Density Functional Theory Analysis of Elementary Reactions in NOx

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Density Functional Theory Analysis of Elementary Reactions in NO Reduction on Rh Surface and Rh Clusters x

Fumiko Deushi, Atsushi Ishikawa, and Hiromi Nakai J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b04526 • Publication Date (Web): 28 Jun 2017 Downloaded from http://pubs.acs.org on June 29, 2017

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The Journal of Physical Chemistry

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Density Functional Theory Analysis of Elementary Reactions in NOx Reduction

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on Rh Surface and Rh Clusters

4 5 Fumiko Deushi a, Atsushi Ishikawa b,d, Hiromi Nakai a-d*

6 7

a

Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda

8 9

University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan b

Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo

10 11

169-8555, Japan c

CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012,

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Japan d

ESICB, Kyoto University, Kyotodaigaku-Katsura, Kyoto 615-8520, Japan (* E-mail address: [email protected], Telephone: +81-3-3205-2504)

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Abstract

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The reduction of NOx is crucial for reducing air pollution from vehicle exhaust. In the presence

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of Rh-based catalysts, the dissociation of NO and formation of N2O and N2 constitute the important

4

elementary steps of NOx reduction. The present study uses density functional theory (DFT) to

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investigate the catalytic performances of Rh(111) surface and Rh55 and Rh147 clusters towards these

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elementary reactions. The NO dissociation reaction was found to have minimum activation barriers

7

(Ea) of 0.63, 0.68, and 1.25 eV on Rh55, Rh147, and Rh(111), respectively. Therefore, it is the fastest

8

on small Rh clusters. In contrast, the N2 formation reaction is relatively inefficient on small clusters,

9

with the corresponding Ea values being 2.14, 1.79, and 1.71 eV. Because of the stronger binding of N

10

atoms to the Rh clusters than to the Rh surface, N2 formation via recombination of N atoms has a

11

higher Ea value on Rh clusters. The calculated reaction rate constants confirmed that small Rh

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clusters are less reactive for N2 formation compared to Rh(111), especially at low temperatures. Our

13

results also suggest that N2O formation is largely endothermic, and thus thermodynamically

14

unfavored.

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Introduction

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Since the invention of automobiles, air pollution from vehicle exhaust has been a serious

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environmental problem, particularly in urban areas. To reduce harmful gases from the exhaust,

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catalytic converters are now widely used.1 Typically, CO, unburned hydrocarbons (CHx), and NOx

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should be simultaneously converted into harmless gases. This is accomplished by using three-way

6

catalysts (TWCs), which primarily consist of precious metals such as Rh, Pd, and Pt. CO and CHx

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can be removed by oxidation, whereas NOx is removed by reduction with CO or CHx acting as

8

reducing agents. However, the N–O bond is too strong (631.6 kJ/mol) for direct reduction of NOx by

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CO or CHx in the gas phase, and it should be first activated by a metal surface.2 Therefore, the ability

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to dissociate the N–O bond is a key requirement for TWCs.

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Rh catalysts are thought to exhibit high activity towards NOx reduction, due to their high

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capability of facilitating NO dissociation. Hence, the behavior of NO molecules adsorbed on the Rh

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surface has been extensively investigated, mainly from the perspective of surface science. For

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example, it was shown that more than half of the NO molecules adsorbed on the Rh(111) surface

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readily dissociate into N and O atoms at 100 K, whereas this reaction does not take place on Pt(111)

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or Pd(111) surfaces.3-5 This implies that Rh is relatively more effective in promoting NO dissociation

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in the TWCs. However, NO dissociation is only one of the reaction steps involved in NOx reduction,

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and the catalytic activity of Rh towards other elementary steps should also be considered in order to

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evaluate the overall NOx reduction activity. Experimental investigations of the other reaction steps

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frequently employ a model reaction, such as the NO + CO reaction,6-10 which generates N2 and CO2 3 ACS Paragon Plus Environment


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like the exhaust gas conversion. Therefore, it is considered a simplified system for evaluating

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exhaust gas conversion by TWCs. Experimental studies have shown that, compared to other

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transition metal elements in TWCs, Rh exhibits good catalytic performance not only towards the NO

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dissociation but also the NO + CO reactions.11 For example, Kobylinski et al. experimentally

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identified the catalytic activity order of Rh > Pt > Pd towards NO reduction in a CO-H2 gas

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mixture.12 Owing to extensive investigations (most of which are surface science studies), the

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mechanism of the NO + CO reaction has been considerably clarified. The current consensus is that

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the reaction proceeds via the following elementary steps: (i) adsorption of NO and CO, (ii)

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dissociation of NO, (iii) either the removal of surface N atoms via N-N recombination to form N2, or

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the reaction of N + NO → N2O, and (iv) removal of surface O atoms by CO via CO2 formation.13-14

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While elucidation of the reaction mechanism on clean metal surfaces is important, real

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catalysts are often composed of metal clusters or nano-sized particles.15 Therefore, the effect of

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cluster size on the catalytic activity towards the NO + CO reaction is also crucial from a practical

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viewpoint. The effect of Rh particle size on its catalytic activity has been partially revealed by

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experimental studies. For example, Oh et al. suggested that the activity increases with the Rh particle

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size: when the particle size increases from the sub-nano regime to ~70 nm, there is a 45-fold increase

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in the overall reaction rate.16 Further, Peden et al. have shown that the product selectivity for the NO

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+ CO reaction, i.e., the ratio between produced N2O and N2, is significantly different between

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Rh(111) and Rh(110).17 Since the relative surface area of these facets changes with the particle size,

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the product selectivity with Rh particles is also likely to depend on the particle size. 4 ACS Paragon Plus Environment

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In order to fully elucidate the effect of the particle size on the overall catalytic activity, all

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elementary reaction steps in the NO + CO reaction should be considered, instead of only NO

3

dissociation. Many experimental and theoretical studies have shown that NO dissociation is

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accelerated on the step or edge sites.18-20 Therefore, small Rh particles are expected to display more

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facile NO dissociation, since they have a higher density of highly active sites such as edge or corner

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sites. If NO dissociation is the rate-determining step, a smaller (nano-sized) Rh cluster is expected to

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exhibit higher activity towards the overall NO + CO reaction than a larger one. Unfortunately, the

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kinetics of the overall reaction is much more complex; consequently, the catalytic activity and its

9

dependence on the Rh particle size cannot be predicted from the NO dissociation reaction alone. To

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better understand the underlying kinetics, one should also consider the removal of surface N and O

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atoms because these atoms adsorb strongly on the Rh surface and occupy the vacant surface sites

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necessary for the NO decomposition reaction. Several experimental studies suggested that compared

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to N atoms, the O atoms are more easily removed via the O + CO → CO2 reaction. Consequently,

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catalyst poisoning by N is considered more problematic.9, 21 A few elementary reactions have been

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proposed for the removal of surface N atoms. For example, two surface N atoms can combine to

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form N2, and the N + NO → N2O reaction also occurs because NO molecules are abundant on the

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surface. Indeed, N2O is one of the major products, especially at low temperatures.22-24 Furthermore,

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NCO formation has been proposed by several investigators.25-27 Nevertheless, it is well known that

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N2 formation is the main process at moderate to high temperatures.22-23, 28-30

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These experimental studies suggest that the mechanism for each elementary reaction step 5 ACS Paragon Plus Environment


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should be clarified in detail in order to elucidate their dependence on particle size. However, this task

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cannot be accomplished by experimental investigations alone. Theoretical calculation is an important

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complementary methodology, because it provides detailed information about the reaction kinetics as

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well as the thermodynamics of the reactants, products, intermediates, and transition states (TSs). In

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the present study, we investigate NO dissociation and the formation of N2 and N2O on sub-nano sized

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Rh clusters. Since these three reactions are important in the overall NO + CO reaction, they are

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intimately related to the catalytic activity during NOx removal. The present work is carried out in

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order to provide theoretical insights to the relationship between the Rh particle size and the NO + CO

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reaction rate. We compare these three reactions on the Rh surface and two small Rh clusters,

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employing the plane wave-based density functional theory (DFT) method because it can treat both

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metal surfaces and clusters with comparable accuracy. The focus is on the thermodynamic and

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kinetic properties, such as reaction energy and activation barrier, since they are essential for

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understanding and predicting the catalytic activities.

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Theoretical Methods We focused on the following four reactions (Eq. 1–4), which constitute the key elementary steps in the overall NO + CO reaction (Eq. 5):

4

NO + *  → NO*

(NO adsorption)

(1)

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NO* + *  → N* + O*

(NO dissociation)

(2)

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2N*  → N2 + 2*

(N2 formation)

(3)

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N* + NO*  → N2O* + *

(N2O formation)

(4)

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2NO + 2CO  → N2 + 2CO2

(5)

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In the above equations, the asterisk (*) indicates a vacant site on the surface, whereas X* represents

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species X adsorbed on a surface. Rh(111) surface is considered here and compared to the Rh clusters.

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The Rh(111) slab model was constructed using 3 × 3 unit cells with six metallic layers, and the

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adjacent slabs were separated by 20 Å vacuum regions. A model with a single molecule adsorbed on

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the surface corresponds to a surface coverage of 0.11 ML.

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Electronic structure calculations were carried out using DFT with the Perdew-Burke-Ernzerhof

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exchange correlation functional with revised parameters (RPBE functional).31 Projector-augmented

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wave (PAW) method was used to represent the core electrons. Valance electronic wavefunctions were

17

expanded using plane waves with a cutoff energy of 400 eV. Brillouin zone integration of 5 × 5 × 1

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and 1 × 1 × 1 Γ-point centered k-point grids was used for Rh(111) and the Rh clusters, respectively.

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For calculations involving Rh clusters and free molecules (NO, CO, N2, CO2, and N2O), a cubic box

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of 24 Å × 24 Å × 24 Å was used. During geometry optimization, first-order Methfessel-Paxton 7 ACS Paragon Plus Environment


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approximation with σ = 0.2 was employed in the smearing of the near-Fermi levels in the surface

2

calculations and Gaussian smearing with σ = 0.1 was used for the clusters. At density of state

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calculation, first-order Methfessel-Paxton with σ = 0.1 was employed. Spin-polarized calculations

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were carried out in all cases. Transition state search was carried out by the nudged-elastic-band

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(NEB) method, in which eight images connecting the initial and final structures were acquired. The

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experimental lattice constant of 3.80 Å for bulk Rh was used for the surface calculations.32 Using the

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adsorption energy of NO molecule, the convergence check with respect to vacuum thickness, plane

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wave cutoff energy, and k-point were examined (Figure S1). For the cluster system, the dependence

9

of the energy on vacuum thickness was examined using Rh147 as example (Table S1). Additionally,

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the dependence of the results on exchange-correlation functional was examined for RPBE, PBE, and

11

PW91 functionals, employing the NO adsorption energy on Rh55 as the benchmark (Table S2).

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Convergence threshold for electronic wave function and geometry optimization were 10–4 and 10–5

13

eV, respectively. These results are shown in Supporting Information. All calculations were carried out

14

using the Vienna ab initio simulation package (VASP) version 5.4.

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The Rh55 and Rh147 clusters were assumed to have the icosahedral geometry, primarily because

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the (111) surface which exhibits the closest packing is exposed in these structures. This facilitates the

17

comparison to the (111) surface. The diameters of the Rh55 and Rh147 clusters were 1.02 and 1.54 nm,

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respectively. None of the atoms in the clusters were fixed during geometry optimization, whereas in

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the surface model the topmost two layers were allowed to relax during this step.

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The possible adsorption sites on the Rh(111) surface and Rh clusters are shown in Scheme 1. 8 ACS Paragon Plus Environment

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On the Rh(111) surface, we examined the atop, bridge, and three-fold hollow (fcc and hcp) sites.

2

There are more types of adsorption sites in the Rh clusters, since Rh atoms form not only the terrace

3

but also the edges and corner parts of the clusters. We considered three types of atop sites–the corner,

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edge, and terrace Rh atoms (C-top, E-top, and T-top, respectively), and three types of bridge sites–

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between the corner-edge, edge-edge, and edge-terrace Rh atoms (CE-br, EE-br, and ET-br,

6

respectively). Two types of three-fold hollow sites, namely hcp and fcc hollow sites that are similar

7

to those on the Rh(111) surface, also exist in the clusters. The three-fold hollow sites with

8

corner-edge-edge and edge-edge-edge Rh atoms are hcp sites (denoted as CEE-hcp and EEE-fcc,

9

respectively), whereas those with edge-edge-terrace Rh are either hcp or fcc sites (EET-hcp and

10

EET-fcc, respectively). In the Rh147 cluster, all the above adsorption sites exist except for EEE-fcc.

11

Only 6 of the 10 adsorption sites exist in Rh55, as shown in Scheme 1.

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13 14

Scheme 1: Adsorption sites (blue dots) available on (A) Rh(111) surface, (B) Rh55, and (C) Rh147

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clusters.

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The adsorption energy (Ead) for an adsorbate A could be calculated using the following formula;

2

Ead = E (Surf-A) − [ E (Surf ) + E (A) ]

3

where E(Surf-A), E(A), and E(Surf) are the electronic energy contributions from the

4

surface-adsorbate system, adsorbate, and surface, respectively. According to this definition, negative

5

Ead indicates attraction.

6 7

(6)

The rate constants of surface reactions and desorption were estimated using the Arrhenius equation,  E kfor/rev = A ⋅ exp  − a  RT

8

 . 

(7)

9

where A is the pre-exponential factor, and Ea is the activation energy associated with the

10

transformation of the reactant to the TS, in either the forward or reverse (for/rev) directions. Here, A

11

is evaluated by the transition state theory as A = kB·T/h, where kB and h are the Boltzmann and

12

Planck constants, respectively.33 The rate constant for the adsorption reaction was estimated from

13

collision theory34-35 as

14

k=

ω 2π mX k BT

.

(8)

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The area per active site (ω) was calculated as 1.59 × 10−19 m2 from the density of bulk Rh crystal

16

(12.4 g·cm−3),32 and mX is the molecular mass of species X.

17


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1

Results and Discussion

2

Adsorption geometries and energies of NO, N2, N, and O on Rh

3

The energies associated with the adsorption of NO, N2, N, and O on Rh(111), Rh55, and Rh147

4

are shown in Table 1. We first discuss the adsorption of NO and N2. On Rh(111), there are four

5

available types of sites (atop, bridge, fcc, and hcp three-fold hollow sites), and NO most strongly

6

adsorbs on the latter two types with Ead = −2.11 and −2.15 eV, respectively. These values are in good

7

agreement with the published theoretical values, such as those reported by Gajdos et al.36 The

8

adsorption of NO on the other two sites is weaker (−1.97 eV for bridge and −1.73 eV for atop sites).

9

These values also agree well with previous experimental and theoretical results, which ranked the

10

sites for NO adsorption in the following order: hcp > fcc > bridge > atop.37-39

11

We examined the NO adsorption energy on Rh55 with PBE and PW91 as well (see Table S2 in

12

Supporting Information). The results show that these two functionals produce stronger binding (thus

13

more negative Eads values) than RPBE by 0.37 and 0.81 eV on average, respectively. This tendency

14

is in agreement with previous studies. For example, the Ead for CO on atop site of Rh(111) was

15

estimated by RPBE and PW91 functionals to be −1.68 and −2.04 eV respectively, while the

16

experimental value was −1.65 eV.40,41 Similarly, the Eads value of NO adsorption on Pd(111) was

17

estimated by RPBE, PBE, and PW91 to be −1.84, −2.34, and −2.35 eV, respectively;36 while the

18

experimental value was −1.86 eV.18 These examples indicates the overbinding of PBE and PW91

19

functionals, which is similar to our results in Table S2. Accordingly, we consider that the RPBE

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gives the most reasonable result. 11 ACS Paragon Plus Environment


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The adsorption of NO occurs with higher Ead values on Rh55 compared to Rh(111). Among the

2

six possible sites, the adsorption is the strongest on the C-top sites with Ead = −2.66 eV, which is

3

stronger than that on the hcp hollow sites of Rh(111) by 0.51 eV. NO adsorption also occurs on the

4

bridge and three-fold hollow sites of Rh55 clusters with large Ead values. Except for the B-top sites,

5

all other sites have Ead above −2.50 eV. Similarly, NO adsorption on the Rh147 cluster is strong on the

6

edge and corner sites, with Ead values of −1.96, −2.26, and −2.68 eV on the T-top, E-top, and C-top

7

sites, respectively. Therefore, it is evident that NO adsorption is stronger on open Rh atoms such as

8

corner and edge sites. In particular, the NO adsorption on Rh147 is the strongest on the C-top site, and

9

also strong on the CEE-hcp site.

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1

Table 1. Energies (in eV) Associated with the Adsorption of NO, N2, N, and O Species on Rh55, Rh147,

2

and Rh(111). RPBE functional was used. Values in Bold Font Represent the Most Stable Adsorption

3

Sites. The symbol “–” means that no stable adsorption position was found for these sites during the

4

geometry optimization. type atop Rh55

bridge hollow

atop

Rh147

bridge

hollow

site

N2

N

−0.86 −0.79

−4.34

−5.09

E-top

−2.66 −2.48

−4.18

−4.62

CE-br

−2.52

—

−5.09

−5.23

EE-br

−2.55

−0.16

−5.47

−5.35

CEE-hcp

−2.63

—

EEE-fcc

−2.56

—

−5.91 −5.48

−5.71 −5.36

C-top

−0.86 — —

−4.28

−4.89

−3.83

−4.32

T-top

−2.68 −2.26 −1.96

—

−3.90

CE-br

−2.48

—

−4.96

−5.18

EE-br(I)

−2.43

−0.31

—

—

C-top

E-top

NO

EE-br(II)

—

−0.31

—

−5.24

ET-br

—

—

—

—

CEE-hcp

−2.64

—

−5.41

−5.26

EET-hcp

−2.48

—

−5.43 −5.03

−5.28 −5.04

−2.97 a

−3.14 a

−4.24 a

−3.90 a

−5.19 −4.87 a

−4.99

−5.08

−5.08 −4.31 a

EET-fcc

— −1.73 −1.53 a

atop

−1.86 b −1.97 −1.73 a

bridge

−2.06 b Rh(111) hcp hollow

−2.15 −1.83 a −2.43 b −2.11 c

—

−0.31 −0.34 a 0.26 0.30 a

—

−2.11 fcc

−1.72 a

—

−2.36 b 5

O

a) Ref.37, b) Ref.38, c) Ref.36 13 ACS Paragon Plus Environment

−4.65

a

−4.26 a


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For almost all the sites, NO adsorption is stronger on Rh clusters than on the Rh(111) surface.

2

This is consistent with the current understanding of nano-sized particles. For example, a theoretical

3

study by Ghosh et al. revealed that NO adsorption on small Rhn (n = 1–5) clusters is stronger than

4

that on Rh(111) and Rh(100) surfaces.42

5

Next, we examine the N2 adsorption in these systems. On Rh(111), N2 adsorption on end-on

6

sites is stronger than that on the side-on ones for all four types of sites, with the atop and bridge sites

7

having stable N2 adsorption. However, N2 adsorption is exothermic only on the atop sites (Ead =

8

−0.31 eV). In comparison, N2 adsorption is stronger in the Rh clusters, particularly on the C-top sites

9

of Rh55 and Rh147 (both with Ead = −0.86 eV). N2 adsorption on the bridge sites is also exothermic

10

(e.g., Ead = −0.31 eV on EE-br(I) and (II) sites).

11

For the atomic species N and O, the most preferred adsorption sites on Rh(111) are the hcp and

12

fcc sites, respectively, in good agreement with previous experimental and theoretical results.43-44 In

13

our calculations, stable adsorption was not observed on the atop and bridge sites, since geometry

14

optimization starting at these sites ends up with N adsorbed on the hollow sites. Similar to the

15

molecules, N and O atoms bind more strongly to the two clusters compared to Rh(111). On the

16

clusters, N adsorption preferentially occurs on the three-fold hollow sites, similar to the case of

17

Rh(111). The adsorption energies are −5.91 and −5.48 eV for CEE-hcp and EEE-fcc on Rh55, and

18

−5.41, −5.43, and −5.03 eV for CEE-hcp, EET-hcp, and EET-fcc on Rh147, respectively. Most of

19

these values are substantially larger than that on Rh(111), which is −5.19 eV on hcp sites.

20

The above results show that the N adsorption is stronger on Rh55 compared to Rh147. Indeed, 14 ACS Paragon Plus Environment

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1

the values of Ead are larger on Rh55 than for similar sites on Rh147. For example, N adsorption

2

commonly occurs on C-top, CE-br, and CEE-hcp sites in both clusters, but it is stronger on Rh55 by

3

0.06–0.50 eV. Based on these results, we conclude that smaller Rh clusters exhibit stronger affinity

4

towards N atoms; and therefore, these clusters are more likely to be poisoned by them. Another

5

interesting difference between the Rh surface and clusters arises from the position of the Rh atoms. N

6

adsorption on the corner Rh atoms is stronger than that at the terrace and edge locations. Further,

7

unlike Rh(111), stable adsorption on the atop and bridge sites is possible for the Rh clusters (being

8

relatively stronger on the bridge sites), although the hollow sites are more favored.

9

The adsorption behaviors of O on Rh clusters are similar to those of N atoms. O atoms bind

10

strongly to the hollow sites on Rh55, being the strongest on CEE-hcp (Ead = −5.71 eV) among the six

11

adsorption sites. This is 0.63 eV stronger than that for the fcc sites on the Rh(111) surface. The

12

EEE-fcc sites also have strong adsorption (Ead = −5.36 eV). However, O adsorption on the EET sites

13

on the edge Rh atoms is weaker than that on the CEE sites of corner Rh atoms. Considering that O

14

atoms bind to the fcc and hcp sites of Rh(111) with similar Ead values, the difference in adsorption

15

strengths between the CEE and EET sites can be attributed to the strong preference for adsorption on

16

the corner Rh atoms.

17

Similarly, on the Rh147 cluster the O atom adsorption is strong on the hollow sites, with Ead =

18

−5.26 and −5.28 eV on the CEE-hcp and EET-hcp sites, respectively. The energy gap between them

19

is less than that for Rh55 clusters, indicating that the corner Rh atoms on larger clusters are less

20

favorable for O adsorption. Further, the O atoms bond to Rh55 more strongly than Rh147 for all four 15 ACS Paragon Plus Environment


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1

feasible sites (C-top, E-top, CE-br, and CEE-hcp). Like the N atoms, the O atoms are also more

2

strongly adsorbed on smaller Rh clusters than on larger ones.

3

The stronger binding of NO molecule on Rh55 than Rh(111) can be explained in terms of the

4

electronic properties. Figure 1 shows the projected local density of states (PDOS) onto the NO

5

molecule and the NO coordinating Rh atom. Decomposition of the PDOS into s-, p- and

6

d-components was carried out, and the results revealed that p- and d-components are main

7

contribution in the NO and Rh atom DOSs, respectively.

8

The strength of the chemisorption on transition metal surface was frequently understood in

9

terms of the d-band center. Da Silva and coworkers have shown that this type of analysis can also be

10

used to compare metal surface and clusters.45 In Figure 1, the d-band centers of Rh atom are shown

11

in the vertical bars, and their values are −2.32 and −2.89 eV below the Fermi energy for Rh55 and

12

Rh(111), respectively. From the DOS analysis in Figure 1, Rh55 has a higher d-band center, thus the

13

anti-bonding region between Rh and NO moiety is higher in energy than that of Rh(111). This

14

indicates the anti-bonding state is less occupied in Rh55, leading to stronger adsorption of NO

15

molecule. Therefore, the difference in the NO adsorption energy between Rh cluster and Rh(111) can

16

be explained by the electronic character.


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1 2

Figure 1. Projected density of states (PDOS) of NO molecule adsorbed on Rh55 and Rh(111) at C-top

3

and atop adsorption sites, respectively. The vertical bar represents the d-band center of the Rh atom

4

on which the NO molecule is adsorbed.

5 6

NO dissociation reaction

7

The stronger adsorption of NO, N2, N, and O species on the Rh clusters compared to the Rh

8

surface implies that these species have significantly different relativities between the clusters and the

9

surface. To elucidate the NOx removal activity, the three key elementary reactions of NO dissociation,

10

N2 formation, and N2O formation were examined; the corresponding Ea and reaction energy (∆E)

11

values are summarized in Table 2.

12



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Page 18 of 43

Table 2. Activation Energy (Ea) and Reaction Energy (∆E) of NO Dissociation on Rh(111), Rh55, and Rh147. path

geometry changes

Ea (eV)

∆E (eV)

I

NO(hcp) → N(fcc) + O(fcc)

1.25

−0.49

II

NO(fcc) → N(fcc) + O(fcc)

1.38

−0.53

I

NO(C-top) → N(CEE-hcp) + O(CEE-hcp)

0.63

−1.63

II

NO(CEE-hcp) → N(CEE-hcp) + O(CEE-hcp)

0.84

−1.11

III

NO(EEE-fcc) → N(CEE-hcp) + O(CEE-hcp)

0.63

−1.18

I

NO(CEE-hcp) → N(CEE-hcp) + O(CEE-hcp)

0.68

−1.11

II

NO(EET-hcp) → N(EET-fcc) + O(EE-br(I))

0.96

−0.81

III

NO(EET-hcp) → N(EET-hcp) + O(EET-fcc)

0.73

−0.56

Rh(111)

Rh55

Rh147

1 2

On Rh(111), the reaction pathway starting from the NO molecule adsorbed on three-fold

3

hollow sites was investigated, since these are the preferred NO adsorption sites. Two reaction paths (I

4

and II) were found. In both paths, the NO dissociation occurs via the geometry changes depicted in

5

Figure 2(C): (a) vertically adsorbed NO switches to side-on position on the surface, (b) NO

6

dissociates from the side-on position via TS, where the N and O atoms partially occupy the hollow

7

sites, and (c) dissociated N and O atoms adsorb on the fcc sites. Path I (Ea = 1.25 eV, ∆E = −0.49 eV)

8

is more reactive than path II. Note that NO dissociation on Rh(111) has been extensively studied

9

theoretically by other researchers. For example, the path I calculated here is the same as that

10

determined by Rempel and co-workers,44 who used the RPBE functional to obtain the Ea and ∆E

11

values of 1.56 and −0.67 eV, respectively, in moderate agreement with our results.

12 18 ACS Paragon Plus Environment

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1 2

Figure 2. Geometry changes along the various NO dissociation reaction pathways on (A) Rh55, (B)

3

Rh147, and (C) Rh(111). Red: O, blue: N, and purple: Rh.

4 5

The NO dissociation reaction on Rh55 and Rh147 is remarkably different from that on Rh(111).

6

Our calculations identified three reaction paths (I, II, and III) on Rh55. The associated geometry

7

changes are summarized in Figure 2(A). The Ea value is smaller for paths I and III (0.63 eV)

8

compared to path II. In path I, NO is first adsorbed on the corner Rh atoms in the atop sites, with the

9

N atom sliding into the CEE-hcp position in the TS prior to N-O dissociation. In path III, the

10

vertically adsorbed NO molecule is tilted in the TS, at which point the N-O dissociation takes place.

11

Similar geometry changes also occur in path II with higher activation energy. After N-O dissociation,

12

the N and O atoms occupy the CEE-hcp sites in path I. However, These product atoms diffuse into

13

different faces of the Rh55 cluster in path I, whereas in path III the dissociation takes place within a

14

single face. This difference arises because N-O dissociation occurs in the corner and edge sites in

15

paths I and III, respectively. When the N and O atoms diffuse into different faces (path I), the

16

repulsive interaction between them is reduced; consequently, the N-O dissociation reaction is more

17

exothermic in path I. 19 ACS Paragon Plus Environment


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Page 20 of 43

1

The NO dissociation behavior on Rh147 is similar to that on Rh55, but with lower reactivity. The

2

geometry changes associated with the reaction paths for Rh147 are shown in Figure 2(B). In all three

3

paths, the NO molecule is adsorbed end-on, moves into the side-on configuration near TS, followed

4

by N-O dissociation. Afterwards, the N atom favors the hollow sites, whereas the O atom moves

5

towards either the hollow or bridge sites. Path I has the lowest Ea (0.68 eV) and the largest ∆E (−1.11

6

eV) values. Path III has a similar Ea value but is less exothermic. All three paths have higher NO

7

dissociation activity on Rh147 compared to on Rh(111), since their Ea values are lower (0.68–0.96 eV)

8

on the former.

9

Compared to Rh(111), Rh55 is particularly active towards NO dissociation, as evidenced by its

10

low Ea, which is almost half of that on Rh(111). The reactivity of Rh55 is close to that of the highly

11

active Rh(100) surface. Previous experimental and theoretical reports have suggested that Ea for NO

12

dissociation on Rh(100) (experimental: 0.38 and 0.46 eV,46-47 theoretical: 0.50 and 0.63 eV

13

significantly smaller than that on Rh(111). Additionally, the NO dissociation activity on Rh55 is close

14

to or even better than that on the stepped Rh(111) surface; the Ea value for NO dissociation on

15

stepped Rh(111) obtained from the DFT calculations by Rempel et al. is 1.03 eV (with the RPBE

16

functional), whereas the reaction energy is −0.92 eV.44 Based on the above observations, it can be

17

concluded that the corner parts of the Rh cluster are highly active during the NO dissociation

18

reaction.

48-49

) is

19

The higher NO dissociation activities of Rh55 and Rh147 are also consistent with the theoretical

20

results on smaller Rh clusters. For example, the DFT study by Harding et al. on the Rh6+ cluster 20 ACS Paragon Plus Environment

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1

demonstrated the lowest Ea value for NO dissociation is 0.23 eV, although this value can be as high

2

as 1.33 eV depending on the cluster geometry.50 Using DFT calculations, Xie et al. have reported that

3

NO dissociation occurs on the Rh7+ cluster with Ea = 1.72–2.45 eV, which also depends significantly

4

on the cluster structure.51-52 These studies imply that the flexible structure of small Rh cluster affects

5

the NO dissociation activity to a great extent. Contrary to these small Rh clusters, the structural

6

changes in the larger Rh55 and Rh147 were moderate, although we allowed full relaxation of the Rh

7

atomic positions in our cluster calculations. We consider that both clusters are sufficiently large to

8

retain the (111) facet on their surfaces. Consequently, the extensive structural change observed in

9

small clusters such as Rh6+ or Rh7+ do not take place in our Rh55 and Rh147 systems.

10 11

N2 formation reaction

12

The N2 formation during NOx reduction is generally believed to take place via the N-N

13

recombination reaction pathway on the Rh surface.4, 8, 21, 53-55 Therefore, we considered this process

14

on Rh(111), Rh55, and Rh147. The associated reaction paths and Ea and ∆E values are summarized in

15

Table 3.

16



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Page 22 of 43

Table 3. Ea and ∆E for N2 Formation Reaction on Rh(111), Rh55, and Rh147. path Rh(111)

geometry changes

Ea (eV)

∆E (eV)

I

N(hcp) + N(hcp) → N2 (atop)

1.71

−0.24

I

N(CEE-hcp) + N(CEE-hcp) → N2 (E-top)

2.33

0.42

II

N(CEE-hcp) + N(CEE-hcp) → N2 (EE-br)

2.14

1.06

I

N(CEE-hcp) + N(CEE-hcp) → N2 (E-top)

4.45

−1.09

II

N(CEE-hcp) + N(EEE-hcp) → N2 (EE-br(I))

1.79

−0.55

III

N(EEE-hcp) + N(EEE-hcp) → N2 (E-top)

1.97

0.01

IV

N(EEE-fcc) + N(EEE-fcc) → N2 (EE-br(II))

3.44

0.34

Rh55

Rh147

1 2

On Rh(111), this reaction starts from two N atoms adsorbed on hcp sites, which is the most

3

stable type for N adsorption. The N-N bond is then formed around the Rh bridge sites. After bond

4

formation, the N2 molecule lying parallel to the surface easily changes into the end-on configuration

5

on the atop sites. The overall Ea and ∆E values for this process are 1.71 and −0.24 eV, respectively.

6

The calculated geometry changes, shown in Figure 3(A), agree with the well-known experimental

7

and theoretical information about the N2 formation (or dissociation) process.20

8


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1 2

Figure 3. Geometry changes along the N2 formation reaction pathways on (A) Rh55, (B) Rh147, and

3

(C) Rh(111). Red: O atom, blue: N atom, purple: Rh atom.

4 5

Two reaction paths (I and II) were found for N2 formation on the Rh55 cluster (Figure 3(B)).

6

The associated geometry changes (Figure 3(B)) show that both paths have N atoms adsorbed on the

7

bridge-like positions in the TS, and the product N2 molecule has end-on adsorption geometry. Path II

8

has the lower Ea value, with N-N recombination occurring at the edge sites (Ea = 2.14 eV, ∆E = 1.06

9

eV). Interestingly, N2 formation is exothermic on Rh(111), whereas it is endothermic on Rh55 for

10

paths I and II. Therefore, the Rh55 cluster is less active towards N2 formation than Rh(111) from both

11

kinetic and thermodynamic viewpoints.

12

The N2 formation reaction on Rh147 is similar, with four identified reaction paths I–IV. The

13

geometry changes along the reaction paths are similar for all four paths: the N atoms in the hollow

14

sites move into bridge-like positions in the TS, and the resultant N2 molecule exhibits end-on

15

adsorption configuration. Path II has the lowest Ea (1.79 eV). In path I, N2 formation occurs on the

16

corner atoms of the Rh cluster, whereas it occurs at the edge atoms of the cluster in path III. The 23 ACS Paragon Plus Environment


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1

other two paths (II and IV) involve N2 formation within a single face of the cluster.

2

A remarkable difference for N2 formation on the two clusters is that exothermic reaction paths

3

exist for Rh147 (∆E = −1.09 eV for path I and −0.55 eV for path II), but not for Rh55. The

4

exothermicity and lower Ea value indicate that N2 formation is easier on Rh147 than on Rh55. On the

5

other hand, reaction paths I and IV in Rh147 have considerably larger Ea values and therefore are

6

unfavored. Paths II and III in Rh147 have similar Ea values, the latter is almost thermo-neutral since

7

its ∆E is close to zero. From these results, it is concluded that path II is the most favorable reaction

8

route to form N2 on Rh147, with the reactivity similar to or slightly lower than that on Rh(111).

9 10

N2O formation reaction

11

We have concluded that small Rh clusters are less active towards N2 formation compared to

12

Rh(111), which implies that the latter is more active towards surface N removal. However, N2O

13

formation must be also considered as an elementary step in the NOx reduction in addition to N2

14

formation, since several experimental studies have identified N2O as an intermediate species in NOx

15

reduction.24, 56-58 During NOx reduction with the Rh catalyst, both N2 and N2O formation reactions

16

play important roles since they remove surface N atoms. For this reason, comparison between the N2

17

and N2O formation is quite important for evaluating the overall NOx reduction process. The present

18

study assumes N2O formation via the Langmuir-Hinshelwood mechanism, i.e., involving the surface

19

N and NO moieties, as proposed in several experimental studies.6, 59 The associated reaction paths as

20

well as the Ea and ∆E values are summarized in Table 4. 24 ACS Paragon Plus Environment

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Table 4. Ea and ∆E for the N2O Formation Reaction on Rh(111), Rh55, and Rh147. path Rh(111)

Rh55

Rh147

geometry changes

Ea (eV)

∆E (eV)

I

NO(hcp) + N(hcp) → N2O(η2: hcp, bridge)

1.77

1.53

I

NO(CE-br) + N(CEE-hcp) → N2O(η2: EE-br, E-top)

2.14

2.09

II

NO(CEE-hcp) + N(CEE-hcp) → N2O(η2: EE-br, E-top)

2.13

1.37

III

NO(CEE-hcp) + N(CEE-hcp) → N2O(η2: EE-br, C-top)

1.92

1.90

I

NO(EET-hcp) + N(EET-fcc) → N2O(η2: EE-br(I), T-top)

1.69

1.52

1 2

We have identified the following geometry changes along the N2O formation path on Rh(111):

3

(i) NO and N adsorbed on hollow sites approach each other, (ii) TS structure is formed, and (iii)

4

η2-type product N2O molecule is formed. Since N2O is adsorbed on the Rh atoms via either the η1 or

5

the η2-modes, these two adsorption positions are explicitly distinguished in the reaction path on

6

Rh(111). The geometry changes on Rh55, Rh147, and Rh(111) are shown in Figure 4.

7

8 9 10

Figure 4. Geometry changes along the N2O formation reaction pathways on (A) Rh55, (B) Rh147, and (C) Rh(111). Red: O, blue: N, and purple: Rh.

11



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

1

Three and one reaction paths were identified for N2O formation in the Rh55 and Rh147 clusters,

2

respectively. All the reaction paths have relatively high Ea values (1.69–2.14 eV). More importantly,

3

the reactions are highly endothermic (1.37–2.09 eV), similar to the case for Rh(111). In all the paths,

4

the NO molecule adsorbed on the hollow or bridge sites tends to remain at its initial position while

5

the N atom approaches it. In other words, N2O formation takes place with the surface N atom

6

attacking the NO molecule. Therefore, it is a case of “late transition state,” meaning that the TS

7

geometry resembles the product state. Because of this property, Ea and ∆E takes similar values in

8

many reaction paths in N2O formation.

9

The relative energetics and kinetics of N2 and N2O formation directly affect the selectivity of

10

the overall reaction. On Rh55, N2O formation via path III has lower Ea than the N2 formation reaction.

11

However, the former is highly endothermic (1.90 eV), indicating that the reverse reaction is faster

12

than the forward one. The other reaction paths are also mostly endothermic. Therefore, the formed

13

N2O molecules, if any, easily dissociate into the N and NO species. The same tendency for N2O

14

formation was observed on Rh147. Based on these considerations, we conclude that N2 instead of N2O

15

is formed following NO dissociation under the reaction conditions assumed here, i.e., with small

16

coverage of surface species on the Rh surface or cluster. This conclusion is also supported by the rate

17

constants of the elementary reactions, as is shown later.

18 19 20

Rate constants of the NO dissociation, N2 formation, and N2O formation reactions To compare these three elementary reactions, their rate constants were calculated using the Ea 26 ACS Paragon Plus Environment

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1

values determined from DFT calculations. Assuming the Langmuir-Hinshelwood reaction

2

mechanism, the pre-exponential factor for the surface reaction rate constant can be approximated by

3

kB·T/h. The calculated forward and backward reaction rate constants (the highest values among

4

different possible paths) are plotted for comparison in Figure 5, and the numerical values are listed in

5

Table S3 of Supporting Information.

6

7 8

Figure 5. Reaction rate constants for elementary steps (NO adsorption/dissociation, N2

9

formation/desorption, and N2O formation/desorption) on Rh55, Rh147, and Rh(111). Both forward and

10

reverse rate constants are shown.

11 12

As expected from the large endothermicity of N2O formation, the reverse reaction is faster than

13

the forward one in most cases. The difference between these rate constants is particularly amplified

14

at lower temperatures. On both Rh clusters and Rh(111) surface, the rate constants for N2O

15

dissociation and N2O desorption have similar orders of magnitude. This indicates that the two

16

reactions take place simultaneously. In contrast, the reverse reaction of N2 formation is much slower

17

than the forward reaction. Thus, the desorption of N2 instead of its decomposition takes place. 27 ACS Paragon Plus Environment


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1

Based on the large endothermicity of N2O formation, it may be concluded that N2 formation is

2

preferred, particularly on Rh(111). In fact, N2 formation is faster than N2O formation on Rh(111) at

3

all temperatures. Although forward formation rate of the N2O formation is faster than N2 formation

4

on Rh55 and Rh147 clusters, its endothermicity indicates backward reaction i.e. N2O decomposition is

5

favored.

6

In the entire temperature range of 300–700 K, the N2 formation rate constant is smaller than

7

that of NO dissociation for Rh(111) and Rh clusters. This implies that N2 formation is a strong

8

candidate for the rate-determining step in the overall reaction. According to the rate constants, the Rh

9

activity toward N2 formation may be ordered as follows: Rh(111) (6.88 s−1) > Rh147 (1.83 s−1) > Rh55

10

(2.37 × 10−4 s−1). This order can be understood from the fact that smaller clusters have larger Ea

11

values for N2 formation, as discussed in the previous section.

12 13


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1


Conclusions

2

Key elementary reaction steps in the NO + CO reaction, namely NO dissociation, N2 formation,

3

and N2O formation, were investigated on the Rh(111) surface and Rh55 and Rh147 clusters (with

4

diameters of 1–2 nm) using the DFT method. For the adsorption processes, our results suggest that

5

NO, N, and O bind stronger to the Rh clusters than to Rh(111). The more open types of Rh sites (i.e.,

6

corner or edge Rh atoms as opposed to terrace Rh atoms) are favored for adsorption. Rh55 displays

7

stronger adsorption compared to Rh147. The adsorption energies of NO, N2, N, and O on the most

8

favorable sites on Rh147 are larger than those on Rh(111) by an average of 0.38 eV, whereas those on

9

Rh55 are larger than Rh(111) by 0.60 eV. In particular, strong binding of N atoms on the Rh55 cluster

10

implies that small-sized Rh clusters are more easily poisoned by N atoms.

11

The energetics of the three elementary steps were also examined. The activation energy for NO

12

dissociation is lower on Rh clusters than on Rh(111), being 0.63, 0.68, and 1.25 eV for Rh55, Rh147,

13

and Rh(111), respectively. Therefore, NO dissociates more easily on smaller Rh clusters than on Rh

14

surface. The N2O formation reaction was found to be thermodynamically unfavorable in all Rh

15

systems, since this process is highly endothermic, and the corresponding activation energies on the

16

Rh clusters are also significantly high (1.92 and 1.69 eV for Rh55 and Rh147, respectively). The N2

17

formation reaction also has high activation energies, but is exothermic on Rh147 and Rh(111). These

18

results indicate that N2 formation reaction is favored over N2O formation.

19

Based on calculated energetics and rate constants, N2O dissociation is faster than its

20

formation since the latter is very endothermic. Also, since N2O only weakly adsorbs on Rh(111) or 29 ACS Paragon Plus Environment


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1

Rh clusters, it can easily desorb as the corresponding rate constant is high. Thus, our results suggest

2

that N2O either decomposes or desorbs from the Rh catalyst. The alternative pathway for surface N

3

atom removal, i.e., the N2 formation reaction, is slower than NO dissociation especially at low

4

temperature. This suggests that the N2 formation is a strong candidate for the rate-determining step in

5

the overall NOx reduction, although additional elementary reaction steps should be considered before

6

reaching a final conclusion. The N2 formation activity can be ordered as: Rh(111) > Rh147 > Rh55,

7

indicating that smaller clusters are less active for NOx reduction at lower temperatures. On the other

8

hand, at higher temperatures NO dissociation is slower than N2 or N2O formation. Since the desorbed

9

state is favored at higher temperatures, NO adsorption on Rh is less likely to occur. This trend is

10

similar among the Rh surface and clusters.

11

Our results imply that small Rh clusters display faster NO dissociation, while the reaction rate

12

of the N2 formation step is low. Thus, insights gained from this study suggest that the activity of the

13

Rh clusters can be improved by inhibiting the strong adsorption of N atoms. We hope that the

14

experimental studies in this direction will be carried out in the future.

15 16


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1

Acknowledgments

2

Parts of the calculation were performed at the Research Center for Computational Science (RCCS),

3

the Okazaki Research Facilities, and the National Institutes of Natural Sciences (NINS). This study

4

was supported in part by the Core Research for Evolutional Science and Technology (CREST)

5

program from the Japan Science and Technology (JST) Agency; Grants-in-Aid for Challenging and

6

Exploratory Research ‘‘KAKENHI 16K17860”; Strategic Programs for Innovative Research

7

(SPIRE); and Computational Materials Science Initiative (CMSI) from the Ministry of Education,

8

Culture, Sports, Science, and Technology (MEXT), Japan.

9 10

Supporting Information

11

Change of NO adsorption energy on Rh(111) with vacuum region thickness, plane-wave cutoff

12

energy, and number of k-points; the total energy change of Rh147 and its dependence on the vacuum

13

region; the NO adsorption energy on Rh55 evaluated with RPBE, PBE, and PW91; the total and s-, p-,

14

d-decomposed densities of states of Rh55 and Rh147; the forward and reverse rate constants of each

15

elementary reaction step on Rh55, Rh147, and Rh(111).

16 17



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1

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Sci. Rep. 1997, 29, 35–90.



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Table of Contents Graphic

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TOC_Graphic 84x35mm (300 x 300 DPI)

ACS Paragon Plus Environment


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Fig. 1 137x75mm (300 x 300 DPI)


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Fig. 2 235x68mm (300 x 300 DPI)



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Fig. 3 228x87mm (300 x 300 DPI)


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Fig. 4 235x71mm (300 x 300 DPI)



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Fig. 5 292x90mm (300 x 300 DPI)


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Scheme 1 238x88mm (300 x 300 DPI)


Density Functional Theory Analysis of Elementary Reactions in NOx

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