Size-dependent reactivity of Rh cationic clusters to reduce NO by CO in the gas phase at high temperatures †

The reactivity of the reduction of NO pre-adsorbed on Rh 2–9+ clusters by CO was investigated using a combination of an alternate on–off gas injection method and thermal desorption spectrometry. The reduction of Rh n N x O y + clusters by CO was evaluated by varying the CO concentration at T = 903 K. Among the Rh n N x O x + clusters, the Rh 3 N 2 O 2+ cluster exhibited the highest reduction activity, whereas the other clusters, Rh 2,4–9 N x O x + , showed lower reactivity. Density functional theory (DFT) calculations for Rh 3+ and Rh 6+ revealed that the rate-determining step for NO reduction in the presence of CO was NO bond dissociation through the kinetics analysis using the RRKM theory. The reduction of Rh 3 N 2 O 2+ is kinetically preferable to that of Rh 6 N 2 O 2+ . The DFT results were in qualitative agreement with the experimental results.


Introduction
3][14] They found size-dependent trends in the reaction mechanism and efficiency of NO decomposition.For small clusters (n = 7-16), once two NO molecules are coadsorbed on a cluster, N 2 is evolved, generating the corresponding oxide cluster. 15Hirabayashi and Ichihashi studied the effect of doping with a second metal (Al, V, or Co) on the NO reactivity of small Rh cluster cations. 17They examined the reactions of Rh 5 X + (X = Al, V, Co, and Rh) with NO under multiple-collision conditions and observed the cluster dioxide formation and N 2 release.In particular, V doping was the most effective for NO decomposition.An important step in the catalytic reaction is the rupture of the N-O bond.Indeed, the release of the N 2 molecule from Rh n N x O x + requires the NO molecule to dissociate, forming two or more N atoms, which then migrate to form an N-N bond. 18he presence of the N-O bond in the NO-attached Rh metal clusters was observed using vibrational spectroscopy. 19,20hen Rh metal clusters react with NO gas, the prominent products obtained are Rh n (NO) m + . 18Note that this notation does not indicate that the NO molecule retains the N-O bond after adsorption on the rhodium cluster.In the case of Rh 6 + clusters, the first NO molecule is molecularly adsorbed onto an on-top site of the octahedral skeleton. 19The second NO molecule adsorbs either molecularly on another on-top site or dissociates into N and O atoms in a ratio of approximately 1 : 0.4.
In contrast to the N atoms, the O atoms, resulting from NO bond dissociation, bind much more strongly to the Rh cluster. 21,22Therefore, the oxidation of CO by the O atom is an essential step for completing the catalytic cycle.Recently, Chen et al. reported a catalytic cycle for the conversion of NO and CO into N 2 and CO 2 , mediated by gas-phase neutral rhodium-aluminum oxide clusters. 12They observed the oxidation of CO by RhAlO 0-3 and RhAl 2 O 1-4 clusters after singlephoton ionization using VUV light (118 nm, 10.5 eV).Previous studies on rhodium metal clusters have shown a size dependence of the reaction rate. 15,18Information regarding the temperature dependence of the reaction is essential for further understanding.Therefore, it is important to analyze the reactivity of clusters under high-temperature conditions using mass spectrometry.
In this study, we investigated the size dependence of the reactivity of NO reduction by CO on Rh clusters that pre-reacted with NO under multi-collision conditions.The thermal desorption of NO and/or N 2 from Rh n N x O y + clusters and their CO reactivity were evaluated by alternate on-off gas injection of CO. 23 The observed difference in CO reactivity between Rh 3 N 2 O 2 + and Rh 6 N 2 O 2 + was explained using density functional theory (DFT) calculations.

Experimental methods
The reduction of NO by CO on Rh n + clusters under thermalized conditions at high temperatures was investigated using an alternate on-off CO gas injection method developed by our group in combination with thermal desorption spectrometry (TDS) (Fig. 1). 23Gas-phase clusters were prepared by laser ablation of a rhodium metal rod using a focused second harmonic (532 nm; 10 Hz) of a Nd:YAG pulse laser at a typical pulse energy of 10 mJ.The Rh metal atoms were then cooled in an NO-seeded He gas flow (He purity 499.99995%;NO concentration 0.017%) from a solenoid pulse valve (General Valve; stagnation pressure 0.65 MPa) to form Rh n N x O y + .A slush bath made from ethanol and liquid nitrogen was used to trap impurities (N 2 O, NO 2 , and H 2 O) in the carrier gas. 24Here, the number of N atoms, x, was assumed to be the same as the number of O atoms, y, because NO molecules were adsorbed onto Rh n + .However, few O-rich clusters (y 4 x) were generated, 18 likely because of the pre-oxidation of the Rh rod surface.The mass flow and pressure controllers maintained the NO concentration at the desired level.
Rh n N x O y + clusters prepared in the carrier gas were introduced into an extension tube before expansion in a vacuum chamber.The tube was heated to 300-1000 K using a resistive heater and the temperature was monitored using type-K thermocouples.The residence time of the cluster ions and the density of the He gas in the extension tube were estimated to be approximately 100 ms and 10 18 molecules cm À3 , respectively.In the tube, the clusters were heated through collisions with the surrounding He gas, which was considered to have achieved thermal equilibrium. 25The reactant CO gas was injected from the nozzle through a pulse valve near the end of the extension tube at a stagnation pressure of 530 Torr to ensure that the heated clusters reacted with CO.The volume of the CO gas pulse was adjusted based on the duration of the pulse valve and the time delay, achieving both a significant mass spectral change and sufficient signal intensity.The CO gas injection was alternated by turning it on for 600 shots (corresponding to two mass spectra) and off for 900 shots (three mass spectra) while the temperature was adjusted for the TDS measurement.This asymmetric alternation of the reactant gas injection displays a clear distinction in the TDS plot.A residual gas analyzer (RGA; MKS e-Vision2) was used to monitor the volumes of NO and CO introduced into the vacuum chamber through the valves.When measuring the CO concentration dependence, the CO concentration in the mixed gas was controlled by scanning the flow rates of the CO and He gases using two mass flow controllers and removing the excess gas using a pressure controller to maintain a constant pressure.The product ions, which were expanded in a vacuum, were accelerated by a pulsed electric field to gain a kinetic energy of 3.5 keV using a time-of-flight spectrometer for mass analysis.The ions were detected using a Hamamatsu double-microchannel plate detector after passing through a 1 m field-free flight tube.The signals were amplified using a preamplifier and digitized using an oscilloscope.Each mass spectrum was obtained by accumulating signals for 300 shots.The mass resolution was sufficiently high (m/Dm 4 1000 at m/z = 1000) to distinguish the Rh, C, N, and O atoms in the mass spectra.

Computational methods
Systematic calculations were performed using the artificial force induced reaction (AFIR) method, as implemented in the GRRM program, to search for cluster structures and reaction pathways. 26The calculations were performed using the DFT method with the TURBOMOLE program package. 27For the reactant, intermediate, and product states, the local minima were searched using the single component AFIR (SC-AFIR) method with the model collision energy parameter g = 100 kJ mol À1 .The NO dissociation and CO oxidation paths were searched starting from the obtained dissociative adsorption structures using the SC-AFIR method and applying an artificial force between N and O and between O and C, respectively, with g = 1000 kJ mol À1 .All the obtained AFIR paths were re-optimized using the in-house modified locally updated plane (LUP) path optimization method. 28he highest energy points along the LUP paths (the approximate TSs), except those higher than 20 kJ mol À1 above the lowest approximate TS, were optimized to the true TSs.Path connections were confirmed using intrinsic reaction coordinate (IRC) calculations.Structure optimization and IRC calculations were performed without any geometric constraints.0][31] During the search calculations, the lowest spin states were targeted and identified using the Fermi option of the TURBOMOLE program.The same procedure was used in our previous work on transition metal hexamer-assisted bond activation. 32or small Rh clusters, the TPSSh functional provided accurate geometries and reaction energies with respect to the experimental results. 33Therefore, the low-lying reactant, intermediate, product, and transition-state structures in the PBE results were further optimized at the TPSSh-D3/def2-SV(P) level of theory using the RI-J technique. 34,35In these calculations, the lowest spin states were manually identified based on a comparison with the calculations for a wide range of spin states.Normal mode analysis was performed on all of the optimized structures.Finally, single-point energy calculations were performed at the TPSSh-D3/def2-TZVP level of theory using the RI-JK technique (TPSSh-D3/def2-TZVP//def2-SV(P)). 36Rate constants based on the Rice-Ramsperger-Kassel-Marcus (RRKM) theory [37][38][39][40][41] were evaluated to validate the thermalization of intermediates in the reaction pathway through comparison with the collision rate of He gas.Gibbs free energy values under the experimental conditions (903 K and 0.04 atm) were also computed.  .The TDS curve observed in the experiment was better reproduced by adding a reaction channel that desorbs two NO molecules at a time to the model in which Based on these intensity changes, concomitant changes in the reactant and product cluster pairs were observed.NO molecules were sequentially released from the clusters on heating, as shown in the following reaction scheme:

Results
Additionally, the data points in Fig. 3 with open circles show the intensities of the clusters when the CO gas was turned on.At 300-700 K, the intensity of Rh 3 N 6 O 6 + decreased and that of Rh 3 N 4 O 4 (CO) 3 + increased when the CO gas was on.A detailed examination of the mass spectrum revealed that when CO gas was added, a group of peaks with compositions in which NO was gradually replaced by CO, for example, from Rh   After showing an abrupt change in the low-concentration region, no change in the intensity was observed with increasing CO concentration.This may be due to the presence of a certain percentage of less reactive isomers.In the experimental setup, we observed reactions within the extension tube with a residence time of B100 ms.Conceivably, more time is required to observe further reactions.

Size and composition dependence of the reactivity of reduction by CO
As previously mentioned, the reduction reactivity of CO is size dependent.The fractions of the clusters for n = 6-9 varied slightly as the CO concentration increased, indicating that they were less reactive for reduction by CO.To understand the size and composition dependence of reactivity, the relative rate constant k rel (n, x, y) of the reduction reaction of Rh n N x O y + was calculated by assuming a pseudo-first-order reaction between CO at T = 903 K.In this experiment, because cluster ions were not massselected, the intensities of multiple clusters changed concurrently because of the reaction with CO.The rate constants for the selected clusters were estimated by analyzing the concentration dependence, as shown in Fig. 5 and summarized in Fig. 6.Generally, the rate constants for oxygen-rich clusters, Rh n N x O x+1 + , are larger than those for the corresponding In particular, Rh 2 N 2 O 3 + , which contains excess oxygen, exhibited the highest reaction rate observed in this study.This cluster is considered to be reduced by the following reaction: The clusters produced by the above equation did not undergo further reduction with CO under the present conditions.The rate constant for the Rh n N x O x + clusters was low at n = 2, highest at n = 3, and decreased with increasing n.Thus, the reactivity for n = 3 is markedly higher than that of the other clusters.In particular, the Rh 6 structures at TS1a/b and TS2 correspond to metastable isomers, namely capped square pyramid and boat structures, respectively, which have been considered in spectroscopic and DFT studies for the gas-phase Rh 6 + cluster. 43It is worth noting that the octahedral structures at TS1a/b and TS2 are less stable than the lowest energy TS structures by 0.46, 1.00, and 0.31 eV, respectively (Fig. S9, ESI †).A previous study on transition metal hexamerassisted bond activation highlighted the importance of metastable cluster structures in assisting bond activation. 32The active sites for NO dissociation and CO 2 formation were identified at the hollow site for n = 3 and the 4-fold hollow site for n = 6.In particular, the active sites for NO dissociation at n = 6 are similar to those on the Rh(100) surface. 7,44or n = 3, the NO bond dissociation step with/without CO adsorption is endothermic by 0.07/0.18eV with an activation energy of 0.94/1.11eV.The CO oxidation step is also endothermic by 0.34 eV with an activation energy of 0.79 eV.For n = 6, the NO dissociation step with/without CO adsorption is exothermic by À1.17/À0.63eV with an activation energy of 0.39/0.92eV, while the CO oxidation step is endothermic by 1.50 eV with an activation energy of 1.64 eV.It should be noted that for n = 6, the actual activation energy for NO dissociation with CO adsorption is 0.85 eV (Fig. S8, ESI †), and this may be attributed to the presence of another high barrier that causes a shape change of the Rh 6 moiety before NO dissociation.However, this value is still smaller than the activation energy of 1.64 eV for CO oxidation.In short, NO dissociation and CO oxidation are endothermic/exothermic and endothermic/endothermic, respectively, for n = 3/6.The RRKM rate constants for the NO dissociation and CO oxidation steps, with the total energy of the reactants (electronic energy plus zero-point energy) as the total energy, are estimated to be 4.7 Â 10 10 and 7.5 Â 10 11 s À1 for n = 3, and 1.6 Â 10 9 and 5.0 Â 10 9 s À1 for n = 6, revealing that the reduction for n = 3 is kinetically preferable to that for n = 6.Furthermore, NO bond dissociation was identified as the rate-determining step for both sizes.Comparing to the collision rate of He (around 10 9 s À1 ), the structural changes of intermediates could proceed with higher frequency than the collision with He.It is, thus, considered that the clusters might not reach thermal equilibrium in the extension tube.The Rh 3,6 (NO) 2 (CO) + clusters could generate CO 2 with the larger excess energy during the residence time of approximately 100 ms.
A simple kinetic analysis of the reaction profiles presented in Fig. S7 and S8 in the ESI, † based on the rate constant matrix construction method, 45 shows that the ratio of k rel (n, x, y) is (3, 2, 2) : (6, 2, 2) = 1 : 0.03.Thus, our DFT results are in qualitative agreement with the experimental results for the rate constant ratio, as shown in Fig. 6.According to Fig. 7, the N-Rh 6 -O moiety in INT1 and INT2 for n = 6 represents the lowest-energy dissociatively adsorbed structures, which are identified by both spectroscopic and DFT methods. 19In these structures, the N and O atoms are adsorbed at different hollow sites in the octahedral Rh 6 motif.Conversely, in the N-Rh 3 -O moiety, the N and O atoms were adsorbed on different edge sites of the triangular Rh 3 motif because of the presence of only a single hollow site for adsorption, and were not sufficiently stabilized.The site-specific binding energies of the N and O atoms were strongly correlated with the relative stabilities of the dissociatively adsorbed states. 21he stabilization energy caused by dissociative adsorption increased with the binding energies of the N and O atoms.In addition, Fig. 7 shows that as NO dissociation becomes more exothermic, the NO dissociation barrier decreases, and the CO oxidation barrier increases.Thus, the relative stability of the dissociatively adsorbed states would be involved in the difference in the reactivity between Rh 3 N 2 O 2 + and Rh 6 N 2 O 2 + .
In particular, for n = 6, the order (10 9 s À1 ) of RRKM rate constants for the NO dissociation and CO oxidation steps could be comparable to the collision frequency of He gas.These collision rates may be influenced by the CO concentration in the tube.Therefore, the kinetics of n = 6 should be carefully investigated with both rate constants based on the RRKM theory and transition state theory.If the collision frequency decreases slightly because of the higher CO concentration, the cluster ions might not achieve thermal equilibrium, leading to the active Rh 6 (NO) 2 (CO) + species generate CO 2 , as mentioned above.On the other hand, if the collision frequency increases slightly under a lower CO concentration, the cluster ions might be thermalized.From the free energy evaluation, shown in Fig. 7b, the CO oxidation from 4 INT2 (1.82 eV and 1.31 Â 10 3 s À1 ) is identified as a rate-determining step, revealing that the intermediate cannot get over the barrier within the residence time.These discussions might relate with the observed fraction change of Rh 6 N 2 O 1 + in Fig. 5.

Conclusions
The size-dependent reactivities of rhodium oxynitride clusters, Rh n N x O y + (n = 2-9), and carbon monoxide were studied by gasphase thermal desorption spectrometry using the alternate onoff gas injection method.The loss of O atoms from the reaction with CO can be explained by the reduction by CO, which resulted in the formation of CO  This journal is © the Societies 2024 evaluation of RRKM rate constants.From comparing the order of the rate constants, the reduction for n = 3 is kinetically preferable to that for n = 6.In addition, the DFT results were in qualitative agreement with the experimental results for the relative rate constant.

Fig. 1
Fig.1Experimental setup of the alternate on-off CO gas injection method developed by our group in combination with TDS.

3. 1 . 4 + 2 +, 3 +,
Fig. 2a shows the mass spectrum focusing on the n = 3 mass region of the nascent Rh n N x O y + cluster ions generated by the adsorption of NO on the Rh clusters at 303 K.The ion peaks assigned to Rh 3 N 4 O 4 + , Rh 3 N 5 O 5 + , Rh 3 N 6 O 6 + , Rh 3 N 6 O 7 + , and Rh 3 N 7 O 7 + were observed in the spectrum.After heating the extension tube to 903 K, the ion peaks shifted to lower masses in the spectrum, which were mainly assigned to Rh 3 NO + , Rh 3 N 2 O 2 + , and Rh 3 N 3 O 4 + (Fig. 2b).Mass spectra of the whole region are shown in Fig. S1-S3 (ESI †).It is speculated that the NO molecules adsorbed at 300 K were desorbed from the clusters when they were heated.Upon introduction of CO gas into the extension tube at 903 K, peaks assignable to Rh 3 + , Rh 3 N + , Rh 3 NO + , Rh 3 N 2 O + , and Rh 3 N 2 O 2 + appeared.The intensities of Rh 3 NO + and Rh 3 N 2 O 2 + decreased, whereas those of Rh 3 N + and, most prominently, Rh 3 N 2 O + increased.These findings suggest that the CO molecules extract O atoms from Rh 3 NO + and Rh 3 N 2 O 2 + to form CO 2 .This pair of increased and decreased compositions observed for n = 3 in response to the removal of one oxygen atom by CO was also clear for n = 4 and weaker for n = 5 and 6 (Fig. S6, ESI †).

3. 2 .
Thermal desorption and alternate on-off gas injection of CO 3.2.1.CO reactivity of Rh 3 N x O y + .The relative intensities of Rh 3 N x O y + were measured as a function of the temperature in the extension tube (TDS plot; Fig. 3).The cluster ions were grouped with the same y À x value (y À x = +1 to À6) and are shown from top to bottom.The intensity changes of the clusters were caused by the heat and/or reactions with CO in the extension tube.By alternate on-off gas injection of CO, the intensities of specific clusters changed accordingly, which provided comb-like response signals in the plots.First, let us examine the reactions caused by heat by examining the data points depicted by filled circles corresponding to the reactions in the absence of CO.At 303 K, Rh 3 N 6 O 6 + was dominant.A small amount of Rh 3 N 7 O 7 + present at room temperature quickly disappeared upon heating.The intensity of Rh 3 N 6 O 6 + gradually decreased with increasing temperature from 400 to 500 K, which was accompanied by an increase in the intensity of Rh 3 N 4 O 4 + before Rh 3 N 5 O 5 + gained intensity.Subsequently, the intensity of Rh 3 N 4 O 4 + decreased above 650 K, and the intensity of Rh 3 N 2 O 2 + increased rapidly before that of Rh 3 N 3 O 3 + .In addition, the intensity of Rh 3 N 2 O 2 + decreased at temperatures above 850 K, whereas that of Rh 3 NO + increased.The changes in the ion intensities can be explained by NO desorption from the clusters by heat.The apparent N 2 O 2 loss can be attributed to the binding energy of NO release.Presumably, the binding energy of an NO molecule in Rh 3 N 5 O 5 + is lower than that of the binding energy in Rh 3 N 6 O 6 + , and the binding energy of an NO molecule in Rh 3 N 3 O 3 + is lower than that of the binding energy in Rh 3 N 4 O 4 + .When the clusters were heated to a sufficiently high temperature to allow the NO molecule in Rh 3 N 6 O 6 + to be readily released from Rh 3 N 6 O 6 + , the less weakly bound NO molecule in Rh 3 N 5 O 5 + was released simultaneously, resulting in the indistinctive appearance of the peaks for Rh 3 N 5 O 5 + and Rh 3 N 3 O 3 + .However, the activation energies of NO desorption estimated by fitting were, as expected, lower for Rh 3 N 5 O 5 + than for Rh 3 N 6 O 6 + but much higher for Rh 3 N 3 O 3 + than for Rh 3 N 4 O 4 +

Fig. 2
Fig. 2 (a) Mass spectrum of nascent Rh 3 N x O y + cluster ions generated by the adsorption reactions of NO on Rh clusters at 303 K. (b) Mass spectrum after heating in an extension tube at 903 K.The blue line corresponds to the case of no reaction with CO and the red line corresponds to the reaction with CO.The area filled in black is the area that appeared in both cases.Clusters with increased/decreased intensities due to CO are indicated by red and blue labels, respectively.

3 +,
Fig. 5 shows the fraction of Rh n N x O y + clusters produced for each value of n as a function of CO concentration.The temperature of

Fig. 3
Fig. 3 TDS plots with alternate on-off gas injection of CO for n = 3 in the temperature range of 300-1000 K. Cluster ions, Rh 3 N x O y + , grouped with the same y À x value (y À x = +1 -À6), are shown from top to bottom.Even when a CO molecule is presumed to be originally attached, our mass resolution cannot distinguish it from two N atoms attached.Here, for the purpose of plotting in one figure, a cluster with k CO molecules attached is categorized as if the cluster had 2k N atoms instead of the k CO molecules.The intensities in the presence and absence of CO are depicted by the open and filled circles, respectively.The number of N atoms in the cluster is color-coded as red, green, blue, orange, brown, purple, and pink.

4 . Discussion 4 . 1 .
Thermal desorption of NO and reduction by CO Based on the experimental results, a reaction scheme for the thermal desorption of NO and reduction of Rh 3 N x O y + by CO is presented in Scheme 1. Rh 3 N x O x + and one-O-atom-rich Rh 3 N x O x+1 + , generated at low temperatures, formed Rh 3 N + above 900 K in the presence of CO.The reaction schemes for n = 4 and 5 are similar to that for n = 3.For n = 7 and 8, several O-rich clusters, including Rh 7duced by thermal desorption in the absence of CO, which is consistent with our previous study. 18These O-rich clusters were formed by N 2 released from Rh 7 N x O x + and Rh 8 N x O x + .We expected that these clusters would be effectively reduced by CO, forming clusters with fewer O atoms and increasing the N-rich clusters.However, the oxygen-rich clusters Rh 7 9 NO 6 + were rapidly depleted in the low CO concentration region, as shown in Fig. 5.The pair of decrease and increase in intensity induced by mixing CO may have induced the following oxygen release reactions: Rh 7 NO 5 + + CO -Rh 7 NO 3 + + CO + O 2 (6)

Fig. 4 Scheme 1
Fig. 4 Intensity changes of one-O-atom-deficient Rh n N x O xÀ1 + (n = 2-6), the main products of the reduction reaction by CO, as a function of temperature in the range of 600-1000 K. Intensities in the presence and absence of CO are depicted by open and filled circles, respectively.The number of N atoms in the cluster is color-coded as red, green, blue, orange, brown, purple, and pink.Fig. 5 Fractions of Rh n N x O y + clusters (n = 2-9) produced by the reaction of CO at 903 K as a function of CO concentration.Lines in the plots were added for visibility.The colors khaki, red, green, and blue correspond to compositions containing zero, one, two, and three N atoms, respectively.

4 . 3 .
Fig. 5 and 6 show that the cluster with Rh 3 N 2 O 2 + exhibited the highest reduction activity, whereas the clusters with Rh 6-9 N x O x + exhibited lower reactivity.To investigate the observed size dependency, we performed theoretical calculations on the reactivity of n = 3 and n = 6 clusters.Using DFT in combination with a systematic pathway search method, we calculated the geometrical structures and energy barriers of the reactions of Rh 3 N 2 O 2 + and Rh 6 N 2 O 2 + with CO.

Fig. 7
Fig. 7 shows the zero-point corrected energy profiles and structural changes in the NO dissociation and CO oxidation steps involved in the reduction of Rh 3 N 2 O 2 + and Rh 6 N 2 O 2 + by CO.The complete energy profile, including adsorbate migration and Rh cluster shape changes, is shown in Fig. S7 (ESI †) for n = 3 and Fig. S8 (ESI †) for n = 6.For the reactions of n = 3 and n = 6, two reaction mechanisms are proposed based on the difference in the order of dissociation of the NO molecules and adsorption of CO: (1) two NO molecules, which adsorb molecularly on Rh 3 + or Rh 6 + (RCTa), dissociate (INT1), followed by CO adsorption (INT2).(2) It is also possible that NO dissociation occurred after the co-adsorption of the two NOs and CO (RCTb).In both cases, a single O-deficient cluster (PRD) is generated by CO 2 formation and desorption.Bare Rh 3 + and Rh 6 + clusters exhibit triangular and octahedral geometries, respectively.As shown in Fig. 7a, the Rh 3 cluster retains its triangular geometry throughout RCT, INT, PRD, and TS.In contrast, the Rh 6 cluster retained its octahedral geometry at RCT, INT, and PRD, while forming different geometries at TS1a/b and TS2.In particular, the Rh 6 structures at TS1a/b and TS2 correspond to metastable isomers, namely capped square pyramid and boat structures, respectively, which have been considered in spectroscopic and DFT studies for the gas-phase Rh 6 + cluster.43It is worth noting that the octahedral

Fig. 6
Fig. 6 Relative rate constant k rel (n, x, y) of the reduction reaction of Rh n N x O y + at 903 K was estimated by measuring the decreasing rate of the fraction of Rh 3-7 N 2 O 2 + , Rh 2,4 N 3 O 3 + , and Rh n N x O x+1 + with the CO concentration for each n.Rate constants were normalized to that of Rh 3 N 2 O 2 + .Red circles, blue triangles, and green triangles correspond to Rh n N 2 O 2 + , Rh n N 3 O 3 + , and Rh n N x O x+1 + , respectively.To indicate the sizedependence of Rh n N 2 O 2,3 + , the lines are shown as a guide.

Fig. 7
Fig. 7 Zero-point corrected energy profiles of the reduction reactions of (a) Rh 3 N 2 O 2 + and (b) Rh 6 N 2 O 2 + by CO, calculated at the TPSSh-D3/def2-TZVP//def2-SV(P) level of theory using the RI technique.The cluster structures correspond to the lowest energy structures at the reactant RCT, intermediate INT, product PRD, and transition state TS for NO dissociation and CO oxidation processes.Superscripts on the labels indicate spin multiplicity.The energy levels are expressed relative to the sum of the energies of the bare Rh cluster, 2NO, and CO.Relative Gibbs free energy (T = 903 K, P = 0.04 atm) is additionally shown in square brackets.
2 .The rate constants for the Rh n N x O x + cluster and CO were approximately zero at n = 2, were highest at n = 3, and decreased with n.DFT calculations of the geometrical structures and energy barriers for the reactions of Rh 3 N 2 O 2 + and Rh 6 N 2 O 2 + with CO revealed that NO bond dissociation is identified to be a rate-determining step through the