On the Catalytic Activity of [RuH2(PPh3)3(CO)] (PPh3=triphenylphosphine) in Ruthenium‐Catalysed Generation of Hydrogen from Alcohols: a Combined Experimental and DFT study

Using density functional theory calculations (at the B97‐D2//BP86 level) and measurements of kinetic isotope effects, we explored the mechanism of [RuH2(PPh3)3(CO)] (22) in catalytic acceptor‐less dehydrogenation of methanol to formaldehyde. 22 is found to exhibit a similar activity as the previously studied [RuH2(H2)(PPh3)3] (1 b) complex. On the computed pathway, η2→η1 slippage of Ru‐bound formaldehyde prior to decoordination is indicated to be rate‐limiting, consistent with the low kH/kD KIE of 1.3 measured for this reaction. We also explored computationally the possibility of achieving complete dehydrogenation of methanol (into CO2 and H2), through subsequent decarbonylation of formaldehyde and water‐gas shift reaction of the resulting carbonyl complex. Complete pathways of this kind are traced for 22 and for [RuH2(PPh3)2(CO)2]. An alternative mechanism, involving a gem‐diol intermediate (obtained upon attack of OH− to coordinated formaldehyde), has also been investigated. All these pathways turned out to be unfavourable kinetically, in keeping with the lack of CO2 evolution experimentally observed in this system. Our calculations show that the reactions are hampered by the low electrophilicities of the CO and HCHO ligands, making OH− uptake unfavourable. Consequently, the subsequent intermediates are too high‐lying on the reaction profiles, thus leading to high kinetic barriers and preventing full dehydrogenation of methanol to occur by this kind of mechanism.


Introduction
Regenerative biomass is an attractive source for the generation and storage of hydrogen gas (H 2 ), in the context of sustainable power management. In particular, if carbohydrates (such as cellulose) contained in plants could be fully decomposed into H 2 and CO 2 , an overall "carbon-neutral" process could be envisaged, where the light harvesting apparatus of photosynthesis would be used to regenerate carbohydrates and consume the CO 2 produced in the first reaction. The resulting H 2 could fuel combustion engines or fuel cells, regenerating the water from which it was created. If such an overall sequence were possible, it would provide us with a more appealing way to produce hydrogen, compared to current industrial processes that are essentially based on fossil fuels as starting products. However, direct H 2 production from carbohydrates still remains challenging. Known reactions generally proceed via prior decomposition of the substrates. [1] In this context, a significant research effort has been accomplished to design efficient (homogeneous) catalytic systems allowing for H 2 generation from carbohydrate derivatives, such as formic acid [2] or alcohols. [2b,3] Among them, methanol is a particularly attractive hydrogen source, [4] as it contains a higher hydrogen content than formic acid (12.5 wt% vs 4.3 wt%). In principle methanol can be catalytically dehydrogenated to three different products. Loss of one equivalent of H 2 gives formaldehyde (step i in Scheme 1), which could undergo subsequent reactions, e. g. to methyl formate. [5] Alternatively, the formaldehyde could be dehydrogenated to give a metal carbonyl complex and a second equivalent of H 2 (step ii). The carbonyl could be expelled from the metal as CO, possibly photochemically, [6] to regenerate the catalyst. Alternatively, it can be envisaged that the bound CO could undergo water gas shift reaction (WGSR) to give a third molecule of hydrogen and CO 2 (step iii). [7] molecule, and are thus unable to achieve the full decomposition of alcohols into H 2 and CO 2 . [2b] Further developments in this field would benefit from a deeper understanding of the mechanisms underlying the catalytic reactions. The latter are multiple-step processes, and thus involve a broad number of short-lived intermediates that are challenging to characterize experimentally. As a result, detailed mechanistic information is still limited, and is essentially obtained with the help of computations.
We recently undertook a comprehensive mechanistic study of the catalytic system developed by Morton and Cole-Hamilton, involving the [RuH 2 (X 2 )(PPh 3 ) 3 ] (X 2 =H 2 (1 b), PPh 3 or N 2 ) complexes as catalyst precursors. This system was among the first being very active for acceptor-less dehydrogenation of alcohols, and allows for an efficient conversion of aliphatic alcohols under basic conditions, at 150°C. [12] Interestingly, the reaction rate increases with the length of the alkyl chain of the substrate (going from methanol to butanol), and the presence of complex 22 (resulting from decarbonylation, see Scheme 3) has been detected. 22 has been also be identified to be a catalyst for dehydrogenation in this system. [12] A series of [RuH 2 (X 2 )(PPh 3 ) 3 ] complexes was also considered regarding the overall sequence shown in Scheme 1, and their propensity to promote decarbonylation and WGSR reactions have been studied by measuring the quantity of produced CO, CH 4 (resulting from decarbonylation) and CO 2 (resulting from WGSR), during conversion of ethanol. [9] Interestingly, a significant amount of methane was produced, but no CO 2 has been detected (even after neutralisation of the solution with concentrated HCl). This revealed that the overall cycle shown in Scheme 1 should not be achievable with these pre-catalysts, since only steps 1 and 2 take place, but WGSR is not operating (step 3).
Our previous mechanistic investigations on this system [13] were based on Density Functional Theory (DFT) calculations, coupled to experimental determinations of Kinetic Isotope Effects (KIEs). In a first report, we focused on the dehydrogenation step itself (i. e. the first step of the overall cycle shown on Scheme 1), in which 1 b plays the role of pre-catalyst. We showed that the reaction mechanism is, in fact, complex, as four different reaction channels have been identified. The latter are strongly interlocked and possess close overall activation barriers. These results suggest that multiple reaction pathways should be considered to explain the reactivity of 1 b regarding dehydrogenation. [13a] In a second report, we focused on the decarbonylation reaction (i. e. the second step of the cycle shown in Scheme 1), leading to the formation of the carbonyl complex 22. We proposed a detailed mechanism for decarbonylation and we found that the latter is indeed kinetically facile with methanol and ethanol substrates. The overall activation barriers are found to be close to the one for dehydrogenation, indicating that the two reactions should be competitive. Also, a significant driving force was found for the formation of 22. [13b] Interestingly, a kinetic isotope effect has been measured for a decarbonylation pathway, suggesting that the rate-limiting step is the first α-H abstraction from the coordinated formaldehyde (namely, the dehydrogenation product of methanol), in keeping with our computational results. [13b] Very recently, some of us characterized isotopomers of 22 (obtained from reaction between 1 b and CD 3 OD in presence of Na) by 1 H NMR, [14] and showed that their relative population in solution is consistent with one of the decoordination pathways (pathway G) that has been previously established from computations. [13b] A summary of pathways A-G, as obtained in our previous studies, is provided in supporting information (see Scheme S1).
Herein, we extend our mechanistic studies to explore the reactivity of 22 in the catalytic system (see Scheme 3). First, we investigate its potential role as dehydrogenation catalyst precursor, i. e. ensuring step 1 of the overall cycle shown in Scheme 1, with [M]=[RuH 2 (PPh 3 ) 2 (CO)]. We report a detailed mechanism describing its reactivity towards methanol, considering that the carbonyl ligand remains coordinated in all intermediates involved in the catalytic cycle. The results of the experimental determination of Kinetic Isotope Effects (KIE) are also presented. Next, we explore the propensity of 22 to undergo WGSR (i. e. corresponding to the third step of the overall cycle shown in Scheme 1, with [M]=[RuH 2 (PPh 3 ) 2 (H 2 )]), with the aim to better understand what are the limiting factors that prevent this reaction, as no CO 2 evolution is found for this catalyst. [9] For completeness, the possibility of a gem-diolate pathway (GDP) mechanism was as also considered (i. e. involving the sequence described in Scheme 2). Finally, we investigated the viability of a full catalytic cycle allowing for full decomposition of methanol, as shown in Scheme 1, considering 22 as pre-catalyst.

Results
This section is organized as follows: first, we report DFT and experimental results on the propensity of 22 to catalyse methanol dehydrogenation. Next, we describe DFT results on CO 2 evolution involving 22, considering both WGSR (third step of the overall cycle described in Scheme 1) and GDP. Finally, DFT results on the full decomposition of methanol involving 22 as pre-catalyst (see Scheme 1) are presented.
In pathways involving diphosphine complexes, two variants were considered, differing in the relative position of PPh 3 and CO ligands at the metal centre, so that a first mechanism involves isomers where the two ligands are in axial positions, while the second mechanism involves isomers where PPh 3 is in an axial position and CO is equatorial. For simplicity only the most favourable variant of each path is presented in the text, the other pathways, labelled with primes, are provided in the Supporting Information (ESI).
In all pathways considered herein, we assume that ligand exchange reactions follow a fully dissociative mechanism, i. e. taking place via the formation of five-coordinate Ru(II) complexes. Also, the latter are assumed to undergo facile isomerisation, by intramolecular rearrangement via turnstile-or pseudo-rotation. [15] The labelling of all species and pathways reported herein are continuing those of our two preceding studies, focused on the dehydrogenation (pathways AÀ D) [13a] and decarbonylation (pathways EÀ G; see also Scheme S1 for details) [13b] reactions. Consequently, the labelling of new species starts with 32. When applicable, the "a" and "b" suffixes denote classical and nonclassical hydrides, respectively, whereas the "ax" subscript refers to stereoisomers where PPh 3 and CO are both in axial positions.
After a detailed description of the catalytic cycles, their kinetics is analysed compared to the previously established mechanisms. [13] Additionally, the results of CH 3 OH/CD 3 OD competition experiments for the determination of the rate-limiting step of methanol dehydrogenation catalysed by 22 are presented, along with a comparison between experimental and computed KIEs.
Unless otherwise specified, all energies mentioned in the text are free energies computed at the B97-D2/ECP2 level and corrected for basis set superposition error (BSSE, see Eq. (8) in Computational details). The model solvent is methanol and the temperature is 150°C throughout. Free energies of every elementary step are gathered in Tables S1 and S3-S7.

Description of pathway H, established from DFT calculations
Based on the reaction pathway C previously reported for alcohol dehydrogenation catalysed by [RuH 2 (H 2 )(PPh 3 ) 3 ] (1b), [13a] we investigated an analogous path, denoted H (Figure 1), for methanol dehydrogenation catalysed by complex 22, in which all intermediates feature a (single) carbonyl ligand. The active species 27 can arise from 22 (which acts as a catalyst precursor) by dissociation of a phosphine ligand. This initiation step is found to be only moderately unfavourable thermodynamically (by 52.3 kJ/mol at the ECP2 level and 43.6 kJ/mol at the ECP3 level; see Tables S1 and 1, respectively), suggesting that intermediate 27 should still be present to a small extent in the catalytic system. Since the dehydrogenation reaction occurs under basic conditions, [12] 27 can coordinate MeO À to afford the anionic methoxy intermediate 32. [16] This step is thermodynamically uphill (ΔG 27!32 = 20.5 kJ/mol), but the subsequent dissoci-ation of the phosphine ligand can easily occur (ΔG 32!33 = À 9.7 kJ/mol). This process affords the five-coordinate species 33 via a reorganisation of the methoxy, carbonyl and hydrido ligands.

Kinetics of the dehydrogenation pathway H and comparisons with the previously studied pathway C (DFT results)
In order to compare the kinetics of pathways H (and H') to the ones previously described, [13] the initiation steps and overall activation barriers have been recomputed at the higher ECP3 level of theory, as done previously. [13] The BSSE corrections (noted δE' BSSE ) were recalculated using a more elaborated approach, allowing for a better estimation of the error when the (de)coordination of more than one ligand is occurring during the overall reaction (see Section II.2 in the ESI for details). All energy components (except δE G ) to the overall free energies were recomputed at the B97-D2/ECP3 level, and are reported in Table 1.
The overall activation energy computed for pathway H is 114.2 kJ/mol (see Table 1), i. e. comparable with (and even slightly lower than) that for the analogous path C (131.0 kJ/ mol). [13] Pathway H' appears to be somewhat less favourable (overall barrier 134.9 kJ/mol). Our DFT results thus confirm that complexes 1b and 22 should both be catalysts for methanol dehydrogenation with comparable activity, and that 22 could potentially be even slightly more active than 1b. Interestingly, while a switch from pathway C to H is possible through decarbonylation forming 22, [13b] the reverse is not possible because of the high thermodynamic stability of the carbonyl complexes. For instance, switching from intermediate 32 on path H to intermediate 11 on path C (through CO dissociation) would require an overall free energy barrier of ΔG � = 245.8 kJ/ mol to be overcome to achieve turnover (via subsequent TS 13-14 , see Table 1). Such a barrier should certainly be out of reach under actual reaction conditions.

Experimental determination of H/D KIE and comparison with DFT results
The experimental H/D KIE for methanol dehydrogenation catalysed by 22 (pathways H and H') could be estimated by following the destiny of the formaldehyde product, bearing in mind the "one-pot" catalytic system we have proposed in reference, [17] where the formaldehyde obtained as a product of Overall free energy barriers C [b] 1b + MeO À !TS  [c] 22 and pathway H presented in Figure 1). When the reaction is performed using equal amounts of CH 3 OH and CD 3 OD, the formation of non-deuterated and bisdeuterated formaldehyde should be observed. The latter compound, in turn, can undergo intramolecular H/D exchange to generate the mono-deuterated derivative. The three isotopomers, CH 2 O, CHDO and CD 2 O, once involved in the subsequent condensation step will afford the non-, mono-and To determine the deuterium isotope effect, the reaction was carried out using tert-butyl propanoate (t-BuP) as substrate and sodium tert-butoxide (t-BuONa) as base (so that the only source of methanol/methoxide was the added methanol) and equal amounts of CH 3 OH and CD 3 OD (see Scheme 5 for detailed reaction conditions). The crude product was analysed via GC-MS spectroscopy.
The analysis of the [MÀ OMe] + fragment of MMA (peaks at 69, 70 and 71 m/z respectively depicted in Figure 2), showed that the methylene group contained zero (56.3 %), one (23.0 %) or two (20.7 %) deuterium atoms. By assuming that the contribution of the non-deuterated species to the peak at 70 m/z is negligible, these percentages could be used to determine the ratio of [MMA : (MMA-d + MMA-d 2 )] that directly equates to a kinetic isotope effect (k H /k D ) of 1.3 for the dehydrogenation pathway under study. This result is in good agreement with the computed values (as obtained from free energies of activation, see Table 2), which are 1.3 for pathway H and 1.9 for pathway C [13a] (see Table 2), i. e. considering either 22 or 1b as pre-catalyst, respectively.
Such very small H/D KIEs typically arises from isotopic substitution at a bond that does not undergo cleavage during the rate-determining step (secondary kinetic isotope effect), [18] in good accordance with our DFT results where the highest barrier corresponds to the partial decoordination of the formaldehyde product, while much larger values of the order of 6 or more denote the breaking or formation of CÀ H bonds in the rate-determining step.

II. DFT investigations on hypothetical CO 2 evolution catalysed by 22
In this section, we explore the possibility of 22 to catalyse CO 2 formation from methanol. For the WGSR part, a stoichiometric amount of water would be needed, which, under the strongly basic conditions, would be deprotonated to afford hydroxide (cf. eq 4, driving force computed at the B97-D2/ECP3 level). In the original Cole-Hamilton system NaOH was added as base directly, [12] therefore we will use OH À as reactant in our study.
We considered three catalytic cycles, labelled Cycle-1, Cycle-2 and Cycle-3 (see Scheme 6), all affording hydrogen and carbon dioxide via the following overall reaction (with ΔG computed at the ECP3 level): We first investigate the WGSR (pathway I), that would allow closing of the overall catalytic cycle for the full decomposition of methanol (see step iii. of Cycle-1 in Scheme 6), as expected in the case of ethanol dehydrogenation catalysed by [Rh(bipy) 2 ] Cl 2 . [9] Next, we considered the GDP mechanism, where the nucleophilic attack of the base takes place at the coordinated HCHO rather than at the carbonyl ligand (pathways J A -J B and J' A -J' B ). In the production of MMA from methanol and methylpropanoate (MEP) catalysed by 22, deprotonated MEP is proposed to attack coordinated formaldehyde in the presence of coordinated CO. 13

Water gas shift reaction (WGSR) involving 22 (pathway I)
From the base and any traces of water that might be present, OH À would form, which, after nucleophilic attack at the CO ligand could afford a metallacarboxylic acid intermediate that  eventually releases CO 2 . Such reactivity is well-known for parent Ru carbonyl complexes, [19] and is considered herein in the present system. Such OH À attack on 22 would afford 38 ( Figure 3a). After decarboxylation and protonation, neutral 1b could be re-formed, re-connecting to the dehydrogenation cycles promoted by this catalyst. A variety of pathways were trialled computationally to investigate the possibility of an intramolecular transfer of the À COOH hydrogen to the metal (see discussion on paths I a , I b and I c in section II.3 in the ESI, and related Figure S2 and Table S4), but such processes turn out to be less favourable than the solvent-mediated proton transfers shown in pathway I (Figure 3). This feature points to a low acidity of 38, in keeping the wide range of pK a observed for hydroxycarbonyl complexes, depending on the nature of the metal and of ancillary ligands. [20] Surprisingly, this route turned out to be extremely endergonic with a prohibitively high barrier (ΔG � [22!TS 40-41 ] is 191.9 kJ/mol at the ECP2 level and 184.5 kJ/mol at the ECP3 level; see Figure 3c and Table 1, respectively). The main reason is that the initial uptake of OH À to form the metalla-acid 38 is highly unfavourable (ΔG = 152.0 kJ/mol; see Figure 3 and Table S3), with the barriers of the subsequent steps adding to the overall kinetic hindrance. Considering that "naked" OH À might only be poorly described by a continuum model, we explored adding explicit MeOH solvent molecules or a counterion, Na + in this case (see Sections II.2 and II.3 in the ESI, and related Figure S3 and Table S5). The latter proved to have a stabilizing effect on the energetics of the initial nucleophilic attack, but even in this case (i. e. using NaOH as nucleophile), the resulting intermediate 38 . Na + is still endergonic by 95.5 kJ/ mol (light grey curve in Figure 3c). If a similar stabilisation by counterions of ca. 32.2 kJ/mol would apply to all subsequent steps, the overall barrier via TS 40-41 would still exceed 150 kJ/ mol. As this stabilisation by the counterion in form of contact ion pairs is likely to be overestimated in these model complexes (in solution solvent-separated ion pairs with rather weaker cation-anion interactions are to be expected), it appears that the hypothesised WGSR is not viable, in accord with the lack of CO 2 evolution occurring with 22 as catalyst. [9] Also, taking together pathways C, G and I to give Cycle-1 (see Scheme 6), the overall free energy span is as high as 207.6 kJ/mol (see Table 1), thus indicating that the full decomposition of methanol should not be achievable via this route.

Full decomposition of methanol following the Gem-Diolate Pathway (GDP): Cycle-2.
Inspired by recent studies of Beller and co-workers, [10] we investigated another possibility to afford CO 2 and H 2 from methanol, via the formation of a gem-diol intermediate, as schematically described in Scheme 2. Again, complex 22 could be a starting point of a such mechanism, and could afford complex 35, in which HCHO is π-coordinated to the metal, i. e. following the first steps of pathway H (see Figure 1). Then, OH À attack on the coordinated HCHO could be envisaged, to afford the dianionic gem-diolate intermediate 43 (see Figure 4). After  Figure 4). Subsequent CO 2 evolution proceeds via pathway J B (see Figure 5), and requires a prior reorganisation of the formato ligand, where concerted RuÀ O bond breaking and RuÀ H coordination afford 49 via TS 48-49 . CO 2 release takes place via elongation of the HÀ C bond, up to full dissociation. This process follows the reverse reaction sequence reported in reference [21] in the case of CO 2 hydrogenation to formic acid. The resulting complex 50 is a "nonclassical" pentahydride, from which H 2 decoordinates to afford 37. The following reaction steps, regenerating complex 22, are identical to those previously described in Pathway H (see Figure 1).
The reaction profiles computed for these two pathways (J A and J B ) indicate that OH À uptake is again enderogonic (by 37.0 kJ.mol À 1 ; see Figure 4), and so are the subsequent H 2 dissociation and β-H transfer steps. Conversely, proton exchange from 46 to afford 48 is significantly exergonic (by 123.2 kJ.mol À 1 ). Calculations at the ECP3 level (see Table 1) show that the overall activation barrier for Cycle-2 is 166.1 kJ/ mol, and corresponds to loss of H 2 from 44. As a result, this pathway should not be viable kinetically, indicating that 22 is little active for full methanol decomposition via a GDP mechanism (Cycle-2). The analogous pathway Cycle-2', involving isomers, is computed even less favourable (see paths J' A and J' B in the SI, in Figures S4-S5 and Table S6), with an overall activation barrier of 180.2 kJ/mol (see Table 1).

III. Full decomposition of methanol involving dicarbonyl complexes as intermediates (Cycle-3)
Taking together that the decoordination of HCHO from complex 35 in pathway H (or 35 ax in pathway H') is both kinetically and thermodynamically difficult (they are the intermediates right before the rate-limiting barrier), and that a new decarbonylation reaction may be envisaged at this stage, we investigated the possibility that dicarbonyl complexes could be involved to potentially catalyse the formation of CO 2 .
The resulting pathway (referred to as Cycle-3 in the following) is composed of three parts (namely, H, G CO and I CO ; see Scheme 6), and would allow for full decomposition of  Table S6.

ChemCatChem
Full Papers doi.org/10.1002/cctc.202000159 methanol. The latter are fully described in Supporting Information (see section II.5 and Figures S6-S10 and Table S7). For the complete cycle, 55 is indicated to be the TOF-determining intermediate (according to Shaik's energy span analysis), [22] and the highest point (the TOF-determining transition state) is formation of the acyl intermediate on the decarbonylation leg G CO (via TS 51-52 ). This raises the total energy span for Cycle-3 to 208.1 kJ/mol (Table 1). The energy span of the analogous mechanism involving H', G' CO and I ' CO (labelled Cycle-3') is similar, albeit slightly smaller (197.2 kJ/mol, see Table 1). Thus, the full decomposition of methanol via these routes should be very slow, indicating that 22 should not be very active for that process in the present catalytic system.

Discussion and Conclusions
We report a comprehensive DFT study of the reactivity of 22 in the context of H 2 generation from methanol. Its potential role in dehydrogenation, decarbonylation and water gas shift have  Table S6.

ChemCatChem
Full Papers doi.org/10.1002/cctc.202000159 been carefully investigated. We have presented detailed reaction pathways for these processes, thus completing further the overall picture of the reactivity of this system. [13] First, DFT calculations, supported by KIE measurements, show that partial dehydrogenation of methanol can effectively be catalysed by 22. The activity of 22 as catalyst should be very similar to that of 1b, as comparable overall activation barriers are obtained for the two corresponding mechanisms (in the range of ca. 112-131 kJ/mol; compare C and H in Table 1). Interestingly, dissociations of phosphine ligands are key steps in pathways C and H, so that bis-and mono-phosphine complexes are predicted to be active species. Phosphine dissociation processes are generally reasonably endergonic (e. g. 52.3 kJ/mol for PPh 3 dissociation from 22, whereas PPh 3 dissociation from 32 is slightly exergonic, by À 9.7 kJ/mol, because it is concomitant to a reorganisation of the first coordination sphere of Ru), resulting in the formation of di-and mono-phosphine intermediates. This feature is reminiscent of previous DFT studies where, e. g. low-ligated Pd(0), possessing a single phosphine as ancillary ligand, are predicted to be the active species, undergoing oxidative addition reactions. [23] Also, a direct comparison between catalytic cycles involving either mono-or bis-ligated triphenylphosphine-rhodium complexes has been reported for the parent hydroformylation reaction, showing that mono-phosphine complexes are more active. [24] When 22 is considered as (pre)catalyst, the decarbonylation reaction (following pathway G CO ) is found to be competitive to dehydrogenation (111.2 kJ/mol vs 115.7 kJ/mol for dehydrogenation via H' and decarbonylation via G CO , see Table 1). A similar feature was obtained in our previous study (involving 1b as precatalyst). [13b] The latter reaction affords dicarbonyl complexes, namely the anionic trihidride 55 and the neutral dihydride 58. Both are found to be relatively low-lying intermediates on the reaction profile (see Figure S6 and initiation Free energies reported in Table 1). We note that ruthenium(II) diphosphine dicarbonyl complexes can be readily synthetized and characterized by IR spectroscopy. [25] Additionally, the intermediacy of di-and tri-carbonyl complexes has been proposed, recently, in the dehydrogenation of formic acid. [26] However, such di-(or tri-)carbonyl complexes are not detected experimentally (under turnover conditions) in the system studied herein, presumably because the formation of 58 and 58 ax from 22 exhibit only very small driving forces (namely, À 13.9 kJ/mol and À 6.8 kJ/mol, respectively, see Table 1). As a result, there is no "thermodynamic sink" corresponding to their formation, and the latter complexes are therefore expected to be present in very low concentration. In contrast, a strong driving force was obtained for the formation of 22 from 1b (À 84.5 kJ/mol, via 1b + MeOH!22 + 3 H 2 ). [13b] 22 is therefore expected to be more populated than 58 (or 58 ax), so that its characterisation becomes achievable. However, the catalytic activity of these low-coordinated phosphine complexes for full methanol dehydrogenation is found to be too low (vide infra).
We have investigated two WGSR pathways, starting either from the mono-carbonyl (namely 22; see pathway I) or dicarbonyl complexes (namely 58; see Pathway I CO ). Significantly higher barriers are computed for these processes compared to dehydrogenation and decarbonylation. We found that the main factor preventing the reaction is a large thermodynamic hindrance for OH À attack on the coordinated CO, which is the very first step of the WGSR. Uptake of OH À by 22 and 58 is predicted to be endergonic by 152.0 kJ/mol and 90.2 kJ/mol, respectively (Figures 3 and S8, respectively). As a result, the WGSR reaction could not be achieved in this system, even though it is well known in parent Rh [9] or Ru [19] complexes. Some of us recently showed that the formation of metallacarboxylic acids through OH À attack on [L n M(CO)] complexes (M = Fe, Ru, Os, and L = CO, PMe 3 , PF 3 , py, bipy, Cl, H) can exhibit a large span of driving forces (ΔG = À 144 kJ/mol to + 122 kJ/mol). [27] The π-acidity of the co-ligands has been recognized as a key factor in the process, and the more electron-withdrawing ligands were predicted to favour OH À uptake. [27] Because the WGSR pathways are unfavourable, the resulting cycles for full dehydrogenation of methanol and water, Cycle-1 or Cycle-3 (Scheme 6), have prohibitively high overall activation barriers (between 197.2 and 208.1 kJ/mol, see values for Cycle-1, Cycle-3 and Cycle-3' in Table 1). The similar barriers observed between Cycle-1 and Cycle-3 indicates that substituting PPh 3 by CO in the precatalyst is not beneficial for the process.
Nucleophilic attack at coordinated HCHO (e. g. in 35) is not kinetically viable either, so that CO 2 evolution via a gem-diolate intermediate (namely 43), as anticipated in other Ru complexes, [10] could not be expected as well. Our DFT results are therefore consistent with the lack of CO 2 evolution with (pre)catalysts 1b and 22. We note, however, that the overall cycle for full methanol dehydrogenation has a significantly lower overall barrier when involving such a GDP route (Cycle-2 in Scheme 6, overall barrier 166.1 kJ/mol, see Table 1) as compared to cycles involving WGSRs (Cycle-1 and Cycle-3, overall barriers exceeding 197 kJ/mol, see Table 1). If, through appropriate ligand design, the barrier of the GDP route could be lowered by some 30 kJ/mol without compromising the viability of the dehydrogenation pathways, a one-pot catalyst for full methanol dehydrogenation based on the Cole-Hamilton system might be within reach. Calculations along these lines are in progress.
To summarize, the new mechanistic insights presented herein emphasise the extreme complexity of this catalytic system, where many competitive reaction channels (including many "crossings" and, sometimes, "dead-ends") are encountered to afford H 2 generation. Our main results are: i) 22 should be active as a methanol dehydrogenation catalyst, and its activity should be comparable to that of 1b, as is observed experimentally. [11] Also, a detailed reaction mechanism for the process has been elucidated and is supported by KIE measurements. ii) The lack of CO 2 evolution in this system has been rationalised by the fact that neither coordinated CO nor HCHO ligands are electrophilic enough to undergo attack by the base (OH À ). As a result, neither WGSR nor GDP reactions are viable. As a result, the full decomposition of methanol, as schematically described in Scheme 2, cannot be achieved with the original, Cole-Hamilton catalyst, in keeping with experimental findings. [9] We hope that this study will stimulate further development of this interesting system, including the rational design of new ligands, and further theoretical and experimental mechanistic studies. Beyond the case of the Ru/PPh 3 complexes presented here, our results may also be useful better to understand the reactivity of analogous dehydrogenation catalysts, [2][3] that may exhibit similar reactivity.

General materials, methods and instruments
All manipulations and reactions were carried out under N 2 gas (dried through a Cr(II)/silica packed glass column) using different techniques including a standard Schlenk, vacuum line and a glove box. Solvents were dried and degassed prior to use. [RuH 2 (CO) (PPh 3 ) 3 ] (22), t-OBuNa, methanol, methanol-d 4 and tert-butyl propanoate were purchased from Sigma-Aldrich. tert-Butyl propanoate was dried over Na 2 SO 4 and distilled under dinitrogen. Na 2 CO 3 (anhydrous) was purchased from Fisher Scientific.
Toluene was dried using a Braun Solvent Purification System. Methanol was dried and degassed by distillation from magnesium under dinitrogen. All gases were purchased from BOC gases.

Determination of KIE's
A Hastelloy™ autoclave was fitted with a magnetic stirrer and charged under a dinitrogen atmosphere with catalyst 1 (0.124 g, 0.135 mmol) and t-BuONa (2.6 g, 27.0 mmol). Toluene (10 mL) and t-BuP (15.64 mL, 103.9 mmol) were added through the injection port together with methanol (3.8 mL, 93.5 mmol), methanol-d 4 (3.8 mL, 93.5 mmol) and 2,4-dimethyl-6-tert-butylphenol (Topanol A, 0.01 mL, in order to prevent MMA polymerisation). The autoclave was sealed, pressurised with ethene (6 bar) and heated to 170°C for 3 hours. The autoclave was then cooled to room temperature, vented to the atmosphere and the obtained product mixture analysed by GC-MS spectroscopy.

Computational Details
The exact same computational protocol as in our two previous studies has been employed herein. [13] The latter has been previously described and validated. [28] Briefly, geometry optimizations are performed at the BP86 level with a medium-sized basis set, then energies are refined with a larger basis set and a dispersioncorrected functional [29] in order to account for the critical noncovalent interactions involved when bulky ligands are considered. [30] This protocol has been successfully employed to model catalytic systems involving Ru [13] and Rh [31] complexes with voluminous triphenylphosphine ligands. We also performed additional methodological tests herein to further validate our protocol (see Section IV in Supporting Information). Briefly, the following steps are involved:

Geometries and thermodynamic corrections
Geometries of all complexes were fully optimized at the RI-BP86/ ECP1 level, i. e. employing the exchange and correlation functionals of Becke [32] and Perdew, [33] respectively, in conjunction with the SDD basis on Ru, denoting the small-core Stuttgart-Dresden relativistic effective core potential (ECP) together with its valence basis set, [34] and the standard 6-31G(d,p) basis for all other elements, except for the carbon and hydrogen atoms of the phenyl rings for which a smaller 3-21G basis set were employed, and suitable auxiliary basis sets for the fitting of the Coulomb potential. [35] Harmonic frequencies were computed analytically and were used without scaling to obtain enthalpic and entropic corrections at the experimentally used temperature of 150°C. [12] The corresponding correction terms δE G were estimated at the RI-BP86/ECP1 level and have been obtained as the difference of the reaction energy of a given step (ΔE RIÀ BP86/ECP1 ) and the corresponding free energy (ΔG RIÀ BP86/ECP1 ), Eq. (6): The entropic contributions have been evaluated at a pressure of 1354 atm in order to model the changes in entropy for a condensed phase. [36] This approach has been validated in Ref, [28] where we showed that such an increased pressure allows for the modelling of binding entropies in CH 2 Cl 2 in excellent accord with the experiment. The corresponding correction terms (δE G ) for each step of the catalytic cycles are gathered in Tables S1 and S3-S7 along with other correction terms (vide infra).
The transition states (denoted TS xÀ y ) were characterized by a single imaginary frequency and visual inspection of the corresponding vibrational mode ensured that the desired minima x and y were connected. The reaction pathways have been investigated more closely by following the Intrinsic Reaction Coordinate (IRC) [37] starting from TS xÀ y and leading to the intermediates x and y.
The initial structures of the complexes were constructed by hand and were derived from structures stemming from our previous studies, [13] following the reaction path.

Refined energies
Refined energies were obtained from single-point calculations (on the RI-BP86/ECP1 geometries) using the same SDD ECP on Ru [34] and a larger basis set (hereafter noted ECP2), namely 6-311 + G(d,p), on all elements except for the carbon and hydrogen atoms of the phenyl rings, for which the 6-31G(d,p) basis set was used. The refined energies are computed with the B97-D2 functional, [29] that follows the DFTÀ D2 general approach of Grimme, [29,38] in which the functional energies are corrected by an atomic pair-wise additive term accounting for the long-range non-covalent interactions. B97-D2 has been successfully employed to study Ru [13,39] and Rh [31,40] catalysed reactions, and has been recently shown to perform well at describing several "bulky" transition metal-complexes. [41] Energies have been corrected for the basis set superposition error (BSSE) using the counterpoise method. [42] The BSSE energy corrections are noted δE BSSE . Estimates of the solvation effects were computed using the Conductor-like screening model (COSMO), [43] with a dielectric constant ɛ = 32.63 to model the experimentally used methanol solvent. [12] The δE solv energy correction is defined as the difference between the reaction energy in the continuum (including the outlaying charge correction; [44] noted ΔE COSMO ) and in the gas phase (ΔE), at the B97-D2/ECP2 level, Eq. (7):