Ru‐Catalyzed Hydrogenolysis of Methanol: A Computational and Kinetics Study

In spite of numerous kinetic studies, the mechanism of the polyol hydrogenolysis on a Ru catalyst surface is still not fully understood. Here, the decomposition of the C1 alcohol methanol can serve as an entry to the clarification of the mechanism. Therefore, kinetic experiments using a Ru/C catalyst and periodic DFT calculations on a Ru(0001) model surface were performed. A modeling of the Ru surface revealed that the surface is most likely covered with hydrogen adsorbates under experimental conditions. On a clean Ru model surface, the overall activation barrier is lower if less dehydrogenation steps occur on the substrate methanol before the C−O bond cleavage. Transferring the results from the clean to the hydrogen‐saturated Ru surface, the pathway via CH2O O−H formation and subsequent C−O cleavage is found to be the most favorable. This study shows that the surface coverage has a significant influence on the activation barrier.


Introduction
The depletion of fossil carbon feedstocks as well as concerns about their environmental impact demand the employment of alternative resources. Biomass is one promising and abundant carbon source that can be utilized for the CO 2 -neutral production of chemicals and fuels. [1] Lignocellulosic biomass in particular holds the advantage of low cost and noncompetitiveness with food plants. The cellulosic and hemicellulosic fractions of biomass can efficiently be converted to C 6 and C 5 polyalcohols, respectively, by combining acid-catalyzed hydrogenolysis with metal-catalyzed hydrogenation. Further hydrogenation performed at elevated temperatures in the presence of metal catalysts leads to short-chained polyols by hydrogenolytic CÀ C and CÀ O bond scission (Scheme 1). [2] These polyalcohols find wide applications as building blocks in polymer synthesis, in pharmaceutical industry and as additives in food industry. [2a] Even though in heterogeneous catalysis various and extensive experimental studies on the hydrogenolysis of polyols were carried out, the molecular reaction on the catalyst surface is yet not fully understood. Computational chemistry can be a helpful tool to gain mechanistic insights on the polyol reactivity on catalytically active metal surfaces. [3] The mechanism of the hydrogenolysis of polyols has been investigated extensively. [4] In particular, two publications by our group elucidate the polyol decomposition performed on a Ru catalyst under neutral reaction conditions. [5] Here, sorbitol, xylitol and erythritol were converted in the presence of Ru/C and molecular hydrogen towards various polyols comprising hexitols, pentitols, tetritols, triols and diols. Based on the experimental results, stereoisomerization, decarbonylation and deoxygenation were proposed as the three main decomposition pathways (Scheme 2). These reactions take place simultaneously on the substrate and all of the subsequent products. Within the stereoisomerization (Scheme 2a), it is generally accepted that one of the hydroxy groups connected to a stereocenter changes its configuration by reversible (de)hydrogenation via successive OÀ H and CÀ H cleavage reactions to a carbonyl species. [6] The CÀ C bond scission between a terminal and an adjacent carbon atom is referred to as decarbonylation and results in a polyol that is shortened by one carbon atom (Scheme 2b). It is probably initiated by dehydrogenation of the polyol towards an aldehyde. [4f] A polyol exhibiting one hydroxy group less at a terminal position can be obtained by CÀ O bond cleavage in a deoxygenation step (Scheme 2c). The experimental evidence on the deoxygenation reaction revealed the racemization of one stereocenter, therefore it was proposed that this reaction could occur via the formation of an enol and a ketone, subsequently. In general, a fourth decomposition pathway leading to CÀ C bond scission at any position in the carbon chain is described by several authors and denoted as a retro-aldol mechanism. [4a,e] However, the applied Ru/C catalyst cannot catalyze this reaction under the given neutral conditions and therefore, this mechanism was not observed in the studies. [5] Based on the C 1 alcohol methanol, we herein report a model study on the decomposition mechanism using computational chemistry. As methanol contains a hydroxy group, which is one of the main characteristics of polyols, we elucidate the reaction mechanism under realistic reaction conditions including solvation effects and the coverage of the catalyst surface and compare computational results to our experimental findings. In contrast to current publications, we investigate the methanol decomposition towards methane, which is in line with our experimental results.
To date, computational studies regarding the hydrogenolysis of polyols and also the Ru-catalyzed decomposition of polyand monoalcohols in particular are scarce. On Ru surfaces, only publications dealing with the methanol decomposition exist. The works by García-Muelas et al. [7] and Moura et al. [8] describe the formation of CO from methanol on a clean Ru(0001) surface. Both studies report quite similar results. The alcohol H activation towards methoxy was identified as the first reaction step, even though García-Muelas et al. found a lower activation barrier for the methanol CÀ H cleavage. Since the alkoxide species has a significantly higher thermodynamic stability and only methoxy is observed experimentally, [9] they state the decomposition pathway via methoxy as predominant. Subsequent CÀ H scissions yield CO and molecular hydrogen as the final products. In the work of García-Muelas et al. [7] CO is formed via successive CÀ H cleavage reactions from H 2 CO, whereas according to Moura et al. [8] the same reaction occurs in one step. In both publications, the methoxy CÀ H cleavage demands the highest activation barrier between 61 and 87 kJ mol À 1 . On the contrary, the steps regarding the formation of CO from formaldehyde require only minimal activation energy (0-6 kJ mol À 1 ). Further publications partly deal with the aforementioned steps of the methanol decomposition. [10] These studies confirm the low activation barriers found for the formaldehyde and formyl CÀ H cleavages. However, in all these publications the reaction was investigated on a clean Ru surface in vacuum conditions. Based on the work of García-Muelas et al., [7] the same group analyzed the effects of solvation in water on the reaction by applying an implicit solvation model combined with two explicit solvent molecules. [11] Due to proton transfer to the water adsorbate, the methoxy formation requires no activation energy and the activation barrier of the methoxy CÀ H bond cleavage is lowered by 16 kJ mol À 1 . Regarding the methanol decomposition, no studies consider interactions with other adsorbates except water.
Several publications study the effect of solvation and surface coverage on the reactivity of polyols. When water is used as a solvent, the metal catalyst exhibits a wetting layer caused by adsorption of water molecules. [12] Therefore, wet surfaces cannot be modeled by a vacuum/metal interface. Michel et al. found that in the presence of another water or alcoholic substrate molecule the formation of a hydrogenbonded dimer is usually more favorable than generating an additional metal-O bond. [13] This facilitates the OÀ H bond scission for the weakly adsorbed hydrogen bond acceptor due to preorganization of the transition state (TS). On the contrary, the CÀ H bond cleavage is slightly inhibited by this effect. Furthermore, Sinha et al. [10c] stated that higher surface coverages of the substrate and hydrogen would result in lateral repulsive interactions and consequently, decrease the activation barriers for hydrogenation.
In the following we present a kinetic analysis of the hydrogenolysis of methanol over Ru/C at different temperatures and the obtained apparent activation energies. Subsequently the reaction pathways are studied comprehensively using periodic DFT on a Ru(001) surface with implicit solvation on a clean and hydrogen covered surface, to obtain reaction pathways with the lowest energetic spans. Finally the experimental and theoretical results are compared.

Kinetics of the Ru/CÀ Catalyzed Hydrogenolysis of Methanol
Hydrogenolysis experiments of methanol were performed in an aqueous solution using a Ru/C catalyst in the presence of high pressures of molecular hydrogen. Prior to the kinetic measurements, blank experiments without catalyst were performed and proved the necessity of the catalyst for the hydrogenolysis reaction. The experimental hydrogenolysis of methanol led to methane as the only decomposition product ( Figure S1). Consequently, other possible products or intermediates such as CO and CO 2 were not generated or completely hydrogenated on the Ru catalyst. The kinetics of the methanol decomposition to methane was studied by determining the pseudo-first order rate constant k mm from the methanol concentrations at different reaction temperatures (Figure 1, left). The second order rate constant k was obtained by taking into account the experimentally measured Ru dispersion of 0.175 of the Ru/C catalyst in the catalyst concentration. Thereof, the apparent activation enthalpy DH � app , the entropy of activation DS � app and the Gibbs energy of activation DG � app were calculated using the Eyring method (Figure 1, right). [14] The methanol hydrogenolysis to methane on Ru/C has a DH � app of about 110 kJ mol À 1 (Table 1). This value is in the same order of magnitude as other apparent activation enthalpies for the decarbonylation and deoxygenation on the same catalytic system. Our group found a DH � app of 118 kJ mol À 1 and 122 kJ mol À 1 for the first decarbonylation of xylitol and sorbitol, respectively. Furthermore, the deoxygenation of xylitol has a DH � app of 83 kJ mol À 1 . [5b] However, these results are hardly comparable since the C 5 and C 6 polyols have far more possibilities for interactions with the catalyst surface due to their several hydroxy groups.
The experimental DG � app of 115 kJ mol À 1 is very similar to DH � app since the value of DS � app is quite low (Table 1). This experimentally determined Gibbs energy of activation serves as a reference for the computational results.

Modeling of the Most Stable Ru Surface
Since under experimental conditions the Ru catalyst surface is not clean but covered with adsorbates like the substrates methanol and hydrogen as well as the solvent water, the most stable and thus, the most probable surface has to be identified. Methanol is preferably adsorbed by dissociation of the OÀ H bond to methoxy and hydrogen (Figure 2 a). This corresponds to a coverage of 2/9 monolayer (ML), as two adsorption sites are occupied in a cell with 9 Ru surface atoms. As a cell with 9 Ru surface atoms has 9 fcc threefold hollow sites, which are preferred for the investigated substrates, 9 sites are used as a reference for adsorption sites. At a coverage of 2/9 ML, a stabilization by G ads = 83 kJ mol À 1 is reached under the given reaction conditions (Table 2 a). A higher coverage, however, destabilizes the adsorption probably due to steric repulsion between the methyl groups ( Figure S3 Due to lower steric demands, water can be bound with a significantly higher coverage of 6 water molecules per 9 Ru atoms (2/3 ML), which is denoted as a bilayer. [12] The most stable arrangement of water on a 3 × 3 Ru slab is a partially dissociated bilayer (Figure 2 b), which reaches a stabilization of 110 kJ mol À 1 (Table 2 b). This finding is in line with computational and experimental findings. [12,15] Molecular hydrogen adsorbs preferably dissociatively on fcc threefold hollow sites with a maximum coverage of 1 ML of H, [16] which can be confirmed by our results showing an energy stabilization of 398 kJ mol À 1 (Table 2c). However, the adsorption energies for the fcc and hcp threefold hollow sites deviate only slightly and consequently, both adsorption modes are feasible.
Probing surfaces mixed with different adsorbates revealed that a (3 × 3) slab composed of one water molecule and seven hydrogen adsorbates has the highest stability (Table 2d), though it is less favored than the hydrogen-saturated surface. Accordingly, the ruthenium slab has an energy minimum, if all fcc threefold hollow sites are occupied with hydrogen atoms. [17] Therefore, this structure will be regarded as the starting point of the reactions.
In analogy with Pd-H hydrides [18] , the incorporation of hydrogen atoms in the Ru lattice could be possible, but to our knowledge no publications regarding RuÀ H hydrides are present. This is supported by calculations showing that the incorporation of H in the Ru(0001) slab is unfavorable (Table S2).

Mobility of Adsorbates on the Ru Catalyst Surface
Even though the Ru catalyst surface fully covered with H adsorbates is the thermodynamic energetic minimum, metastable energetic states with vacant adsorption sites will be present under the given reaction conditions (# > 150°C, #: temperature). However, an identification of the actual coverage of hydrogen on the surface would require kinetic modelling using Kinetic Monte Carlo simulations. Nevertheless, in order to ensure the most favorable coverage of H atoms on the investigated slab, the mobility of adsorbed H atoms on the Ru catalyst surface was investigated. By this means, hydrogen atoms could migrate into the slab to fill vacant sites after consumption of hydrogen atoms in hydrogenation steps or they could migrate into a neighboring slab, if an additional vacancy is required for a bond cleavage. The migration of hydrogen from one fcc threefold hollow site to another takes place via a local minimum on a hcp threefold hollow site. The transition states connecting these minima are located on the bridge sites between those hollow sites ( Figure S5). The barrier for migration (ΔE mig � ) of H atoms on a clean Ru(0001) surface amounts to only 14 kJ mol À 1 (Table 3). In addition, the barrier for migration of vacant sites on an almost fully H-covered surface is very similar (21 kJ mol À 1 ), since lateral interactions are small ( Figures S6-7).
Furthermore, the mobility of the oxygen containing products of the hydrogenolysis was tested. If O and OH adsorbates have low migration barriers on the Ru surface, the hydrogenation of the C and O fragments can be treated separately, since migration between neighboring surface unit cells is possible. While the migration of OH requires a similarly low activation energy as the H atom, the barrier for migration of O is significantly higher and migration between different threefold hollow sites would be slow (Table 3). Consequently, we can assume that the oxygen atom remains on its adsorption site until being hydrogenated. However, O atoms adsorbed in proximity to a carbonaceous fragment have only a minor influence on the activation barrier of the CÀ H bond formation (cf . Table S3).

Methanol Decomposition Mechanisms on a Clean and a Hydrogen-Saturated Ru(0001) Surface
The mechanism of the methanol hydrogenolysis is investigated on both a clean and a hydrogen-saturated Ru(0001) model surface since the calculations are significantly simplified on the clean surface. Theoretically possible products of the decomposition reaction of methanol are either carbon monoxide, carbon dioxide or methane (Scheme 3). However, in our hydrogenolysis experiments of methanol on Ru/C methane was the only decomposition product (see Figure S1). Besides, the formation of methane is the only reaction that shows a negative Gibbs free energy (Scheme 3). Therefore, we focus on reaction pathways leading to methane in this study, which is in contrast to previous works on the methanol decomposition. [7][8] The most stable adsorption sites and geometries of all reactants, reaction intermediates and products were identified (Table S1) and this knowledge was considered in the computation of the catalytic cycles.
A combination of dehydrogenation and hydrogenation reactions at the carbon and oxygen atom as well as the cleavage of the CÀ O bond are necessary to convert methanol into methane (Scheme 4). Since experiments revealed that methoxy is the predominantly adsorbed species on the Ru catalyst surface, it is very likely that the reaction sequence of the methanol decomposition starts with an OÀ H bond cleavage to methoxy. [9,19] Therefore, reaction pathways via methanol CÀ O and CÀ H bond cleavages are not considered. In general, the CÀ O bond scission can take place at any dehydrogenation stage of methanol. The direct CÀ O cleavage of these intermediates as well as the CÀ O cleavage after an OÀ H formation can be distinguished (Scheme 4). After cleavage of the CÀ O bond, the obtained fragments are stepwise hydrogenated to methane and water. As CÀ H bond formations were found to have lower activation barriers than OÀ H bond formations (Table S3), the hydrogenation of carbonaceous fragments is considered before the formation of water.
All reaction pathways (note: all pathways start at I and end at VI) presented in Scheme 4 were calculated on a clean Ru(0001) surface. As these are preliminary studies for the mechanism on a hydrogen-saturated Ru surface, dispersion interactions were neglected. The respective energy profiles and images of the stationary points can be found in the Supporting information ( Figures S8-18). The mechanism of the complete dehydrogenation of methanol to CO coincides with the pathways discussed in the literature ( Figure S16). [7][8] Comparably high activation barriers for the methanol OÀ H and the methoxy CÀ H cleavage were found, while the CÀ H bond scissions of formaldehyde and formyl have likewise minor activation barriers (cf.   (II-III) however is less favorable, which is probably due to the steric hindrance of the methyl group ( Figure S9). In all considered pathways, the formation of OÀ H bonds needs considerably high activation energies between 100 kJ mol À 1 and 166 kJ mol À 1 , while CÀ H bond formations have lower activation barriers between 46 kJ mol À 1 and 79 kJ mol À 1 (Table S3). The reason for these relatively high barriers could be that the formation of OÀ H and CÀ H bonds requires the detachment of RuÀ H bonds, similar to the formation of H 2 , which already requires 38 kJ mol À 1 on a per H basis. This destabilization of the Ru surface accounts for a considerable portion of the activation barrier of the hydrogenation steps. The high barriers for OÀ H bond formations on the clean Ru surfaces could be reduced, if the assistance of water or methanol molecules would be considered on a clean surface [13] or if the surface coverage is included in the calculations as shown in the following sections.
In general, the stability of local minima increases with each dehydrogenation step of methanol and otherwise decreases after each hydrogenation reaction. This is due to the generation and consumption of hydrogen adsorbates in the reaction steps, which either stabilizes or destabilizes the surface afterwards (cf. Figure S16). This can be confirmed by the fact that for all investigated pathways the energetic span (ES, which is the difference between the highest transition state and the lowest intermediate and a measure for the total activation energy of a reaction pathway) [20] is determined by the TS of the water formation (V-VI), which represents the most hydrogenated stage in the catalytic cycle, and local minima at strongly dehydrogenated stages (Figures S8, S10, S13 and S16). A comparison of the ESs of the potential reaction pathways on the clean Ru model surface shows that the ES decreases, if the  CÀ O bond cleavage takes place at an early dehydrogenation stage of methanol (Table 4). The reason is that less hydrogen adsorbates are formed at early dehydrogenation stages and thus, the surface is less stabilized, which would otherwise result in an increased ES.
The methanol decomposition pathways to methane via CH 3 O (1), CH 2 OH (2) and CH 2 O (3) CÀ O cleavage have the smallest ESs on the clean Ru surface and are therefore recalculated on a Ru(0001) surface saturated with hydrogen adsorbates to represent the experimental conditions and improve the computational results. Since hydrogen adsorbates showed a high mobility on the catalyst surface, H atoms are considered to migrate in or out of the investigated Ru slab in order to maintain the most favorable hydrogen coverage on the catalyst surface. Consequently, the highest possible coverage of hydrogen is considered for each reaction step. If additional vacancies are required for the following reaction step, a migration of a vacancy from a different slab containing a vacancy is assumed, as the barrier is comparatively small (cf. Table 3). On the other hand, if a vacant site is generated in a reaction step, this vacant site is filled with a hydrogen adsorbate that migrates from another cell into the investigated slab.
In general, the mechanisms and the single reaction steps of the methanol decomposition on a Ru(0001) surface covered with hydrogen adsorbates are very similar compared to the clean surface. For all three investigated pathways, at first the methanol OÀ H bond is cleaved (i-ii) leading to a methoxy and a hydrogen atom. As an alternative to the surface-mediated cleavage of methanol, the concerted methanol OÀ H bond cleavage and recombination of the H atom with a surface hydrogen was probed (Figures S25-26). Since the repulsion between the adsorbates is too high on a fully hydrogencovered surface, this reaction step was tested on a Ru slab with two vacant sites. However, the direct recombination of the methanol H with a surface hydrogen resulting in desorbed H 2 is less favorable than the homolytic cleavage of the methanol OÀ H bond. Following the decomposition pathway via CH 2 OH CÀ O cleavage (2) (Figure 4), the formaldehyde species formed after the CÀ H bond cleavage of methoxy (vii) has to migrate on the surface to form the reactant geometry (x) of the following OÀ H bond formation. This migration coincides with the CH 2 O rotation on the clean Ru model surface (cf. Figure S10) and the activation barriers are extremely low compared to the overall activation barrier ( Figure S21). This again indicates that adsorbed molecules are quite mobile on the catalyst surface. Obviously stationary point x is less stable than vii since the CH 2 O molecule is located in proximity to a H adsorbate. This repulsion can already be recognized from the fact that this hydrogen atom moves away from the threefold hollow to a bridge site ( Figure S22). In contrast to the clean surface, the adsorption of one H 2 molecule that is required in the reaction does not take place at the beginning of the reaction, but most probably after the consumption of the hydrogen adsorbates that were generated from dehydrogenation of methanol. For pathway (2) via CH 2 OH, this is the case after the hydrogenation of CH 2 to CH 3 (xiii). For all three investigated pathways, this leads to a fluctuating number of vacant sites by two in the course of the catalytic cycles.  When comparing the activation energies of the single reaction steps on the clean and the hydrogen-covered Ru(0001) surface, it becomes obvious that most barriers are comparable (Table 5). However, some hydrogenation reactions are facilitated significantly on the H-saturated surface (iii-iv, x-xi). This could be because many other hydrogen adsorbates can still stabilize the surface and repulsion can be reduced by forming an OÀ H or CÀ H bond. The activation barriers of OÀ H bond formations (iv-v, v-vi) however, are only slightly decreased on the hydrogen-covered surface. These TSs determine the ES for the pathways (2) and (3). This leads to a smaller energetic span for the CH 2 OH pathway (2) compared to CH 2 O (3) since TS iv-v is slightly higher in energy than v-vi and the formation of OH from O (iv-v) can be avoided in pathway (2). In addition, the ES for the CH 2 OH pathway (2) is determined by stationary point v containing adsorbed OH, while the pathways via CH 2 O (3) has a more stable intermediate with an adsorbed O atom (iv). Consequently, a reaction sequence that avoids the formation of O adsorbates and the formation of OH is the most favorable. For pathway (1) via CH 3 O, the ES is very similar to pathway (3) (Table 6). However, the activation barrier determined by TS ii-iii of the CÀ O bond cleavage and the adsorbed O species has a slightly higher barrier ( Figure S19). Among the three investigated reaction pathways on the H-covered Ru surface, the CH 2 OH pathway (2) shows the best ES of 80 kJ mol À 1 (Table 6) and is consequently the most probable reaction pathway. A separation of the Gibbs free energies of activation in enthalpic and entropic contributions reveals that the entropic contribution to the ES is quite small which is in accordance with the experimental result. This indicates that the rate-determining step does not include the adsorption or desorption of a molecule to or from the surface.
Compared to the ESs of the respective mechanisms on the clean Ru surface, a reduction can be observed by considering hydrogen co-adsorbates on the catalyst surface. When comparing the ESs in Tables 4 and 6 it has to be mentioned that the ESs in Table 6 were calculated for cycles that contain dispersion corrections while the ESs of the pathways calculated in Table 4 do not. However, even without consideration of dispersion interactions the ES decreases by about 20 kJ mol À 1 for the pathways via CH 3 O (1) and CH 2 OH (2) and by about 40 kJ mol À 1 for the CH 2 O pathway (3). This effect can be explained by the fact that higher surface coverages result in lateral repulsive interactions. [10c] Consequently, the adsorbates are less stabilized on the surface, which reduces the activation barriers of the reaction steps.
Finally, a comparison of the computationally and experimentally determined activation barriers of the methanol hydrogenolysis reveals that ES of 80 kJ mol À 1 on the H-saturated Ru(0001) surface via the CH 2 OH intermediate is underestimated compared to the experimentally determined Gibbs free energy of activation (DG � app = 115 � 10 kJ mol À 1 ). Possibly, the consideration of different crystal planes including steps and edges instead of the plane Ru(0001) surface could have an impact on the reaction. Furthermore, the approximations made for the entropic contributions could play a non-negligible role.
Nevertheless, periodic DFT is a suitable tool for the mechanistic analysis of this surface-catalyzed reaction. Moreover, this indicates that the consideration of the catalyst surface coverage is of high importance in order to obtain more reasonable energetic results.

Conclusion
To summarize, we reported a combined computational and experimental study on the Ru-catalyzed hydrogenolysis of methanol. A kinetics study on the methanol hydrogenolysis was performed on a Ru/C catalyst and gave a Gibbs energy of activation of DG � app = 115 � 10 kJ mol À 1 . As only methane was observed as a decomposition product experimentally, we investigated the methanol decomposition to methane on a Ru(0001) model surface using periodic DFT. In order to , which is smaller than the experimentally determined Gibbs free energy of activation. Nevertheless, the results of this study emphasize the importance of modeling reactions under realistic conditions. Based on the results of this publication, the hydrogenolysis mechanism of higher polyols such as ethylene glycol or glycerol can be investigated to elucidate the surface mechanism. In this regard, the dependence of the apparent activation energies on the position of the reacting group and the polyol chain lengths as observed previously [5b] can be examined.

Experimental Methods
Methanol (> 99.8 5 %), acetic anhydride (> 97 %) and pyridine (> 99 %) were obtained from ChemSolute. Ru/C (5 wt. %) was obtained from Sigma-Aldrich. Molecular hydrogen (> 99.999 %) was obtained from Linde. The hydrogenolysis of methanol was performed in high-pressure stainless steel autoclaves of 50 mL volume with a sampling tube equipped with a Teflon inlet and a magnetic stirrer. In a typical experiment, 0.525 g (16.4 mmol) methanol and 0.400 g Ru/C (5 wt. %) were added to the autoclave and dispersed in 20 mL water. After flushing the autoclave with H 2 , it was pressurized with 80 bar H 2 . Subsequently, the autoclave was heated in an aluminum cone to reaction temperature (413 K, 423 K, 433 K, 443 K or 453 K) at a stirrer speed of 750 rpm. Samples were taken 0 min, 15 min, 30 min, 60 min, 120 min and 180 min after the reaction temperature was reached. The catalyst was filtered out over a polyamide filter with a pore size of 0.45 μm. 0.167 mL of the filtrate were dissolved in 2 mL acetic anhydride/pyridine (1 : 1 vol/vol). After stirring over night at room temperature, the samples were measured by gas chromatography (GC) [Thermo Scientific Trace GC system equipped with an Agilent DB-23 column (internal diameter: 0.25 mm; length: 60 m; film thickness: 0.25 mm; isobaric: 0.1 MPa He; temperature gradient: 353-527 K)]. Methanol was calibrated using the external standard method. All reactions were performed twice in order to prove reproducibility. The dispersion of the Ru/C catalyst was determined by a CO-pulse titration assuming a Ru:CO stoichiometry of 1 : 1. For an extensive characterization of the commercial Ru/C catalyst, the reader is referred to the publication by Haus et al. [21]

Determination of the Gibbs Energy of Activation
The rate constants of the methanol decomposition k mm were calculated under the assumption of a pseudo-first order kinetics (Equation 1). For the fitting to the experimental data, an induction period at the beginning of the reaction is not considered in the fit, as the Ru/C catalyst most probably needs to be activated by an in situ reduction of the oxidic overlayer on the Ru surface. In addition, a certain time is needed until the reaction temperature is reached inside the autoclave. [5a] Therefore, the time zero was set 15-30 min after the beginning of the reaction. The methanol concentration was calculated numerically at intervals of 1 min. These concentrations were fitted to the experimental data by variation of k mm by means of the MS Excel Solver Add-In with the solving method 'Generalized Reduced Gradient (GRG) non-linear' using the least square method. [5b] dc m dt ¼ À k mm � c m (1)

m: Methanol; mm: Methanol/methane
The second order rate constant k of the methanol decomposition is calculated by division of k mm by the concentration of accessible Ru atoms c Ru (Equation 2). c Ru is determined according to Equation 3 considering the mass fraction of Ru (ω) and the metal dispersion (δ).
The apparent activation enthalpy DH � app and the entropy of activation DS � app were calculated using the Eyring method. [14] Therefore, a linear regression of ln k = T versus 1/T of the linearized form of the Eyring equation (Equation 4) was carried out. The Gibbs energy of activation DG � app was determined according to Equation 5. The standard error on DH � app and DS � app was calculated by division of the standard deviation by the square root of the number of data points. The standard error on DG � app is determined by a Gaussian error propagation of the errors on DH � app and DS � app .

Computational methods
All DFT calculations were carried out in a periodic framework using the VASP program series (revision 5.4.4) [22] combined with the PBE exchange-correlation functional [23] within the generalized-gradient approximation (GGA). In most cases, the PBE functional was complemented by the Grimme D3 correction with BJ damping [24] to account for dispersion. Preliminary studies such as the investigation of Ru hydrides, the estimation of migrational barriers and the study of catalytic cycles on a clean Ru surface do not contain dispersion corrections. This is indicated at the respective results. The electronion interactions were described by the PAW method. [25] In order to ensure accurate energies, the energy cut-off of the plane wave basis was set to 400 eV. The metal surface was modeled by a Ru(0001) slab, which is the thermodynamically most favorable surface. [26] A RuÀ Ru distance of 2.71 Å was obtained from relaxation of Ru bulk. The slab consisted of a four-layered (3 × 3) cell of which the two top layers describing the surface were allowed to relax. The lower two layers were fixed during the optimization process to represent the bulk phase. The Brillouin-zone was sampled by a Γcentered 7 × 7 × 1 Monkhorst-Pack grid [27] together with a secondorder Methfessel-Paxton smearing of 0.2 eV. [28] In order to avoid interactions between slabs a 15 Å vacuum overlayer was implemented. Geometry optimizations of local minima on the potential energy surface were performed with convergence criteria for the electronic self-consistent energy and the ionic relaxation of 10 À 6 eV and 0.02 eV Å À 1 , respectively. The TSs of minimum energy paths were localized by employing the NEB method [29] with four movable images between the fixed initial and final stationary points. Every TS was optimized with the improved dimer method [30] using a smaller convergence criterion for ionic relaxation of 0.01 eV Å À 1 . Frequency calculations verified that every localized TS exhibits exactly one imaginary frequency corresponding to the investigated reaction step. Since the substrate methanol contains only one O atom that interacts with the surface, hydrogen bond interactions were assumed to be negligible in this study and therefore, solvation effects were calculated implicitly by using the VASPsol code [31] on preoptimized geometries. The zero-point energy and thermal contributions to the electronic energy were computed from frequency calculations of the free molecules and all adsorbates using statistical thermodynamics at a temperature of 150°C and a pressure of 80 bar (see Supporting information). [32] Thermal contributions of adsorbed molecules and atoms were calculated according to the harmonic limit. Low-frequency modes of adsorbed systems below 100 cm À 1 were shifted to 100 cm À 1 for the calculation of the vibrational entropy and enthalpy to avoid a large error on the entropic terms. Adsorption energies G ads were calculated using Equation 6, where G denotes the Gibbs energy of the isolated adsorbate (A), the clean Ru(0001) surface (Ru) or the adsorbed system (A/Ru).
The activation barrier of the multistep reaction sequence is determined according to the ES model by Kozuch and Shaik. [20]