Mechanism of the Facile Nitrous Oxide fixation by Homogeneous Ruthenium Hydride Pincer Catalysts

Solving ozone depletion and climate change problems requires the development of effective methods for sustainably curbing them. With this aim, Milstein and co-workers developed a PNP pincer ruthenium catalyst for the homogeneous hydrogenation of nitrous oxide (N2O), an ozone-depleting substance and the third most important greenhouse gas, to generate dinitrogen and water as resultant products. The mechanism of this promising transformation was unveiled by means of experiments together with density functional theory (DFT) calculations, which inspired Milstein and co-workers to use similar (PNN)Ru-H pincer catalysts for the reduction of N2O by CO to produce N2 and CO2. The use of the latter type of catalysts resulted in the proposition of a new reaction protocol and allowed to work under milder conditions. Here we describe the detailed mechanism of the last transformation catalyzed by a (PNN)Ru-H catalyst by means of DFT calculations, and not only this, but we also discover the way to block undesired parasitic reactions. Apart from that, we have explored a new evolution of this family of catalysts to go beyond previous experimental outcomes. The mechanism consists of a cascade of easy steps, starting from an insertion of the N2O oxygen into the Ru-H bond generating a hydroxo intermediate and releasing N2 and ending with a β-hydride elimination to form CO2 and regenerate the catalyst. The whole process occurs in a facile way with the exception of two steps: the formation of the hydroxyl ligand and the final β-hydride elimination to form CO2. However, the energy barriers of these two steps are not the bottleneck in the catalysis but rather the ease of the pyridyl group bonded to Ru to isomerize by C-H activation. We propose to solve this drawback by tuning the PNN ligand to block the pyridyl free rotation.


I.
Isomerization Analysis

I. Isomerization Analysis
The initial geometries for the complexes 5, 7 and 8 were obtained from the crystallographic information file provided in the supporting information of the experimental work of D. Milstein and coworkers (J. Am. Chem. Soc. 2018, 140, 7061-7064). In that work, they provided 2 isomers, E1 and E2, of complex 5, the corresponding form E1 of complex 7 and E2 isomer of complex 8 (see Figure S1). Therefore, our first step before starting the study of the catalytic cycle was to determine the relative stability of the two isomers for different species involved in the catalytic cycle A and B (Figure and Tables S1).
Figure S1. Intermediates 5-8, 10 and 10' of the PNN-pincer Ru based catalysts involved in the oxidation of CO by N2O, in two isomeric forms, E1 and E2. Table S1. Relative Gibbs energies (in kcal/mol) of the intermediates depicted in Figure S1 for the CO oxidation by N2O homogeneously catalyzed by ruthenium complex, referred to the initial intermediate 6+CO+N2O E2. All data shown were calculated at T = 70 ºC, using solvent corrections (solvent: THF) and M06-L/cc-pVTZ~sdd//BP86-D3BJ/SVP~sdd level of theory. We found that, the differences between isomers were smaller than 1 kcal/mol for most of the intermediates. Same results were suggested by the experimental evidences, since in previous work they obtained E1 and E2 X-ray structures. Therefore, we can assume that both isomers will be present in the media during the catalytic process. Moreover, they do not present large structural differences, thus we decided to study the hole process just for the E2 form in order to simplify the study. Figure S3. Reaction profile of the full mechanism for N2O reduction catalyzed by Ru-H pincer 8 following cycle B (relative Gibbs energies for THF media in kcal/mol and referred to catalyst 6+CO+N2O, and P = P(tBu2)). All data shown were calculated at T = 70 C using M06-L/cc-pVTZ~sdd//BP86-D3BJ/SVP~sdd level of theory. Figure S4. Optimized geometry at the BP86/SVP~sdd level of theory of the intermediate 13+THF.

III. Test of other Catalysts and Reaction Conditions
As we mentioned in the main manuscript, we have experimental results from previous work done by Milstein and coworkers, and we know the TONs for catalysts 2-5 and 15 in toluene at 100 °C. Even the best reactions conditions found experimentally were the ones used for the main study (solvent = THF at 70 °C), the previously mentioned catalyst were not tested in the laboratory using these conditions. Therefore, in order to be coherent with the experimental data we have computed the Gibbs energies of the crucial intermediates of the cycle at these conditions, the results obtained are presented in Table S2.    Figure S6. Schematic Reaction profile for the catalysis together with the isomerization from 7 to 8 with the differences between intermediates and TS of the main steps. The names of the barriers correspond to the ones in Table S4. S7 Table S4. Gibbs free energy barriers of the main steps for the CO oxidation by N2O catalyzed by ruthenium hydride complex. Energies in kcal/mol for all the steps shown in Figure S6. All data shown were calculated at T = 70 °C using THF as solvent with the exeption of (a) that were calculated at T = 100 °C using toluene as solvent.
catalyst 7-9 7-10+H2O 9-10+H2O 7-10 9-10 10-11axial  Figure S7. Comparison of the key steps in the CO oxidation by N2O catalyzed by different Ru-H pincer catalysts, substituted with -OMe and -CF3 (relative Gibbs energies for THF media at 70 C in kcal/mol and referred to the complex equivalent to catalyst 6+CO+N2O, and P = P(tBu2)).  Figure S8. Comparison of the isomerization process from 7 to 8 using different -OMe and -CF3 substituted Ru-H pincer catalysts (relative Gibbs energies for THF media at 70 C in kcal/mol and referred to the complex equivalent to catalyst 6+CO+N2O, and P = P(tBu2)).

IV. Effective Oxidation State Analysis and Atomic Charges
The effective oxidation state (EOS) analysis allowed us to compute the oxidation state (OS) of the Ru and the ligands. In the EOS method, effective atomic orbitals (eff-AOs), with their respective occupations are computed. To get the OS of each fragment, the electrons are assigned to the eff-AOs used to assign the electrons to the fragments with eff-AOs in order to get the OS. More information about the EOS method can be found in the corresponding references cited in the computational details section of the main manuscript.
According to the calculations, the OS of the Ru is +2, the CO ligands are 0, and the hydride and the pincer are -1 each, in both intermediates (7 and 8), this assignation its clear with a R% larger than 60% (Tables S5 and S6). Even though, some differences between intermediates 7 and 8 can be appreciated if we divide the pincer ligand in different fragments (fragments 5, 6, 7 and 8 in Figure S9). In the case of intermediate 7, the reduced part of the pincer, whit an OS of -1, is the side ring while in intermediate 8, the central ring has an OS of -2 and the phosphine (fragment 8) ligand is +1. This is a surprising result taking into account that in complex 8 the lateral ring is coordinated to the metal trough the C, so we expected this fragment to have an OS of -1 in this case. However, it has to be noted that for this Ru-H pincer complexes, especially if we want to separate the PNN into different fragments, the assignation of the electrons is not clear. The difference in occupation number between the last occupied and first unoccupied eff-AOs, and , is small, in the case of system 7, the las electron was assigned to fragment 5, with of 0.466 having a small difference of just 0.055 with the of the C bridge (fragment 7). This also gives a low reliability index values close to 55% 1 in the cases that the PNN is fragmented. The latter values can be better understood if we look at the shape of the eff-AOs depicted in Figures  10 and 11, we can observe that the last electron pain assigned in intermediate 7 went to an orbital placed in the C-C bond joining the pyridyl rings of the pincer, and the first unoccupied orbital is an s-type like orbital of the P. In the case of intermediate 8, Figure S9. Fragments selected for the EOS and charge calculations, with the corresponding labels.
In the external ring of the PNN ligand X = N, CH or C. Table S5. Alpha electrons, occupation number of last occupied and first unoccupied eff-AOs ( and , respectively) and Effective Oxidation State (EOS) for the fragments depicted in Figure S9 in intermediate 7. The reliability index R(%) of the EOS assignment for each calculation are also given. This is a closed-shell singlet, thus, alpha and beta frontier eff-AOs are equivalent (beta results are omitted). Table S6. Alpha electrons, occupation number of last occupied and first unoccupied eff-AOs ( and , respectively) and Effective Oxidation State (EOS) for the fragments depicted in Figure S9 in intermediate 8. The reliability index R(%) of the EOS assignment for each calculation are also given. This is a closed-shell singlet, thus, alpha and beta frontier eff-AOs are equivalent (beta results are omitted).  Figure S11. Eff-AOs ( and ) with occupation numbers between 0.200 and 0.700 in intermediate 8. The orbitals were obtained from a calculation considering fragments 1, 2, 3, 4, 5 and a last fragment grouping 6, 7 and 8, having an R% = 57.7. Table S7. Corresponding 3-D space and Mulliken electron populations and charges for the fragments depicted in Figure S9 Table S8. Corresponding 3-D space and Mulliken electron populations and charges for the fragments depicted in Figure S9 in intermediate 8.

V. Aromaticity analysis of the pincer ligand.
A part from the HOMA and EDDB aromaticity measures that we presented in the main manuscript we also checked the aromaticity by means of FLU, PDI, MCI and Iring electronic indices. We wanted to characterize the aromaticity of the pincer ligand in their different coordination, through the N (PNN) or the C of the external ring (PNC). For this reason, we analyzed the aromaticity in the two 6-member rings (MR) present in the ligand and the two 5-MR that are formed after the coordination to the metal, all of them shown in Figure S12. The results of the different aromaticity indices can be interpreted as following. On the one hand, in the case of indices based on references (HOMA and FLU), the maximum aromaticity is achieved when the system resembles more the references molecules, i.e. benzene for C-C or pyridine for C-N bonds. In the case of HOMA the maximum aromaticity is achieved at a value of 100, while in FLU, the closer the value to zero the more aromatic the compound is. The fact that these indices are based on references suppose a drawback in this case, since we do not have references for Ru-C, Ru-N, and Ru-P bonds, thus we cannot compute the aromaticity of rings III and IV. On the other hand, we have the multicenter indices PDI, Iring, and MCI, which measure the delocalization without using references. In the three cases, high positive values (close to those obtained for pyridine in the case of the 6-MR) will be indicative aromatic character, whereas smaller values will correspond to non-aromatic species. It has to be noted that in the case of PDI, just the delocalization between atoms situated in the para positions is taken into account, therefore this index just cab be measured for 6-MRs. Table S9. HOMA, FLU, PDI, Iring and MCI aromaticity results (in a.u.) of the studied intermediates 7, 13, 14 and 8 systems. Taking into account the 6 and 5-member rings depicted in Figure S12.

S14
Finally, we used the EDDB method which provides both visual and quantitative results. The visual results are the EDDB(r) isosurfaces, which in the case of having delocalized electrons (aromaticity) we will observe a continuous thick surface, like the one observed for pyridine in Figure S13 or for the 6-MRs of the ruthenium complexes in Figure 3b in the main manuscript, while in the case of non-aromatic this surface will have discontinuities. Then we also have the number of delocalized electrons, which together with the Hückel and Baird rules can tell us if the compound is going to be aromatic or not (e.g. for benzene and pyridine we expect 6 delocalized electrons).  S15 VI. Egas, Ggas, Esolv., Gsolv. and frequencies Table S11. Egas and Ggas at BP86-D3BJ/SVP~sdd level of theory, Esolvent at M06-L/cc-pVTZ~sdd level of theory and Gsolvent computed as Ggas -Egas + Esolvent all of them in Hartree for the compounds involved in cycle A and the isomerization process from 7 to 8 starting from catalyst 6. Number of negative frequencies found for each optimized structure at BP86-D3BJ/SVP~sdd level of theory, and the corresponding frequency in the cases when there is a negative one (frequencies in cm -1 ).  Table S13. Egas and Ggas at BP86-D3BJ/SVP~sdd level of theory, Esolvent at M06-L/cc-pVTZ~sdd level of theory and Gsolvent computed as Ggas -Egas + Esolvent all of them in Hartree for the compounds involved in the main steps of catalyzed reduction of N2O and the isomerization process of the catalyst starting from system P(iPr)2 (4). Number of negative frequencies found for each optimized structure at BP86-D3BJ/SVP~sdd level of theory, and the corresponding frequency in the cases when there is a negative one (frequencies in cm -1 ).  Table S14. Egas and Ggas at BP86-D3BJ/SVP~sdd level of theory, Esolvent at M06-L/cc-pVTZ~sdd level of theory and Gsolvent computed as Ggas -Egas + Esolvent all of them in Hartree for the compounds involved in the main steps of catalyzed reduction of N2O and the isomerization process of the catalyst starting from system P(CH3)2.
Number of negative frequencies found for each optimized structure at BP86-D3BJ/SVP~sdd level of theory, and the corresponding frequency in the cases when there is a negative one (frequencies in cm -1 ).  Table S15. Egas and Ggas at BP86-D3BJ/SVP~sdd level of theory, Esolvent at M06-L/cc-pVTZ~sdd level of theory and Gsolvent computed as Ggas -Egas + Esolvent all of them in Hartree for the compounds involved in the main steps of catalyzed reduction of N2O and the isomerization process of the catalyst starting from system P(CF3)2. Number of negative frequencies found for each optimized structure at BP86-D3BJ/SVP~sdd level of theory, and the corresponding frequency in the cases when there is a negative one (frequencies in cm -1 ).  Table S16. Egas and Ggas at BP86-D3BJ/SVP~sdd level of theory, Esolvent at M06-L/cc-pVTZ~sdd level of theory and Gsolvent computed as Ggas -Egas + Esolvent all of them in Hartree for the compounds involved in the main steps of catalyzed reduction of N2O and the isomerization process of the catalyst starting from system external o-CF3. Number of negative frequencies found for each optimized structure at BP86-D3BJ/SVP~sdd level of theory, and the corresponding frequency in the cases when there is a negative one (frequencies in cm -1 ).  Table S17. Egas and Ggas at BP86-D3BJ/SVP~sdd level of theory, Esolvent at M06-L/cc-pVTZ~sdd level of theory and Gsolvent computed as Ggas -Egas + Esolvent all of them in Hartree for the compounds involved in the main steps of catalyzed reduction of N2O and the isomerization process of the catalyst starting from system external p-CF3. Number of negative frequencies found for each optimized structure at BP86-D3BJ/SVP~sdd level of theory, and the corresponding frequency in the cases when there is a negative one (frequencies in cm -1 ).  -1924.236348 -1923.882353 -1925.483207 -1925.129211 0 -Intermediate: 11equatorial -1924.246516 -1923.889382 -1925.487882 -1925.130748 0 -TS: 11equatorial-6 -1924.196266 -1923.846646 -1925.437278 -1925 -1924.240282 -1923.886416 -1925.488143 -1925.134276 0 -Intermediate: 11equatorial -1924.249924 -1923.892320 -1925.492466 -1925.134862 0 -TS: 11equatorial-6 -1924.199615 -1923.849926 -1925.441798 -1925 Table S19. Egas and Ggas at BP86-D3BJ/SVP~sdd level of theory, Esolvent at M06-L/cc-pVTZ~sdd level of theory and Gsolvent computed as Ggas -Egas + Esolvent all of them in Hartree for the compounds involved in the main steps of catalyzed reduction of N2O and the isomerization process of the catalyst starting from system p-CF3. Number of negative frequencies found for each optimized structure at BP86-D3BJ/SVP~sdd level of theory, and the corresponding frequency in the cases when there is a negative one (frequencies in cm -1 ).  Table S20. Egas and Ggas at BP86-D3BJ/SVP~sdd level of theory, Esolvent at M06-L/cc-pVTZ~sdd level of theory and Gsolvent computed as Ggas -Egas + Esolvent all of them in Hartree for the compounds involved in the main steps of catalyzed reduction of N2O and the isomerization process of the catalyst starting from system external o-OMe. Number of negative frequencies found for each optimized structure at BP86-D3BJ/SVP~sdd level of theory, and the corresponding frequency in the cases when there is a negative one (frequencies in cm -1 ).  Table S21. Egas and Ggas at BP86-D3BJ/SVP~sdd level of theory, Esolvent at M06-L/cc-pVTZ~sdd level of theory and Gsolvent computed as Ggas -Egas + Esolvent all of them in Hartree for the compounds involved in the main steps of catalyzed reduction of N2O and the isomerization process of the catalyst starting from system external p-OMe. Number of negative frequencies found for each optimized structure at BP86-D3BJ/SVP~sdd level of theory, and the corresponding frequency in the cases when there is a negative one (frequencies in cm -1 ).  Table S22. Egas and Ggas at BP86-D3BJ/SVP~sdd level of theory, Esolvent at M06-L/cc-pVTZ~sdd level of theory and Gsolvent computed as Ggas -Egas + Esolvent all of them in Hartree for the compounds involved in the main steps of catalyzed reduction of N2O and the isomerization process of the catalyst starting from system central p-OMe. Number of negative frequencies found for each optimized structure at BP86-D3BJ/SVP~sdd level of theory, and the corresponding frequency in the cases when there is a negative one (frequencies in cm -1 ).  Table S23. Egas and Ggas at BP86-D3BJ/SVP~sdd level of theory, Esolvent at M06-L/cc-pVTZ~sdd level of theory and Gsolvent computed as Ggas -Egas + Esolvent all of them in Hartree for the compounds involved in the main steps of catalyzed reduction of N2O and the isomerization process of the catalyst starting from system p-OMe. Number of negative frequencies found for each optimized structure at BP86-D3BJ/SVP~sdd level of theory, and the corresponding frequency in the cases when there is a negative one (frequencies in cm -1 ).  -1925- .683854 -1925- .269189 -1926- .903881 -1926- .489216 1 -52.0 Intermediate: 9 -1925- .714678 -1925- .295230 -1926- .941996 -1926.522548 0 -TS: 9- 10+H2O -200210+H2O - .086937 -200110+H2O - .651973 -200310+H2O - .367118 -200210+H2O - .932154 1 -544.8 TS: 9-10 -192510+H2O - .673560 -192510+H2O - .262351 -192610+H2O - .888406 -1926 -1929- .619435 -1929- .197996 -1930- .847614 -1930- .426175 0 -TS: 12-7 -1929- .547924 -1929- .134630 -1930- .770731 -1930 Table S27. Egas and Ggas at BP86-D3BJ/SVP~sdd level of theory, Esolvent at M06-L/cc-pVTZ~sdd level of theory and Gsolvent computed as Ggas -Egas + Esolvent all of them in Hartree for the compounds involved in the main steps of catalyzed reduction of N2O starting from system 16. Number of negative frequencies found for each optimized structure at BP86-D3BJ/SVP~sdd level of theory, and the corresponding frequency in the cases when there is a negative one (frequencies in cm -1 ).  Table S28. Egas and Ggas at BP86-D3BJ/SVP~sdd level of theory, Esolvent at M06-L/cc-pVTZ~sdd level of theory and Gsolvent computed as Ggas -Egas + Esolvent all of them in Hartree for the intermediates used (5, 6, 7, 8 10 and 10') in the conformational studies of the complex in section I of the SI. Number of negative frequencies found for each optimized structure at BP86-D3BJ/SVP~sdd level of theory, and the corresponding frequency in the cases when there is a negative one (frequencies in cm -1 ).  Table S29. Egas and Ggas at BP86-D3BJ/SVP~sdd level of theory, Esolvent at M06-L/cc-pVTZ~sdd level of theory and Gsolvent computed as Ggas -Egas + Esolvent all of them in Hartree for the reactants, products, salts and solvent molecules involved in the process. Number of negative frequencies found for each optimized structure at BP86-D3BJ/SVP~sdd level of theory, and the corresponding frequency in the cases when there is a negative one (frequencies in cm -1 ).