DFT Investigation into the Role of Superbases as the Auxiliary Groups in CO₂ Reduction ^†

Abstract

Non-metallic hydride donors have emerged as an interesting, highly tunable class of compounds capable of CO₂ reduction, with benzimidazoles being simple, yet efficient and regenerable, representatives. In this work, the role of superbases as auxiliary groups attached to the benzimidazole framework was investigated using the CPCM(CH₃CN)/ωB97xD/aug-cc-pVTZ//CPCM(CH₃CN)/ωB97xD/6-31+G(d,p) approach. Three modes of operation were assessed through hydricity calculations and the modeling of two different CO₂ reduction mechanisms. Among the superbases considered, phosphazene substituents yielded the largest increase in the hydride donation ability, lowering hydricity by 6 kcal mol⁻¹ relative to 2-methylbenzimidazole, with the α-substitution exerting a stronger effect than β-substitution. For most systems, changes in hydricity correlate with changes in aromaticity, except in systems where steric congestion limits optimal substituent alignment. CO₂ activation pathways encompassing guanidine/CO₂ hydrogen bonding and guanidinium carboxamidine formation were modeled. In the former, transition state structures were significantly stabilized, and the overall exergonicity of the reduction is enhanced. Also, utilizing the longer and more flexible linker additionally decreases the barrier for the reaction. The carboxamidine pathway is disfavored because of the high stability of the carboxamidine intermediate and low barrier for the C–N bond cleavage, which reverses the mechanism to the reduction of isolated CO₂.

1. Introduction

Global warming is one of the greatest ecological challenges. Carbon dioxide is recognized as one of the main contributors to this phenomenon as its atmospheric concentration continuously increases [1]. Much effort has been devoted to optimizing the circular economy of CO₂, thereby reducing the carbon footprint as much as possible. In general, the conversion of CO₂ into value-added chemicals represents an important scientific challenge, and researchers across all fields are working hard to achieve this goal while preserving process sustainability and adhering to the 12 principles of green chemistry [2]. Among various strategies, treating CO₂ as a feedstock chemical for polymer processing and liquid fuel production is considered a highly promising use [3].

Despite its high thermodynamic stability and significant electrochemical potential needed for its reduction, CO₂ can be converted into valuable organic chemicals both electrochemically and non-electrochemically using appropriate activators [4,5,6,7]. The non-electrochemical strategies commonly used today involve the reaction of CO₂ with strong nucleophiles, such as hydride anions, metal hydrides, and superbases. Studies indicate that amines and other nitrogen-based nucleophiles form carbamate intermediates; these are essential in the synthesis of organic carbonates and polycarbonates, which serve as green solvents or biodegradable polymers [8,9,10,11,12,13]. In this context, guanidines—as archetypal superbases—exhibit high catalytic activity while remaining cost-effective, readily accessible, and free of heavy metal ions [10,14]. Besides that, cyclic guanidines have been recognized as effective catalysts for the CO₂ reduction with hydrides [15,16], as well as potent hydride donors [17,18]. It has been proposed that the guanidinium cation effectively stabilizes the development of the negative charge during CO₂ reduction [19]. Motivated by this idea, a guanidine-rich metal–organic cage (MOC) was designed and employed as the active catalyst for the electrochemical activation of CO₂ [20].

Bioinspired organic hydrides have emerged as a promising class of reductants capable of converting CO₂ into formic acid and its derivatives. These species are particularly attractive because they can be regenerated through electrochemical reduction [21]. Their capacity to transfer hydride anion to an acceptor is determined by hydricity (ΔG°_H⁻), defined as the Gibbs energy for the hydride transfer half-reaction (Equation (1)).

DH → D⁺ + H⁻  Δ_rG° = ΔG°_H⁻(DH)

(1)

The experimental hydricity of CO₂ in acetonitrile was determined to be 184 kJ mol⁻¹ (44 kcal mol⁻¹), and it was measured by bracketing against [HPt(diphosphine)₂]⁺ hydride donors [22,23]. The hydride donors (DH) with hydricity values lower than this threshold are thermodynamically capable of reducing CO₂ to formic acid. The general mechanism for this process employing a neutral hydride donor is illustrated in Scheme 1. As noted by Glusac and coworkers, mechanisms such as aromatization or the addition of electron-donating substituents stabilize the resulting cation and shift the equilibrium toward the products [21].

Guanidines and other strong bases are recognized as powerful π–electron donors and employed as the building blocks in the design of highly basic phosphines [24,25]. Analogous to the effect of NMe₂ on the hydricity of the benzimidazole derivatives [26], and the recent results in the design of bisphosphine-type hydride donors [27], the incorporation of superbasic groups into the hydride donor framework is expected to lower their hydricity (Role 1). Furthermore, given the beneficial role of the guanidinium cation in stabilizing charge, we envisioned that it could serve as a functional auxiliary group. Specifically, we postulate that it may promote hydride transfer to CO₂ by stabilizing the transition state and the final product through hydrogen bonding with CO₂ and formate anion (Role 2), thereby increasing the reaction rate and overall exergonicity of the reaction. Alternatively, neutral guanidines are known to bind CO₂ and form carboxamidines (Role 3). This process eliminates the energetic penalty for CO₂ deformation during reduction and may lower the kinetic barrier [15].

This study explores how guanidine and related superbases affect the hydricity of benzimidazole derivatives, focusing specifically on aromaticity as a primary driver of cation stabilization and its changes upon the hydride transfer. Additionally, we evaluate the viability of guanidines in cooperative CO₂ reduction through a detailed analysis of the most probable reaction pathways.

2. Results

2.1. Influence of Superbases on the Hydricity of the Selected Benzimidazole Derivatives (Role 1)

The analysis started by comparing the hydricities of known hydride donors based on the benzimidazole framework (1H–7H). The initial set of benzimidazole systems (BIM group) was further enlarged to include hexacyclic analogs 8H and 9H (BIG group) and triaminomethane derivatives 10H and 11H (TAM group). This selection covers three distinct cation stabilization modes: (i) varying the π-electron donation power at position 2 of the imidazole subunit (1H–5H), (ii) extended delocalization over the polycyclic backbone (6H–9H), and (iii) formation of a tricyclic guanidium cation (10H and 11H). The hydricities for all compounds were calculated in acetonitrile at the CPCM(CH₃CN)/ωB97xD/aug-cc-pVTZ//CPCM(CH₃CN)/ωB97xD/6-31+G(d,p) level of theory. This computational approach demonstrated very good correlation between the experimental and computed hydricities [17,21,28]. The structures and the calculated data are presented in Figure 1, while the energy data are given in Table S1a (Supplementary Materials).

The calculated hydricities for 1H, 2H, and 4H–7H are, on average, 3 kcal mol⁻¹ lower than the experimental data measured in DMSO [26], while the relative trend is well preserved with a correlation coefficient of r² = 0.967 (Figure S1). Replacing the phenyl subunit with 4-NMe₂Ph (going from 2H, 6H, and 8H to 4H, 7H, and 9H) decreases the hydricity by 3.5, 5.6, and 5.6 kcal mol⁻¹, respectively. The more pronounced substituent effect observed in 7H/7⁺ and 9H/9⁺ systems is expected, as these cations adopt a fully planar conformation. Planarity facilitates efficient charge delocalization across the entire carbocyclic framework and maximizes the π-donating contribution of the NMe₂ group. In contrast, the phenyl ring in 2⁺ and 4⁺ is nearly perpendicular to the benzimidazole plane, which restricts charge transfer. This is qualitatively evidenced by the shortening of the d_NC bond (Figure 1) by 0.028 Å in 7H to 7⁺ or 9H to 9⁺, compared to 0.020 Å for the 4H/4⁺ pair. Additionally, NBO analysis indicates that nitrogen lone-pair donation in 4⁺ (quantified by the E²_ij stabilization energy in the NBO framework) is 3–4 kcal mol⁻¹ smaller than in the other two cations. This finding supports a more substantial increase in the double-bond character of the d_NC bond in the fully planar systems.

Three groups of hydride donors (BIM, BIG, and TAM) were further expanded to include derivatives bearing dimethylamino (DMA) or superbase substituents at the α- and β-position of the benzimidazole subunit. Electron-rich superbases were chosen because they are expected to lower hydricity by stabilizing the cation formed after the hydride transfer. The structures are shown in Figure 2, and energies are given in Table S1b (Supplementary Materials).

Incorporating dimethylamino or superbasic groups into the benzimidazole subunit generally decreases hydricity (Figure 1 and Figure 2), with a more pronounced effect observed for derivatives (MaH) compared to β-analogs (MbH). Among the groups studied, the influence of the P1 phosphazene substituent was the largest. For instance, substitution with the P1 group at the α- and β-positions lowers the hydricity of 1H by 6.2 and 4.6 kcal mol⁻¹, respectively. While the two guanidine moieties (TMG and ImIm) show similar impacts on ΔG*_H⁻(1H), the effect of CPI falls between that of P1 and TMG. Interestingly, the DMA group exhibits the opposite trend: hydricities for α-substituted derivatives (12aH, 17aH, and 20aH) are equal to or higher than those calculated for the parent structures. Conversely, DMA substitution at the β-position lowers the hydricities by up to 3.7 kcal mol⁻¹; the effect is slightly weaker than P1 but larger than that of TMG, ImIm, or CPI.

The reduced effectiveness of α-substitution stems from the inability of the DMA group to remain coplanar with the aromatic ring. Consequently, a nitrogen lone-pair is rotated to 49° (42° for the cation) relative to the benzene ring plane. Also, the degree of pyramidalization (DP) at the nitrogen atom of the DMA group is significant, measuring 20.1° (12aH) and 21.0° (12a⁺) (Figure 3). These geometrical constraints diminish π-conjugation, echoing patterns observed in strained guanidines [29]. Inspection of the geometries of 16aH and 16bH reveals that the optimal conformation favors π–π rather than n–π overlap across the substituent–framework (C-SB) junction bond. This is supported by the frontier orbital analysis of the parent structures P1H, TMGH, and CPIH, where HOMO is π-orbital delocalized across the guanidine or phosphazene double bond (Supplementary Materials, Figure S2). Due to the quasi-spherical geometry of the P1 group, structures 16aH and 16bH, and their cationic forms, can achieve a coplanar arrangement of the π- systems, facilitating the effective delocalization across the junction bond. Furthermore, the nitrogen lone-pair in 16a is oriented toward the N_im-Me methyl group, forming an [N∙∙∙H-C] hydrogen bond. This interaction is supported by the identification of corresponding (3,−1) bond critical points (BCPs) along both its covalent and noncovalent bond paths (Supplementary Materials, Figure S3). In contrast, the geometry of the TMG, ImIm, and CPI groups hinders planarization and enforces the less effective n–π delocalization. A similar rationalization applies to the β-substituted derivatives. In these systems, the DMA and P1 groups can adopt geometries that maximize π-donation, resulting in lower hydricities than those of the TMG, ImIm, and CPI derivatives. Despite the significant changes in hydricities caused by the substitution, no significant changes in the partial charges and the C2-H bond lengths in either the BIM or TAM groups of compounds were observed (Table S2 in Supplementary Materials).

The hydricity differences between 22aH and 22bH are essentially identical to those observed for 16aH and 16bH, suggesting that similar geometric and electronic effects are at play. Conversely, the BIG family of structures exhibits an opposing trend. In these systems, significant steric congestion arises from the proximity of the lateral backbone methyl groups to the superbasic subunit. Consequently, the hydricities of the 17bH–19bH derivatives are lower than those of their corresponding α-isomers.

For the next step, the impact of the substitution on aromaticity was examined, utilizing the MCI [30] and NICS(1)_zz [31] indices. While no general correlation between these indices was observed, the results are consistent with known trends. Krygowski and coworkers previously established that strongly aromatic systems are generally resistant to the substituent effect, becoming more sensitive as the aromaticity decreases [32]. Consequently, the observed variation within 7 units for NICS and 1.5 units for MCI is not surprising. Both indices confirm that all studied systems remain highly aromatic, with a slight increase in the aromaticity of the benzene ring following hydride transfer; additionally, the imidazolidine ring gains aromatic character as expected. Substituents attached to the benzimidazole subunit generally reduce aromaticity, with P1 exerting the most significant influence. The changes in the indices are more pronounced for the cationic structures than for neutrals, a finding that seems to oppose the claims of Krygowski and coworkers mentioned above, but this phenomenon needs to be re-examined in more detail on a larger set of molecules. Finally, it is noteworthy that β-substitution triggers more substantial changes in aromaticity than α-substitution (Figure S4 in Supplementary Materials).

Having confirmed that certain structural groups exhibit systematic changes in aromaticity upon substitution, we investigated whether this trend consistently extends to hydricity. For this purpose, we calculated total changes in aromaticity (Δ(MCI), Equations (2)–(4)) and compared the values with the calculated ΔG*_H⁻ (Figure 1 and Figure 2).

Δ(MCI)₆ = MCI(DH)₆ − MCI(D⁺)₆

(2)

Δ(MCI)₅ = MCI(DH)₅ − MCI(D⁺)₅

(3)

Δ(MCI) = Δ(MCI)₆ + Δ(MCI)₅

(4)

(ΔG*_H⁻)_fit = 5.01 × Δ(MCI)₆ + 9.96 × Δ(MCI)₅ + 18.45

(5)

where indices 5 and 6 refer to the 5- and 6-membered rings, respectively. Equation (5) was derived via multiple linear regression using two independent variables (Δ(MCI)₆ and Δ(MCI)₅) across the set of 35 investigated hydride donors. The resulting data are tabulated in Tables S3 and S4 (Supplementary Materials), and the observed trends are shown in Figure 4.

While both approaches show systematic changes for specific groups of compounds, multiple linear regression indicates better overall agreement. The parent structures and their β-substituted derivatives generally correlate well with the established trend line. In contrast, α-substitution results in significant deviation from the correlation line, except for most members of the TAM series. However, α-P1-substituted derivatives (outlined triangles in Figure 4) consistently act as outliers in all categories, including TAM. Significant outliers and a distinct regression slope are observed for structures where the cation is delocalized over large polycyclic systems (BIG group, red dots in Figure 4). This divergence suggests that their electronic properties are governed by factors requiring further investigation. These trends demonstrate that the perturbations in aromaticity induced by the substitution systematically influence hydricity.

2.2. CO₂ Reduction Assisted by Guanidinium Cation (Role 2)

The second role of the superbases examined in this work is their potential application as activators of CO₂ reduction through hydrogen bonding interactions. Our selection was restricted to a protonated guanidine capable of forming two hydrogen bonds with the formate anion. The influence of the guanidinium cation on the kinetics and thermodynamics of CO₂ reduction was investigated using 1H as the hydride-donating component tethered to a tetrahydropyrimidin-2(1H)-imine via ethylene or propylene bridges, as shown in Figure 5.

A preliminary conformational search was performed using the xTB/GOAT approach, [33,34] implemented in the ORCA 6.1 software [35,36]. Twelve lowest-energy conformations were re-optimized at the ωB97xD/6-31+G(d,p) level of theory in combination with the CPCM(ACN) continuum solvation model (Section S4, Table S5a–c in Supplementary Materials). The resulting conformations for the neutral (23H or 24H) and protonated (23H₂⁺ and 24H₂⁺) forms were divided into three distinct sets based on the pyramidalization of the imidazole nitrogen atoms and the position of the guanidine subunit relative to the C2-H bond. The search for the lowest-energy structures was further performed by varying the spacer conformation (gauche vs. all-antiperiplanar), the tautomeric form (endocyclic vs. exocyclic C=N double bonds in the neutral guanidine subunit), and the syn/anti isomerism at the exocyclic nitrogen atom.

Regardless of the spacer length, the most stable structures (c1 conformer, Figure 5) feature the guanidinium cation preferentially positioned “below” the benzimidazole ring (C2-Me side). The structures are characterized by the intermolecular hydrogen bonding between the guanidine and benzimidazole moieties, as evidenced by NBO second-order perturbation energies (E_ij⁽²⁾ = 14.42 kcal mol⁻¹). Additionally, conformations c2 and c3 (Figure 5) were evaluated to account for the expected synergistic effect of the two subunits during the CO₂ binding and reduction. Conversely, in the lowest-energy conformations of 23H and 24H, the neutral guanidine subunit resides “above” the plane (C2-H side). Notably, these most stable neutral conformers closely correspond to conformer c3 of the protonated forms.

In the context of CO₂ reduction, the guanidinium subunit in conformer c1 cannot assist the CO₂ binding but influences reaction thermodynamics by modulating the hydricity of the benzimidazole fragment. Specifically, calculated hydricities of 23H and 24H are comparable to that of 1H, amounting to 41.1 and 43.8 kcal mol⁻¹, respectively, implying their similar capacity to reduce CO₂. On the other hand, hydricities of their protonated forms are 51 and 47 kcal mol⁻¹, respectively (Table S6 in Supplementary Materials). This shift can be attributed to the energetically unfavorable formation of the dictations.

The CO₂ reduction mechanism was modeled by following the reaction coordinate for hydride transfer from the benzimidazole subunit to CO₂. The resulting barriers and reaction Gibbs energies were evaluated against the parent 1H. Given that c2 and c3 are interconvertible via imidazole ring puckering, they likely share a transition state for the reduction step. All energies were calculated relative to the lowest-energy conformer with CO₂ separated by 10 Å (23_ref and 24_ref), the distance at which no intermolecular interactions are expected. The reaction schemes and thermodynamic profiles are summarized in Figure 6, while the energies of all species are presented in Tables S7 and S8 in the Supplementary Materials.

The lowest transition state (TS) energies were obtained for conformers c2 (23H₂⁺_TS) and c3 (24H₂⁺_TS), amounting to 19.8 and 16.8 kcal mol⁻¹, respectively. These values are noticeably lower than in 1H_TS. In contrast, the energy of the 23H₂⁺_TS(c1) conformer is 1.9 kcal mol⁻¹ higher than that of 1H_TS, while the calculated barrier for 24H₂⁺ is nearly the same as that of 1H_TS. Here, we recall that the guanidinium cation—CO₂ hydrogen bond in c1 conformers is absent. These results indicate that hydrogen bonding and greater conformational flexibility are beneficial for the reduction process. We should emphasize that our calculated ΔG^‡(1H_TS) is slightly higher than the previously reported value (ΔG^‡(1H_TS) = 20.3 kcal mol⁻¹) [37]. A discrepancy arises from the treatment of the entropy contribution, which can be a significant source of error [38]. However, as this study focuses on relative trends, any potential systematic errors are expected to be consistent across all structures. Here, we can mention that the sum of the Gibbs energies of 1H and CO₂ is 13.2 kcal mol⁻¹ lower than our reference point, which would lead to a much higher barrier (28.8 kcal mol⁻¹) for CO₂ reduction, comparable to that obtained by Lee and coworkers [17].

Beyond their superior kinetics, the product formed from c2 or c3 conformers of 23H₂⁺ is more stable than that from the c1 isomer by more than 11 kcal mol⁻¹. Furthermore, the spatial orientation of the guanidinium group in the c3 conformer (Figure 5) facilitates the reorientation of the resulting formate, allowing for the formation of two hydrogen bonds. This interaction additionally stabilizes the product by 5 kcal mol⁻¹, resulting in an overall exergonicity of −13.2 kcal mol⁻¹. Similarly, the reduction of CO₂ with 24H₂⁺(c3) is exergonic by −13.5 kcal mol⁻¹. However, in this case, two hydrogen bonds were formed during the IRC calculations, with no evidence of another minimum.

2.3. CO₂ Reduction via Carbamates (Role 3)

The reaction profile for CO₂ reduction via intramolecular hydride transfer is illustrated in Scheme 2 and Figure 7. As in the previous section, the energies of all minima were referenced to the CO₂-separated structure (26_ref, Figure 7 and Table S8 in Supplementary Materials). The calculations show that the most stable conformers of carboxamidines 25 and 26, formed from two tautomeric forms of 23H, are essentially isoenergetic and lie 16.5 kcal mol⁻¹ below the CO₂-separated structure (26_ref). Accordingly, the energies of the intermediates and the products, as well as activation barriers, were evaluated relative to 25 and 26. The results indicate that the reaction does not take place at the carboxamidine stage. Instead, attempts to locate a transition state for hydride attack at the carboxamidine carbon led to C–N bond cleavage and identification of the TS2(M) structure. IRC calculations starting from TS2(M) converged to the expected products and to the intermediate complexes 23Hn1_CO₂ or 23Hn2_CO₂ (Figure 7), which can subsequently undergo intramolecular hydride transfer through transition states located 21 kcal mol⁻¹ above these intermediates. However, due to the stability of the carboxamidines 25 and 26, the calculated barriers for the reduction step are 35.5 kcal mol⁻¹ for TS2(25) and 35.0 kcal mol⁻¹ for TS2(26), which are 11–15 kcal mol⁻¹ higher than those obtained for 23H₂⁺ (Figure 6). To complete the reaction profile, the TS1(25) and TS1(26) structures were also optimized. The calculated barriers for the formation of 25 and 26 from the intermediate complexes 23Hn1_CO₂ and 23Hn2_CO₂ are approximately 2 kcal mol⁻¹, whereas the C-N bond cleavage (the reverse process) is significantly more demanding, with calculated barriers of 11.6 and 13.9 kcal mol⁻¹, respectively.

These results indicate that, if reduction occurs, it proceeds via the noncovalent 23H_CO₂ complex (path “a” in Scheme 2) rather than through the carboxamidine intermediate (path “b” in Scheme 2). Overall, within the proposed mechanism, the presence of neutral guanidine leads to a bifurcation of the CO₂ pathway, with carboxamidine formation emerging as the dominant process. For the conversion of CO₂ to formate to take place, a tandem sequence involving carboxamidine cleavage followed by hydride transfer would be required. However, the thermodynamics of this sequence are highly unfavorable, being endergonic by 13–14 kcal mol⁻¹ (the initial step) and 9 kcal mol⁻¹ (the overall process). Given both the relatively high activation barrier and the endergonic nature of the overall transformation, CO₂ reduction would require significantly harsher reaction conditions. Taken together, these computational findings suggest that carboxamidine formation inhibits rather than promotes CO₂ reduction, and that neutral guanidines are not suitable candidates for the auxiliary groups.

3. Discussion

This study explores the utility of guanidine and other superbases as auxiliary functional groups that can assist in the reduction of CO₂ using non-metallic, benzimidazole-based hydride donors. Two different motifs of substitution were considered: (i) direct substitution on the benzimidazole subunit, and (ii) a guanidine substituent linked to the benzimidazole moiety by a linker.

The first type of substitution primarily modulates the hydricity, which was taken as an indication of the substituent effect. Based on the “push–pull” concept developed by Raczynska and Gal [39], it was hypothesized that a stronger π-donating group would lead to a greater decrease in hydricity. This reasoning is further supported by recent results on bisphosphines, in which P1-substituted phosphines exerted a greater effect on hydricities than TMG and amidine groups [27]. In our case, the following trend in substituent effects was observed for the β-substitution pattern: P1 > DMA > TMG ≈ ImIm ≈ CPI. This trend is unexpected, given the trend in the basicity of phosphines and phosphazenes with the same electron-donating substituents, in which the DMA substituent has the weakest influence [25,40,41]. According to the results presented in the previous section, this is most likely due to the inability of the guanidine-based and CPI substituents to achieve the conformation with the optimal π-π overlap across the C-N junction bond. A more detailed insight into this observation requires a rigorous analysis of the electronic structure in these systems and in properly selected analogs, which is beyond the scope of this paper. In contrast, α-substitution yielded less predictable trends due to steric congestion, which prevents the substituents from adopting the optimal geometry for π-donation. Nevertheless, the α-substitution exerted a more pronounced impact on hydricity, with α–P1 (16aH) showing a maximal decrease of 6.2 kcal mol⁻¹ relative to 1H. Interestingly, the changes in partial charges at C2 and the adjacent hydrogen atoms remain practically constant. The attenuated effects were observed in systems in which the resulting cation could delocalize over a larger aromatic framework, prompting an analysis of changes in aromaticity. While specific groups of molecules showed reasonably strong correlations, the systematic deviations observed in α–P1 derivatives suggest that a more detailed dissection of energy changes is required.

The second substitution motif introduces monocyclic guanidine or its protonated form as an auxiliary group that can assist in CO₂ activation during the reduction step. In agreement with data from the literature [37], transition state structures for CO₂ reduction exhibit pronounced bending of the O=C=O angle (145–148°), indicative of significant substrate activation. However, a substantial decrease in the activation barrier by 5.5 kcal mol⁻¹ is observed only when a propylene linker is employed. Assuming the same pre-exponential factor, the rate constant would approximately increase by a factor of 10⁴. In contrast, the shorter ethylene linker appears insufficient to provide the conformational flexibility required to achieve optimal geometry during the reduction step.

The results also indicate that hydrogen-bonding interactions exert a stronger influence on the reaction’s thermodynamics than on its kinetics. Formation of the HB with the formate anion lowers the Gibbs energy of the reaction by up to 11 kcal mol⁻¹ if two HBs are formed. Our computations further suggest that formation of the carboxamidine intermediate may serve as a side pathway that effectively sequesters CO₂ and maintains its proximity to the reaction center. The carboxamidine moiety is cleaved during the reduction step, and the overall process proceeds similarly to the noncovalent complexes described above (Role 2). However, activation barriers are higher and have pronounced endergonicity. These findings strongly suggest that the protonated guanidine is a more effective auxiliary group than its neutral counterpart, thereby limiting the structural variability achievable through combining the different functional roles of the superbasic groups investigated in this work. Notably, the basicity of the guanidine subunit limits its possible combination with substituents playing Role 1 to those of lower basicity than guanidine itself.

4. Materials and Methods

Computational details: All DFT calculations were performed using the Gaussian16 software [42], while the conformational analysis was done using the GOAT routine implemented in the ORCA 6.1 program package [33,34,35,36]. The structures were fully optimized using ωB97xD density functional [43] in combination with the 6-31+G(d,p) basis set. The nature of the stationary points was verified with vibrational analysis (NImag = 0 for minima or NImag = 1 for the TS structures). Electronic energies were refined by the single-point calculations at the ωB97xD/aug-cc-pVTZ levels of theory. Calculations were performed in acetonitrile approximated as the dielectric continuum, and treated by employing the CPCM approach (ε(CH₃CN) = 35.688) [44]. This computational model is very good at calculating hydricities, which was confirmed earlier [17,28,45]. The employed model is also benchmarked against the experimental hydricities of 21 known hydride donors taken from Ref. [45], providing the linear correlation function given in Equation (6) with R² = 0.994 and the mean unsigned error of 1.8 kcal mol⁻¹. This function was used for calculating the hydricities in this work.

ΔG*_H⁻(exp) = 0.996 × ΔG*_HHR − 404.134

(6)

ΔG*_HHR = G*(DH) − G*(D⁺)

(7)

The details of the calculations and the comparison with several other density functionals have been submitted to another journal.

The Gibbs energy was corrected for low-energy vibrations (<100 cm⁻¹) according to the recommendations of Truhlar and coworkers [46]. The second-order perturbation energies were calculated using the NBO 3.1 routine within the Gaussian16 software, and the bond critical points were identified using AIM2000 software, version 2 [47,48,49]. The Multiwfn 3.8 program was used for the calculation of MCI indices from HF/6-31G(d) wavefunction and with iMCBOtype = 1 setting [50]. NICS(1)_zz values were taken from the NMR GIAO calculations at the B3LYP/6-311+G(d,p) level of theory at 1.0 Å above the geometrical center of each ring. Visualization of the geometries was done by Molden 6.9 and Avogadro², version 1.102.1 [51,52,53].

5. Conclusions

The computational results presented here demonstrate two complementary strategies for enhancing CO₂ reduction by benzimidazole-based hydride donors using superbasic groups.

Superbases act as strong electron-donating substituents that modulate hydricity, with their effectiveness being affected by steric and conformational factors. Changes in the aromaticity of the benzimidazole core, as interpreted by MCI aromaticity indices, provide a useful descriptor that correlates with hydricity, provided the size of the aromatic system remains essentially unchanged. Notably, α-substituted derivatives—especially bulky phosphazenes—show significant deviations from this correlation, highlighting steric limitations. These findings offer insight into the origin of hydricity and will support the rational design of improved donors.

The second approach involves lowering the barrier for CO₂ reduction by incorporating a guanidinium cation as an auxiliary group that assists in CO₂ binding through hydrogen bonding. This effect is particularly pronounced near the transition state, where an increase in the polarity of CO₂ is expected due to its deformation. Our calculations show that the barrier can be lowered by more than 5 kcal mol⁻¹ when a propyl linker is used.

Although these two approaches appear orthogonal, the applicability of hybrid systems (combining both a superbasic substituent and a guanidine auxiliary group) may be limited due to possible intramolecular proton transfer. Investigation of such systems, along with potential side processes, is currently underway.

In view of ongoing efforts to optimize the CO₂ reduction process, our results expand the scope of potential hydride donors, particularly non-metallic ones. They also demonstrate that hydrogen bonding can facilitate the reduction process despite the nonpolarity of CO₂.