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Minimum-energy pathways for the demethanation reaction CH3OH + Nin+ (n=3,4) → NinO+ + CH4 have been computed to examine why this reaction occurs preferentially on Ni4+. Stationary points of paths for the demethanation of CH3OH on Nin+ (n=3,4), which provide possible reaction pathways, were characterized and the associated activation barriers were evaluated on both Ni3+ and Ni4+ via density-functional theory calculations. On Ni4+, all the transition states along the minimum-energy path are energetically below the reactant asymptote, whereas on Ni3+, the transition states are above it.
A number of experimental and theoretical studies have been conducted to examine the gas-phase reactions catalyzed by small transition metal clusters [1-30]. Of particular interest are the reactions involving small nickel clusters that have been extensively studied [1-19,31,32]. From these studies, it has been found that the catalytic activity and product branching are controlled by the size and geometry of the metal clusters. For instance, Nin+ (n= 2,5-20) reacts with ethylene, whereas Nin+ (n= 3,4) does not . Size-specific reactions have also been reported on Nin+ (n= 4-31) with carbon monoxide, where only Nin+ were found to be active [1,7].
More recently, Ichihashi et al.  studied the reaction of Nin+ (n= 3-11) with methanol under single-collision conditions and found that the reaction changes with the size of the nickel clusters. The crossed molecular beam technique was employed to study the reaction in the gas phase at collision energies of less than 1.0 eV. Dominant reactions were methanol chemisorptions, demethanation, and carbide formation. A different reaction takes place on each cluster; demethanation on Ni4+, carbine formation on Ni7,8+ and only chemisorption on Ni6+. The products detected for the Ni4+ cluster were 35% of methane with nickel oxide and 65% of other complexes, such as Ni4+(CH3OH). For the other cluster Nin+ (n = 3, 5-11), however, methane and nickel oxide formation was very small, and methane production decreases with decreasing size of the cluster. Subsequent density-functional theory (DFT)-based theoretical examination of the geometry and energetics of the different nickel clusters by the same authors found an anti-correlation between the HUMO-LUMO gap and the reaction cross section of Nin+ (n= 3-11) with methanol .
Hirabayashi et al.  extended the investigation to examine the mechanism and intermediate species in the reaction of Nin+(n=3,4) with methanol. Using Infrared Photodissociation Spectroscopy technique (IR-PD), they measured the OH stretching frequency of methanol absorbed on nickel clusters, Ni3+(CH3OH)1-3 and Ni4+(CH3OH)1-4 in gas phase. In each IR-PD spectrum, they observed a single peak at a wavelength of 3634 cm-1 for Ni3+(CH3OH), which blue-shifts by ca. 10 cm-1 for Ni3+(CH3OH)2-3 and a single peak at 3640 cm-1 for Ni4+(CH3OH)m. The assignment of these peaks to the O-H stretching was confirmed by DFT calculations.
Despite the numerous experimental and theoretical studies, the underlying mechanism for the size-specific demethanation that occurs on Ni4+, but not on Ni3+, remains unclear. In the present study, a DFT study is conducted for the reaction of Nin+ (n=3,4) with CH3OH to map the minimum-energy reaction pathways for the demethanation on these nickel clusters, and examine why the reaction occurs preferentially on Ni4+.
All geometries (reactants, products, and intermediate complexes) were optimized in DFT calculations using Dmol3 from Accelrys Inc. . The Perdew-Burke-Ernzerhof (PBE)  exchange and correlation functionals were employed. The Kohn-Sham  orbitals were expanded in the DNP basis sets - numerical basis sets as defined in the Dmol3 program . All electrons were included in the present calculations to obtain the correct energetics. The transition states were found by combining the Nudged Elastic Band (NEB) , Quadratic Synchronous Transit (QST) and partial optimization methods. All transition and minimum-energy states were confirmed by vibrational frequency analysis. The activation energies and reaction pathways were computed including the zero-point energies.
Results and discussion
Various geometrical isomers of Ni3+ and Ni4+ were fully optimized to determine the ground-state geometry for each cluster. To examine the reliability of the present calculation, the Ni2+ dimer was also studied and compared with available experimental data. The calculated ground state of the nickel dimer cation has an spin multiplicity of 4, in agreement with previous theoretical studies [8,17,37,38]. The calculated equilibrium internuclear distance, Re, was 2.254 Å, in good agreement with the measured value of 2.242 ± 0.001 Å . The calculated dissociation energy, Do, of Ni2+ was 2.716 eV, somewhat overestimating the experimental value 2.245 ± 0.025 eV [40,41]. The ground-state geometry of Ni3+ is a triangular structure with interatomic distances of 2.28, 2.28 and 2.21 Å. The dissociation energy of Ni3+ (Ni3+ → Ni2+ + Ni) is 3.05 eV, in agreement with experimental results . For Ni4+, the ground-state geometry is a tetrahedral structure with interatomic distance of 2.30-2.32 Å, and dissociation energy of 2.73 eV, also in agreement with experimental value . Based on the agreement between experiment and the present calculations, one can conclude that the present computational method correctly describes the chemistry of small nickel clusters.
3.1 Demethanation CH3OH + Ni3+ → CH4 + Ni3O+
The first step in the demethanation on Ni3+ is the chemisorption of methanol to form Ni3+(CH3OH). Figure 1 shows the energy profile of the methanol chemisorption on Ni3+. The chemisorption process is spontaneous with an exothermicity of 31.76 kcal/mol. The structure of the Ni3+(CH3OH) complex was optimized from various initial structures - methanol adsorbed ontop, bridge and three-fold site by either the methyl or OH group on Ni3+ - all of which converged to the structure (Ni3+-C1) shown in Figure 1. In Ni3+-C1, methanol is adsorbed at atop site of Ni3+ through the O atom of methanol forming a Ni-O bond of 1.99 Å. The structure of the nickel cluster remains unchanged upon chemisorption. These results for the chemisorption of methanol on Ni3+ cluster agrees with the previous calculations on Ni3,4+  and other metals, Au  and Cu .
Upon chemisorption of methanol on Ni3+, the subsequent isomerizations of the Ni3+-C1 complex in Figure 1 can lead to the demethanation products, CH4 and Ni3+O. To determine the minimum-energy pathway between the Ni3+-C1 and the final demethanation products, we first identified and optimized the structures of a large number of complexes that arise from the isomerizations of Ni3+-C1. In Figure 2, the eight most energetically favorable isomeric complexes are displayed. These complexes may be classified into two groups, based on the metal-bound fragments of methanol on the nickel ion. Ni3+-C2 through Ni3+-C7 comprises the first group (Group I in Fig. 2), with the six isomers arising from the different positions on the Ni ion cluster to which the hydroxyl (OH) and methyl (CH3) subunits are adsorbed. Group II is comprised of two complexes, Ni3+-C8 and Ni3+-C9, with the O and CH4 fragments adsorbed on the nickel ion cluster. The isomerizations of Ni3+(CH3OH) complex (Ni3+-C1, Fig. 1) into the Group I complexes require the C-O bond breaking of the adsorbed methanol, which demands a high activation energy. The two lowest-energy isomerization pathways leading to Ni3+-C3 and Ni3+-C5 require the activation energies of ca. 32 kcal/mol (Ni3+-TS1, Fig. 3) and 37 kcal/mol (Ni3+-TS2, Fig. 3), respectively. For the isomerizations of Group I complexes to Group II complexes, the O-H bond needs to be broken, again requiring high activation energies, ca. 61 kcal/mol and 32 kcal/mol, respectively, leading to Group II complexes Ni3+-C8 and Ni3+-C9. The final products Ni3O+ and CH4 are formed from complex of Group II by desorption of methane. To calculate the activation energies for the C-O bond breaking, the transition states between Ni3+-C1 and all the complexes in Group I were identified by all three different methods mentioned in Section 2. The same procedure was used to determine the activation energy for the O-H bond breaking process.
Figure 3 displays two lowest minimum-energy pathways for methanol demethanation on Ni3+. In these two pathways, two energy barriers must be overcome to generate the final products. The first energy barrier arises from the C-O bond breaking. The transition states for C-O bond breaking-Ni3+-TS1 and Ni3+-TS2-are 0.27 kcal/mol and 5.86 kcal/mol above the reactant asymptote, respectively. Under the experimental conditions of Kondow et al. experiment [11,32], where the initial kinetic energy for reactants is 2.3 kcal/mol, the activation energy to overcome Ni3+-TS1 may be achieved. On the other hand, Ni3+-TS2 is 3.56 kcal/mol above the reactant asymptote plus the initial kinetic energy. The second energy barrier arises from the O-H bond breaking. The transition state Ni3+-TS3 for this process from Ni3+-C3 is 21.87 kcal/mol above the reactant asymptote. For the other pathway, Ni3+-C5 complex must reach the transition state Ni3+-TS4, which is 4.88 kcal/mol above the reactant asymptote. The final step for the formation of methane and Ni3+O involves desorption of the metal-bound methane, both Ni3+-C8 and Ni3+-C9 complexes smoothly dissociating into the products. In the two most energetically favorable minimum-energy pathways found in the present study, all the transition states are energetically above the reactant asymptote, indicating that the demethanation reaction is unfavorable, particularly under the single-collision condition in which the experiments were carried out [11,32]. Even though the Ni3+-TS1 is below the reactant asymptote plus the initial relative kinetic energy of the reactants, the second transition state in the pathways are energetically well above the reactant asymptote. The calculations support the experimental results of Kondow et al. [11,32], where only the chemisorption of CH3OH on Ni3+ was detected.
3.2 CH3OH + Ni4+ → CH4 + Ni4O+
Like Ni3+, the first step for the demethanation on Ni4+ is the chemisorption of methanol by the O atom. Figure 4 shows an energy diagram for the formation of Ni4+(CH3OH) complex (Ni4+-C1) via the chemisorption of methanol on the Ni4+ cluster. The chemisorption process occurs spontaneously with an exothermicity of 35.04 kcal/mol, only 3.28 kcal/mol lower than the methanol adsorption on Ni3+. The minimum-energy pathway for the demethanation on Ni4+ was evaluated by first identifying a large number of possible isomeric complexes arising from Ni4+-C1 complex (Figure 4).
A number of energetically favorable isomeric complexes are identified and collected in Figure 5. These eighteen complexes are classified into five groups, based on the metal-bound fragments of methanol on the nickel ion. The isomerizations of Ni4+-C1 to the complexes of Group I, II and III require C-O bond breaking of the adsorbed methanol, which demands activation energy. For the isomerizations of the complexes in Group I-III to the complexes of Group IV and V, the O-H bond must be broken, requiring another activation energy. The final demethanation products are formed from the complexes of Group V via desorption of methane. To calculate the activation energies required for the C-O bond breaking, the transition states between Ni4+-C1 and all complexes of Group I - III were identified by three different methods mentioned in Section 2. The same procedure was used to determine the transition states and the activation energies for the O-H breaking processes.
Figure 6 displays the most favorable minimum-energy pathway for methanol demethanation on Ni4+. In this particular isomerization pathway, three energy barriers have to be overcome to generate the final demethanation products. The first energy barrier is for the C-O bond breaking, in which the transition state (Ni4+-TS1) lies 27.83 kcal/mol above Ni4+(CH3OH) complex (Ni4+-C1), but 7.21 kcal/mol below the reactant asymptote, or 9.51 kcal/mol below the reactant asymptote plus the initial relative kinetic energy of the reactants. Under the experimental conditions [11,32], the initial center-of-mass kinetic energy for reactants is 2.3 kcal/mol. Therefore, the reactants and the complex Ni4+-C1 have the total energy well above that of the activated complex Ni4+-TS1 and isomerize into Ni4+-C5. The second energy barrier - a small barrier at ca. 7.6 kcal/mol - corresponds to the facile migration of adsorbed OH from Ni4+-C5, where both OH and the methyl group are coordinated to the same nickel atom, to Ni4+-C8. (((This energy barrier is relatively small, only 7.57 kcal/mol.))) The final energy barrier corresponds to the O-H bond breaking and is high. The transition state Ni4+-TS3 for the O-H bond breaking process is 29.37 kcal/mol above Ni4+-C8, but again as much as 10.87 kcal/mol below the reactant asymptote, or 13.17 kcal/mol below the reactant asymptote plus the initial relative kinetic energy of the reactants. The final step in the formation of methane and Ni4+O from Ni4+-C18 is an endothermic process that involves desorption of the metal-bound methane, the complex smoothly dissociating into the products. In the minimum-energy pathway for the demethanation on Ni4+, all the transition states are energetically well below the reactant asymptote, indicating that the process would readily occur under the single-collision condition. The calculations support the experimental results of Kondow et al. [11,32], where the dominant final product of methanol-nickel reaction were methane and Ni4+O.
A density functional theory study of the minimum energy pathway for the CH3OH + Nin+ (n=3,4) → Nin+O + CH4 demethanation reaction has been carried out to elucidate why the demethanation reaction occur preferentially on Ni4+. The reaction mechanism and activation barriers for methanol decomposition on both Ni3+ and Ni4+ clusters are computationally elucidated. On Ni4+, all transition states in the minimum-energy pathway are below the reactant asymptote, while on Ni3+ the transition states are above it. The present study explicates the experimental results of Kondow et al. [11,32], where only the chemisorption of CH3OH was detected on Ni3+, while methane and Ni4+O formed on Ni4+. The results support previous conclusions by Ichihashi et al. - the size-dependent demethanation on Nin+ is controlled by the energy barrier for bond breaking and formation in the chemical processes.
The authors gratefully acknowledge the financial support from the NASA-UPR Center for Advanced Nanoscale Materials under NASA-URC Grant NNX08BA48A. This work was also supported in part by the Fondo Institucional para la Investigación (FIPI) of the University of Puerto Rico Grant No. 8-80-218.