Theoretical Study of Reversible Hydrogenation of CO 2 to Formate Catalyzed by Ru(II)–PN 5 P, Fe(II)–PN 5 P, and Mn(I)–PN 5 P Complexes: The Effect of the Transition Metal Center

: In 2022, Beller and coworkers achieved the reversible hydrogenation of CO 2 to formic acid using a Mn(I)–PN 5 P complex with excellent activity and reusability of the catalyst. To understand the detailed mechanism for the reversible hydrogen release–storage process, especially the effects of the transition metal center in this process, we employed DFT calculations according to which Ru(II) and Fe(II) are considered as two alternatives to the Mn(I) center. Our computational results showed that the production of formic acid from CO 2 hydrogenation is not thermodynamically favorable. The reversible hydrogen release–storage process actually occurs between CO 2 /H 2 and formate rather than formic acid. Moreover, Mn(I) might not be a unique active metal for the reversible hydrogenation of CO 2 to formate; Ru(II) would be a better option.


Introduction
The significant consumption of fossil fuels has led to an increase in atmospheric CO 2 concentrations from 317 ppm in 1960 to 428 ppm in 2024 [1,2].Although CO 2 poses various environmental problems, it is also a relatively abundant and non-toxic carbon source that can be used to produce value-added chemicals such as methanol and formic acid [3].Hydrogen energy is currently attracting considerable attention as a renewable and clean energy.However, the transportation and storage of hydrogen are problematic due to its physical and explosive properties in oxygen-containing mixtures.CO 2 hydrogenation to formic acid, which can convert hydrogen into a liquid organic hydrogen carrier, presents a promising solution to this problem [4,5].Therefore, in recent years, extensive research has been performed to improve the hydrogenation of CO 2 to formic acid or formate and the subsequent dehydrogenation of formic acid [6][7][8][9].
For CO 2 hydrogenation, Inoue et al. conducted a preliminary study on the hydrogenation of CO 2 to formate using transition metal catalysts [10].Since then, the application of transition metal homogeneous catalysts in CO 2 hydrogenation has gained significant attention, though catalytic efficiency remains a challenge [11][12][13][14].Until 2009, Nozaki et al. achieved efficient catalytic CO 2 hydrogenation to formate using an Ir-PNP (PNP = 2,6-(di-iso-propylphosphinomethyl)-pyridine) complex, with a turnover number (TON) of 3500,000 and a turnover frequency (TOF) of 120,000 h −1 at 200 • C and 5.0 MPa [15].In 2014, Pidko et al. synthesized a Ru-PNP complex by substituting Ir with Ru and used this complex to catalyze the hydrogenation of CO 2 to formate (TOF = 1,100,000 h −1 at 120 • C and 40 bar with DMF as the solvent and DBU as the base) [16].Other Rubased complexes have also been shown to be highly efficient catalysts for the hydrogenation of CO 2 to formic acid (in ionic liquids) or formates (in the presence of organic bases) [17][18][19].For non-precious metals, Milstein et al. synthesized an Fe-based complex, ( t BuPNP)Fe(H) 2 (CO), which demonstrated catalytic activity comparable to that of precious metals, Ir and Ru, achieving low-pressure (10 bar) conversion to formate [20].Then, a series of other Fe(II) carbonyl hydride complexes and Fe-PN 3 P (PN 3 P = 2,6-diaminopyridine scaffold) complexes were used for CO 2 hydrogenation [21,22].In 2017, Gonsalvi et al. reported, for the first time, the synthesis of two Mn(I)-based complexes, Mn(PN 3 PNH i Pr)(H)(CO) 2 and Mn(PN 3 PNMe i Pr)(H)(CO) 2 , and achieved a maximum conversion of 10,000 and a yield of more than 99% at 80 • C and 80 bar [23].
Several studies have explored the dehydrogenation of formic acid [24,25].For precious metals, Nozaki et al. catalyzed the dehydrogenation of formic acid (FA) using Ir-PNP complexes to obtain a TOF of 120,000 h −1 [26].In 2014, Pidko et al. used the Ru-PNP complex, which demonstrated excellent stability and the highest FA dehydrogenation reaction rate in DMF.In the presence of triethylamine (Et 3 N), the maximum TOF was 257,000 h −1 , and the maximum TON was 326,500 [16].Huang et al. achieved better results using the Ru-PN 3 P complex in dimethyl sulfoxide solvent [27].For non-precious metal complexes, Milstein et al. used the Fe-PNP complex for FA dehydrogenation and obtained a TON of 100,000 and a TOF of 417 h −1 at 40 • C [28].Other Fe-based complexes also show high catalytic activity in formic acid dehydrogenation reactions [29,30].Boncella et al. used an aliphatic Mn-PNP complex for FA dehydrogenation without a base, achieving a TON of 190 [31].
Although various noble and non-precious metal complexes have been used for CO 2 hydrogenation and FA dehydrogenation, these processes were carried out under different conditions.In 2022, Beller and coworkers achieved the reversible hydrogenation of CO 2 to formic acid by using a Mn(I)-PN 5 P complex in mixed solution (H 2 O:THF = 1:1) with excellent activity and the reusability of the catalyst (CO 2 hydrogenation: TON = 230,000; FA dehydrogenation: TON = 29,000) [32].This is the first time this result was achieved under the same reaction conditions (additives and solvents).
For the reaction mechanism for CO 2 hydrogenation, some theoretical studies have been performed [33][34][35].In 2014, Pidko et al. showed that the intermediate (Ru-OCHO) after the rotation of formate had the lowest energy based on theoretical calculations [36].But the mechanism proposed by Pathak et al. using aliphatic Mn-PNP complexes showed that formic acid is formed directly without the rotation of formate [37].And in 2022, when Batista et al. suggested the mechanism for CO 2 hydrogenation to formic acid, they considered the rotation of formate but did not study this intermediate further [38].In Beller's paper, the authors proposed a mechanism for CO 2 hydrogenation and FA dehydrogenation where formic acid is formed directly from formate [32].However, previous work has shown that the formate intermediate is so stable that the formation of formic acid directly from formate is energetically unfavorable.Therefore, the detailed mechanism for the reversible hydrogenation of CO 2 to FA is still in doubt [39][40][41].
In addition, the Ru-based complexes are the most frequently used for CO 2 hydrogenation and FA dehydrogenation.And among non-precious metals, the Fe-based complexes exhibited excellent catalytic efficiency.However, Beller et al. accomplished the reversible hydrogenation of CO 2 to FA for the first time using the Mn(I) complex.In order to make clear whether the Mn(I) complex is a unique catalyst for this reversible reaction, we compared the catalytic activity of the Fe(II) and Ru(II) complexes with the Mn(I) complex, as shown in Scheme 1.
also been shown to be highly efficient catalysts for the hydrogenation of CO2 to formic acid (in ionic liquids) or formates (in the presence of organic bases) [17][18][19].For non-precious metals, Milstein et al. synthesized an Fe-based complex, ( t BuPNP)Fe(H)2(CO), which demonstrated catalytic activity comparable to that of precious metals, Ir and Ru, achieving low-pressure (10 bar) conversion to formate [20].Then, a series of other Fe(II) carbonyl hydride complexes and Fe-PN 3 P (PN 3 P = 2,6-diaminopyridine scaffold) complexes were used for CO2 hydrogenation [21,22].In 2017, Gonsalvi et al. reported, for the first time, the synthesis of two Mn(I)-based complexes, Mn(PN 3 PNH i Pr)(H)(CO)2 and Mn(PN 3 PNMe i Pr)(H)(CO)2, and achieved a maximum conversion of 10,000 and a yield of more than 99% at 80 °C and 80 bar [23].
Several studies have explored the dehydrogenation of formic acid [24,25].For precious metals, Nozaki et al. catalyzed the dehydrogenation of formic acid (FA) using Ir-PNP complexes to obtain a TOF of 120,000 h -1 [26].In 2014, Pidko et al. used the Ru-PNP complex, which demonstrated excellent stability and the highest FA dehydrogenation reaction rate in DMF.In the presence of triethylamine (Et3N), the maximum TOF was 257,000 h -1 , and the maximum TON was 326,500 [16].Huang et al. achieved better results using the Ru-PN 3 P complex in dimethyl sulfoxide solvent [27].For non-precious metal complexes, Milstein et al. used the Fe-PNP complex for FA dehydrogenation and obtained a TON of 100,000 and a TOF of 417 h -1 at 40 °C [28].Other Fe-based complexes also show high catalytic activity in formic acid dehydrogenation reactions [29,30].Boncella et al. used an aliphatic Mn-PNP complex for FA dehydrogenation without a base, achieving a TON of 190 [31].
Although various noble and non-precious metal complexes have been used for CO2 hydrogenation and FA dehydrogenation, these processes were carried out under different conditions.In 2022, Beller and coworkers achieved the reversible hydrogenation of CO2 to formic acid by using a Mn(I)-PN 5 P complex in mixed solution (H2O:THF = 1:1) with excellent activity and the reusability of the catalyst (CO2 hydrogenation: TON = 230,000; FA dehydrogenation: TON = 29,000) [32].This is the first time this result was achieved under the same reaction conditions (additives and solvents).
For the reaction mechanism for CO2 hydrogenation, some theoretical studies have been performed [33][34][35].In 2014, Pidko et al. showed that the intermediate (Ru-OCHO) after the rotation of formate had the lowest energy based on theoretical calculations [36].But the mechanism proposed by Pathak et al. using aliphatic Mn-PNP complexes showed that formic acid is formed directly without the rotation of formate [37].And in 2022, when Batista et al. suggested the mechanism for CO2 hydrogenation to formic acid, they considered the rotation of formate but did not study this intermediate further [38].In Beller's paper, the authors proposed a mechanism for CO2 hydrogenation and FA dehydrogenation where formic acid is formed directly from formate [32].However, previous work has shown that the formate intermediate is so stable that the formation of formic acid directly from formate is energetically unfavorable.Therefore, the detailed mechanism for the reversible hydrogenation of CO2 to FA is still in doubt [39][40][41].
In addition, the Ru-based complexes are the most frequently used for CO2 hydrogenation and FA dehydrogenation.And among non-precious metals, the Fe-based complexes exhibited excellent catalytic efficiency.However, Beller et al. accomplished the reversible hydrogenation of CO2 to FA for the first time using the Mn(I) complex.In order to make clear whether the Mn(I) complex is a unique catalyst for this reversible reaction, we compared the catalytic activity of the Fe(II) and Ru(II) complexes with the Mn(I) complex, as shown in Scheme 1.

Results and Discussion
Three complexes, Mn(I)-PN 5 P, Fe(II)-PN 5 P, and Ru(II)-PN 5 P, were considered for the theoretical study of the formation of formic acid and the regeneration of the catalyst throughout the catalytic cycle.In addition, the mechanism for the reversible operation of hydrogen storage and release was further discussed.All calculations in this paper were performed in mixed solutions (H 2 O:THF = 1:1).

The Metal Centers' Effects on the Formation of Formic Acid from CO 2 Hydrogenation
The reaction mechanism for CO 2 hydrogenation to formic acid or formate has been extensively studied.The whole process includes the coordination of CO 2 , the direct addition of hydride to CO 2 , and the rotation of formate [42][43][44].Herein, we propose a complete catalytic cycle for the hydrogenation of CO 2 to formic acid, as shown in Scheme 2. Initially, CO 2 interacts with the hydride on the metal center of complex 1 to form complex 2. Secondly, the hydride can be added directly to CO 2 to form complex 3.The formate moiety then rotates itself to form a very stable intermediate complex 4. The rotated formate attracts a proton from the arm of the PN 5 P ligand to form complex 5, which leads to the dearomatization of the PN 5 P ligand.Subsequently, after FA is released, complex 6 is yielded.The final step, 6→1, is the regeneration of the catalyst.The optimized geometries of all species in CO 2 hydrogenation to formic acid catalyzed by the Ru(II)-PN 5 P complex are shown in Figure 1.The optimized geometries of all species involved under the Fe(II)-PN 5 P and Mn(I)-PN 5 P complexes are provided in the Supporting Information (Figures S1 and S2).

Results and Discussion
Three complexes, Mn(I)-PN 5 P, Fe(II)-PN 5 P, and Ru(II)-PN 5 P, were consid the theoretical study of the formation of formic acid and the regeneration of the throughout the catalytic cycle.In addition, the mechanism for the reversible oper hydrogen storage and release was further discussed.All calculations in this pap performed in mixed solutions (H2O:THF = 1:1).

The Metal Centers' Effects on the Formation of Formic Acid from CO2 Hydrogenatio
The reaction mechanism for CO2 hydrogenation to formic acid or formate h extensively studied.The whole process includes the coordination of CO2, the dire tion of hydride to CO2, and the rotation of formate [42][43][44].Herein, we propose a co catalytic cycle for the hydrogenation of CO2 to formic acid, as shown in Scheme 2. I CO2 interacts with the hydride on the metal center of complex 1 to form complex ondly, the hydride can be added directly to CO2 to form complex 3.The formate then rotates itself to form a very stable intermediate complex 4. The rotated form tracts a proton from the arm of the PN 5 P ligand to form complex 5, which lead dearomatization of the PN 5 P ligand.Subsequently, after FA is released, comp yielded.The final step, 6→1, is the regeneration of the catalyst.The optimized geo of all species in CO2 hydrogenation to formic acid catalyzed by the Ru(II)-PN 5 P c are shown in Figure 1.The optimized geometries of all species involved under th PN 5 P and Mn(I)-PN 5 P complexes are provided in the Supporting Information (Fig and S2).The first step in the formation of FA is CO2 coordination.CO2 interacts with the hydride of the M-H bond on complex 1 to form complex 2. The distances between CO2 and The first step in the formation of FA is CO 2 coordination.CO 2 interacts with the hydride of the M-H bond on complex 1 to form complex 2. The distances between CO 2 and the hydride on the Ru, Fe, and Mn center are 2.951 Å, 3.039 Å, and 3.354 Å, respectively.The O-C-O bond angles are 178.8 • , 179.0 • , and 179.7 • , respectively.The Gibbs free energy changes in CO 2 coordination to Ru(II)-PN 5 P, Fe(II)-PN 5 P, and Mn(I)-PN 5 P complexes are 2.4 kcal/mol, 2.4 kcal/mol, and 2.2 kcal/mol, respectively.After CO 2 is fixed, the hydride can be directly added to CO 2 to form complex 3.The formed C−H bond distances in complex 3 with the Ru, Fe, and Mn centers are 1.216 Å, 1.214 Å, and 1.219 Å, respectively.The O-C-O bond angles are 135.1 • , 134.9 • , and 135.5 • , respectively.For the Ru(II)-PN 5 P complex, the activation energy for this step is 3.5 kcal/mol.For the Fe(II)-PN 5 P and Mn(I)-PN 5 P complexes, the activation energies are 3.1 kcal/mol and 4.3 kcal/mol, respectively.The following step is the rotation of the HCOO − moiety to form a more stable formate complex 4. For the Ru(II)-PN 5 P complex, this step is exergonic by 10.2 kcal/mol with an activation energy of 2.8 kcal/mol.For the Fe(II)-PN 5 P complex, this step is exergonic by 12.9 kcal/mol with an activation energy of 3.0 kcal/mol.For the Mn(I)-PN 5 P complex, this step is exergonic by 7.6 kcal/mol with an activation energy of 8.7 kcal/mol.From complexes 4 to 5, the formation of FA is endergonic by 14.7 kcal/mol and has an activation energy of 13.7 kcal/mol on the Ru(II)-PN 5 P complex.On the Fe(II)-PN 5 P complex, this step is endergonic by 15.7 kcal/mol with an activation energy of 14.3 kcal/mol.On the Mn(I)-PN 5 P complex, this step is endergonic by 10.8 kcal/mol with an activation energy of 10.0 kcal/mol.Finally, formic acid is removed from complex 5, and the free energy changes for this step are 5.3 kcal/mol, 6.8 kcal/mol, and 10.0 kcal/mol, respectively.
As shown in Figure 2, for the overall process of CO 2 hydrogenation to FA, the highest barrier occurs at the stage from 4 to 6.For the Ru(II)-PN 5 P complex, it is 20.0 kcal/mol.And, for the Fe(II)-PN 5 P and Mn(I)-PN 5 P complex, it is 22.5 kcal/mol and 20.8 kcal/mol, respectively.These values indicate that the Ru(II)-PN 5 P complex exhibits the best catalytic activity, but the Mn(I)-PN 5 P complex is comparable to the Ru(II)-PN 5 P complex; the activity of the Fe(II)-PN 5 P complex is the worst.The reverse process of CO 2 hydrogenation to FA is just the dehydrogenation of FA.Thus, 6→5→4→3→2→1 is the pathway for FA dehydrogenation.For FA dehydrogenation, the highest overall barrier occurs at step 4→TS3/4.It is 13.0 kcal/mol, 15.9 kcal/mol, and 16.3 kcal/mol on the Ru(II)-PN 5 P, Fe(II)-PN 5 P, and Mn(I)-PN 5 P complexes, respectively, suggesting that the order of catalytic activity for FA dehydrogenation is Ru(II)-PN 5 P > Fe(II)-PN 5 P > Mn(I)-PN 5 P.
The O-C-O bond angles are 178.8°,179.0°, and 179.7°, respectively.The Gibbs free energy changes in CO2 coordination to Ru(II)-PN 5 P, Fe(II)-PN 5 P, and Mn(I)-PN 5 P complexes are 2.4 kcal/mol, 2.4 kcal/mol, and 2.2 kcal/mol, respectively.After CO2 is fixed, the hydride can be directly added to CO2 to form complex 3.The formed C−H bond distances in complex 3 with the Ru, Fe, and Mn centers are 1.216 Å, 1.214 Å, and 1.219 Å, respectively.The O-C-O bond angles are 135.1°,134.9°, and 135.5°, respectively.For the Ru(II)-PN 5 P complex, the activation energy for this step is 3.5 kcal/mol.For the Fe(II)-PN 5 P and Mn(I)-PN 5 P complexes, the activation energies are 3.1 kcal/mol and 4.3 kcal/mol, respectively.The following step is the rotation of the HCOO − moiety to form a more stable formate complex 4. For the Ru(II)-PN 5 P complex, this step is exergonic by 10.2 kcal/mol with an activation energy of 2.8 kcal/mol.For the Fe(II)-PN 5 P complex, this step is exergonic by 12.9 kcal/mol with an activation energy of 3.0 kcal/mol.For the Mn(I)-PN 5 P complex, this step is exergonic by 7.6 kcal/mol with an activation energy of 8.7 kcal/mol.From complexes 4 to 5, the formation of FA is endergonic by 14.7 kcal/mol and has an activation energy of 13.7 kcal/mol on the Ru(II)-PN 5 P complex.On the Fe(II)-PN 5 P complex, this step is endergonic by 15.7 kcal/mol with an activation energy of 14.3 kcal/mol.On the Mn(I)-PN 5 P complex, this step is endergonic by 10.8 kcal/mol with an activation energy of 10.0 kcal/mol.Finally, formic acid is removed from complex 5, and the free energy changes for this step are 5.3 kcal/mol, 6.8 kcal/mol, and 10.0 kcal/mol, respectively.As shown in Figure 2, for the overall process of CO2 hydrogenation to FA, the highest barrier occurs at the stage from 4 to 6.For the Ru(II)-PN 5 P complex, it is 20.0 kcal/mol.And, for the Fe(II)-PN 5 P and Mn(I)-PN 5 P complex, it is 22.5 kcal/mol and 20.8 kcal/mol, respectively.These values indicate that the Ru(II)-PN 5 P complex exhibits the best catalytic activity, but the Mn(I)-PN 5 P complex is comparable to the Ru(II)-PN 5 P complex; the activity of the Fe(II)-PN 5 P complex is the worst.The reverse process of CO2 hydrogenation to FA is just the dehydrogenation of FA.Thus, 6→5→4→3→2→1 is the pathway for FA dehydrogenation.For FA dehydrogenation, the highest overall barrier occurs at step 4→ TS3/4.It is 13.0 kcal/mol, 15.9 kcal/mol, and 16.3 kcal/mol on the Ru(II)-PN 5 P, Fe(II)-PN 5 P, and Mn(I)-PN 5 P complexes, respectively, suggesting that the order of catalytic activity for FA dehydrogenation is Ru(II)-PN 5 P > Fe(II)-PN 5 P > Mn(I)-PN 5 P.  The global minimum of the total free energy profile corresponds to complex 4, the rotated formate species, with relative values of -8.8 kcal/mol, -12.0 kcal/mol, and -11.1 kcal/mol, respectively.At the same time, the relative values of FA + 6 are 11.2 kcal/mol, 10.5 kcal/mol, and 9.7 kcal/mol, respectively.This means that the formation of FA is energetically unfavorable; if FA is not removed from the reaction system, the final product will be complex 4 rather than complex 6 and FA.

The Metal Centers' Effects on the Regeneration of Catalysts
The regeneration of catalysts can proceed down two primary routes: (1) direct H 2 cleavage after its coordination on complex 6, which is actually a process of proton transfer; (2) water molecules in solution can accelerate the process as a bridge for proton transfer, as shown in Scheme 3. Firstly, H 2 is bound to the metal center in complex 6 to form complex 7.Then, H 2 is broken on complex 7 to regenerate complex 1 by direct cleavage (route 1).Route 2 shows the cleavage of H 2 with the help of a water bridge.The optimized geometries of selected species in the regeneration process on the Ru(II)-PN 5 P complex are illustrated in Figure 3.The optimized geometries of selected species on the Fe(II)-PN 5 P and Mn(I)-PN 5 P complexes during the regeneration process are given in Figures S3 and S4.plex 7.Then, H2 is broken on complex 7 to regenerate complex 1 by direct cleavage (route 1).Route 2 shows the cleavage of H2 with the help of a water bridge.The optimized geometries of selected species in the regeneration process on the Ru(II)-PN 5 P complex are illustrated in Figure 3.The optimized geometries of selected species on the Fe(II)-PN 5 P and Mn(I)-PN 5 P complexes during the regeneration process are given in Figures S3 and  S4.
As shown in Figure 4, for the regeneration of catalysts, the first step is H2 coordination.The bond distance of free H2 molecules is 0.762 Å, while the distance increases to 0.841 Å, 0.829 Å, and 0.815 Å, respectively, after bonding on Ru(II)-PN 5 P, Fe(II)-PN 5 P, and Mn(I)-PN 5 P complexes.This step is endergonic by 3.1 kcal/mol, 3.9 kcal/mol, and 8.2 kcal/mol, respectively, for the Ru(II)-PN 5 P, Fe(II)-PN 5 P, and Mn(I)-PN 5 P complexes.In route 1, the direct cleavage of H2 on the Ru(II)-PN 5 P complex is exergonic by 5.4 kcal/mol with an activation energy of 31.2 kcal/mol.On the Fe(II)-PN 5 P complex, this step is exergonic by 5.6 kcal/mol with an activation energy of 30.0 kcal/mol.On the Mn(I)-PN 5 P complex, this step is exergonic by 9.1 kcal/mol with an activation energy of 24.3 kcal/mol.For the overall process of catalyst regeneration, the apparent activation barrier is 34.3 kcal/mol, 33.9 kcal/mol, and 32.5 kcal/mol, respectively.In route 2, with the help of a water bridge, the activation barrier is lowered to 22.8 kcal/mol, 20.5 kcal/mol, and 18.7 kcal/mol, respectively.As shown in Figure 4, for the regeneration of catalysts, the first step is H 2 coordination.The bond distance of free H 2 molecules is 0.762 Å, while the distance increases to 0.841 Å, 0.829 Å, and 0.815 Å, respectively, after bonding on Ru(II)-PN 5 P, Fe(II)-PN 5 P, and Mn(I)-PN 5 P complexes.This step is endergonic by 3.1 kcal/mol, 3.9 kcal/mol, and 8.2 kcal/mol, respectively, for the Ru(II)-PN 5 P, Fe(II)-PN 5 P, and Mn(I)-PN 5 P complexes.In route 1, the direct cleavage of H 2 on the Ru(II)-PN 5 P complex is exergonic by 5.4 kcal/mol with an activation energy of 31.2 kcal/mol.On the Fe(II)-PN 5 P complex, this step is exergonic by 5.6 kcal/mol with an activation energy of 30.0 kcal/mol.On the Mn(I)-PN 5 P complex, this step is exergonic by 9.1 kcal/mol with an activation energy of 24.3 kcal/mol.For the overall process of catalyst regeneration, the apparent activation barrier is 34.3 kcal/mol, 33.9 kcal/mol, and 32.5 kcal/mol, respectively.In route 2, with the help of a water bridge, the activation barrier is lowered to 22.8 kcal/mol, 20.5 kcal/mol, and 18.7 kcal/mol, respectively.

The Metal Centers' Effects on Hydrogen Storage and Release
In Beller's experiment, the H2 storage-release cycle started from the dehydrogenation of FA, catalyzed by complex 6 at 90 °C, in which the pressure was carefully decreased to release H2.Then, CO2 was reloaded under high pressure (20 bar), followed by fulfilling H2 (80 bar) at 85 °C.After the H2 storage step, H2 release took place when the pressure decreased to start a new cycle.According to our computational study mentioned above,

The Metal Centers' Effects on Hydrogen Storage and Release
In Beller's experiment, the H 2 storage-release cycle started from the dehydrogenation of FA, catalyzed by complex 6 at 90 • C, in which the pressure was carefully decreased to release H 2 .Then, CO 2 was reloaded under high pressure (20 bar), followed by fulfilling H 2 (80 bar) at 85 • C.After the H 2 storage step, H 2 release took place when the pressure decreased to start a new cycle.According to our computational study mentioned above, the pathway for FA dehydrogenation is 6→5→4→3→2→1→9→8→7→6, and the pathway for CO 2 hydrogenation is 6→7→8→9→1→2→3→4.This is the first cycle, and the end of this cycle is complex 4 as the stable-rotated formate complex.When the pressure decreases, CO 2 is released first, and then H 2 is released (4→3→2→1→9→8→7→6).The H 2 storage operation is the reverse process 6→7→8→9→1→2→3→4.This provides the details of the second cycle.We find that the H 2 storage in the second cycle is the same as that in the first cycle, but the H 2 release is different.In the first cycle, H 2 is released from FA dehydrogenation (6→5→4→3→2→1→9→8→7→6); however, in the second cycle, H 2 is released from formate dehydrogenation (4→3→2→1→9→8→7→6).All of the subsequent H 2 storage-release cycles occur as the second cycle.The free energy profile for the H 2 storage-release cycle is presented in Figure 5.The apparent activation barriers (6→TS8/9) for H 2 storage on the Ru(II)-PN 5 P, Fe(II)-PN 5 P, and Mn(I)-PN 5 P complexes are 18.7 kcal/mol, 20.5 kcal/mol, and 22.8 kcal/mol, respectively, as collected in Table 1.And for the reverse H 2 release, the apparent activation barriers (9→TS8/9) for H 2 release on the Ru(II)-PN 5 P, Fe(II)-PN 5 P, and Mn(I)-PN 5 P complexes are 24.4 kcal/mol, 25.7 kcal/mol, and 27.5 kcal/mol, respectively.It can be seen that the Mn(I)-PN 5 P complex is not the most highly active catalyst even for H 2 storage or for H 2 release; the Ru(II)-PN 5 P complex may have the best catalytic efficiency, and the second-best option is the Fe(II)-PN 5 P complex.
H2 storage-release cycles occur as the second cycle.The free energy profile for the H2 storage-release cycle is presented in Figure 5.The apparent activation barriers (6→TS8/9) for H2 storage on the Ru(II)-PN 5 P, Fe(II)-PN 5 P, and Mn(I)-PN 5 P complexes are 18.7 kcal/mol, 20.5 kcal/mol, and 22.8 kcal/mol, respectively, as collected in Table 1.And for the reverse H2 release, the apparent activation barriers (9→TS8/9) for H2 release on the Ru(II)-PN 5 P, Fe(II)-PN 5 P, and Mn(I)-PN 5 P complexes are 24.4 kcal/mol, 25.7 kcal/mol, and 27.5 kcal/mol, respectively.It can be seen that the Mn(I)-PN 5 P complex is not the most highly active catalyst even for H2 storage or for H2 release; the Ru(II)-PN 5 P complex may have the best catalytic efficiency, and the second-best option is the Fe(II)-PN 5 P complex.

Computational Methods
All calculations were performed with the Gaussian 09 program [45].Geometry optimization and frequency analyses were carried out using the B3LYP hybrid functional [46].To obtain more accurate single-point energy, the B3LYP-D3(BJ) functional with dispersion corrections was further applied [47].For Ru, Fe, and Mn, the Stuttgart-Dresden pseudopotential basis set (SDD) was employed, which was supplemented by two sets of f functions and a set of g functions [48].And the Dunning cc-pVDZ [49] basis set was applied for the other main group elements.Frequency analyses were performed to determine the minimum or transition state at each stationary point and to obtain the thermochemical properties of all species.Gibbs free energy was calculated at 298.15 K and 1 atm.All

Computational Methods
All calculations were performed with the Gaussian 09 program [45].Geometry optimization and frequency analyses were carried out using the B3LYP hybrid functional [46].To obtain more accurate single-point energy, the B3LYP-D3(BJ) functional with dispersion corrections was further applied [47].For Ru, Fe, and Mn, the Stuttgart-Dresden pseudopotential basis set (SDD) was employed, which was supplemented by two sets of f functions and a set of g functions [48].And the Dunning cc-pVDZ [49] basis set was applied for the other main group elements.Frequency analyses were performed to determine the minimum or transition state at each stationary point and to obtain the thermochemical properties of all species.Gibbs free energy was calculated at 298.15 K and 1 atm.All transition states were verified by intrinsic reaction coordinate (IRC) calculations.In order to keep in accord with the experimental conditions, we modeled the mixed solvent (H 2 O:THF = 1:1) in this paper.To deal with the solvent effects of the mixed solution (H 2 O:THF = 1:1), the polarizable continuum model (PCM) [50,51] was applied by defining the static dielectric constants (eps = 42.8905) and the dynamic dielectric constant (epsinf = 1.875937) of the solvent, respectively.All structural plots in this paper were drawn using VMD software (version 1.9.2, 29 December 2014) [52].

Conclusions
In this study, the reversible hydrogenation of CO 2 was investigated by theoretical calculations.For the process of CO 2 hydrogenation to FA, the highest barrier occurs at stages 4 to 6.This means that the formation of FA is energetically unfavorable; if FA is not removed from the reaction system, the final product will be complex 4 rather than complex 6 and FA.The Ru(II)-PN 5 P complex exhibits the best catalytic activity, but the Mn(I)-PN 5 P complex is comparable, and the Fe(II)-PN 5 P complex is the worst.For FA dehydrogenation, the highest overall barrier occurs at step 4→TS3/4.And the order of catalytic activity is Ru(II)-PN 5 P > Fe(II)-PN 5 P > Mn(I)-PN 5 P.During catalyst regeneration, the activation barrier is lowered with the help of a water bridge.
We also further investigated the mechanism of H 2 storage and release.We found that H 2 storage in the second cycle was the same as that in the first cycle, but H 2 release was different.In the first cycle, H 2 is released from FA dehydrogenation.However, in the second cycle, H 2 is released from formate dehydrogenation.All of the subsequent H 2 storage-release cycles occur as the second cycle.In the process of H 2 storage and release, it is the formate rather than formic acid that participates in the reversible cycle.The Mn(I)-PN 5 P complex is not the most highly active catalyst; the Ru(II)-PN 5 P complex may have the best catalytic efficiency, and the second-best option is the Fe(II)-PN 5 P complex.The calculations demonstrate that the Mn(I)-PN 5 P catalyst does not have a special presence, while Ru(II)-PN 5 P is more favorable.This study provides a theoretical basis for experimental research by expanding the range of catalysts through theoretical studies.

Supplementary Materials:
The following supporting information can be downloaded at https://www.mdpi.com/article/10.3390/catal14070440/s1. Figure S1.The optimized geometries of all species in CO 2 hydrogenation to formic acid catalyzed by the Fe(II)-PN 5 P complex; Figure S2.The optimized geometries of selected species in the regeneration of Fe(II)-PN 5 P complexes; Figure S3.The optimized geometries of all species in CO 2 hydrogenation to formic acid catalyzed by the Mn(I)-PN 5 P complex; Figure S4.The optimized geometries of selected species in the regeneration of Mn(I)-PN 5 P complexes; and Table S1.Cartesian coordinates for optimized geometries of all the species of the three complexes in the mixed solution (H 2 O:THF = 1:1).

Figure 1 .
Figure 1.The optimized geometries of all species in CO2 hydrogenation to formic acid catalyzed by the Ru(II)-PN 5 P complex.The R1 groups in TS4/5 and complex 5 are omitted for clarity.The bond distances are in angstrom (Å), and the bond angles are in degrees (•).(Ru: pink; C: cyan; P: orange; O: red; N: blue; H: white.)

Figure 1 .
Figure 1.The optimized geometries of all species in CO 2 hydrogenation to formic acid catalyzed by the Ru(II)-PN 5 P complex.The R 1 groups in TS4/5 and complex 5 are omitted for clarity.The bond distances are in angstrom (Å), and the bond angles are in degrees (•).(Ru: pink; C: cyan; P: orange; O: red; N: blue; H: white).

Figure 3 .
Figure 3.The optimized geometries of selected species in the regeneration of the Ru(II)-PN 5 P complex.The R 1 groups in the TS7/1 and TS8/9 are omitted for clarity.The distances are angstrom (Å) (Ru: pink; C: cyan; P: orange; O: red; N: blue; H: white).

Figure 3 .
Figure 3.The optimized geometries of selected species in the regeneration of the Ru(II)-PN 5 P complex.The R1 groups in the TS7/1 and TS8/9 are omitted for clarity.The distances are angstrom (Å) (Ru: pink; C: cyan; P: orange; O: red; N: blue; H: white).

Figure 5 .
Figure 5. Free energy profile for the reversible hydrogen storage-release catalyzed by Mn(I)-PN 5 P, Fe(II)-PN 5 P, and Ru(II)-PN 5 P complexes.

Table 1 .
The activation energy for the reversible hydrogen storage-release catalyzed by the three complexes.

Figure 5 .
Figure 5. Free energy profile for the reversible hydrogen storage-release catalyzed by Mn(I)-PN 5 P, Fe(II)-PN 5 P, and Ru(II)-PN 5 P complexes.

Table 1 .
The activation energy for the reversible hydrogen storage-release catalyzed by the three complexes.