Structural Evolution of the Rhodium-Doped Silver Clusters AgnRh (N

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Structural Evolution of the Rhodium-Doped Silver Clusters AgnRh (N # 15) and Their Reactivity Towards NO Peter Ludwig Rodríguez-Kessler, Sudip Pan, Elizabeth Florez, Jose Luis Cabellos, and Gabriel Merino J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b05048 • Publication Date (Web): 11 Aug 2017 Downloaded from http://pubs.acs.org on August 11, 2017

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The Journal of Physical Chemistry

Structural Evolution of the Rhodium-Doped Silver Clusters AgnRh (n ≤ 15) and their Reactivity Towards NO P. L. Rodríguez-Kessler,1,* Sudip Pan,1 Elizabeth Florez,2 José Luis Cabellos,1 and Gabriel Merino.1,*

1

Departamento de Física Aplicada, Centro de Investigación y de Estudios Avanzados,

Unidad Mérida, Km 6 Antigua Carretera Progreso, Apdo. Postal 73, Cordemex, 97310, Mérida, Yucatán, México 2

Departamento de Ciencias Básicas, Universidad de Medellín, Medellín 050010, Colombia

*

To whom correspondence should be addressed: [email protected] (PLRK), [email protected] (GM)

1

ACS Paragon Plus Environment


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ABSTRACT Structural properties of AgnRh (n ≤ 15) clusters are investigated using a successive growth algorithm coupled with density functional theory computations. The structures of the clusters are revisited, including a detailed discussion of their electronic properties. In contrast to these previous contributions, the lowest energy structures of the clusters are planar for n = 3-6, while three-dimensional for n = 7 onward. Our present searches identify new lowest energy structures for n = 3-6, and 9-13. The most stable isomers are selected to study the adsorption of NO. The size-dependent reactivity of the clusters indicates that Rh atom acts as a more effective adsorption site for NO than Ag. Since the transition from Rhexposed to Rh-encapsulated structures occurs at n = 9, the reactivity towards NO for AgnRh clusters with n ≤ 8 is considerably higher than that for the larger homologues. Further, the results show that doping Agn clusters with Rh increases the reactivity toward NO adsorption.

INTRODUCTION Silver clusters serve as building blocks for fabricating nanostructured materials due to their potential applications in optics1,2 and catalysis.3-7 In 2005, Janssens et al.8 reported experimentally the effect of the early transition metal (TM) dopants in silver clusters and found evidence of their enhanced stability. The same group noted a quenching in the magnetic moment of Ag10Co+,9 which is attributed to the fulfilled 18 electronic shell 2


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configuration.10 Motivated by these experimental findings, a number of theoretical studies analyzed the size dependency behavior for Agn doped clusters with metallic (Fe, Co) and semiconductor (Si) impurities.11–14 These studies clearly suggest that doping a silver cluster can induce modifications into its structural and electronic properties. However, most of these reports were devoted in exploring the effect of the early 3d transition metals as dopants, and so far, a very little attention has been paid for the noble metals as impurities. Kohaut and Springborg15 analyzed the structural and energetic properties of Rh-doped Agn clusters with n = 2-19 by first-principles computations, and found compact structures throughout the complete series of these clusters. These results caught our attention because no drastic sizedependent induced effects were reported, although Rh and Co have the same number of valence electrons (4d85s1 and 3d74s2, respectively). Herein, we systematically explore the potential energy surfaces (PES) of the AgnRh clusters via density functional theory (DFT) computations. In contrast to the results of Kohaut and Springborg,15 the growth pattern is planar for n = 3-6, while for n = 9-11, the cluster growth is directed toward the formation of endohedral geometries, which are distinct to the previously reported ones.15 Evaluation of the various energetic parameters like binding energy per atom, second order energy differences, dissociation energy, the HOMO-LUMO energy gap, and the ionization potential reveals that Ag9Rh has a closed-shell electronic structure with 18 valence electrons, in which Rh is situated at the center of a symmetric Ag9 cage. In order to analyze the structural implications on cluster reactivity, we further investigate the NO adsorption on the lowest-lying energy forms of AgnRh clusters. The interest in NO adsorption is because it is one of the principal pollutants emitted by automobiles. Previous DFT studies explored NO adsorption on small clusters such as Agn (n = 1-8),16 Pdn (n = 1-6),17 Fen (n = 1-6),18 Rh6,19 Cu4, Ag4, and Cu2Ag2.20 Recently, Tian et al.21 analyzed the NO adsorption on Pdn (n = 8, 13, 19, 25) clusters and found that the adsorption does not depend on the cluster size but rather on the structure. Further, systematic 3



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DFT studies were performed to investigate the molecular and dissociative adsorption of NO on Rh6+ and other Rhn± (n = 3, 4, 6, and 13) clusters.22,23 Hirabayashi and Ichihashi24 carried out experimental studies on the reaction of Ti-doped Cun+ clusters with NO and O2 and showed that the size dependence reactivity toward NO correlates with the adsorption energy. Herein, our calculations show that NO is adsorbed preferably via its N-end and Rh atom acts as a more effective adsorption site than Ag. Since the structural transition from Rh-exposed structure to Rh-encapsulated one occurs at n = 9, the reactivity towards NO is higher for the smallest clusters with n ≤ 8 than that for the larger analogues. For n = 9-15, as Ag center interacts with NO, the adsorption energy is more or less similar to that in pure Agn clusters, indicating the position of the Rh dopant as a determining factor for the reactivity. These present results are useful for the interpretation of the experimental observations in rhodiumsilver catalysts. COMPUTATIONAL DETAILS Our computations are based on the Kohn-Sham DFT,25,26 as implemented in the Gaussian 09 program.27 The exchange and correlation energies are treated with the PBE0 functional28 in conjunction with the def2-TZVP basis set.29 The lowest energy structures for AgnRh (n = 1-15) clusters are obtained by calculating individually a large number of structures generated by the combination of different techniques. For small cluster sizes (for n ≤ 7), the graph theory is used, which allows us to explore efficiently the configuration space to identify the global minima and gathers a large set of cluster isomers.30 Since the number of spatial structures increases exponentially with size, for larger sizes, the consideration of all structures for calculation is very limited, and efficient methods are needed to correctly predict the structure of the clusters.31-34 For n = 8 onward, we have used a ‘successive growth algorithm’, which constructs the structures of large clusters based on the preceding small ones.35 The geometries of AgnRh are generated from the lowest energy arrangements of Agn4


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1Rh

by adding an extra Ag atom. In particular, our algorithm identifies all planes formed by

three atoms on the surface of the clusters to deposit one Ag atom at three different binding sites such as the hollow, bridge and atop, respectively. However, this procedure generates a large number of structures, increasing the computational cost. Therefore, we have only considered those isomers of Agn-1Rh which lie inside the relative energy (∆E) window of 1 eV from the ground state. The principle of this procedure is that the clusters follow a growth pattern from the preceding ones, in which the near imposible task of exploring the configuration space of a large cluster is reduced to determine the lowest energy configuration when adding a single atom on all inequivalent sites on the cluster surface. This technique has proven to be an effective geometric search method for determining the lowest energy structures on Ni and Ti clusters among others.36,37 For each combination, the PESs for the first five spin multiplicities are explored. The harmonic vibrational frequencies are also evaluated to ensure that the clusters are true minima on their corresponding PESs. The average bond length (rav) is calculated by considering smaller distances than the sum of the covalent radii of two atoms forming the bond.

RESULTS Our computations show that the lowest energy structure of the AgRh dimer is a triplet, while the corresponding singlet and quintet states are higher in energy by 1.13 and 1.56 eV, respectively. The average binding energy (EB) in AgRh is 0.69 eV/atom, which is lower than that in the Ag2 dimer (with 0.76 eV/atom), the latter in excellent agreement with those of the reported theoretical and/or experimental values (see Table S1).14-16,38-41 The bond length in AgRh (2.599 Å) is larger than that in Ag2 (with 2.578 Å), despite a slightly lower radius of Rh than Ag, consistent with the EB result, however, this feature is limited to 5



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only dimers, while for larger clusters (starting from Ag2Rh) the Ag-Rh bond is energetically more favorable than the Ag-Ag one. Structures In the case of triatomic clusters, the most stable form (2d.1) adopts a C2v symmetric triangle in the doublet spin state, whereas the second low-lying isomer (2d.2) is an irregular triangle in quartet state with a ∆E value of 0.75 eV (see Figure 1). The EB in 2d.1 is 1.15 eV/atom, while for the pure Ag3 it is 1.01eV /atom.

2d.1, C2v , 2 (0.00) a

2d.2, Cs, 4 (0.75)

3d.1, C2v , 3 (0.00)

3d.2, C2v , 1 (0.51) a

4d.1, C2v , 2 (0.00)

4d.2, C2v , 2 (0.23) a

5d.1, C2v , 3 (0.00)

5d.2, C2v , 3 (0.15)

6d.1, D 3d, 2 (0.00)

6d.2, C2v , 2 (0.17) a

7d.1, Cs, 3 (0.00) a

7d.2, C3v , 3 (0.22)

8d.1, C2v , 2 (0.00) a

8d.2, Cs, 2 (0.12)

9d.1, D 3h , 1 (0.00)

9d.2, Cs, 3 (0.75) a

Figure 1. UPBE0/def2-TZVP structures of the first and second lowest energy isomers of AgnRh clusters with n = 2-9, along with their isomer label, point group, spin multiplicity, and relative energy (eV), respectively. The xd.y notation is used for each cluster, where x corresponds to the number of Ag atoms, d the Rh impurity and y the isomer number. a Previously structures of AgnRh clusters reported in Ref 15.

The first and second lowest energy isomers of Ag3Rh are a planar rhombus (3d.1) and tetrahedron (3d.2) structures in triplet and singlet states, respectively. Notice that even for small cluster like 3d.1 Kohaut and Springborg15 predicted 3d.2, as the most stable one, 6


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which may raise question about the reliability of their adopted SIESTA code.42 However, a recheck of the results using the same code coincides with our present results showing that the planar structure is energetically favored (by 0.8 eV) over 3d.2. Therefore, the final outcome is independent of the code, which hints that, perhaps, the differences are associated with the employed structure search method where Kohaut and Springborg15 described the initial potential energy surface by a tight-binding based scheme and a Gupta many-body potential. In its next larger-sized cluster, the global minimum structure is a trapezoid in the doublet state (4d.1), whereas the second isomer is a trigonal bipyramid (4d.2). It is worth noting that for n = 1-4, the AgnRh clusters adopt the similar 2D structures like pure Agn+1 clusters in which the Rh impurity occupies the highest coordinated position. Interestingly, for n = 5 onward, the replacement of one Ag atom in the Agn+1 clusters by one Rh atom results in a significant structural rearrangement. From the growth point of view, by attaching one Ag atom on 2d.1, both 3d.1 and 3d.2 isomers can be formed. Starting from these tetraatomic clusters, two routes of growing pattern are identified (see Figure S1) in which one of them forms planar clusters starting from 3d.1 up to the 6d.1 cluster. Note that 5d.1 is not a planar system, rather it adopts a pentagonal pyramid in the triplet state with C2v symmetry. On the other hand, 6d.1 is a practically planar D3d structure in the doublet state with a hexacoordinate Rh atom. Further, by attaching Ag atoms on 3d.2, three-dimensional structures can be formed up to the 6d.2 pentagonal bipyramid (PBP), which are found as the second most stable isomers for n = 3-6. For n = 7 and 8, a pentagonal growth pattern is energetically favored in which 7d.1 and 8d.1 possess a capped and bicapped PBP structure, respectively. For clusters with n = 9-15, AgnRh clusters favor the low spin configurations. From 9d.1 up to 12d.1, the cluster growth is directed toward the formation of endohedral geometries, which are distinct 7



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to the previously reported ones.15 In this context, 9d.1 adopts an endohedral cage structure with Rh at the center in the singlet state, which is significantly more stable (by 0.75 eV) than a tricapped PBP structure (9d.2). Its next neighbor-sized cluster, 10d.1, has a C2v structure, whereas the additional silver atom is capped over an Ag triangle of 10d.1 to form 11d.1 (see Figure 2).

10d.1, C2v , 2 10d.2, C2v , 2 (0.00) a (0.07)

11d.1, Cs, 1 (0.00) a

11d.2, Cs, 1 (0.08)

12d.1, Cs, 2 (0.00)

12d.2, I h , 4 (0.09) a

13d.1, Cs, 1 (0.00)

13d.2, C3, 3 (0.07) a

14d.1, C2v , 2 14d.2, C2v , 2 (0.21) (0.00) a

15d.1, Cs, 1 (0.00) a

15d.2, Cs, 1 (0.15)

Figure 2. UPBE0/def2-TZVP structures of the lowest and second lowest energy isomers of AgnRh clusters with n = 10-15, along with their isomer label, point group, spin multiplicity, and relative energy (eV), respectively. aPreviously structures of AgnRh clusters reported in Ref 15.

For 12d.1 and 13d.1 clusters, the global minima correspond to capped and bicapped incomplete icosahedra, respectively. Previous works reported by Gong et al.,43 and Zhang et al.,44 used the icosahedral structure (12d.2) as a model to investigate the properties of the Ag12M cluster, where M = Rh among various dopants. Contrastingly, we found that 12d.2 is 0.09 eV less stable than 12d.1. Since the cluster properties are quite sensitive to the structure, the latter would behave differently from the former. Note that from Ag10Rh to Ag13Rh clusters, the ∆E values between two competitive isomers range from 0.07 to 0.09 eV, which are relatively small compared to others, e.g., Ag2Rh, Ag3Rh, and Ag9Rh (see Figure S2). For 8


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Ag14Rh and Ag15Rh, icosahedral based structures are the most stable ones. Therefore, our present searches identify more stable structures than those reported by Kohaut and Springborg for n = 3-6, and 9-13.15 The average bond distances (rav) of AgnRh clusters are presented in Figure 3a. A reduced rav value in Rh-doped clusters, compared to pure Agn analogues, shows the ability to adopt more compact structures in the AgRh alloy than the latter ones. There is a node in the curve at n = 6, corresponding to the high symmetric structure of the 6d.1 cluster. Furthermore, the smallest rav value is attained at n = 9, implying the strongest interactions between atoms. Noticed that the Ag-Rh bond distances in the clusters are related to the charge transfer from the Agn host to the Rh impurity. The charges on each atom, computed by following the natural bond orbital scheme, show that for n ≥ 4 the electron charge is transferred from the Agn host to the Rh impurity (see Figure 3b). Such charge transfer (∆q) increases with the increment in the size of the clusters. The maximum ∆q value is attained for n = 9, which suggests that among all the present clusters, the 5s and 5p orbitals of Rh in Ag9Rh cluster experience the largest acceptance of electrons from Ag moiety (see Figures 3b and 3c). These findings motivate us to explore the electronic properties of the doped clusters (vide supra).

9



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Figure 3. (a) The average bond distance (rav) of AgnRh clusters with n=1-15. (b) Charge transfer (∆q) of Rh atom on AgnRh cluster. (c) Natural population (Npop) of 5s and 5p orbitals of Rh atom on AgnRh clusters.

Stability In order to determine the effects of the Rh impurity on the stability, various energetic descriptors of the title clusters are compared with pure Agn+1 clusters. The structures of Agn+1 clusters are reported in a number of papers.45-49 We also explored the PESs of Agn+1 (n = 115) clusters and our results for the largest clusters coincide with those reported by Yang et al.,45 which were obtained by using a genetic algorithm (see Figure S3). The relative stability of AgnRh and Agn+1 clusters is investigated by calculating EB value, second order energy differences (∆2E), and dissociation energy (Ed), which are defined as follows:

EB[Agn+1] = ((n + 1)E[Ag] - E[Agn+1])/(n + 1),

(1)

∆2E[Agn+1] = E[Agn+2] + E[Agn] - 2E[Agn+1],

(2) 10


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Ed[Agn+1] = E[Agn] + E[Ag] - E[Agn+1],

(3)

for the pure Agn clusters, and

EB[AgnRh] = (nE[Ag] + E[Rh] - E[AgnRh])/(n + 1),

(4)

∆2E[AgnRh] = E[Agn+1Rh] + E[Agn-1Rh] - 2E[AgnRh],

(5)

Ed[AgnRh] = E[Agn-1Rh] + E[Ag] - E[AgnRh],

(6)

for the Rh-doped Agn clusters, where E[Ag], E[Rh], E[Agn+1], and E[AgnRh] are the energies of Ag (4d105s1) atom, Rh (4d85s1) atom, Agn+1 cluster, and AgnRh cluster, respectively. Figure 4 shows the variation of EB of pure Agn+1 and AgnRh clusters as a function of the cluster size n + 1 (see Table S2 for absolute values of EB in AgnRh clusters). For Agn+1 clusters, EB presents an oscillating increment as the cluster size increases. For Rh-doped Agn clusters, EB is higher than that in the pure silver analogues from the trimer onward. The reason behind a larger EB value in Ag2 than that in AgRh but the reverse trend in the larger clusters lies in the fact that for dimer cases, the bonding is an s-s interaction in both dimers, which is slightly polarized in AgRh, because of the electronegativity difference between Ag and Rh. This is responsable to weaken the Ag-Rh bond in comparison to the non-polar AgAg bond in Ag2. However, for the larger clusters, the interplay of the unpaired d orbital electrons of Rh comes into the picture, which makes Rh superior to Ag to be located at the most coordinated position maximizing the interaction. In fact, EB increases rapidly up to n = 11



9 and then onwards the increment becomes less pronounced. For comparison, we have also included the previously reported structures of AgnRh clusters.15 It is apparent from the Figure 4 that these structures with n = 3-6 and 9 possess notably less EB values than the presently reported lowest energy isomers, while for n = 10-13 the corresponding EB values are only slightly smaller than the present cases. 2.0 1.8 1.6

EB (eV/atom)

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1.4 1.2 1.0

Agn+1 AgnRh

0.8

AgnRh

0.6

a

0

2

4

6

8

10

12

14

16

n

Figure 4. Comparison of the average binding energies (EB) of AgnRh (circles) and Agn+1 (squares) clusters. The EB values (at PBE0 level) of the previously structures of AgnRh clusters reported in aRef 15, are shown for comparison.

The ∆2E and Ed quantities help us to determine the relative stability of AgnRh clusters compared to their neighbors. For pure Agn clusters, ∆2E and Ed (in the channel leading to Agn-1Rh + Ag) plots (as shown in Figure 5) show the usual even-odd pattern with higher stability for clusters with even valence electrons, whereas for AgnRh clusters, the size variation of these parameters is less pronounced, with the maximum values for Ag6Rh and Ag9Rh clusters. Those sizes may correspond to the magic numbers with closed-shell electronic structures, which are usually characterized by having unusual stability and large HOMO-LUMO energy gaps (∆H-L) (vide infra).

12


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Figure 5. (a) The comparison of second energy differences (∆2E) of AgnRh (circles) and Agn+1 (squares) clusters with n = 1-15. (b) The dissociation energy (Ed) of AgnRh and Agn+1 clusters.

To understand these energetic trends, ∆H-L and ionization potential (IP) are computed to determine the chemical stability of the clusters. Usually, a cluster with higher ∆H-L value exhibits lower reactivity. In our case, the Rh impurity increases the ∆H-L value with respect to that in Agn analogues (see Figure 6a). Note that the highest ∆H-L occurs for AgRh, Ag6Rh, Ag9Rh, Ag11Rh, and Ag13Rh clusters. However, among them Ag6Rh and Ag9Rh have higher stability, based on the other energetic criteria (vide supra).

13



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Figure 6. (a) HOMO-LUMO energy gap (∆H-L) of AgnRh (circles) and Agn+1 (squares) clusters with n=1-15. (b) The vertical ionization potentials of Agn+1 and AgnRh clusters with n = 1-15. The experimental data (curve with error bars) for the IP of Agn clusters is included for comparison.50

For n = 10, 12 and 14, the smallest ∆H-L values are obtained for the Rh-doped clusters, implying their enhanced reactivity. To support these findings, we have further computed the vertical IP as shown in Figure 6b, by using the following expresions:

IP = E[Agn+1+] – E[Agn+1],

(7)

IP = E[AgnRh+] – E[AgnRh],

(8)

where E[Agn+1+], E[AgnRh+] are the energies of the cationic clusters with the neutral geometries. Experimentally, Jackschath et al.50 measured the vertical IP of Agn clusters (n ≤ 36). In Figure 6b, the computed IP values of pure Agn clusters are compared with those experimentally obtained ones and it is found that our theoretical prediction is in excellent agreement with the experimental curve for n ≤ 8 clusters. For n = 9 onward, the relative deviation between computed and experimental values increases but the computed curve maintains a similar pattern as that of the experimental one. This larger deviation may be due to the increase in isoenergetic isomers for the larger clusters sizes (the observables depend on multiple cluster structures instead of one). These results help us to validate our approximation to further analyze the effect of the Rh impurity on Agn clusters. It is known that for metal clusters when a new shell starts getting occupied, the IP drops sharply, suggesting that the n-1 cluster corresponds to a closed-shell electronic 14


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structure.9 These features are found at n = 7 and 10, suggesting that Ag6Rh and Ag9Rh clusters may possess closed electronic shells. Nevertheless, due to the odd number of electrons, the increased stability in Ag6Rh cluster could be due to a dominant geometric effect, in which the stability is determined more by the number of atoms rather than by the number of electrons. Previously, the similar effect was noted in Au6V by Nhat and Nguyen.51 The effect would be more pronounced when both the geometric effect and closed shell phenomenon come together in the picture. Therefore, we attribute the enhanced stability of Ag6Rh to the compact symmetric structure, whereas for Ag9Rh, the exceptional stability is originated from the both 18-electron rule and geometric effect. In terms of the phenomenological shell model, it has a closed-shell structure with configuration [1S21P61D10], in which the Rh impurity delocalizes its 4d and 5s electrons and each Ag atom contributes its one valence 5s electron. Metal clusters with 18 and 20 valence electrons were reported for numerous clusters including Ag10Co+,9 Al7+,52 Si16Ti,53 Ge10Ni,54 among others, which exhibit greater stability than their neighbors.

NO Adsorption on AgnRh Clusters In 2002, Kotsifa et al.55 found that the substitution of Ag by Rh in silver nanoparticles results in a significant increase in the catalytic activity for the reduction of NO. To provide insights into the reactivity of the clusters towards the adsorption of NO, we have computed the adsorption energy (Eads), defined as: Eads = E[sys] − E[catalyst] − E[species],

(9)

where E[species], E[catalyst], and E[sys] are the total energies of the isolated species (NO), the catalyst (Agn+1, AgnRh with n = 1-15) and the adsorption system, respectively (notice that a negative value in Eads implies an energy gain during adsorption). The interaction of the 15



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clusters with NO is investigated approximating the NO molecule to the global minimum of each title cluster. In principle, NO can be adsorbed in several places on the AgnRh cluster. Of course, the number of adsorption sites increases with n. In order to understand the most proclive sites for adsorption, all possible adsorption sites were explored for clusters with n ≤ 8, whereas for n = 9 onward, at least three different top and bridge sites were considered. For instance, Figure 7 depicts some structures of the Ag7Rh-NO after considering several adsorption sites in multiple spin configurations. First, the adsorption does not modify the skeleton of the cluster. Second, Rh atom is turned out as the most stable NO adsorption site, in which the NO molecule gets bound via N-end. The O-Rh bonding is also possible but considerably less stable than the N-Rh one. The adsorptions on Ag atoms lead to about 2 eV higher energy isomer than that on Rh atom. Similarly to previous works that investigated NO adsorption in TM clusters, it has been found that the N atom adsorbs on the cluster surface while the O atom moves to a free position.16-23 Piotrowski and Piquini56 addressed the interaction of NO with Rh, Pd, Ir, and Pt 13-atom clusters and found a clear trend of N-TM bonding formation which also occur on the TM(111) surface.

(0.00), 2

(0.04), 2

(1.27), 4

(1.53), 2

(1.54), 2

(1.61), 4

(1.82), 4

(1.87), 2

(1.92), 4

(1.97), 2

(1.97), 2

(1.98), 2

Figure 7. NO adsorption on Ag7Rh cluster. For each configuration, the relative energy (in eV) and spin multiplicity are given. Silver, rhodium, oxygen and nitrogen atoms are in 16


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gray, dark cyan, red, and blue, respectively.

The most stable isomers of NO adsorbed AgnRh clusters and the related results are provided in Figure 8. For clusters with Rh-exposed structures (n = 1-8), NO is adsorbed preferably with N bonding on Rh. The comparatively larger Eads values are found for n = 1-6, ranging from -2.13 to -3.21 eV. In the bound state, the N-O bond length gets slightly elongated, compared to that in the free NO (1.13 Å), but irrespective of the adsorbing clusters it remains almost unchanged (from 1.15 to 1.17 Å). We found that the deepest adsorption is performed in the Rh top site by the Ag2Rh triangle and the Ag6Rh PBP, with an adsorption energy of -3.21 eV/NO and -2.96 eV/NO, respectively. Note that although the 6d.1 is most stable and magic cluster, it turns out that the 6d.1-NO adsorption complex is not that much stable, rather it would prefer to undergo isomerization during NO adsorption on Rh, in which the planar structure transforms into a 3D one. This is why we are not presenting this cluster in Figure 8. For the AgRh dimer (not shown), the NO molecule adsorbs in the Rh top site as well, with adsorption energy of -2.00 eV/NO.

17



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Structure

Label

˚) r N− O ( A

E ads (eV)

ν(cm− 1)

2S + 1

2d.1-NO

1.16

-3.21

1854

3d.2-NO

1.16

-2.47

4d.2-NO

1.15

6d.2-NO

Page 18 of 30

Label

˚) r N− O ( A

1

3d.1-NO

1.15

-2.13

1840

2

1837

2

4d.1-NO

1.15

-2.56

1901

1

-2.57

1893

1

5d.1-NO

1.15

-2.88

1906

2

1.15

-2.96

1911

1

7d.1-NO

1.16

-2.07

1806

2

8d.1-NO

1.17

-1.47

1691

1

9d.1-NO

1.14

-0.24

1907

2

9d.2-NO

1.17

-1.24

1686

2

10d.1-NO

1.17

-0.29

1688

1

11d.1-NO

1.15

-0.25

1704

2

11d.2-NO

1.20

-0.55

1583

4

12d.1-NO

1.20

-0.55

1573

3

12d.2-NO

1.18

-0.31

1582

3

St ructure

E ads (eV) ν(cm− 1)

2S + 1

Figure 8. Structures of AgnRh-NO complexes, the N-O bond length, the adsorption energy (Eads), the N-O stretching frequency (ν), and spin multiplicity (2S+1), respectively.

For n = 7 onward, the Eads starts to decrease, since the coordination of the Rh atom increases. Interestingly, for n = 9, the Eads becomes minimum, with -0.24 eV/NO, in which the NO is adsorbed by the Ag site. Although in the previous section we emphasized that the 9d.1 cluster is magic, we attribute the low Eads value due to the encapsulation of the more active Rh center. Note that for the 9d.2 isomer, the Eads value is considerable (-1.24 eV). For larger clusters, with n = 10-12, the Eads is quite low, lying within the range from -0.29 to 0.55 eV, since the Rh atom is not available for binding. For these clusters, the NO molecule gets adsorbed at the bridge site, except for 11d.1. Because of the low Eads the results for n = 13-15 clusters are not further included. The vibrational frequency (ν) of the NO attached molecule decreases with the increase of coordination, e. g., for n = 2-9 the highest N-O stretching frequency are found, ranging from 1691 to 1911 cm-1 (ν = 2030 cm-1 for the 18


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isolated NO molecule), indicating some amount of red-shift in the frequency. Due to the bridge adsorption site for n=10-12, ν decreases, while the lowest value (with ν = 1582 cm-1) is found for the icosahedron cluster 12d.2 in which the NO molecule attaches to the 3-fold hollow site with ν = 1582 cm-1. In ref 20, the vibration of gas-phase NO was reported to be 2076 cm-1. It is worth noting that, due to the preferred Rh-NO adsorption, for the larger clusters (with encapsulated Rh) the most stable AgnRh-NO systems could likely have the AgnRh unit geometries different (such as the exohedral motif) from those without the adsorbed molecule. This may well interchange the relative stabilities of the isomers upon NO adsorption (as, e.g., for the n=9 case). It thus seems possible that in reality (for nonzero-temperature conditions making the clusters less rigid) the interaction with NO will alter the cluster geometry. In this context, the location of the exohedral structures is important to guarantee the adsorption behaviour of larger clusters, and those with n=10-13, which possesses the lower energy gaps between the most stable structure and the lowest energy isomer (see Figure S2). To prove the stability of the clusters, in Figure 9 it is shown the structures of different AgnRh (n=10-13) cluster isomers (it is not intended to show all possible isomers but only a selection). The results show that for n=11-13, the first exohedral structures start from 0.42 to 1.03 eV, which confirms the stability of the clusters in real conditions.

Ag10Rh 0.0, 2

0.07, 2

0.42, 2

0.45, 2

0.53, 2

0.74, 2

0.0, 1

0.08, 1

0.1, 3

0.67, 3

0.68, 1

0.75, 1

Ag11Rh

Ag12Rh 19



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Page 20 of 30

0.0, 2

0.09, 4

0.33, 2

0.50, 2

0.67, 2

0.79, 4

0.0, 1

0.07, 3

0.19, 1

0.23, 1

0.34, 1

1.03, 1

Ag13Rh

Figure 9. Structures of AgnRh (n=10-13) clusters isomers. For each structure the relative energy (in eV) and spin multiplicity are given.

Now let us compare the previous results with the adsorption of NO on pure silver clusters (Figure 10). For small clusters (Agn+1 = 1-6), we reoptimized the configurations reported by Grönbeck et al.16 at the PBE0/def2-TZVP level, while for n = 7-12, we have explored the possible number of adsorption sites. Of course, there is no guarantee that we are successfully located the most stable adsorption site for these clusters, because of their irregular structure and the number of possible adsorption sites increasing with n. NO is found to be adsorbed on the border sites for pure Ag clusters. Interestingly, the Eads value ranges from -0.75 to -0.10 eV, being the largest for Ag3 and Ag5 clusters.

-0.19, 2

-0.74, 3

-0.50, 2

-0.75, 3

-0.10, 2

-0.31, 3

-0.12, 2

-0.29, 3

-0.17, 2

-0.35, 3

-0.19, 2

-0.27, 3

20


Page 21 of 30

Figure 10. NO adsorption on Agn+1 (n = 1-12) clusters. The adsorption energy (in eV) and spin multiplicity are given. Clearly, the size-dependent Eads values show that for n = 1-8 (clusters with Rhexposed structures), an enhanced reactivity for NO occurs, while for n = 9-12 the reactivity remains more or less unchanged upon the the Rh-doping (see Figure 11). 3.5

Agn+1-NO AgnRh-NO

3.0 2.5

| Eads | (eV)

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


2.0 1.5 1.0 0.5 0.0

1

2

3

4

5

7

6

8

9

10

11

12

n

Figure 11. Size-dependent NO adsorption on AgnRh and Agn+1 clusters. CONCLUSIONS Structure and stability of AgnRh clusters with n = 1-15 atoms are investigated using density functional theory with the generalized gradient approximation. The lowest energy structures of AgnRh clusters are determined by extensive searches for each cluster size. The calculations have shown that the AgnRh clusters adopt planar structures up to n = 3-6, while for n > 7 onward, they possess more compact structures than pure silver in which the Rh impurity occupies the highest coordinated position. Our present searches identify new lowest energy forms for n = 3-6, and 9-13. The most stable isomers are selected to explore their efficacy for NO adsorption. The size-dependent reactivity of the clusters indicates that Rh atom acts as a more effective adsorption site than Ag. Because of the structural transition 21



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Page 22 of 30

from Rh-exposed structure to Rh-encapsulated occurs at n = 9, the reactivity towards NO for the clusters with n = 1-8 is considerably larger than the other larger homologues. Our results suggest that the position of the Rh dopant is a key factor for reactivity. Therefore, maximizing the number of Rh atoms at the surface of the catalyst may increase its efficiency. However, there is a strong tendency for the Rh atoms to be encapsulated in the rhodiumsilver catalyst, which may explain why the highest catalytic activity occurs for Rh-rich nanoparticles, e.g., for compositions of ca. 95% Rh-5%Ag, according to the experimental observations.55 Supporting Information Available: Comparison of the bond length and dissociation energy of Ag2 and RhAg dimers between the theoretical and experimental ones, the average binding energies per atom in AgnRh clusters, growth pattern of AgnRh clusters, relative energy of AgnRh cluster isomers, structures of the lowest energy isomers of Agn clusters and cartesian coordinates of the studied systems.

NOTES The authors declare no competing financial interest.

ACKNOWLEDGMENTS PLRK and SP thank CONACYT for postdoctoral fellowship. This work is funded by Conacyt (Grant CB-2015-252356). The CGSTIC (Xiuhcoalt) and ABACUS at Cinvestav (Conacyt grant EDOMEX-2011-COI-165873) are acknowledged for allocation of computational resources.

REFERENCES 22


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TOC 3.5

Agn+1-NO AgnRh-NO

3.0 2.5

| Eads | (eV)

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2.0 1.5 1.0 0.5 0.0

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Structural Evolution of the Rhodium-Doped Silver Clusters AgnRh (N

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