% and 58%), respectively. The TDI (6ONRh4CO) is in charge of the NO and CO coadsorbed on the Rh4 cluster. In 6ONRh4CO, the Mülliken spin densities of −Rh4, −CO, and −NO moieties are 5.08, 0.04, and −0.12, respectively, and the occupancies of Rh− N and Rh−C bond orbitals are 4.73 and 1.96 e from NBO analysis. It is indicated that there are approximately one doublebond of Rh−N and one single-bond of Rh−C in 6ONRh4CO. The TDI (3NbRh4NO) is representative of the NO adsorbed on Rh4Nb cluster. In 3NbRh4NO, the Mülliken spin densities of −Rh4Nb and −NO moieties are 2.19 and −0.18, respectively. It is indicated that the unpaired electrons mainly locate on the −Rh4Nb moiety. The TDTSs (3TS5a-1, 3TS5b-1, 4TS4b-2, and 4 TS4c-2) are responsible for the N−O bond cleavage on the triangle facet site, N−O bond cleavage on the edge site, C−O bond formation, and synchronous N−O bond cleavage and C− O bond formation, respectively. For the gross eq 1 2NO + 2CO → N2 + 2CO2 the rate constants of 3NbRh4NO → 3TS5a-1 (k4), 3NbRh4NO → 3 TS5b-2 (k5), 6ONRh4CO → 4TS4b-2 (k6), and 6ONRh4CO → 4TS4c-2 (k7) are representative of the whole reaction constants of the reaction pathways RP-CO-3Rh-N2 (k4), RPCO-3Rh-N2O (k5), RP-CO-2Rh-N2 (k6), RP-CO-2Rh-N2O (k6), RP-CO-1Rh-N2 (k7), and RP-CO-1Rh-N2O (k7 or k5), respectively. Over the 300−900 K temperature range, the rate constants k6 and k7 can be fitted by the following expressions (in s−1) k4 = 1.403 × 1011 exp( − 181 203/RT )

(vii)

k5 = 5.033 × 1012 exp( − 230 880/RT )

(viii)

k6 = 4.875 × 1010 exp( − 267 100/RT )

(ix)

k 7 = 5.608 × 1010 exp(− 218 900/RT )

(x)

Over the 300−900 K temperature range, the rate constant k7 is calculated to be eight to two magnitude orders greater than the rate constant k6. As mentioned earlier, for RP-CO-1Rh-N2 (k7), the TDTS of 4TS4c-2 is associated with the synchronous N−O bond cleavage and C−O bond formation, while for RPCO-2Rh-N2 (k6), the TDTS of 4TS4b-2 is characteristic of the C−O bond formation. In other words, the RP-CO-1Rh-N2 of synchronous N−O bond cleavage and C−O bond formation is kinetically more favorable than the RP-CO-2Rh-N2 of stepwise N−O bond cleavage and C−O bond formation. This embodies the reducibility of CO toward NO and the cooperativity of Rh− Rh in the Rh4 cluster, which makes CO readily reduce NO. This result on the Rh4 cluster differs from that on the Rh atom, in which CO plays a dominating role in the RhO reduction to regenerate Rh atom.31 It is indicated that the formation of CO2 should originate partly from the reaction between the adsorbed CO and NO on the edge site of Rh4 cluster, which is in accordance to the experimental phenomena by Brandt et al.15 Moreover, the rate constant k5 is almost 1 to 18 times greater the rate constant k7, and the rate constant k4 is calculated to be eight to two magnitude orders greater than the rate constant k5. For RP-CO-1Rh-N2O, since k5 (3NbRh4NO → 4TS5b-2 with the degrees of TOF control 58%) is greater than k 7 (6ONRh4CO → 4TS4c-2 with the degrees of TOF control

Figure 6. Branch ratios of k2/(k2 + k4), k4/(k2 + k4), k1/(k1 + k7), and k7/(k1 + k7) as a function of temperature.

Both RP-1NO-3Rh and RP-CO-3Rh-N2 are referred to the facet site of Rh4 cluster. As shown in Figure 6, with the increase of temperature (300−900 K), the branch ratio of k4/(k2 + k4) gradually decreases from 100% to 60% whereas the branch ratio of k2/(k2 + k4) gradually increases from 0% to 40%. In particular, over the catalytic converter operating temperatures of 600−800 K, the branch ratio of k4/(k2 + k4) gradually decreases from 90% to 70% whereas the branch ratio of k2/(k2 + k4) gradually increases from 10% to 30%, that is, over the usual experimental temperature of 600−800 K, RP-CO-3RhN2 is kinetically more favorable than RP-1NO-3Rh, while both RP-1NO-3Rh and RP-CO-3Rh-N2 coexist. Both for the dominate RP-CO-3Rh-N2 and the secondary RP-1NO-3Rh, the TDIs of 3NbRh4NO and 3NbRh4Ob(NO) are associated with the nitrogen-atom molecular complex, which is in agreement with the experimental observation of surface nitrogen.16,17 Furthermore, the formation of CO2 stems solely from recombination of CO and the O atom, the latter L


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Figure 7. Geometric structures of the reactants, intermediates, TSs, and products, and schematic energy diagrams for the two reactions of Rh4Nb + CO → Rh4 + NCO and Rh4 + NCO → Rh4Ob + CN calculated at the B3LYP/6-311+G(2d),SDD level, respectively. Bond lengths are reported in Angstroms and bonds angles in degrees. Relative energies (kJ mol−1) for the corresponding species plus CO2 relative to 7Rh4 + NO + 2CO are shown.

temperature (560−900 K), RP-1NO-2Rh is predominant, in which the TDTS is associated with the first N−O bond cleavage. The formation of CO2 should stem solely from the surface reaction between the adsorbed CO and the O atom, the latter being originated from NO decomposition, which is in agreement with the experimental observation.12−14 3.3. Formation of the NCO and CN Side Products. These side reactions are composed of the two reactions 10 and 11, that is, Rh4Nb + CO → Rh4 + NCO and Rh4 + NCO → Rh4Ob + CN. The geometric structures and schematic energy diagrams for reactions 10 and 11 are depicted in Figure 7. As indicated in Figure 7, reactions 10 and 11 are calculated to be endergonic by 162.2 and 367.4 kJ mol−1 on their MERPs, respectively. Accordingly, these two reactions are thermodynamically hampered. However, the formation of the intermediates Rh4NCO and ORh4CN are calculated to be endergonic by only 22.9 and 54.7 kJ mol−1 on their MERPs in reactions 10 and 11, respectively. As mentioned earlier, reactions 2 and 3, that is, NO + 2CO → NCO + 2CO2 and NO + 3CO → CN + 2CO2, are calculated to be exergonic by 114.1 and 74.5 kJ mol−1, respectively. It is indicated that the two side reactions 2 and 3 are thermodynamically favorable. 3.3.1. Rh4Nb + CO → Rh4 + NCO. As depicted in Figure 7, first, when one CO molecule is adsorbed on Rh4Nb through the C-end, a molecular complex NbRh4CO is generated with a stabilization energy of 118.6 kJ mol−1. Next, from NbRh4CO, C−N bond formation takes place via a five-membered ring TS6-1, resulting in a molecular complex Rh4NCO. Then Rh4NCO releases the NCO molecule free, leaving Rh4 behind. As indicated in Figure 7, the MERP should start at the quartet state and terminate on the septet via one MECP between 5Rh4 and 7Rh4, with the HEB of 175.4 kJ mol−1 at the reaction step

originating from the dissociation of NO. For the dominate RPCO-3Rh-N2, the TDTS of 4TS5a-1 is associated with the second N−O bond cleavage and formation of N2 originates from recombination of two N atoms. Alternatively, for the secondary RP-1NO-3Rh, the TDTS of 3TS1e-1 is associated with N−N bond formation for intermediate N2O formation. Overall, on the Rh4 cluster, N2 originates partly from recombination of two N atoms and partly from decomposition of N2O. Except for the reaction pathways on the facet site of the Rh4 cluster, there are two main reaction pathways on the edge site of the Rh4 cluster, RP-1NO-2Rh (k1) and RP-CO-1Rh-N2 (k7). As shown in Figure 6, RP-CO-1Rh-N2 (k7) is dominant at low temperature (300−560 K) whereas RP-1NO-2Rh (k1) is governed at high temperature (560−900 K). With the increase of temperature (300−900 K), the branch ratio of k1/(k1 + k7) gradually increases from 3% to 83%, whereas the branch ratio of k7/(k1 + k7) gradually decreases from 97% to 17%. On the edge site of the Rh4 cluster, at low temperature (300−560 K) RPCO-1Rh-N2 is dominant, in which the TDTS is related to the synchronous N−O bond cleavage and C−O bond formation. The presence of CO in some degree decreases the catalytic reduction temperature of NO on the Rh4 cluster. This embodies the reducibility of CO toward NO, which promotes the reduction of NO. This result on the Rh4 cluster differs from that on the Rh atom, in which CO plays a dominating role in the RhO reduction to regenerate Rh atom.31 This may stem from the cooperativity of Rh−Rh in the Rh4 cluster, which makes CO readily reduce NO. It is indicated that CO2 should originate partly from the reaction between the adsorbed CO and NO, which is in accordance to the experimental phenomenon by Brandt et al.7 On the other hand, at high M


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CO → Rh4NCO is kinetically more favorable than the reaction Rh4Nb + NO → Rh4 + N2O because of its low EHHP (−225.0 vs −191.4 kJ mol−1), while the reaction Rh4Nb + CO → Rh4NCO is kinetically more inferior than the reaction Rh4Nb + NO → Rh4Ob + N2 by virtue of its high EHHP (−225.0 vs −231.7 kJ mol−1). These results can qualitatively explain the N2, N2O, NCO, and CN contained species observed from reduction of NO by CO on surfaces of other d metals.34,65 In summary, for the overall reaction 2NO + 2CO → N2 + 2CO2, the facet site of the Rh4 cluster exhibits better catalytic performance than the edge site of the Rh4 cluster, especially for N−O bond cleavage. Both the dominant RP-CO-3Rh-N2 and the secondary RP-1NO-3Rh are associated with the facet site of the Rh4 cluster. The TDTSs are characteristic of the second N−O bond cleavage and N−N bond formation for the intermediate N2O formation for the former and latter, respectively. On the facet site of the Rh4 cluster, formation of CO2 stems solely from the recombination of CO and the O atom, the latter originating from dissociation of NO, while N2 originates partly from recombination of two N atoms and partly from decomposition of N2O. Alternatively, on the edge site of the Rh4 cluster, at low temperature (300−560 K), RP-CO-1Rh-N2 is dominant, in which the TDTS is associated with the synchronous N−O bond cleavage and C−O bond formation. The formation of CO2 should originate partly from the reaction between the adsorbed CO and NO and partly from recombination of CO and the O atom, whereas N2 originates from recombination of two N atoms. On the edge site of the Rh4 cluster, at high temperature (560−900 K), RP-1NO-2Rh is predominant, in which the TDTS is associated with the first N−O bond cleavage. The formation of CO2 stems solely from recombination of CO and the O atom, whereas N2 stems from N2O intermediate. It is predicted that the nitrogen species (3NbRh4NO and 3 NbRh4Ob(NO)) and N2O, NCO, and CN contained species should be observed from reduction of NO by CO on the Rh4 cluster. 3.4. Comparison of Rh4 Cluster with the Rh4+ Cluster. To explain the difference of two charge states, Rh4 and Rh4+, regarding their catalytic behavior, the HOMO and LUMO molecular orbitals for Rh4 and Rh4+ are depicted in Figure S2 of the SI. As shown in Figure S2, the HOMO−LUMO gaps are 2.79 and 2.26 eV for the ground septet Rh4 cluster and the ground sextet Rh4+ cluster, respectively. It is apparent that the HOMO−LUMO gap for the ground 7Rh4 is larger than that for the ground 6Rh4+. It is indicated that the neutral Rh4 cluster possesses lower reactivity and higher kinetic stability than the cationic Rh4+ cluster. Furthermore, for 7Rh4, the HOMO of αMO no. 38 involves 99% d-orbital contribution and the LUMO of α-MO no. 39 includes 95% p-orbital and 5% d-orbital contributions. For 6Rh4+, the HOMO of α-MO no. 37 involves 99% d-orbital contribution and the LUMO of α-MO no. 38 includes 13% s-orbital, 82% p-orbital, and 6% d-orbital contributions. It is indicated that there exists different HOMO−LUMO orbital interactions between 7Rh4 and 6Rh4+. Therefore, these differences in the HOMO−LUMO gap and HOMO−LUMO orbital interactions should make them have different catalytic reactivity. Here, we will compare their catalytic reactivity for the crucial reaction step in the catalytic cycle. As mentioned earlier, on the Rh4 cluster, the TDTSs of the optimal reaction pathways are associated with N−O bond

of 4Rh4NCO → 5Rh4 + NCO and the EHHP of −114.1 kJ mol−1 at 5Rh4 + NCO. As shown in Figure 7, 4NbRh4CO posits −394.9 kJ mol−1 in a deep well. TOF analysis shows that for the NCO species formation the TDI is 4NbRh4CO with the TDTS at the exit (7Rh4 + NCO). In 4NbRh4CO, the occupancies of BD(σ)Rh−C are 1.937 e, indicating a complete σ bond in Rh−C. Thus, 4 NbRh4CO has a large complexation energy of 118.6 kJ mol−1 relative to 4Rh4Nb + CO. Such large complexation energy traps the 4NbRh4CO complex in a deep well. In 4Rh4NCO, the dominant stabilization energies of LP(5) Rh → RY*(7)C, LP(5)N → LP*(4)Rh, and BD(σ)Rh−Rh → BD*(π)C−O are 253.0, 120.3, and 65.9 kJ mol−1, respectively. These results show that there is a dominant hyperconjugative interaction in the Rh−N−C−O−Rh five-membered ring cycle, thereby making an extremely stable complex 4Rh4NCO with a complexation energy of 139.3 kJ mol−1 relative to 7Rh4 + NCO. Such large complexation energy hampers the release of NCO species from 4Rh4NCO. This emphasizes that release of NCO molecule is the TOF-determining reaction step. Moreover, this result can qualitatively explain the NCO-contained species observed from reduction of NO by CO on Rh/Al2O3 catalyst.34 3.3.2. Rh4 + NCO → Rh4Ob + CN. As shown in Figure 7, when one NCO molecule is adsorbed on the Rh4 cluster, a molecular complex (μ-1,3-O,N)-Rh4NCO is obtained with a stabilization energy of 139.3 kJ mol−1 on its MERP. From Rh4NCO, C−O bond cleavage occurs via a four-membered ring TS6-2, leading to ORh4CN. Last, from ORh4CN, the direct Rh−C bond cleavage decomposes into the Rh4O moiety and CN radical. As mentioned earlier, the top Rh4O can convert to the bridge Rh4Ob via TS2-2, as shown in Figure 2. As indicated in Figure 7, the MERP should begin at the septet state and terminate at the quintet one via one MECP between 7Rh4O and 5Rh4O with the HEB of 334.9 kJ mol−1 at the 6ORh4CN → 7Rh4O + CN reaction step and the EHHP of 143.0 kJ mol−1 at 5TS2-2. In 6ORh4CN, the occupancies of BD(σ)Rh−C are 1.786 e, indicating a complete σ bond in Rh−C. Thus, 6ORh4CN involves a large complexation energy of 334.9 kJ mol−1 relative to 7Rh4O + CN. Such large complexation energy impedes the releasing CN species from 6ORh4CN, trapping the 6ORh4CN complex in a deep well. TOF analysis shows that for CN species formation the TDI is 4NbRh4CO and the TDTS is 5 TS2-2. This emphasizes that the [1,2]-O shift is the TOFdetermining reaction step. As shown in Figures 5 and 7, a glance to the reaction pathways reveals that the 4 N b Rh 4 NO and 4 N b Rh 4 CO intermediates are thermodynamically preferred. For NO deoxygenation with CO on the Rh4 cluster, the reaction traps the extremely stable complexes 4NbRh4NO and 4NbRh4CO in a deep well, thereby hampering the further process. However, since the intermediates do not lose all of their energy in a gasphase experiment, the relevant barrier is not that of the bottom of the well but that from the reactants.64 If so, once Rh4Nb is formed, it is necessary to compare the reactions of Rh4Nb with NO and CO. The reactions of Rh4Nb + NO → Rh4 + N2O, Rh4Nb + NO → Rh4Ob + N2, and Rh4Nb + CO → Rh4NCO are calculated to be exergonic by 62.9 kJ mol−1, exergonic by 84.7 kJ mol−1, and endergonic by 22.9 kJ mol−1, respectively. It is indicated that the reactions of Rh4Nb + NO → Rh4 + N2O and Rh4Nb + NO → Rh4Ob + N2 are thermodynamically preferable, while the reaction Rh4Nb + CO → Rh4NCO is not thermodynamically preferable. However, the reaction Rh4Nb + N


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investigated. The following conclusions can be drawn from the present calculations. For the overall reaction of 2NO + 2CO → N2 + 2CO2, the main reaction pathways take place on the facet site rather than the edge site of the Rh4 cluster. The TDTSs are characteristic of the second N−O bond cleavage and N−N bond formation for intermediate N2O production. The TDIs of 3NbRh4NO and 3 Nb Rh4 Ob (NO) are associated with the nitrogen-atom molecular complex, which is in agreement with the experimental observation of surface nitrogen. On the facet site of the Rh4 cluster, formation of CO2 stems solely from recombination of CO and the O atom while N2 originates partly from recombination of two N atoms and partly from decomposition of N2O. Alternatively, on the edge site of the Rh4 cluster, at low temperature (300−560 K) the TDTS is associated with the synchronous N−O bond cleavage and C−O bond formation. Formation of CO2 should originate partly from reaction between the adsorbed CO and NO and partly from recombination of CO and the O atom, whereas N2 originates from recombination of two N atoms. At high temperature (560−900 K), the TDTS is associated with the first N−O bond cleavage. Formation of CO2 stems solely from recombination of CO and the O atom, whereas N2 stems from N2O intermediate. For N−O bond cleavage or synchronous N−O bond cleavage and C−O bond formation, the neutral Rh4 cluster exhibits better catalytic performance than that of the cationic Rh4+ cluster. Alternatively, for N−N bond formation, the cationic Rh4+ cluster possesses better catalytic performance than the neutral Rh4 cluster.

cleavage on the facet site or N−N bond formation for N2O production. Unfortunately, on the Rh4+ cluster, the reaction pathways on the facet site have not been reported.32 To shed light on the charge effect of the cluster, we made up the corresponding transition states, which are associated with the N−O bond cleavage on the facet site of the Rh4+ cluster. On the Rh4+ cluster, the geometric structures and relative energies of some species are shown in Figures S4 of the SI. For comparison, the lowest energy barriers for N−O bond cleavage and N−N bond formation on the neutral Rh4 cluster and the cationic Rh4+ cluster are listed on Table 2. Table 2. Lowest Energy Barrier (LEB) for the N−O Bond Cleavage and N−N Bond Formation Reaction Step on the Neutral Rh4 Cluster and the Cationic Rh4+ Cluster reaction step Rh4NO → TS1b-1, N−O bond cleavage Rh4(NO)2 →TS 1d-1, N−O bond cleavage ONRh4CO → TS4a-1, N−O bond cleavage NbRh4NO →TS5a-1, N−O bond cleavage NbRh4Ob(NO) → TS1e-1, N−N bond formation a

LEB (kJ mol−1) Rh4

LEB (kJ mol−1) Rh4+

177.8 142.2

184.9 207.0

145.5

181.2

190.6

226.8

197.7

160.6a

Reference 32.

As shown in Table 2, in view of the facet site, the energy barriers for N−O bond cleavage on the neutral Rh4 cluster are lower, 7.1, 64.8, 35.7, and 36.2 kJ mol−1, than those on the cationic Rh4+ cluster. It is indicated that the neutral Rh4 cluster exhibits better catalytic performance for N−O bond cleavage than the cationic Rh4+ cluster. This may stem from the fact that the neutral Rh4 cluster involves higher reducibility than the cationic Rh4+ cluster, where the reducibility is beneficial to N− O bond cleavage. Alternatively, with regard to N−N bond formation for N2O production, the energy barrier on the cationic Rh4+ cluster is 37.1 kJ mol−1 lower than that on the neutral Rh4 cluster. It is indicated that the cationic Rh4+ cluster possesses better catalytic performance for N−N bond formation than the neutral Rh4 cluster. This may originate from the fact that the cationic Rh4+ cluster has higher oxidizability than the neutral Rh4 cluster, where the oxidizability is helpful to the N−N bond formation for N2O production. On the other hand, with regard to the edge site, the optimal reaction pathways are RP-CO-1Rh-N2 (k7) on the neutral Rh4 cluster and PR-Ps (kPs) on the cationic Rh4+ cluster with the TDTS of the synchronous N−O bond cleavage and C−O bond formation for CO2 production. The rate constant k7 on the Rh4 cluster is calculated to be seven to one magnitude orders greater than kPs on Rh4+ cluster32 over the 300−900 K temperature range. It is indicated that for the synchronous N− O bond cleavage and C−O bond formation, the neutral Rh4 cluster exhibits better catalytic performance than the cationic Rh4+ cluster. This may be ascribed to the fact that the neutral Rh4 cluster possesses higher reducibility than the cationic Rh4+ cluster, where the reducibility is conducive to the synchronous N−O bond cleavage and C−O bond formation.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b07713. Calculated gas-phase ion energetics and difference percentage of the calculated value relative to the experimental value at the B3LYP/6-311+G(2d),SDD, M05/6-311+G(2d),SDD, and M06/6-311+G(2d),SDD levels for some typical species; thermal correction to Gibbs free energy, sum of electronic and thermal free energies, and relative energies various species with respect to the ground reactants calculated at the B3LYP/6-311+G(2d),SDD level in the gas phase under room temperature and atmospheric pressure (300 K and 1 atm); standard orientations of various species calculated at the B3LYP/6-311+G(2d),SDD level in the catalytic reduction of NO by CO on Rh4 cluster; Arrhenius plots of calculated rate constants for the crucial reaction step in the catalytic reduction of NO by CO on Rh4 cluster; geometric structures and relative energies of some species at the B3LYP/6-311+G(2d),SDD level in the catalytic reduction of NO by CO on Rh4+ cluster; see DOI: 10.1039/b000000x/ (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: 028-85411105. Phone: 028-85411105.

4. CONCLUSIONS The catalytic reduction mechanism of NO by CO on the tetrahedral Rh4 subnanocluster has been systematically

Author Contributions

This manuscript was written through contributions of all authors. H.-Q.Y. is responsible for part computation, analysis, O


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and writing, H.-Q.F. for main computation, B.-F.S. for part computation, B.X. for part computation, Q.-Q.X. for part computation, and C.W.H. for design and revision. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful for financial support by the National Natural Science Foundation of China (nos. 21343001 and 21573154) and the Applied Foundation Research of Sichuan Province (nos. 2011JY0024 and 2014JY0218).

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