Theoretical Study of NO Dissociative Adsorption onto 3d Metal Particles M55 (M = Fe, Co, Ni, and Cu): Relation between the Reactivity and Position of the Metal Element in the Periodic Table.

NO dissociative adsorption onto 3d metal particles M55 (M = Fe, Co, Ni, and Cu) was investigated theoretically using density functional theory computations. A transition state exists at higher energy in the Cu case but at lower energy in the Fe, Co, and Ni cases than the reactant (sum of M55 and NO), indicating that Cu55 is not reactive for NO dissociative adsorption because NO desorption occurs more easily than the N-O bond cleavage in this case, but Fe55, Co55, and Ni55 are reactive because NO desorption needs a larger destabilization energy than the N-O bond cleavage. This result agrees with the experimental findings. The energy of transition state E(TS) becomes higher in the order of Fe < Co < Ni ≪ Cu. Exothermicity E exo (relative energy to the reactant) decreases in the order of Fe > Co > Ni ≫ Cu. These results indicate that the reactivity for NO dissociative adsorption decreases kinetically and thermodynamically in this order. In addition, the E(TS) and E exo values show that 3d metal particles are more reactive than 4d metal particles when a comparison is made in the same group of the periodic table. Charge transfer (CT) from the metal particle to NO increases as the reaction proceeds. The CT quantity to NO at the TS increases in the order of Cu < Ni < Co < Fe, identical to the increasing order of reactivity. The negative charges of the N and O atoms of the product (N and O adsorbed M55) increase in the order of Ni < Co < Cu < Fe, identical to the increasing order of E exo except for the Cu case; in the Cu case, the discrepancy between the order of E exo and those of the N and O negative charges arises from the presence of valence 4s electron of Cu because it suppresses the CT from N and O to Cu55. From these results, one can infer that the d-valence band-top energy of M55 plays an important role in determining the reactivity for NO dissociative adsorption. Truly, the d valence orbital energy decreases in the order of Fe > Co > Ni ≫ Cu and the 3d metal > 4d metal in the same group of the periodic table, which reflects the dependence of reactivity on the metal element position in the periodic table.

Introduction

The reduction of nitrogen monoxide, NO, to N2 is one of the important reactions in a three-way catalyst (TWC) for cleaning automobile exhaust gas, as is well known.[1−6] Rh metal particles have been used as one of the key components of TWC for NO reduction for a long time.[7−10] However, the rhodium resources on the earth are extremely limited. As the dissociative adsorption of NO onto Rh metal particles is believed to be the first step of NO reduction, it is crucially important to understand whether and how NO dissociative adsorption occurs on various metals, in particular, on cheap and abundant 3d transition metals.

Many reports of the relevant literature have described experiments elucidating NO reaction behavior on metal particles and surfaces.[11−15] Summarizing those reports, the reaction behavior of the NO molecule on metal particles and surfaces can be classified into three categories, (i) NO dissociative adsorption with the N–O bond cleavage, (ii) NO molecular adsorption without the N–O bond cleavage, and (iii) NO dimerization through N–N bond formation. It is particularly interesting that the NO reaction behavior depends on the metal element position in the periodic table.[12] For instance, NO dissociative adsorption was reported to occur on group VI (Mo and W), VII (Re), VIII (Fe and Ru), and IX (Co, Rh, and Ir) metal surfaces at room temperature and even at lower temperatures.[12] In the case of group X metal elements, however, NO dissociative adsorption was reported to occur on the Ni metal surface, but NO molecular adsorption was reported on Pd and Pt metal surfaces. In the case of group XI metal elements, NO dimerization was reported to occur on Cu[16,17] and Ag metal surfaces,[18,19] whereas the Au metal surface is expected to be inert for NO dimerization and to undergo only NO molecular adsorption.[12]

Differences in the reactivities of metal elements for NO dissociative adsorption were discussed in terms of the melting point of bulk metals, as follows:[12] when the d-shell is half occupied, metal–metal bonds are the strongest. Therefore, the cohesive energy is large and the melting point is high. Such metal particles and surfaces can form strong M–N and M–O bonds because the half-occupied d-shell contributes well to the M–N and M–O bonds. Therefore, the melting point is related to the reactivity for NO dissociative adsorption. Nevertheless, this understanding is not perfect. For instance, the Pd metal melting point is slightly higher than those of Fe, Co, and Ni, whereas the Pd metal is not reactive for NO dissociative adsorption but Fe, Co, and Ni metals are reactive, as described above. Such phenomena lead us to pose one important open question: Do more general properties of metal elements explain the NO dissociative adsorption reactivity?

Another noteworthy point is that the reactivity of Ni for NO dissociative adsorption differs greatly from those of Pd and Pt, although these elements belong to the same group X. Regarding group IX elements, however, Co, Rh, and Ir are all reactive for NO dissociative adsorption.[12] These results present us with a second open question: Why does Ni differ so much from Pd and Pt for NO dissociative adsorption in group X, whereas Co exhibits similar reactivity to those of Rh and Ir in group IX?

To obtain correct answers to the questions presented above, one must perform theoretical studies of NO dissociative adsorption onto metal particles and surfaces. NO molecular adsorption has been investigated theoretically many times.[20−36] Nevertheless, theoretical studies of NO dissociative adsorption onto metal particles and surfaces have been limited except for a few works. For instance, NO dissociative adsorption onto Rh metal particles and Rh(111) surface has been investigated theoretically by Nakai and co-workers.[37] In addition, a first-principles microkinetic study of NO dissociative adsorption and NO–CO reaction on the Rh(111) surface has been reported by Ishikawa and Tateyama.[38] Recently, NO dissociative adsorption and NO dimerization on M55 and M13 (M = Ru, Rh, Pd, and Ag) have been investigated theoretically.[39,40] In the case of 3d metals, NO dissociative adsorption onto Cu13 and Cu38 has been discussed in recent theoretical works,[41,42] but no systematic theoretical study of NO dissociative adsorption onto other 3d metal particles and surfaces has been reported yet. Consequently, a systematic theoretical study of NO dissociative adsorption onto 3d metal particles is necessary for obtaining theoretical answers to the open questions posed above and for understanding the differences and similarities in reactivity for NO dissociative adsorption between 3d and 4d metal particles.

For this work, we theoretically investigated NO dissociative adsorption onto 3d metal particles such as Fe55, Co55, Ni55, and Cu55, where the icosahedral structure (Scheme ) was used; the section “Computational Details and Models” below presents the reason. Our purposes here are (i) to explore the reactivity of these metal particles for NO dissociative adsorption, (ii) to compare the reactivity for NO dissociative adsorption between 3d and 4d metals, in particular, between Ni and Pd (group X) and between Co and Rh (group IX), (iii) to ascertain what property of metal particle determines the reactivity for NO dissociative adsorption, and (iv) to elucidate the relation between the metal particle reactivity for NO dissociative adsorption and the metal element position in the periodic table based on the metal particle electronic structure. Although NO dissociative adsorption onto Cu clusters has been investigated theoretically using Cu13 and Cu38,[41,42] we re-investigated NO dissociative adsorption onto Cu55 for a better comparison with Ag55, which was employed as a model in a theoretical study of NO reactions on 4d metal particles.[39] Throughout this work, we intended to present general knowledge of the relation between the electronic structure of the metal particle and reactivity for NO dissociative adsorption.

Scheme 1

Icosahedral Structure of the M55 Particle (M = Fe, Co, Ni, or Cu) Investigated Here (a) and Edge and Vertex Positions on the Surface (b)

Results and Discussion

Geometry Changes in NO Dissociative Adsorption onto Fe55, Co55, Ni55, and Cu55

NO is adsorbed onto M55 at both the vertex and edge sites, where the adsorption at the vertex site is moderately more stable than at the edge site. Table S1 of the Supporting Information presents a comparison of these two adsorption sites. As shown in Figure , NO adsorption at the vertex site occurs through the N atom in an end-on adsorption manner in all these 3d M55 particles like that in 4d M55 particles (M = Ru, Rh, Pd, and Ag).[39] This adsorption species is designated as 1; the extent of spin polarization is presented in Table S2 of the Supporting Information. NO has an almost linear adsorption structure (M–N–O angle = 179–180°) in the Fe and Co cases and a slightly bending structure (175°) in the Ni case, whereas NO is adsorbed onto Cu55 in a somewhat bending structure (M–N–O angle = 161°). The reason for this difference is discussed in the section below. The M–N distance is 1.63–1.64 Å in Fe55, Co55, and Ni55, but somewhat longer in Cu55 by 0.12 Å, which is consistent with the lower adsorption energy in the Cu case, as discussed below. The N–O distance is moderately longer than that of a free NO molecule (1.172 Å), but it does not differ much among these metal particles. The NO stretching frequency is a useful property for investigating the interaction of the NO molecule with the metal surface, but its computed value does not agree well with the experimentally obtained value.[12] The disagreement is not unreasonable because M55 was used for the calculations, but the bulk metal surface was used for experimental measurements; Table S3 of the Supporting Information presents a comparison.

Figure 1

Geometry changes in N–O dissociative adsorption onto Fe55, Co55, Ni55, and Cu55. Distances are in angstrom. In Ni55 and Co55, transition states of two kinds were located, whereas in Fe55 and Cu55, only one transition state was located. R1, R2, R3, and A1, respectively, represent the N–O, M–N, and M–O distances (in angstrom) and M–N–O angle (in degree). R2 and R3 are the averaged values of M–N and M–O distances because N and O atoms exist at the bridge or hollow site in 2, TS, and 3.

The N–O bond cleavage is likely to occur starting from the NO side-on adsorption structure. Therefore, we investigated the side-on adsorption structure 2 (Figure ). The N–O distance is somewhat elongated in Fe55 and Co55 but only moderately so in Ni55 and Cu55. The M–N distance is shorter than the M–O distance in all these intermediates. Then, the N–O bond is cleaved via a transition state to afford an N, O-adsorbed species 3 in which N and O atoms exist at the hollow site of the surface. In the reaction on Fe55, only one transition state (TS1) was located, whereas in the Co55 and Ni55 cases, transition states of two kinds, TS1 and TS2, were located. In TS1, each of the N and O atoms exists at a bridging position between the vertex and edge M atoms. In TS2, the N atom exists at a hollow position of vertex and two edge M atoms, but the O atom exists at a bridging position between the vertex and edge M atoms. In the reaction on Cu55, only one TS3 was located. In this TS3, the N and O atoms exist, respectively, at atop positions of vertex and edge Cu atoms. At all these TSs, the N–O distance is elongated considerably; it lengthens in the order of Fe55 < Co55 < Ni55 in TS1. However, the N–O distance at TS2 is somewhat shorter than that at TS1 in the Co and Ni cases, indicating that the character of TS2 differs from that of TS1. TS3 of the Cu case is more product-like than either TS1 or TS2 of the Co and Ni cases because the N–O bond is longer in TS3 than in either TS1 or TS2. This geometrical feature of TS3 suggests that NO dissociative adsorption is difficult in the Cu case, as discussed below. In product 3, the M–N and M–O distances lengthen in the order of Ni55 < Co55 < Fe55 ≪ Cu55. This order does not fit the decreasing order of reaction energy, as discussed below, but this order seems reasonable because the 3d atomic orbital becomes larger as Ni < Co < Fe.[43,44] In the case of Cu, the much larger 4s orbital participates in these bonds.[43,44]

It is noteworthy here that the N–O distance at TS is somewhat shorter in the 3d metal case than in the 4d metal case; 1.744 Å for Ru55, 1.982 Å for Rh55, 2.764 Å for Pd55, and 3.137 Å for Ag55.[39] This difference between 3d and 4d metals suggests that the NO dissociative adsorption onto the 3d metal particle occurs through an earlier (more reactant-like) transition state than that onto the 4d metal particle, which is expected to be related to the differences in reactivity between 3d and 4d metal particles, the discussion of which is presented below.

Energy Changes in NO Dissociative Adsorption onto Fe55, Co55, Ni55, and Cu55

In this section, we mainly used potential energy without zero-point energy correction for discussion because the Gibbs energy and frequencies were evaluated approximately here, as described below in the section “Computational Details and Models”. Only for the discussion of NO adsorption/desorption, the Gibbs energy was used, because the entropy change is very large in these process and because the entropy change mainly comes from the entropy in the gas phase, which can be evaluated in a usual manner.

For all these 3d metal particles, NO molecular adsorption is exergonic, as shown in Figure . The end-on adsorption energy increases in the order of Cu55 ≪ Ni55 < Fe55 ≤ Co55. The side-on adsorption structure 2 is moderately less stable than the end-on adsorption 1. The energy of transition state E(TS), defined as the difference in potential energy between the transition state and the sum of reactants (M55 + NO), becomes higher in the order of Fe55 < Co55 < Ni55 ≪ Cu55 (Figure and Table ), where the energy of TS2 is shown for Co55 and Ni55 because TS2 exists at a moderately lower energy than TS1. The activation barrier (Ea), defined as the difference in potential energy between the TS and the most stable NO molecular adsorption species 1, increases in the order of Fe55 < Ni55 < Co55 ≪ Cu55, almost identical to that of E(TS), except for the different orders of Co55 and Ni55, as presented in Table . The difference between the order of Ea and that of E(TS) for Co55 and Ni55 is attributable to the larger NO end-on adsorption energy to Co55 than that to Ni55. It is noteworthy that TS3 of the reaction on Cu55 is calculated at a much higher Gibbs energy than the sum of reactants (Cu55 + NO). By contrast, for the other metal particles, TS is calculated at a lower Gibbs energy than the reactant (Figure ). Consequently, it should be concluded that NO dissociative adsorption occurs on Fe, Co, and Ni particles but not on Cu particles even though 3 is more stable than the reactant in the Cu case. This conclusion agrees with experimental results.[12] In addition, it is noteworthy too that the Ni metal is reactive but Pd metal is not,[39] as reported from experiments,[12] although both belong to group X. This contrast between Ni and Pd metals is discussed below.

Figure 2

Energy changesa in NO dissociative adsorption onto M55 particles (M = Fe, Co, Ni, and Cu). Energies are shown in kcal mol–1 unit. For Co and Ni cases, the energy of TS2 is shown because TS2 is more stable in energy than TS1. aPotential energies without correction of zero-point energy are presented without parentheses; the Gibbs energies are presented in parentheses. The Gibbs energy changes are approximately evaluated, as described in the section “Computational Details and Models”.

Table 1

Activation Barrier (Ea), Energy of Transition State (E(TS)), and Reaction Energy (ΔE) of NO Dissociative Adsorption onto 3d and 4d Metal Particles

	group
	VIII	IX	X	XI
	Fe	Co	Ni	Cu
Eaa	14.0	25.2d (27.6)e	18.2d (22.2)e	90.4
E(TS)b	–49.6	–40.2d (−37.8)e	–37.7d (−33.7)e	+65.8
ΔEc	–126.6	–107.5	–98.8	–51.9

Activation barrier (kcal mol–1) defined as the energy difference between the transition state and the most stable intermediate before the transition state, where the potential energy without correction of zero-point energy is used.

Energy of transition state relative to the sum of M55 and NO.

Reaction energy defined as the energy difference between the product and the sum of M55 and NO.

For lower energy TS2.

For higher energy TS1.

Cited from ref (39).

The reaction is markedly exothermic compared to both the sum of reactants (M55 + NO) and the most stable NO adsorption structure 1. The reaction energy ΔE increases (becomes more negative) in the order of Cu55 ≪ Ni55 < Co55 < Fe55. This order is the same as the decreasing order of E(TS), as expected from the Hammond rule, leading one to infer that the reactivity for NO dissociative adsorption increases in the same order both kinetically and thermodynamically; the same conclusion is obtained based on the Gibbs energy changes, as described in page S8 of the Supporting Information.

The other important result is that the E(TS) value is higher and the Ea value is larger in the 4d metal case than in the 3d metal case, when a comparison is made in the same group of the periodic table (Table ). The ΔE values of Fe55 and Co55 are moderate to somewhat more negative than those of Ru55 and Rh55. The ΔE values of Ni55 and Cu55 are considerably more negative than those of Pd55 and Ag55. Consequently, one can conclude that the 3d metal particle is more reactive than the 4d metal particle in the same group of the periodic table both kinetically and thermodynamically.

Changes in Electron Distribution in NO Dissociative Adsorption

For better understanding NO dissociative adsorption, we investigated the changes in atomic charge by NO dissociative adsorption using Bader charges. In the end-on adsorption structure, the NO molecule is strongly negatively charged, as shown in Table . The negative charge is considerably larger in the side-on adsorption structure 2 than in the end-on one 1, indicating that charge transfer (CT) occurs from the metal particle to the NO molecule and that it is much larger in the side-on than in the end-on. The larger CT in the side-on than in the end-on is reasonable because one completely empty π* orbital of NO overlaps more with the d-valence band in the side-on adsorption structure than in the end-on. This explanation is understood by considering that the π* orbital in the M–N–O plane overlaps well with the M d orbitals in the case of the side-on structure but does not well in the end-on structure. The negative charge of NO increases further when going from 2 to 3 through TS. This finding is consistent with our understanding that the CT to anti-bonding MO plays an important role in σ-bond cleavage.[45] At TS1, the NO negative charge increases in the order of Cu55 < Ni55 < Co55 < Fe55, in reverse to the increasing order of TS energy E(TS) (Table ). Although TS2 is moderately more stable than TS1 for the Co and Ni cases, we employed TS1 here for comparing the NO charge among Fe, Co, and Ni cases because CT depends considerably on the TS structure, as indicated by the NO charge of the Co and Ni cases at TS1 and TS2. This comparison is not unreasonable because E(TS) does not differ much between TS1 and TS2. Actually, the increasing order of E(TS) does not change even if we use TS2 for comparing the Co and Ni cases with the Fe case. In the 4d metal case, the NO negative charge at TS is also related to the reactivity of M55 (M = Ru, Rh, and Pd) for N–O bond cleavage, except for Ag55. These results of NO negative charges at 2, TS, and 3 suggest that the CT from M55 to NO is a determining factor of reactivity for the N–O bond cleavage. In the lower energy TS2 of Co and Ni cases, the NO molecule is more negatively charged than in TS1. The TS2 geometry is likely to be more favorable for CT interaction with M55 than the TS1 would be. In the reaction on Fe55, only TS1 was located, but TS2 could not be, suggesting that the reaction on Fe55 need not have the TS2 geometry because Fe55 can have strong CT interactions with NO even in TS1. However, the reactions on Co55 and Ni55 need to have the TS2 geometry to have strong CT interactions because Co55 and Ni55 are less favorable for the CT than Fe55 is, as discussed below.

Table 2

Changes in the Bader Charge (in e) by NO Dissociative Adsorption onto M55 (M = Fe, Co, Ni, and Cu)

			TS
	1	2	TS1	TS2	3
Fe55–NO
q(NO)	–0.365	–0.978	–1.170		–1.978
q(N)	+0.099	–0.422	–0.491		–0.929
q(O)	–0.464	–0.536	–0.679		–1.049
Co55–NO
q(NO)	–0.338	–0.731	–1.160	–1.241	–1.815
q(N)	+0.268	–0.144	–0.491	–0.594	–0.887
q(O)	–0.606	–0.587	–0.669	–0.647	–0.927
Ni55–NO
q(NO)	–0.233	–0.462	–1.123	–1.132	–1.682
q(N)	+0.143	+0.014	–0.464	–0.476	–0.809
q(O)	–0.376	–0.476	–0.659	–0.656	–0.872
Cu55–NO
q(NO)	–0.256	–0.466		–1.036a	–1.874
q(N)	+0.126	+0.059		–0.362a	–0.922
q(O)	–0.382	–0.525		–0.676a	–0.951

Bader charge at TS3.

In product 3, N and O atoms, respectively, have negative charges of −0.81 to −0.93 and −0.87 to −1.0 e. Their negative charges increase in the order of Ni55 < Co55 < Cu55 < Fe55. This order is parallel to the increasing order (becoming more negative) of ΔE, except for Cu55, suggesting that the large negative charges of the N and O atoms in 3 are related to the larger (more negative) ΔE value, the reason of which is discussed in the next section. However, the Cu case is exceptional because the N and O atoms are more negatively charged at 3 in the Cu case than in the Co and Ni cases (Table ) despite its much smaller ΔE than in the Co and Ni cases (Table ). This is a seemingly unreasonable discrepancy of the Cu case, but it is attributable to the electronic structure, as we discuss below.

Table 3

d-Valence Band-Top Energy ε(d-top),a d-Band Center Energy ε(d-c),a M55–N and M55–O Bond Energies BDE(M55–N), and BDE(M55–O)b (M = Fe, Co, Ni, Cu, Ru, Rh, Pd, and Ag)c

	Fe	Co	Ni	Cu
ε(d-top)	–3.30	–3.20	–3.60	–5.40 (s: −3.60)d
ε(d-c)	–5.00	–5.67	–6.27	–7.21
BDE(M55–N)	142.7	129.0	130.1	100.8
BDE(M55–O)	150.1	137.6	133.7	117.4

In eV. ε(d-c) is calculated using d-valence band.

BDE(M55–X) (X = N or O) = Et(M55) + Et(X) – Et(M55–X), where X = N or O and Et is the total energy (in kcal mol–1).

From ref (39) for 4d metals.

s-Band top energy.

Electronic Structure of M55 (M = Fe, Co, Ni, and Cu)

The CT from M55 to NO generally depends on the energy level of the valence band. Therefore, we investigated the density of states (DOS) and the partial DOSs (PDOS). As shown in Figure , Fe55 and Co55 exhibit very large spin polarization because their 3d-shells are not fully occupied. By contrast, the spin polarization is moderate in Ni55 and tiny in Cu55 because their 3d-shells are, respectively, almost and completely occupied. The d-band center, which is calculated using d-valence band, is found at the very low energy in Cu55 and its energy ε(d-c) becomes higher in the order of Cu55 ≪ Ni55 < Co55 < Fe55, as shown in Figure and as presented in Table . The d-valence band-top energy ε(d-top) is also very low in Cu55, where the first peak of DOS is defined as the band-top. It then rises following the same order. In the Cu case, the valence band-top exists at high energies, similarly to that of Ni55, but it is not a 3d band but a 4s band. The presence of the 4s-valence band-top in the Cu case differs completely from the 3d-valence band-top of other particles, which arises from a 3d104s1 electron configuration of the Cu atom at the ground state. In other words, the difference in electron configuration is the reason why the results of Cu case differ considerably from those of other metal particles. Details are discussed below.

Figure 3

DOS and PDOS of s, p, and d bands of Fe55, Co55, Ni55, and Cu55 particles. Energies of d-valence band top (red arrow), s-band top (green arrow), and d-band center (in eV) are represented, respectively, as ε(d-top), ε(s-top), and ε(d-c). The Fermi level is shown as a dashed line. ε(d-c) is calculated using d-valence band.

The CT quantity at TS1 is parallel to the orders of ε(d-top) and ε(d-c) (Tables and 3). In addition, the sum of negative charges of N and O atoms of 3 increases (more negative) in the order of Ni55 < Co55 < Fe55, which is parallel to the orders of ε(d-top) and ε(d-c). These results suggest that the 3d valence orbital energy is an important property for determining the reactivity of M55. It is noteworthy that the Cu case is excluded from the discussion presented above because its electronic structure differs completely from those of the others.

The 3d metal particle has higher energy ε(d-top) than the 4d metal particle does when a comparison is made in the same group of the periodic table. However, the ε(d-c) of Pd55 is almost identical to that of Ni55 (Table ), although the ε(d-c) values of the other 3d metal particles are higher than those of the other 4d metals of the same group. Based on these results, one can reasonably conclude that the ε(d-c) does not always explain the difference in reactivity between 3d and 4d metal particles; moreover, the ε(d-top) is better for discussion than the ε(d-c). We use the ε(d-top) for discussion hereinafter. Because of this higher energy ε(d-top), the 3d metal particle forms stronger CT to the NO moiety from the metal particle than the 4d metal. The CT to anti-bonding MO is needed in σ-bond cleavage.[45] Therefore, the smaller Ea and lower energy E(TS) of the 3d metal particle than those of the 4d metal particle (Table ) are inferred to arise from the higher energy ε(d-top) of the 3d metal particle.

Another important feature is that the ε(d-top) decreases from Fe to Cu, from Ru to Ag, and from the 3d metal to the 4d metal (Table ). These features are consistent with the general trends observed for 3d and 4d orbital energies of metal atoms[44−46] and the d-ionization potentials of 3d and 4d metal atoms.[47] Because of these general features observed in the periodic table, it can be said that the reactivity of metal particles for NO dissociative adsorption decreases from Fe to Cu, from Ru to Ag, and from a 3d to a 4d metal in the same group of the periodic table.

At the end of this section, we discuss several features of Cu55 that are different from those of Fe55, Co55, and Ni55. The first of those different features is the smaller Cu–N–O angle of the NO adsorption structure than the M–N–O angle of the other M55 particles. Because the Cu atom has a 3d104s1 electron configuration in the ground state, the valence band-top consists of a Cu 4s orbital, as discussed above (Figure ). The NO molecule has a lone-pair orbital on the N atom, one singly occupied π* orbital, and the other empty π* orbital. In the on-top end-on adsorption structure, the lone-pair orbital forms σ-donation to the conduction band and the π* orbital forms back-donation from the d-valence band, as discussed earlier.[48,49] Fe55, Co55, and Ni55 have low-energy conduction bands consisting of 3d, 4s, and 4p orbitals around −2.5 eV in Fe55 and Co55 and −2.8 eV in Ni55. However, Cu55 has it around −2.4 eV, a little bit higher energy than in the other metal particles. In addition, the DOS of the low-energy conduction band becomes smaller in the order of Fe55 > Co55 > Ni55 > Cu55; it is particularly small in Cu55. This feature arises from the increasing order of the number of valence electrons, Fe < Co < Ni < Cu. In other words, the very small low-energy conduction band of Cu55 is attributable to a fully occupied 3d-shell (3d10 electron configuration) and the presence of one 4s electron. These features of Cu55 are not favorable for the CT from the lone-pair orbital of NO to Cu55. Instead, the lone-pair orbital of NO gives rise to the exchange repulsion with the 4s-type valence band-top of Cu55 when the Cu–N–O angle is 180°. To reduce the exchange repulsion, NO changes the direction of the lone pair orbital by decreasing the Cu–N–O angle. In addition, the CT from NO to Cu55 is weak because the conduction band exists at a higher energy and its DOS is smaller than those of Ni55. Accordingly, the negative charge of the NO moiety becomes larger than in the Ni55 case. In product 3 of the Cu case, the sum of N and O atomic charges is more negative than those of the Co and Ni cases despite the considerably smaller (less negative) ΔE than those of the Co and Ni cases. The more negatively charged N and O atoms of 3 in the Cu case are also attributed to the presence of the 4s-conduction band-bottom at the high energy and its small DOS because the CT from the N and O atoms to Cu55 is weak in such a case. These results show that the high-energy 4s-valence band-top and 4s-conduction band-bottom and the small DOS of the 4s-conduction band-bottom are origins of the different features of Cu case from other particles such as the smaller Cu–N–O angle, the more negatively charged NO in 1, and more negatively charged N and O atoms in 3.

Reaction Energy of NO Dissociative Adsorption and DOS Features

The reaction energy ΔE is related strongly to the M55–N and M55–O bond energies. Therefore, those bond energies are one of the important factors for NO dissociative adsorption. The sum of those bond energies decreases in the order of Fe55 > Co55 > Ni55 > Cu55, as shown in Table , identically to the decreasing order of the ΔE value (Table ). Here, the M55–X (X = N or O) bond energy is defined as a difference between the total energy of M55–X and the sum of total energies of M55 and X. In addition, the sum of those bond energies is smaller in the 4d metal particles than in the 3d metal particles except for the Fe and Ru cases (Table ), which is consistent with the smaller (less negative) ΔE of the reaction with 4d metal particles than that of the reaction with 3d metal particles (Table ).

The discussion of whether these bond energies depend on the d valence orbital energy is important. The bond energy of a polarized covalent bond is represented approximately by eq based on the simple Hückel method,[50]where εA and εB, respectively, denote the Coulomb integrals of A and B atoms and β is the resonance integral. This equation is consistent with our understanding that the covalent bond becomes stronger when the difference in electronegativity increases between A and B atoms. The M–alkyl, M–silyl, and similar bonds (M = transition metal atom)[51−56] and the binding energy of oxygen-containing species with metal particles[39,57,58] are discussed and analyzed using this eq . It is likely that the β does not differ much among the M55 particles investigated here because all these atoms belong to the first-row late-transition-metal elements. In such a case, the larger εA–εB term engenders the larger A–B bond energy and more negatively charged N and O atoms in 3. Based on this understanding, eq provides a reasonable explanation for the decreasing order of M–N and M–O bond energies Fe55 > Co55 > Ni55 and the same decreasing order of the negative charge, as follows. The Coulomb integral εA approximately corresponds to the valence orbital energy. The metal 3d valence orbital exists at a higher energy than the 2p valence orbitals of N and O atoms, as shown in Scheme , because of the much smaller electronegativity of the 3d metal element than those of N and O atoms. Because the highest energy d valence orbital mainly contributes to the M55–X bond according to frontier orbital theory and because the ε(d-top) becomes lower when going from Fe to Ni, as discussed above, the εA–εB term decreases when going from Fe to Ni, resulting in the same decreasing orders of M55–N and M55–O bond energies and the negative charges of N and O atoms in 3, as shown in Table .

Scheme 2

Orbital Energy Diagram between the d-Valence Band-Top and 2p Orbital of N or O Atoms

The Cu case was excluded from the discussion presented above. Next, we must discuss the reason why the Cu55–N and Cu55–O bond energies are much smaller than those of Ni55 despite the presence of Cu55 4s valence band a high energy. For Ag55, we encountered the same problem showing that the Ag55–N and Ag55–O bond energies are much smaller than those of Pd55, Rh55, and Ru55 despite the presence of a Ag55 5s valence band a high energy.[39] Because of the d10 electron configuration, the d-shell of Cu and Ag does not contribute to the metal–metal bond. In such a case, the metal–metal bond is formed only by s electrons. The Cu atom has only one 4s valence electron, which is mainly used for the Cu–Cu bonding interaction. Therefore, the 4s electron cannot contribute greatly to the Cu55–N and Cu55–O bonds. For this reason, Cu55–N and Cu55–O bonds are weaker than the other M55–N and M55–O bonds. We shall end the discussion here because an almost identical explanation has been presented for the Ag case.[39]

Similarities and Differences between 3d and 4d Metal Particles for NO Dissociative Adsorption

As described in the “Introduction” section, Co is reactive for NO dissociative adsorption, similar to Rh in group IX. Moreover, Cu is not reactive like Ag in group XI. However, in group X, Ni is reactive but Pd is not. These experimentally obtained observations[12] are reproduced by the present density functional theory (DFT) calculations. One would reasonably wonder why the reactivity is similar between 3d and 4d metals in groups IX and XI but different in group X. Two important trends should be remembered; in one, the d orbital energy lowers when going from the left-hand side to the right-hand side in the periodic table; while in the other, the 3d orbital exists at a higher energy than the 4d orbital. Consequently, the reactivity of metal particles for NO dissociative adsorption decreases from Fe to Cu, from Ru to Ag, and also from the 3d metal element to the 4d element in the same group. Because of these trends, the reactivity disappears at group XI (Cu) in the 3d metal, but at an earlier group X (Pd) in the 4d metal.

This discussion suggests that the reactivity of the Ni particle differs greatly from that of the Pd particle but rather resembles that of the Rh particle. The reactivity of the Co particle rather resembles that of the Ru particle because of the similarity of ε(d-top). In other words, the left-low diagonal similarity exists between group X of the 3d metal (Ni) and group IX of the 4d metal (Rh) and between group IX of the 3d metal (Co) and group VIII of the 4d metal (Ru). This similarity is possible when ε(d-top) plays an important role in determining the reactivity. This left-low diagonal similarity differs from the right-low diagonal similarity in the periodic table between the first and the second series p-block elements because the right-low diagonal similarity of p-block elements arises from a similar atomic radius, charge density, and electronegativity.

Conclusions

The NO dissociative adsorption onto 3d metal particles M55 (M = Fe, Co, Ni, and Cu) was investigated theoretically. DFT computations here clearly show that NO dissociative adsorption occurs on M = Fe, Co, and Ni (group VIII to X) but not on M = Cu (group X). These results agree with the experimentally obtained findings.[12] It is noteworthy that Ni55 is reactive for NO dissociative adsorption but Pd55 is not, although both belong to the same group X. The transition state becomes lower in energy in the order of Cu55 ≫ Ni55 > Co55 > Fe55 and the reaction energy increases (becomes more negative) in the order of Cu55 ≪ Ni55 < Co55 < Fe55, indicating that the reactivity for NO dissociative adsorption increases in the same order both kinetically and thermodynamically.

When going from the reactant (M55 + NO) to the product (adsorbed N and O atoms), the negative charge of the NO moiety increases. The negative charge of the NO moiety at the transition state increases in the order of Ni55 < Co55 < Fe55, when a comparison is made in the same kind of transition-state structure (TS1). These results indicate that the CT from the metal particle to NO plays an important role in NO dissociative adsorption. This increasing order is parallel to the increasing order of the d-valence band-top energy ε(d-top).

The other important factor is the reaction energy, which is determined by the M55–N and M55–O bond energies. The sum of bond energies increases in the order of Cu55 < Ni55 < Co55 < Fe55. These bond energies increase as the d valence band-top rises in energy. Because the ε(d-top) lowers in the order of Fe > Co > Ni, which is the same as the fundamental characteristics of the periodic table,[46,47] the M55–N and M55–O bonds strengthen in the order of Ni < Co < Fe. The weak Cu55–N and Cu55–O bonds arise from the 3d104s1 electron configuration of the Cu atom.

Summarizing the results of CT from M55 to NO and the M55–N and M55–O bond energies, it should be concluded that ε(d-top) is an important property to determining the reactivity for NO dissociative adsorption in both kinetics and thermodynamics. This ε(d-top) becomes lower when going from Fe to Cu, from Ru to Ag, and from the 3d metal to the 4d metal in the same group. These features are the origin of the reactivity trend of these 3d and 4d metal particles.

At the end of this section, the Cu case must be mentioned because its differs greatly from the other particles; (i) it is not reactive for NO dissociative adsorption; (ii) the Cu55–N and Cu55–O bonds are weaker than those of the other metals; and (iii) its 4s valence band-top exists at a similar energy to the 3d valence band-top of Ni55, but the d valence band-top exists at much lower energy than the other metal particles. These features are mutually consistent. However, 3 has more negatively charged N and O atoms in the Cu case than in either the Co or Ni case. These more negatively charged N and O atoms in 3 are seemingly inconsistent with the smaller (less negative) reaction energy and smaller Cu55–N and Cu55–O bond energies. The reason for that apparent inconsistency is the presence of the 4s conduction band-bottom at high energies and its small DOS. These features are not favorable for the CT from N and O atoms to Cu55. Therefore, much negative charge remains on the N and O atoms. The weak Cu55–N and Cu55–O bonds arise from the 3d104s1 electron configuration of the Cu atom. Because of the 3d104s1 electron configuration, the 3d band does not contribute to the Cu–Cu bond. Only the singly occupied 4s valence shell contributes to the Cu–Cu bond. Consequently, the Cu 4s shell does not contribute well to the Cu55–NO, Cu55–N, and Cu55–O bonds, which result in lower reactivity, smaller Cu55–N and Cu55–O bond energies, and smaller exothermicity of NO dissociative adsorption, but more negatively charged N and O atoms in 3 than those of the other Co55 and Ni55 particles.

Computational Details and Models

Spin-polarized DFT was used with the Perdew–Burke–Ernzerhof (PBE) functional[59] using plane-wave basis sets for representing valence electrons with an energy cutoff of 400 eV and the projector-augmented wave method for representing core electrons.[60,61] The dispersion correction influences slight energy changes in NO dissociative adsorption onto 3d metal particles M55, as shown in Table S4 of the Supporting Information. The HSE06 functional was employed for calculating the DOS[62] because this functional provides a better band-gap in general. The Monkhorst–Pack grid method was used for 1 × 1 × 1 k-point sampling. The metal particle was placed at the center of a 25 × 25 × 25 Å cubic box under the periodic boundary condition, which seems sufficient to neglect the interaction between the metal particle and its periodic image. In geometry optimization, convergence criteria for total energy and maximum force were set, respectively, to 1.0 × 10–4 eV and 0.01 eV/Å. The transition state was optimized using the nudged elastic band method.[63,64] Vibrational frequencies were calculated for all optimized geometries to check that the transition state has one imaginary frequency and that equilibrium geometry has no imaginary frequency, where the NO moiety, N and O atoms, one vertex M atom interacting with the NO moiety, and five M atoms surrounding the vertex M atom are involved in the calculation while the other part was fixed. This approximation was employed here to reduce the computational time because frequency calculations are very time-consuming. In this approximation, many M–M vibrations are neglected, indicating that the Gibbs energy and zero-point energy evaluated by this procedure are approximated values. However, it is likely that this procedure provides important frequencies for understanding whether a species has an equilibrium structure or a transition state. Because of this approximation, we mainly used the potential energy without zero-point energy correction for discussion and used the Gibbs energy only for discussing which of NO desorption and NO dissociative adsorption occurs; remember that the entropy change is very large in adsorption and desorption. All these DFT calculations were conducted using the Vienna ab initio simulation package.[65,66]

We used M55 as a model of metal particles because this particle has been used in the recent theoretical study of NO dissociative adsorption to several 4d metal particles.[39] Although M55 metal particles are small compared to most real catalysts, the use of M55 particle is not so unreasonable because they are of sub-nanometer scale and because M55 metal particles have been employed as model catalysts in theoretical studies of heterogeneous catalytic reactions and related reactions.[37,57,67−74] Also, a recent theoretical study of NO dissociative adsorption onto Rh55, Rh147, and Rh(111) surfaces has indicated that the activation barrier differs little among them and that the reaction energy of the Rh55 case is moderately larger (more exothermic) than those of the others, but it does not differ very much.[37] It is likely that the comparison is reasonably made using M55 among Fe, Co, Ni, and Cu particles and between the 3d metal and 4d metal particles in the same group, although M55 is smaller than real metal particles.

As shown in Schemes a and S1 of the Supporting Information, this particle has symmetrical structures of two kinds: icosahedral (I) and octahedral (O) structures. In our recent work, we used the I structure of a 4d metal particle M55 in theoretical calculations of NO dissociative adsorption because the I structure is more stable than the O in Ru55, Rh55, Pd55, and Ag55.[39] We also investigated the relative stabilities of I and O structures of the 3d metal particle M55, which revealed that the I structure is more stable than the O in Fe55, Co55, Ni55, and Cu55 too. Table S5 of the Supporting Information presents their relative energies. Therefore, we used the I structure of M55 and made comparisons of reactivity and electronic structure between 3d and 4d metals. It is noteworthy that the comparison must be made using the same surface structure because the reactivity toward the NO molecule depends on the metal surface structure.[12]

In the I structure of M55, 42 M atoms exist on the surface. The surface has 30 M atoms at the edge position and 12 M atoms at the vertex position (Scheme b). NO adsorption and NO reaction were investigated at these possible adsorption positions. Geometries of intermediate and transition states were optimized with no constraint, starting from the I-like geometry.