Mechanistic Studies of Oxygen-Atom Transfer (OAT) in the Homogeneous Conversion of N2O by Ru Pincer Complexes

As the overall turnover-limiting step (TOLS) in the homogeneous conversion of N2O, the oxygen-atom transfer (OAT) from an N2O to an Ru-H complex to generate an N2 and Ru-OH complex has been comprehensively investigated by density functional theory (DFT) computations. Theoretical results show that the proton transfer from Ru-H to the terminal N of endo N2O is most favorable pathway, and the generation of N2 via OAT is accomplished by a three-step mechanism [N2O-insertion into the Ru-H bond (TS-1-2, 24.1 kcal mol−1), change of geometry of the formed (Z)-O-bound oxyldiazene intermediate (TS-2-3, 5.5 kcal mol−1), and generation of N2 from the proton transfer (TS-3-4, 26.6 kcal mol−1)]. The Gibbs free energy of activation (∆G‡) of 29.0 kcal mol−1 for the overall turnover-limiting step (TOLS) is determined. With the participation of potentially existing traces of water in the THF solvent serving as a proton shuttle, the Gibbs free energy of activation in the generation of N2 (TS-3-4-OH2) decreases to 15.1 kcal mol−1 from 26.6 kcal mol−1 (TS-3-4). To explore the structure–activity relationship in the conversion of N2O to N2, the catalytic activities of a series of Ru-H complexes (C1–C10) are investigated. The excellent linear relationships (R2 > 0.91) between the computed hydricities (∆GH) and ∆G‡ of TS-3-4, between the computed hydricities (∆GH) and the ∆G‡ of TOLS, were obtained. The utilization of hydricity as a potential parameter to predict the activity is consistent with other reports, and the current results suggest a more electron-donating ligand could lead to a more active Ru-H catalyst.

Milstein and co-workers showed that a dicarbonyl PNN-Ru-H pincer complex (I, Scheme 1, PNN = 6-((di-tert-butylphosphino)methylene)-6H-[2,2 -bipyridin]-1-ide) could serve as an efficient catalyst in the homogeneous conversion of N 2 O and CO [31]. The dicarbonyl PNN-Ru-H complex (I, Scheme 1) catalyzed the conversion of N 2 O and CO to generate N 2 and CO 2 with a turnover number (TON) of up to 579 referenced to N 2 and 561 referenced to CO 2 after heating for 22 h at 70 • C. The overall mechanism of the conversion of N2O and CO by the Ru-H species includes: (1) the generation of N2 and a dicarbonyl Ru-OH complex (II, Scheme 1) via oxygen-atom transfer (OAT), (2) the formation of a dicarbonyl Ru-COOH complex (III, Scheme 1) via the intramolecular nucleophilic attack of OH on the nearby CO group, (3) the release of CO2 and the formation of a monocarbonyl Ru-H complex (IV, Scheme 1) via decarboxylation, and (4) the regeneration of the dicarbonyl PNN-Ru-H active species (I, Scheme 1) via the nucleophilic attack of a free CO. The generation of N2 via oxygen-atom transfer was proposed as the turnover-limiting step (TOLS), which was supported by the observation of a relatively fast formation of CO2 via an intramolecular reaction between the Ru-OH species and CO [31]. This experimentally established turnover-limiting step is also verified by computational studies [34][35][36].
It has come to our attention that the oxygen-atom transfer (OAT) between N2O and the Ru-H complex has not been fully investigated yet. Three categories of reactions between the N2O and Ru-H complex that need to be considered are: (1) the proton transfer from Ru-H to the terminal N of N2O (I, Chart 1), (2) the proton transfer from Ru-H to the terminal O of N2O (II, Chart 1), and (3) the hydride transfer from Ru-H to the central N of N2O (III, Chart 1). The generation of N2 via proton transfer and hydride transfer from Ru-H to N2O must be thoroughly evaluated and compared. Various transition states of proton transfer from Ru-H to N2O could be proposed, as induced by different geometries of N2O adduct (endo vs. exo isomer). The effect of the geometries of N2O (endo vs. exo isomer) in the oxygen-atom transfer (OAT) from N2O to Ru-H to generate N2 and Ru-OH must also be appropriately addressed.
Chart 1. Proton transfer (I and II) and hydride transfer (III) between Ru-H and N2O. The overall mechanism of the conversion of N 2 O and CO by the Ru-H species includes: (1) the generation of N 2 and a dicarbonyl Ru-OH complex (II, Scheme 1) via oxygen-atom transfer (OAT), (2) the formation of a dicarbonyl Ru-COOH complex (III, Scheme 1) via the intramolecular nucleophilic attack of OH on the nearby CO group, (3) the release of CO 2 and the formation of a monocarbonyl Ru-H complex (IV, Scheme 1) via decarboxylation, and (4) the regeneration of the dicarbonyl PNN-Ru-H active species (I, Scheme 1) via the nucleophilic attack of a free CO. The generation of N 2 via oxygen-atom transfer was proposed as the turnover-limiting step (TOLS), which was supported by the observation of a relatively fast formation of CO 2 via an intramolecular reaction between the Ru-OH species and CO [31]. This experimentally established turnover-limiting step is also verified by computational studies [34][35][36].
It has come to our attention that the oxygen-atom transfer (OAT) between N 2 O and the Ru-H complex has not been fully investigated yet. Three categories of reactions between the N 2 O and Ru-H complex that need to be considered are: (1) the proton transfer from Ru-H to the terminal N of N 2 O (I, Chart 1), (2)  The overall mechanism of the conversion of N2O and CO by the Ru-H species includes: (1) the generation of N2 and a dicarbonyl Ru-OH complex (II, Scheme 1) via oxygen-atom transfer (OAT), (2) the formation of a dicarbonyl Ru-COOH complex (III, Scheme 1) via the intramolecular nucleophilic attack of OH on the nearby CO group, (3) the release of CO2 and the formation of a monocarbonyl Ru-H complex (IV, Scheme 1) via decarboxylation, and (4) the regeneration of the dicarbonyl PNN-Ru-H active species (I, Scheme 1) via the nucleophilic attack of a free CO. The generation of N2 via oxygen-atom transfer was proposed as the turnover-limiting step (TOLS), which was supported by the observation of a relatively fast formation of CO2 via an intramolecular reaction between the Ru-OH species and CO [31]. This experimentally established turnover-limiting step is also verified by computational studies [34][35][36].
It has come to our attention that the oxygen-atom transfer (OAT) between N2O and the Ru-H complex has not been fully investigated yet. Three categories of reactions between the N2O and Ru-H complex that need to be considered are: (1) the proton transfer from Ru-H to the terminal N of N2O (I, Chart 1), (2) the proton transfer from Ru-H to the terminal O of N2O (II, Chart 1), and (3) the hydride transfer from Ru-H to the central N of N2O (III, Chart 1). The generation of N2 via proton transfer and hydride transfer from Ru-H to N2O must be thoroughly evaluated and compared. Various transition states of proton transfer from Ru-H to N2O could be proposed, as induced by different geometries of N2O adduct (endo vs. exo isomer). The effect of the geometries of N2O (endo vs. exo isomer) in the oxygen-atom transfer (OAT) from N2O to Ru-H to generate N2 and Ru-OH must also be appropriately addressed. In this contribution, the detailed reaction mechanism for the oxygen-atom transfer (OAT) from N 2 O to Ru-H in the conversion of N 2 O has been comprehensively investigated using density functional theory (DFT) computations. With the detailed reaction mechanism for the conversion of N 2 O to N 2 in hand (Figure 1), the turnover-limiting step for the conversion of N 2 O and CO by a series of Ru-H complexes (Chart 2) with different electrondonating and electron-withdrawing groups have been investigated to explore the structureactivity relationship, and the results provided here are the continuous efforts for the homogeneous conversion of N 2 O by the transition metal complex.
Inorganics 2022, 10, x FOR PEER REVIEW 3 of 12 In this contribution, the detailed reaction mechanism for the oxygen-atom transfer (OAT) from N2O to Ru-H in the conversion of N2O has been comprehensively investigated using density functional theory (DFT) computations. With the detailed reaction mechanism for the conversion of N2O to N2 in hand (Figure 1), the turnover-limiting step for the conversion of N2O and CO by a series of Ru-H complexes (Chart 2) with different electrondonating and electron-withdrawing groups have been investigated to explore the structure-activity relationship, and the results provided here are the continuous efforts for the homogeneous conversion of N2O by the transition metal complex.

Computational Methods
Full gas-phase geometry optimizations were performed using the method of B3LYP [37][38][39][40] [45,46] basis set and LANL2DZ effective core potentials (ECP) were used for Ru, the LANL2DZ(d,p) [45,47] basis set and LANL2DZ ECP were used for P, and the 6-31G(d') [48][49][50] basis sets were used for all other atoms (C, N, O, and H). In basis set 2 (BS2), the Ahlrichs Def2-TZVP [51,52] basis sets and related ECP were used for Ru, and TZVP [53] basis sets were used for all other atoms (C, N, O, P, F, and H). The Gaussian 16 default ultrafine integration grid, 2-electron integral accuracy of 10 −12 , and SCF convergence criterion of 10 −8 were used for all computations, and vibrational frequency computations were performed to verify the nature of all stationary points. All located transition states were obtained with only one imaginary frequency, and minima without any imaginary frequencies were obtained. The default rigid-rotor-harmonic-oscillator (RRHO) approximation was used to calculate the vibrational contribution to entropy. The intrinsic reaction coordinate (IRC) computations from the located transition states were performed, and both directions of the reaction path following the transition state were computed (see SI for the IRC plots) [54,55]. Gibbs free energies of activation (ΔG ‡ ) and free energies of reaction (ΔG°) were determined with standard conditions of 1 atm and 298. 15

Computational Methods
Full gas-phase geometry optimizations were performed using the method of B3LYP [37][38][39][40] with Grimme's D3 [41] [45,46] basis set and LANL2DZ effective core potentials (ECP) were used for Ru, the LANL2DZ(d,p) [45,47] basis set and LANL2DZ ECP were used for P, and the 6-31G(d') [48][49][50] basis sets were used for all other atoms (C, N, O, and H). In basis set 2 (BS2), the Ahlrichs Def2-TZVP [51,52] basis sets and related ECP were used for Ru, and TZVP [53] basis sets were used for all other atoms (C, N, O, P, F, and H). The Gaussian 16 default ultrafine integration grid, 2-electron integral accuracy of 10 −12 , and SCF convergence criterion of 10 −8 were used for all computations, and vibrational frequency computations were performed to verify the nature of all stationary points. All located transition states were obtained with only one imaginary frequency, and minima without any imaginary frequencies were obtained. The default rigid-rotor-harmonic-oscillator (RRHO) approximation was used to calculate the vibrational contribution to entropy. The intrinsic reaction coordinate (IRC) computations from the located transition states were performed, and both directions of the reaction path following the transition state were computed (see SI for the IRC plots) [54,55]. Gibbs free energies of activation (∆G ‡ ) and free energies of reaction (∆G • ) were determined with standard conditions of 1 atm and 298. 15 (Table S1) and the coefficient linear regression (R 2 ) was 0.9967 ( Figure S1) [56][57][58].

Results and Discussion
To fully understand the oxygen-atom transfer (OAT) from N 2 O to an Ru-H complex (Scheme 1), the proposed pathway for the proton transfer from Ru-H to the terminal N of endo N 2 O is presented in the following Section 3.1 (Figure 1) Figure 1) forms the Ru-OH complex (structure 4, Figure 1) and molecular N 2 . The generation of N 2 from the proton transfer (TS-3-4) is the TOLS for the conversion of N 2 O to N 2 . The Gibbs free energy of activation for the overall turnover-limiting steps (TOLS) based on the energetic span/transition state theory is determined as 29.0 kcal mol −1 (3 to TS-3-4, Figure 1) [62,63]. The generation of separated N 2 and the Ru-OH complex (structure 4) from the Ru-H complex and N 2 O is favorable by -65.1 kcal mol −1 (Figure 1). The effect of potentially existing traces of water in the THF solvent in the homogeneous conversion of N 2 O was also considered. Anticipated lower Gibbs free energy of activation in the generation of N 2 (15.1 kcal mol −1 , TS-3-4-OH 2 , Figure 1) with the participation of potentially existing H 2 O serving as a proton shuttle compared to the non-assisted generation of N 2 (26.6 kcal mol −1 , TS-3-4, Figure 1) was obtained. No such assistance of solvent THF was found (34.2 kcal mol −1 , TS-3-4-THF, Figure 1). The result of the H 2 Oassisted generation of N 2 is consistent with Poater's results on the hydrogenation of N 2 O by the PNP-Ru-dihydride pincer complex [35,36].
Another structural isomer that created a pathway for the N 2 generation from the N 2 O oxygen-atom transfer involves an intermediate without an intramolecular hydrogen bond, and is presented in Figure S6. Structures 2b, 3b, and 4b in Figure S6 are the structural isomers of structures 2, 3, and 4 in Figure 1 with a different orientation of diazene substrate and the OH group. For this alternative pathway, slightly higher ∆G ‡ are found (26.5 kcal mol −1 for TS-1b-2b vs. 24.1 kcal mol −1 for TS-1-2, 27.5 kcal mol −1 for TS-3b-4b vs. 26.6 kcal mol −1 for TS-3-4). The effect on the ∆G ‡ for the generation of N 2 from the anionic pyridinyl is relatively small. The possible proton transfer from Ru-H to the terminal O of N 2 O was also investigated (Scheme S2), and significantly higher ∆G ‡ were obtained (40.6 kcal mol −1 for TS-1-2d and 38.6 kcal mol −1 for TS-1b-2c). Compared to the formation of the Ru-O bond in Figure 1, the relatively small electronegativity of terminal N of N 2 O made it difficult to form Ru-N bonds (2c and 2d in Scheme S2), which caused the higher ∆G ‡ . Even higher ∆G ‡ were also obtained for the hydride transfer from Ru-H to the central N of N 2 O (42.7 kcal mol −1 for TS-1-5 and 45.2 kcal mol −1 for TS-1b-5b, Figures S6 and S7).
The above discussed mechanistic studies of the homogeneous oxygen-atom transfer (OAT) from N 2 O to the Ru-H complex to generate an N 2 and Ru-OH complex clearly showed that the pathway of the proton transfer from Ru-H to the terminal N of endo N 2 O is most favorable (Figure 1). It is accomplished by three asynchronous steps including N 2 O insertion into the Ru-H bond (TS-1-2), change of geometry of the formed O-bound diazene intermediate (TS-2-3), and the generation of N 2 from the proton transfer (TS-3-4). The last step (TS-3-4) forming the molecular N 2 and Ru-OH complex is the overall turnover-limiting step (TOLS) in the proposed three-step mechanism.

Hydricity as A Parameter to Predict the Activity
The concept of hydricity has been previously utilized to interpret the structure-activity relationships in transition-metal hydride species involved homogeneous catalysis [64][65][66][67][68][69][70]. The hydrogenation of CO 2 to formate catalyzed by molecular Co-H complexes presented an excellent linear relationship between the logarithm of the catalytic turnover frequency and the hydricity of Co-H complexes (R 2 = 0.9956), and significantly improved activity for Co-H complexes with relatively stronger hydride-donating ability were observed [66]. The model using the relationship between hydricities and the one-electron reduction potential of the transition-metal complexes is also used to study the reactivity of transition-metal hydride complexes in the CO 2 reduction [68]. The hydricity (∆G H − ) of each Ru-H complex was calculated using the equation presented in Scheme 2 [64,65]. pyridinyl is relatively small. The possible proton transfer from Ru-H to the terminal O of N2O was also investigated (Scheme S2), and significantly higher ΔG ‡ were obtained (40.6 kcal mol −1 for TS-1-2d and 38.6 kcal mol −1 for TS-1b-2c). Compared to the formation of the Ru-O bond in Figure 1, the relatively small electronegativity of terminal N of N2O made it difficult to form Ru-N bonds (2c and 2d in Scheme S2), which caused the higher ΔG ‡ . Even higher ΔG ‡ were also obtained for the hydride transfer from Ru-H to the central N of N2O (42.7 kcal mol −1 for TS-1-5 and 45.2 kcal mol −1 for TS-1b-5b, Figures S6 and S7).
The above discussed mechanistic studies of the homogeneous oxygen-atom transfer (OAT) from N2O to the Ru-H complex to generate an N2 and Ru-OH complex clearly showed that the pathway of the proton transfer from Ru-H to the terminal N of endo N2O is most favorable (Figure 1). It is accomplished by three asynchronous steps including N2O insertion into the Ru-H bond (TS-1-2), change of geometry of the formed O-bound diazene intermediate (TS-2-3), and the generation of N2 from the proton transfer (TS-3-4). The last step (TS-3-4) forming the molecular N2 and Ru-OH complex is the overall turnover-limiting step (TOLS) in the proposed three-step mechanism.

Hydricity as A Parameter to Predict the Activity
The concept of hydricity has been previously utilized to interpret the structure-activity relationships in transition-metal hydride species involved homogeneous catalysis [64][65][66][67][68][69][70]. The hydrogenation of CO2 to formate catalyzed by molecular Co-H complexes presented an excellent linear relationship between the logarithm of the catalytic turnover frequency and the hydricity of Co-H complexes (R 2 = 0.9956), and significantly improved activity for Co-H complexes with relatively stronger hydride-donating ability were observed [66]. The model using the relationship between hydricities and the one-electron reduction potential of the transition-metal complexes is also used to study the reactivity of transition-metal hydride complexes in the CO2 reduction [68]. The hydricity (ΔGH − ) of each Ru-H complex was calculated using the equation presented in Scheme 2 [64,65]. To explore the structure-activity relationship in the conversion of N2O to N2, the catalytic pathways of a series of Ru-H complexes (C1-C7, Chart 2) were investigated. The parent PNN-Ru-H complex was modified by the introduced electron-donating (CH3) and electron-withdrawing groups (CF3) on the para positions of these two pyridinyl fragments. For comparison, the structural isomers of the Ru-H complex with the PNC ligand [PNC = 6′-((di-tert-butylphosphino)methyl)-(2,2′-bipyridin)-3-ide] were also modeled (C8-C10, Chart 2). It is noted that the Ru-H complex with the PNC ligand [PNC = 6′-((ditert-butylphosphino)methyl)-(2,2′-bipyridin)-3-ide] was significantly less active than the PNN-Ru-H complex in the homogeneous conversion of N2O and CO [31].
The most favorable intramolecular hydrogen-bond-involved pathway (Figure 1) for the conversion of N2O to N2 catalyzed by Ru-H complexes (C1-C10, Chart 2) is studied. The ΔG ‡ for TS-1-2 (formation of O-bound diazene intermediate from insertion of N2O into the Ru-H bond) and TS-3-4 (generation of N2 from proton transfer) are summarized in Table 1 To explore the structure-activity relationship in the conversion of N 2 O to N 2 , the catalytic pathways of a series of Ru-H complexes (C1-C7, Chart 2) were investigated. The parent PNN-Ru-H complex was modified by the introduced electron-donating (CH 3 ) and electron-withdrawing groups (CF 3 ) on the para positions of these two pyridinyl fragments. For comparison, the structural isomers of the Ru-H complex with the PNC ligand [PNC = 6 -((di-tert-butylphosphino)methyl)-(2,2 -bipyridin)-3-ide] were also modeled (C8-C10, Chart 2). It is noted that the Ru-H complex with the PNC ligand [PNC = 6 -((di-tertbutylphosphino)methyl)-(2,2 -bipyridin)-3-ide] was significantly less active than the PNN-Ru-H complex in the homogeneous conversion of N 2 O and CO [31].
In order to quantitatively explore the structure-activity relationship in the conversion of N 2 O to N 2 , the relationship between the computed ∆G ‡ and Ru-H stretching frequencies (Figure 2), and the relationship between the computed ∆G ‡ and computed hydricities ( Figure 3) were fitted. Good linear relationships between computed ∆G ‡ and Ru-H stretching frequencies (R 2 = 0.9658 for C1-C7, and R 2 = 0.8578 for C8-C10, Figure 2) were obtained, and excellent correlations exist between ∆G ‡ of TS-3-4 and the computed hydricities (R 2 = 0.9158 for C1-C7, and R 2 = 0.9765 for C8-C10, Figure 3). Excellent linear fittings between the ∆G ‡ of TOLS and the computed hydricities (R 2 = 0.9381 for C1-C7, and R 2 = 0.9272 for C8-C10, Figure 4) were also obtained. The structure-activity relationship using hydricity to predict the activity is consistent with the results from studies on the molecular transition-metal hydride involved CO 2 hydrogenation, CO 2 reduction, and H 2 evolution [66][67][68]71,72]. This result suggests that a more active Ru-H catalyst with a higher turnover frequency for the conversion of N 2 O to N 2 would come from introducing a more electron-donating ligand.

Conclusions
A comprehensive theoretical investigation of the reaction between N2O to an Ru-H complex using DFT computations was performed. The proton transfer from Ru-H to the terminal N of endo N2O (Figure 1)

Conclusions
A comprehensive theoretical investigation of the reaction between N2O to an Ru-H complex using DFT computations was performed. The proton transfer from Ru-H to the terminal N of endo N2O (Figure 1)

Conclusions
A comprehensive theoretical investigation of the reaction between N2O to an Ru-H complex using DFT computations was performed. The proton transfer from Ru-H to the terminal N of endo N2O (Figure 1)

Conclusions
A comprehensive theoretical investigation of the reaction between N 2 O to an Ru-H complex using DFT computations was performed. The proton transfer from Ru-H to the terminal N of endo N 2 O (Figure 1) was shown as the most favorable pathway, which includes N 2 O insertion into the Ru-H bond (TS-1-2, 24.1 kcal mol −1 ), change of geometry of the formed (Z)-O-bound oxyldiazene intermediate (TS-2-3, 5.5 kcal mol −1 ), and the formation of an Ru-OH complex and generation of N 2 from a proton transfer step (TS-3-4, 26.6 kcal mol −1 ). Significantly low Gibbs free energy of activation in the generation of N 2 (15.1 kcal mol −1 , TS-3-4-OH 2 ) with the participation of potentially existing traces of H 2 O in the THF solvent serving as a proton shuttle was observed. The excellent linear relationships between the computed hydricities (∆G H − ) and the Gibbs free energies of activation (∆G ‡ ) of TS-3-4, between the computed hydricities (∆G H − ) and the Gibbs free energy of activation (∆G ‡ ) of TOLS (R 2 > 0.91), suggest that hydricity could be utilized as a potential parameter to predict the catalytic activities, and the design of more active Ru-H catalysts could benefit from ligand modification with more electron-donating groups.
Author Contributions: G.L.: conceptualization, investigation, formal analysis, methodology, writingreviewing and editing, and funding acquisition; M.Z.: investigation and formal analysis; C.E.W.: conceptualization, formal analysis, writing-reviewing and editing, and funding acquisition. All authors have read and agreed to the published version of the manuscript.