Solubility of CO in solid-state PET measured by pressure-decay method

Abstract

The solubility of CO₂ in solid-state PET was measured using a pressure-decay method. In order to calculate the solubility of CO₂ in the amorphous region of PET, the crystallinity of solid state PET dissolved in CO₂ at different pressures and temperatures was measured by differential scanning calorimetry (DSC). The solubility increases with increasing pressure and it follows a linear relationship and obeys Henry’s law when the pressure is below 8 MPa. The effect of temperature on solubility is weak and the solubilities at different temperatures are almost the same under low pressures. At higher pressure, the solubility decreases with an increase in temperature. The solubility of CO₂ in the amorphous region of PET at 373.15 K, 398.15 K and 423.15 K was correlated with the Sanchez-Lacombe equation of state with a maximal correlation error of 6.69%.

1 1 Introduction

Addressing global warming and the depletion of fossil fuels represents urgent challenges facing humanity [1−3]. One proposed solution involves converting the primary greenhouse gas, CO₂, into energy carriers supported by renewable sources such as solar, wind, or water power [4,5]. The catalytic electrochemical conversion of CO₂ to CO holds significant importance due to its role as a reagent in various chemical processes, such as methanol, acetic acid, and hydrocarbon-based fuel production [6−8]. An ongoing challenge in catalysis is achieving precise selectivity, guiding a reaction to produce a specific desired product. In the metal-based molecular catalysts domain, considerable research focuses on the impact of the secondary coordination sphere. This sphere refers to the functional groups surrounding the metal center, and understanding how their subtle variations influence the selectivity of these complexes is a key area of investigation [9,10]. While transition metal-based molecular catalysts traditionally exhibit catalytic activity primarily at the metal center, recent considerations include the potential for ligand moieties to play a more substantial role in catalytic reactions, cooperatively interacting with the metal center [11,12]. Both the electronic and steric properties of ligands have been observed to significantly influence catalytic activity [8]. Therefore, developing highly efficient catalysts hinges on leveraging both the metal center and ligand contributions to catalytic activities, driving efforts toward developing complexes with tailored ligands by modifying their electronic and steric characteristics. Despite the progress, some catalysts exhibit low selectivity for the CO₂ reduction reaction (CO₂RR), often leading to concurrent hydrogen evolution reaction (HER) and producing multiple byproducts [8,13,14]. Catalyst modification through coordinated atoms presents a potential alternative to enhance reactivity and selectivity [15,16], although a detailed mechanistic understanding remains lacking, hindering systematic improvement. Mn(I)-based organometallic complexes emerge as promising catalyst systems for CO₂ electroreduction, offering both efficiency and affordability [16−20]. Mn(I) diimine complexes have shown promising results in catalyzing the reduction of CO₂ to CO [21]. Mechanistic insights into these processes are crucial for further development. Notably, Mn-centered complexes have rarely been explored for proton reduction, indicating a significant avenue for investigation. Understanding the mechanistic intricacies of these processes is essential for advancing catalytic systems for CO₂ reduction and HER.

However, our current study primarily concentrates on examining the impacts of promoters. By interacting with catalytic intermediates or transition states, these promoters play a role in influencing reaction rates, efficiency, and stability of molecular catalysts. They achieve this by reducing overpotentials or activation barriers. Experimental and computational reports have highlighted the remarkable catalytic efficiencies observed in electrochemically reducing CO₂ to CO or generating fuels as byproducts [19−22]. Nevertheless, they still fall significantly short of the levels necessary for practical applications. In this study, density functional theory (DFT) calculations were conducted to examine the reaction mechanism and rationalize product selectivity. The work primarily focuses on theoretical investigations of bioinspired homogeneous catalysts and utilizes DFT calculations to explore the mechanisms of CO₂RR and the HER. Our proposed mechanism involves the electro-reduction of MnBr, resulting in Mn^– with two additional electrons. Following this step, competitive CO₂RR and HER occur, forming CO-coordinated and H₂-coordinated products, respectively. Our analysis is focused on comprehending the electronic structure, reactivity of active species, and selectivity for CO₂RR and HER, offering valuable insights into the feasibility of the proposed mechanism. We expect that this comprehension will be pivotal for optimizing comparable homogeneous CO₂RR systems in the future, as shown in the cautiously summarized catalytic cycles of the Mn(I) diimine electrocatalyst [Mn(pyrox)(CO)₃Br] system for both CO₂RR and HER-driven processes.

2 2 Computational methodology

DFT studies were performed on Mn complexes with diamine ligands, specifically focusing on [Mn(pyrox)(CO)₃Br]. We utilized nine distinct DFT functionals in our study: B3LYP [23], B3LYP-D3 [24], BP86 [25], Cam-B3LYP [26], M06L [27], M06 [28], M06-2X [29], PBE1PBE [30], and ωB97X [31]. These functionals were employed to analyze bonding characteristics in relation to the initial geometry of [Mn-Br]⁰ single crystal data acquired experimentally, as detailed in Table S1 (cf. Electronic Supplementary Material, ESM). We discuss the rationale behind selecting B3LYP, M06, and PBE1PBE functionals, and conducted comparisons among these DFT functionals to assess their redox properties, enabling a comparison with experimental findings [16], which is outlined in Tab.1. Among the nine functionals, B3LYP, M06, and PBE1PBE are known for their reliability in determining structural, redox properties, and energetic values. These functionals were used for the CO₂RR process, and additionally, two more functionals (M06L and B3LYP-D3) were employed for the HER process due to their improved accuracy in predicting chemical reaction barrier heights and noncovalent interactions. We utilized the 6-31G(d) [32] basis set for atomic elements H, C, N, and O, and for the Mn center, we applied the Los Alamos effective core potential (LANL2DZ) [33]. Gas phase-optimized geometries were validated to exhibit real harmonic vibrational frequencies for all intermediates based on Gibbs free energy corrections. Transition state geometries, identified with one imaginary frequency, underwent thermodynamic corrections for free-energy calculations at room temperature. We conducted intrinsic reaction coordinate calculations to verify that the identified transition states establish connections between reactants and products [34]. Solvation effects in acetonitrile (CH₃CN) were considered through single-point calculations carried out on gas phase optimized structures using the CPCM solvation model in CH₃CN (ε = 35.688) [35]. The single-point energy calculations were performed using the B3LYP, M06, and PBE1PBE, employing a larger TZVP [34] basis set for the CO₂RR process and including the two additional functionals M06L and B3LYP-D3 for the HER process. Furthermore, redox properties were derived from the reduced and oxidized species using the Born-Haber cycle [34,36−38].

Tab.1 Comparison of computed reduction potentials (in V) with experimentally available data vs. NHE (–4.6 V) at three different functionals with LANL2DZ(6-31G(d)//TZVP in CH3CN medium

Species	B3LYP	M06	PBE1PBE	Experiment
2Mn → 3Mn	−0.927	−1.093	−1.017	−1.29
3Mn → 5Mn	−2.075	−1.976	−1.980	−1.20
9Mn → 11Mn	−1.962	−1.911	−1.913	–
10Mn → 12Mn	−1.528	−1.411	−1.448	–
12Mn → 5Mn	−1.723	−1.903	−1.876	−1.20–1.35

$\begin{array}{rl}& E^0=\frac{\mathrm{\Delta }{G}^0\left(\mathrm{s}\mathrm{o}\mathrm{l}\right)}{n_{\mathrm{e}}F}-E^0\left(\mathrm{R}\mathrm{E}\mathrm{F}\right),\\ & {\mathrm{p}K}_{\alpha }=\frac{\mathrm{\Delta }{G}^{\ast }\left(\mathrm{a}\mathrm{q}\right)}{2.303RT}=\frac{\mathrm{\Delta }{G}^{\ast }\left(\mathrm{a}\mathrm{q}\right)}{1.365}.\end{array}$

The equation used for calculating ΔG⁰ is ΔG⁰ = –nFE⁰, where n represents the number of transferring electrons, F is Faraday’s constant (F = 96.484 kJ·mol^–1 or 23.06 kcal·vol^–1·g^–1), and ΔG⁰ stands for the free energy of reduction with 1 mol·L^–1 standard state. To account for the 1 mol·L^–1 standard state in a CH₃CN solution starting from the gas phase optimized geometries, a concentration correction of 1.89 kcal·mol^–1 [RTln(24.5)] was integrated into the computed reaction profiles [34]. Additionally, the equation ΔG⁰ = –[ln(10)RT]pK_α was utilized to compute pK_α values, where ΔG⁰ denotes the free energy of protonation. The standard state aqueous free energy of a proton, G_aq*(H⁺), was determined using the gas-phase free energy (G⁰_g(H⁺) = –6.29 kcal·mol^–1), while the experimentally measured hydration free energy (G_aq, solv(H⁺) = –265.9 kcal·mol^–1) was obtained from the literature [36]. All reduction potentials were measured relative to the normal hydrogen electrode (NHE) in CH₃CN. The NHE reference value of 4.44 V was used as a reference electrode for experimental purposes [37]. Specifically, an applied potential of –1.20 V vs. NHE was employed experimentally [16] and this value was also used to construct free energy profiles. Vertical excitations were computed using the time-dependent DFT method [39] to determine absorption spectra, and these calculations demonstrated close agreement with available experimental data (Table S2, cf. ESM). The bonding nature of key transition states was investigated using the quantum theory of atoms in molecules (QTAIM) at the same level of theory used for optimization. QTAIM analyses were conducted using the AIM 2000 package [40]. All computations were executed using the Gaussian 09 software package [41].

3 3 Results and discussion

This study delves into diverse reaction pathways concerning the catalytic activity of [Mn(pyrox)(CO)₃Br], employing electronic structure calculations. illustrates the proposed reaction mechanism. The section unfolds as follows: the initial section delineates the catalytic cycle stepwise, commencing with the initial reduction, followed by CO₂ fixation and protonation. The subsequent segment presents and deliberates alternative intermediates concerning their relevance. Christoph Steinlechner’s research group previously introduced a series of Mn diimine catalysts, namely [Mn(pyrox)(CO)₃Br], for CO₂ conversion to CO employing protonated TEOAH⁺ as the proton source. These catalysts feature charged diimine ligands in the primary coordination sphere, displaying superior catalytic activity compared to [Mn(benzox)(CO)₃Br] and [Mn(qinox)(CO)₃Br] [16]. However, elucidating the specific mechanism governing the CO₂RR over the competing HER remains elusive. Leveraging experimental findings and prior theoretical studies [19,20], the proposed mechanistic pathways () for Mn diimine catalyst are discussed. These mechanisms can be summarized as follows: Initially, the electro-reduction of the hexa-coordinated [Mn-Br]⁰ complex (¹Mn) in the singlet state, with an overall charge of 0, leads to the generation of [Mn^I-CH₃CN]⁺ (²Mn) through reductive dehalogenation of the catalyst in the presence of CH₃CN, followed by the liberation of Br^–. Subsequently, the process commences with a ligand-based reduction facilitated by a single electron, yielding either an anion or a neutral hexa-coordinate radical, contingent upon the retention or dissociation of the halide anion (Br^–) during the reduction event, signifying an electrochemical-chemical pathway.

Scheme1 The proposed reaction mechanism for the CO2RR and HER by 1Mn species is illustrated. The protonation-first pathway (PFP) is depicted in red, while the reduction-first pathway (RFP) is indicated in blue.

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The hexa-coordinate [²Mn]⁺ species may arise, potentially allowing a CH₃CN solvent molecule to coordinate with the vacant site of the [³Mn]⁰ species. This mechanism suggests an immediate reduction of the hexa-coordinate radical to the ⁵Mn species, which emerges at the second reduction potential compared to the parent species. The resulting ⁵Mn species undergoes protonation to form the (⁶Mn) Mn-hydride. This implies the feasibility of this mechanism being operational across various systems documented in the literatures [20,22]. Furthermore, after the second reduction step, an intermediate species forms, which could either interact with CO₂ to generate another intermediate or engage with a proton donor to produce a hydride species, Mn-H. This provides a plausible explanation for the notable selectivity of these catalysts toward CO over H₂ or formate (HCOO^–) production. Moreover, the protonation of [Mn-CO₂] to yield [Mn-CO₂H], using TEOAH⁺ as the proton source, is a crucial intermediate of ⁹Mn. Competitive reactions involving CO₂RR and HER then occur, resulting in the production of CO from [Mn-CO] (¹²Mn) and the generation of H₂ and HCOO^– from [Mn]¹⁻ (⁵Mn). Eventually, CO, H₂, and HCOO^– are released, completing the catalytic cycle.

Steinlechner and coworkers [16] outlined two potential pathways for generating CO and H₂O from the ⁹Mn [Mn^I-CO₂H] intermediate, known as the PFP and RFP as shown in . The PFP starts with the heterolytic cleavage of the C–OH bond, facilitated by a proton donor, resulting in H₂O and [Mn-CO]⁺ formation. This intermediate is then reduced to produce the ¹²Mn species. On the other hand, the RFP involves reducing [Mn-CO₂H] followed by the heterolytic cleavage of the C–OH bond, leading to H₂O and the common [Mn-CO] intermediate. Sequential or concerted one-electron reduction steps and CO evolution events complete the catalytic cycle, regenerating the active ⁵Mn catalyst.

3.1 3.1 Activation of catalysis: optimized geometries

Theoretical calculations were undertaken to analyze the characteristics of [Mn(pyrox)(CO)₃Br] (¹Mn). Our computed structural and spectroscopic parameters are consistent with X-ray crystallographic geometrical data and experimental observations (Tables S1 and S2). As elaborated in Table S2 of the supporting information, the structure of ¹Mn closely aligns with experimental results [16] obtained from Fourier transform infrared (FTIR) and UV-visible spectroscopy. Additionally, from the FTIR spectra of [Mn(pyrox)(CO)₃Br] ground state geometry at gas phase, the ν_CO stretching vibrational peaks were observed at 2113.7, 2060.0, 2042.9 cm^–1 when computed (at B3LYP/6-31G(d)/LANL2DZ), which were quite similar to experimental vibrational band at 2028 cm^–1.

Moreover, the UV-visible spectra of [Mn(pyrox)(CO)₃Br] were found to show an intense peak at λ_max = 333.8 nm (f₀ = 0.038) and a broad peak at 434.06 nm (f₀ = 0.002) in CH₃CN solvent. These peaks arose from the charge transfer transitions, which is quite comparable with experimental data [16]. These findings are consistent with experimental evidence and are summarized in Table S2. This table suggests that, computationally, the selection of the functional aligns with the observed trend. Furthermore, the agreement between our computed results and the available experimental data are evident in Tables S1 and S2. Analogous to previously reported diimine Mn complexes [16,22], the Mn center retains an oxidation state of +1, with the organometallic unit exhibiting a six-coordinate pseudo-octahedral geometry. Additionally, the bond lengths of selected bonds in all structures are illustrated in Fig.1. In accordance with previous research, the catalyst is activated through two consecutive one-electron reductions, transferring two additional electrons to the Mn center. The initial geometry reveals a metal-to-ligand charge transfer, transitioning from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO), with an energy gap (E_g) of 3.85 eV. Notably, the HOMO of ¹Mn appears to involve the σ-antibonding orbital between the Br atom and the Mn atom (see Fig.2). The process begins with CH₃CN solvent coordination to form the ²Mn complex, followed by Br^– dissociation to yield ²Mn, consistent with its formation. The calculated first one-electron reduction potentials (–0.927 V (B3LYP), –1.093 V (M06), –1.017 V (PBE1PBE) vs. NHE) align well with the experimental reduction potential of –1.29 V (Tab.1). The more readily reducible ²Mn is promptly reduced to ³Mn (radical species) upon its generation, forming a more active anionic species (⁵Mn) followed by a second electron reduction process. The calculated second one-electron reduction potentials for the transformation of ³Mn → ⁵Mn (–2.075 V (B3LYP), –1.976 V (M06), –1.980 V (PBE1PBE) vs. NHE) are also included in Tab.1. In the electrocatalytic reduction of CO₂ to CO using [Mn(pyrox)(CO)₃Br], the catalytically active intermediate is a five-coordinate anion. This intermediate initiates the formation of a radical, which undergoes rapid protonation (H⁺ from TEOAH⁺) and CO₂ reduction, enabling further analysis.

Fig.1 The optimized geometries, including the bond lengths (in Å), of all the specified species delineated in Scheme 1, are provided.

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Fig.2 The frontier molecular orbital scheme for charge transfer mechanism from HOMO to the LUMO orbitals in 1Mn species.

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3.2 3.2 CO₂ fixation and protonation

Fig.3 illustrates the extensive computed free energy profile (using B3LYP/LANL2DZ(6-31G(d)//TZVP)) for the CO₂ fixation and protonation, with all structures optimized in solution and considering CH₃CN as the solvent. Additionally, we determined the free energies using the TZVP basis set with the M06 and PBE1PBE functionals from the optimized geometries obtained with the B3LYP functional. These results are presented in Table S3 (cf. ESM). The study by Steinlechner et al. [16], confirmed that the parent complex [Mn(pyrox)(CO)₃Br], initially undergoes a pseudo-concerted two-electron ECE (electrochemical-chemical-electrochemical) reduction to generate the five-coordinate radical anion species from ²Mn + 1e^– → ³Mn + CH₃CN and ³Mn + 1e^– → ⁵Mn (anion). The pseudo-concerted two-electron ECE pathway is preferred for ¹Mn. Rapid dissociation of Br^– occurs upon CH₃CN binding with the Mn center. Such a process exhibits an activation energy barrier of 1.46 eV, attributed to electrostatic repulsion within the unstable ²Mn intermediate. This specific transition state (^TS1Mn) indicates a “late” nature, as evidenced by the presence of one imaginary frequency at 90.0i·cm^–1 and a corresponding force constant of 0.0580 mdyn·Å^–1. This transition state exhibits a late nature, as evidenced by the incipient Br–Mn–N bond angle of 67.08°, with Mn–Br and Mn–ACN bond distances of 3.642 and 2.879 Å, respectively.

Fig.3 The reaction free energy (ΔG) profile for CO2 fixation and protonation steps.

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Meanwhile, the one-electron reduction of the resulting ³Mn and ⁴Mn intermediates is exergonic by –3.56 and –6.58 eV, respectively, compared to the parent complex and the two-electron reduction steps. In Fig.3 it shows that upon forming the active species ⁵Mn from ³Mn and ⁴Mn, followed by reduction steps, a vacant site becomes available where CO₂ can potentially be fixed, leading to its reduction. The creation of the Mn-CO₂ intermediate (⁷Mn) is calculated to be exothermic by –6.22 eV and requires overcoming a lower activation energy barrier of 0.82 eV compared to the active species ⁵Mn. The specific transition state (^TS2Mn) involving the vacant site of the ⁵Mn species, which leads to the fixation of CO₂ and the formation of the CO₂-coordinated ⁷Mn species, is characterized by an imaginary frequency of 75.14i·cm^–1 and a force constant of 0.0387 mdyn·Å^–1. The calculated transition state ^TS2Mn shows that CO₂ coordinates to the Mn center via a carbon atom, with the Mn–C bond measuring approximately 2.920 Å, and the O=C=O bond angle approaching 153.8°. Notably, although ⁷Mn could be formally categorized as a Mn⁰-CO₂ complex, this mechanism bears similarities to the interaction expected between the HOMO of the two-electron reduced [Mn(pyrox)(CO)₃Br] complex and CO₂ during its addition process. Furthermore, once CO₂ has coordinated with the Mn center, the reaction can proceed through the protonation of the CO₂ ligand.

3.3 3.3 CO release and catalyst regeneration

Investigations revealed that the ⁷Mn catalyst class necessitates the presence of a suitable proton donor (TEOAH⁺) to facilitate CO₂ binding and the subsequent formation of the neutral Mn(I) six-coordinate metallocarboxylic acid intermediate [Mn-CO₂H]⁰ [16]. Moreover, prior experimental and computational studies have emphasized the requirement of two sequential protonations using H⁺ for the reduction of CO₂ to CO [20,22]. To model the protonation process, TEOAH⁺ (as a proton source) was introduced, as previously documented by Steinlechner et al. [16]. As outlined earlier, the additional electron in ⁷Mn primarily localizes on the CO₂ ligand, resulting in a partial negative charge on the bound CO₂ (Fig.4). Also, the single-point energy calculations were executed utilizing the TZVP basis set in combination with the B3LYP, M06, and PBE1PBE functionals, as specified in Tables S4 and S5 (cf. ESM) within the supporting information. The depicted reaction free energy profile in Fig.4 elucidates the CO₂RR initiated from the active ⁷Mn species, followed by both the PFP and RFP. This prompts protonation from TEOAH⁺ to coordinate with CO₂, leading to the formation of species ⁹Mn. This process is exergonic, with ΔG = –0.85 eV. Protonation of the C–O bond induces weakening of the C–O bond, elongating it from 1.315 Å in ⁷Mn to 1.377 Å in ⁹Mn. This facilitates proton transfer from the TEOAH⁺ to the C–O unit, with an energy barrier of only –0.61 eV (^TS3Mn), which is exothermic compared to ⁷Mn due to the barrier-less process. The subsequent release of N–H (TEOAH⁺) is also exergonic, with ⁹Mn being –0.85 eV more stable than ⁷Mn. Additionally, although the HOMO of ⁹Mn exhibits slightly more delocalization than that of ⁷Mn, a partial negative charge still occupies the COOH unit. This progression drives the reaction forward, culminating in the next protonation step to form [MnCO] (¹²Mn). Next, the [Mn-CO] intermediate (¹²Mn) formation can proceed via two possible pathways, as depicted in Fig.4: the RFP or PFP. As previously mentioned, a partial negative charge remains localized on the COOH ligand of ⁹Mn in the PFP. In this scenario, TEOAH⁺ can coordinate with species ⁹Mn to form ¹⁰Mn. This reaction step involves the exothermic formation of the intermediate (¹⁰Mn), succeeded by an activation barrier of 0.58 eV (^TS4Mn_PFP) compared to ⁹Mn. This transition state is considered “early” and is additionally exergonic by –2.01 eV. Protonation of one of the C–O bonds weakens the C–O bond, elongating it from 1.377 Å in ⁹Mn to 1.390 Å in ^TS3Mn (Fig.4). This process is accompanied by the cleavage of the C–OH bond, with a transition state of ^TS4Mn_PFP. In this context, the breakage of the C–OH bond represents the rate-determining step, although ^TS4Mn_PFP exhibits a hydrogen-bonding network between the CO group and TEOAH⁺, as well as the cleavage of C–OH (1.940 Å) between the COOH and TEOAH⁺. After the OH^– fragment is removed from COOH, it produces species ¹²Mn. This species can then be reduced at –5.23 eV to recreate the active ¹²Mn species and release CO, following a thermodynamically favorable pathway with a ΔG of –8.24 eV. The process has a low activation barrier of 0.19 eV for ^TS5Mn compared to ^12AMn (–7.83 eV), leading to the formation of a [Mn]^1– species. Alternatively, in the context of the reduction-first mechanism, a single-electron reduction occurs on [Mn-COOH] ¹⁰Mn, resulting in ¹²Mn. The calculated reduction potential of –1.962 V, which is more negative than that of –1.528 V (⁹Mn + e^– → ¹²Mn), indicates that the reduction-first step may present a favorable pathway by the less activation barrier of 0.47 eV (^TS4Mn_RFP) compared to the transition state of ^TS4Mn_PFP in PFP. Moreover, the cleavage of the C–OH bond in the RFP occurs at the ^TS4Mn_RFP step with a slightly lower barrier of 0.11 eV compared to ^TS4Mn_PFP. This step is exothermic and facilitates the formation of additional intermediates. As depicted in Fig.4, both ^TS4Mn_PFP and ^TS4Mn_RFP transition states are classified as “early” transitions. Specifically, ^TS4Mn_RFP is deemed more feasible than ^TS4Mn_PFP.

Fig.4 The reaction free energy (ΔG) profile for the CO2RR originating from the active 7Mn species. The PFP is illustrated in red, whereas the RFP is depicted in blue.

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Hence, reduction is deemed necessary and takes precedence over protonation. The reduction step increases the overpotential in the RFP due to its more negative reduction potential. However, it provides a higher reducing capacity to overcome the subsequent rate-determining C–OH bond cleavage protonation step. On the other hand, the PFP, with a reduced overpotential, follows a mechanism where protonation initiates the rate-determining C–OH bond cleavage step at the neutral [Mn-CO₂H]⁰ intermediate. While thermodynamically advantageous due to the subsequent formation of a cationic intermediate in [Mn-CO]⁺ alongside H₂O evolution (), this occurs at a kinetic expense due to its lower intrinsic potential energy compared to the higher overpotential RFP. Subsequent one-electron reduction of [Mn-CO]⁺ allows both pathways to converge at the neutral [Mn-CO]⁰ intermediate, facilitating CO dissociation and producing the free CO product and active species of ⁵Mn. This is followed by an additional one-electron reduction to restore the active catalyst. Additionally, there are low barriers encountered in this process, with ^TS5Mn experiencing a decrease in activation energy by 0.19 eV for the CO formation process. This elucidates the ease of significant CO production via this pathway, achieved through the generation of the active catalyst via one-electron reduction (at –1.723 V). This specific step is found to be thermodynamically more favorable.

3.4 3.4 HCOO^– formation

Fig.5 illustrates the free energy profile of the reaction depicting the formation of HCOO^– through the CO₂RR, initiated from the active ⁵Mn species via CO₂ addition and protonation steps. Additionally, the computed free energies for reducing CO₂ to form HCOO^– are referenced to the ⁵Mn complex and express all the values in eV. All species were optimized using the B3LYP/LANL2DZ(6-31G(d)) method. Single-point energy calculations were performed using the TZVP basis set and the B3LYP, M06, and PBE1PBE functionals, as detailed in Tables S6 and S7 (cf. ESM). The formation of HCOO^– is commonly recognized to occur through CO₂ insertion into metal hydrides [42−44]. In this context, it is noteworthy that HCOO^– indeed arises from the active ⁵Mn species, followed by protonation at the pK_α values of 26.8 (B3LYP), 26.9 (M06), and 25.6 (PBE1PBE), despite the thermodynamically more stable species being Mn-H (⁶Mn), generated by –1.47 eV, which reacts with CO₂ to form HCOO^–. This suggests the necessity of applying a sufficiently high pK_α to facilitate CO₂ insertion and/or release HCOO^– from the catalyst at a notable rate. After the formation of Mn-hydride (⁶Mn) from ⁵Mn, a specific step is recognized with an activation barrier of 2.51 eV (^TS2bMn_HCOO) compared to ⁶Mn for HCOO^– formation, and –7.66 eV for generating a highly thermodynamically stable and more reactive [Mn]^1– species. Another path involves the strong integration of CO₂ with the Mn center (⁵Mn), resulting in the generation of [Mn-CO₂]^1– (⁷Mn) through the transition state of ^TS2Mn. Additionally, the protonation step occurs as follows: ⁷Mn + H⁺ → ^7AMn, resulting in the formation of a highly stable intermediate at –3.48 eV (^7AMn). Following this, a transfer of H⁺ from the proton source of TEOAH⁺ aids in forming HCOO^– through the transition state of ^TS2aMn_HCOO.

Fig.5 The reaction free energy (ΔG) profile for the formation of HCOO– by CO2RR originating from the active 5Mn species through CO2 addition and protonation steps.

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Moreover, this specific phase displays a significant activation barrier of 3.00 eV (at ^TS2aMn_HCOO) when compared to ^7AMn, leading to the removal of HCOO^–. This removal results in the creation of a more stable [Mn]^1– species, effectively regenerating the active species in a thermodynamically favorable manner. In the end, both scenarios result in the release of HCOO^– due to the significant activation energy required and the catalyst’s regeneration through a thermodynamically less favorable pathway. However, the higher selectivity and favorability of CO formation over HCOO^– are attributed to the higher activation barriers involved.

3.5 3.5 H₂ release from HER

Our exploration of the mechanism was extended by scrutinizing the thermodynamic profile of protonation, transitioning ⁵Mn species to Mn-H for the HER. Experimentally, no evidence of Mn-H formation was observed, nor further protonation from TEOAH⁺ to release H₂, and to form the reactivity of active [Mn]^–1 species. Particularly, despite both Mn-hydride serving as an intermediate, this catalyst exhibits selectivity for HCOO^– generation over hydrogen evolution in a CH₃CN medium. In the instance of the Mn-hydride complex, a mere examination of the thermodynamics of intermediates () would suggest feasibility for hydrogen evolution, as all energies are thermally accessible. However, this suggests that the hindrance to hydrogen evolution lies in the reactivity of manganese hydride and its formation, which is also observed in other systems [42−44]. If the HER is not thermodynamically inhibited, it may be constrained by kinetics. Potential routes for hydrogen evolution are contemplated in to explore kinetics. The delineates the protonation of hydride formation by TEOAH⁺ (acting as a proton source), leading to ⁶Mn-H-H, the dihydrogen complex. In the context of the HER, we not only compared results obtained from the original B3LYP, M06, and PBE1PBE functionals but also included other functionals for comparison, such as B3LYP-D3 and M06L. This choice was motivated by the recognition that the M06-L functional offers improved accuracy in predicting chemical reaction barrier heights for the HER. Specifically, in our pursuit of heightened accuracy across the board, we opted for the M06-L functional, tailored to fit similar types of catalysts [45−47] aiming to enhance precision in determining chemical reaction barrier heights for the HER. Initially, the formation of ⁶Mn (Mn-H), two new competitive pathways emerge, allowing either the reaction with CO₂ to yield HCOO^–, which serves as the key intermediate in protonation to generate H₂ [22,48,49]. To comprehend the selectivity of the CO₂RR over the HER, the mechanism of the competitive HER was also computed. Initially, protonation of the Mn-H (⁶Mn) complex is achieved through the addition of a TEOAH⁺, resulting in the formation of a H–H (0.772 Å) fragment at the metal center (⁶Mn-H-H). Fig.6 illustrates the free energy profile of reactions, delineating the formation of Mn-hydride leading to hydrogen evolution, stemming from the active ⁵Mn species through the involved protonation steps. The mechanism initiates with TEOAH⁺, facilitating the cleavage of the N–H bond, resulting in Mn-H formation.

Fig.6 The reaction free energy (ΔG) profile for the formation of Mn-hydride toward hydrogen (H2) evolution originating from the active 5Mn species through the protonation steps involved and also the selected bond lengths and possible hydrogen bond interactions.

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Subsequently, a hydrogen atom transfers from the proton source (TEOAH⁺) to the Mn-H-H unit, forming a dihydrogen fragment in the intermediate ⁶Mn-H-H. This particular step is thermodynamically more stable in the order of M06L (–1.89 eV) > M06 (–1.77 eV) > B3LYP (–1.72 eV) > B3LYP-D3 (–1.68 eV) > PBE1PBE (–1.56 eV), respectively (Table S8, cf. ESM). From Table S8, the computed free energies for H₂ evolution and the estimated energies are referenced to the ⁵Mn complex. All species underwent optimization using the B3LYP/LANL2DZ(6-31G(d)) method. Single-point energy calculations were carried out using the TZVP basis set with the B3LYP, M06, PBE1PBE, M06-L, and B3LYP-D3 functionals. Additionally, the M06-L functional exhibits a lower activation barrier for the transition state of ^TSMn_H-H by 0.06 eV compared to ⁶Mn-H and ${}^{\mathrm{T}\mathrm{S}}{\mathrm{M}\mathrm{n}}_{{\mathrm{H}}_2}$ by 0.19 eV compared to the B3LYP, B3LYP-D3, M06, and PBE1PBE functionals utilized. This distinction is evident in Fig.6. This segment demonstrates a relatively higher favorability toward the formation of the Mn-H-H intermediate when employing the M06-L functional, with a smaller barrier difference of 0.16 eV and 0.37 eV (^TSMn_H-H) compared to B3LYP-D3 and M06. Nevertheless, a comparable pattern was observed when considering the B3LYP and PBE1PBE functionals, featuring elevated activation barriers (0.82 eV with B3LYP and 0.75 eV with PBE1PBE). This observation confirms the reduced feasibility of the HER from a thermodynamic perspective. In contrast, the process appears to be relatively straightforward from a thermodynamic perspective at room temperature. It is noteworthy that the energy barrier for the step involving the release of H₂, which serves as the rate-determining step, is slightly elevated by 0.37 eV (at M06L) for the cleavage of the Mn-H-H–TEOA bond (${}^{\mathrm{T}\mathrm{S}}{\mathrm{M}\mathrm{n}}_{{\mathrm{H}}_2}$) compared to that of the transition state of ^TSMn_H-H. This discrepancy produces heightened selectivity for the HER. The M06-L functional demonstrates commendable and consistent performance, providing a much more accurate activation barrier than other functionals.

Ultimately, the liberation of H₂ from the metallic center facilitates the regeneration of the active species ⁵Mn. The overall findings from the HER show a preference for CO in the CO₂RR over the HER, as well as a preference for H₂ evolution over the formation of HCOO^–. Additionally, the order of selectivity and feasibility, with CO > H₂ > HCOO^– generations (Fig. S1, cf. ESM), was well established and confirmed through theoretical considerations.

3.6 3.6 Comparison with experiments

Steinlechner and coworkers [16] reported on the electrocatalytic reduction of CO₂ using novel Mn(I) diimine complexes [Mn(X)(CO)₃Br], where X represents pyrox, benzox, and qinox. Through a control experiment conducted under an air atmosphere, it was verified that HCOO^–, H₂, and CO were not generated in the absence of CO₂. Eventually, both CO and H₂ were observed as reaction products. The catalyst displayed two consecutive irreversible one-electron reduction potentials at –1.29 and –1.20 V, as determined experimentally. The computational results indicated an initial one-electron reduction followed by Br^– dissociation. The calculated reduction potentials (–1.093 and –1.976 V at M06) agreed with the experimental data. Subsequently, we proposed a couple of electrocatalytic cycles to describe the CO₂RR and HER. The CO₂RR cycles encompassed catalyst activation, CO₂ fixation and protonation, and CO release with catalyst regeneration. The HER cycles involved protonation, Mn-H formation, H₂ release, and catalyst regeneration. Analyzing the overall potential energy profile for the CO₂RR and HER, we observed the highest energy barrier (${}^{\mathrm{T}\mathrm{S}}{\mathrm{M}\mathrm{n}}_{{\mathrm{H}}_2}$) in the HER, attributed to O–H bond cleavage, which constitutes the rate-determining step. However, this step was not significantly challenging at room temperature. This suggests that the transferred electron primarily leads to CO formation, followed by HER initiation. Additionally, in the CO₂RR, the calculated reduction potential of [MnCOOH]⁰ was approximately 1.911 V more negative than that of [MnCO], indicating the necessity of protonation before subsequent reduction at the experimentally applied potential (–1.20 V). Thus, wet conditions are crucial for CO₂ electro-reduction. Moreover, our study’s calculated charge transfer mechanism emphasized the central metal’s electron population’s critical role in describing reactivity. As previously reported in the ligand pyrox, substituents increase electron delocalization on the Mn center compared to benzox and qinox, favoring CO₂ fixation and reduction [16]. This finding suggests that coordinated atoms can be tailored to facilitate electron reduction to catalyst centers and regulate the production ratio of CO, HCOO, and H₂, offering promise for future research.

4 4 Conclusions

In summary, we utilized DFT calculations to explore the electronic structure and selectivity of the CO₂RR compared to the competing HER, catalyzed by the [Mn(pyrox)(CO)₃Br] complex. Two electrons are transferred to the Mn center through two sequential one-electron reductions, facilitating CO₂ fixation via establishing a Mn–C bond. Subsequently, the computed reduction potential from ⁹Mn → ¹¹Mn is more negative than that from ¹⁰Mn → ¹²Mn, indicating the necessity of reduction before subsequent protonation. The subsequent CO release and catalyst regeneration steps proceed along a thermodynamically favorable pathway. For the HER, the mechanistic steps involve (i) protonation and Mn–H formation and (ii) H₂ release and catalyst regeneration. Similar mechanistic pathways are observed in the HER. It can be inferred that the Mn center offers a promising avenue for overcoming the substantial activation energy barrier associated with the cleavage of the C–OH bond (the rate-determining step in the CO₂RR) and the Mn–H bond (the rate-determining step in the HER). The selectivity favoring the CO₂RR over the HER is ascribed to the higher energy barrier involved in producing ⁶Mn-H-H during the formation of H₂ (^TSMnH₂). Conversely, the selectivity of CO over HCOO⁻ is also attributed to the higher energy barrier present in this process. This study elucidates the complete electrocatalytic cycles for CO₂ reduction coupled with water-splitting reactions through detailed calculations. We anticipate that these computational findings will offer valuable insights for designing molecular catalysts capable of modulating the selectivity of the CO₂RR.

References

1. Khan V A Solubilityof gases in molten polymers at high pressuresDissertation for the Doctoral DegreeMichiganWayne State University 1998
2. Tomasko D L Li H Liu D Han X Wingert M J Lee J Koelling K W A review of CO₂ applica-tions in the processing of polymersInd Eng Chem Res 2003 4264316456. doi:10.1021/ie030199z
3. Areerat S Hayata Y Katsumoto R Kegasawa T Egami H Ohshima M Solubilityof carbon dioxide in polyethylene/titanium dioxide composite underhigh pressure and temperatureJ Appl PolymSci 2002 86282288. doi:10.1002/app.10944
4. Newitt D M Weale K E Solution and diffusion of gasesin polystyrene at high pressuresJ ChemSoc 1948 IXl541l549
5. Koros W J Paul D R Rocha A A Carbon dioxide sorption and transport in polycarbonateJ Polym Sci, Part B: Polym Phys 1976 14687702
6. Sato Y Yurugi M Fujiwara K Takishima S Masuoka H Solubilities of carbon dioxideand nitrogen in polystyrene under high temperature and pressureFluid Phase Equilibria 1996 125129138. doi:10.1016/S0378‐3812(96)03094‐4
7. Davis P K Lundy G D Palamara J E Duda J L Danner R P New pressuredecay techniques to study gassorption and diffusion in polymers at elevated pressuresInd Eng Chem Res 2004 4315371542. doi:10.1021/ie034075y
8. Michaels A S Bixler H J Solubility of gases in polyethyleneJ Polym Sci 1961 50393412. doi:10.1002/pol.1961.1205015411
9. Brantley N H Kazarian S G Eckert C A In situ FTIR measurement of carbon dioxide sorption intopoly (ethyleneterephthalate) at elevated pressuresJ Appl Polym Sci 2000 77764775. doi:10.1002/(SICI)1097‐4628(20000725)77:4<764::AID‐APP8>3.0.CO;2‐#
10. Reid R C Skierwood T K Prausnitz J M The properties of gases and liquidsNew YorkM cGraw-Hill Book Company 1987
11. Wissinger R G Paulaitis M E Molecular thermodynamic modelfor sorption and swelling in glassy polymer-CO₂ systems at elevated pressuresInd EngChem Res 1991 30842851. doi:10.1021/ie00053a006
12. Garg A Gulari E Manke C W Thermodynamics of polymer melts swollen with supercriticalgasesMacromolecules 1994 2756435653. doi:10.1021/ma00098a019
13. Sanchez I C Lacombe R H An elementary molecular theoryof classical fluidsJ Phys Chem 1976 8023522362. doi:10.1021/j100562a008
14. Lacombe R H Sanchez I C Statistical thermodynamicsof fluid mixturesJ Phys Chem 1976 8025682580. doi:10.1021/j100564a009
15. Sanchez I C Lacombe R H Statistical thermodynamicsof polymer solutionsMacromolecules 1978 1111451156. doi:10.1021/ma60066a017
16. Panayiotou C Vera J H Local compositions and localsurface area fractions: a theoretical discussionCan J Chem Eng 1981 59501505
17. Panayiotou C Vera J H Statistical thermodynamicsof T-mer fluids and their mixturesPolymJ 1982 14681694. doi:10.1295/polymj.14.681
18. Kiszka M B Meilchen M A Mchugh M A Modeling high pressure gas-polymer mixtures using the Sanchez-Lacombeequation of stateJ Appl Polym Sci 1988 36583597. doi:10.1002/app.1988.070360311