Quantum chemical screening of eutectic solvent components for insights into CO₂ complexation mechanisms

Abstract

Developing new negative emission technologies (NETs) to capture atmospheric CO₂ is necessary to limit global temperature rise below 1.5 °C by 2050. The technologies, such as direct air capture (DAC), rely on sorption materials to harvest trace amounts of CO₂ from ambient air. Deep eutectic solvents (DESs) and eutectic solvents (ESs), a subset of ionic liquids (ILs), are all promising new CO₂ sorption materials for DAC. However, the experimental design space for different DESs/ESs/ILs is vast, with the exact CO₂ complexation pathways difficult to elucidate; this creates significant limitations in rationally designing new materials with targeted CO₂ sorption energetics. Herein, the CO₂ complexation pathways for a structural library of different DES/ES components are computed using quantum chemical calculations (i.e., density functional theory). For the entire structure library, we report the energies of elementary CO₂ binding and proton transfer reactions as these reactions are fundamental in DAC within DESs and ESs. These elementary reactions are combined to generate CO₂ complexation pathways and calculate their free energies. The different elementary steps and reaction pathways demonstrate the range of CO₂ complexation free energies and the significance between CO₂ binding and proton transfer reactions. We also report the CO₂ complexation free energies with different functional groups around the CO₂ sorption site, supporting the concept of functionalization for tuning CO₂ complexation thermodynamics. Additionally, our findings suggest potential descriptors, such as proton affinity or pK_a, could be useful when identifying candidate species for ESs and predicting/rationalizing product distributions. Our work has implications for experimental synthesis, characterization, and performance evaluation of new DAC sorption materials.

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Design, System, Application

The development of negative emission technologies (NETs) is crucial for mitigating global climate change by capturing atmospheric CO₂. Among these technologies, direct air capture (DAC) relies on advanced sorbent materials to efficiently harvest CO₂ from ambient air. Deep eutectic solvents (DESs) and eutectic solvents (ESs), as subsets of ionic liquids (ILs), show significant promise as CO₂ sorbents due to their unique properties, including negligible vapor pressures, high thermal stabilities, and chemical tunability. However, the vast experimental design space and complex CO₂ complexation pathways present challenges in rationally designing new materials with targeted CO₂ sorption energetics. In this work, we employ quantum chemical calculations, specifically density functional theory (DFT), to investigate the CO₂ complexation mechanisms within a structural library of DES/ES components. By computing the energies of elementary CO₂ binding and proton transfer reactions, we generate comprehensive CO₂ complexation pathways and calculate their free energies. This approach allows us to explore the impact of various functional groups on CO₂ binding thermodynamics, providing insights into the tunability of CO₂ sorption properties. Our findings highlight the potential of functionalization to enhance CO₂ complexation by modifying the chemical environment around the sorption site. Additionally, we identify potential descriptors, such as proton affinity or pK_a, that could aid in predicting and rationalizing CO₂ sorption performance. This work lays the groundwork for the experimental synthesis, characterization, and optimization of new DAC sorbent materials, ultimately contributing to the advancement of NETs and the global effort to combat climate change.

Introduction

Reducing CO₂ emissions from burning non-renewable fossil fuels is insufficient to remediate global climate change.¹ Therefore, the development of new negative emission technologies (NETs)^2–5 to remove previously emitted CO₂ is essential in limiting global temperature rise.⁶ Direct air capture (DAC), one such NET, is a carbon capture process that relies on novel sorbent materials to efficiently remove atmospheric CO₂ under ambient conditions.^6–9 Promising DAC materials include ionic liquids (ILs),^10–12 deep eutectic solvents (DESs),^10,13–15 metal–organic frameworks (MOFs),^16–20 and covalent organic frameworks (COFs).^21–23 These solid- and liquid-sorbent materials exhibit promising physical and chemical properties for DAC and are tunable. For state-of-the-art DAC materials,²⁴ higher gravimetric CO₂ uptake is achieved when CO₂ binds chemically (e.g., ILs²⁵) instead of physically (e.g., MOFs²⁶). This is particularly important for DAC, where the amount of CO₂ is very small. For DAC, there is a need to develop new materials that exhibit high CO₂ capacities, which requires a deeper understanding of the structure–function relationships that govern the CO₂ sorption process.

Both ILs and DESs are promising liquid sorbents for DAC due to their negligible vapor pressures, high thermal stabilities, and chemical tunabilities.^27–30 ILs are liquid salts comprising of both cationic and anionic components (charges of ±1) that melt below 100 °C.³¹ Both these cationic and anionic components are hydrogen bond acceptors (HBAs). Examples of cationic components (i.e., [HBAc]⁺) are 1-ethyl-3-alkylimidazolium ([EMIM]⁺) and choline ([Ch]⁺), and examples of anionic components (i.e., [HBAa]⁻) are imidazolide ([Im]⁻) and pyrrolide ([Pyr]⁻).³² DESs are similar to ILs in that they contain the cationic and anionic components, but DESs also contain a hydrogen bond donor (HBD), such as ethylene glycol (EG) that contributes to further melting point suppression^33,34 and, generally, lowers the viscosity of the solvent.^14,35 However, even eutectic solvents (ESs), where the exact ‘deep’ eutectic composition is not necessarily known, still exhibit promising properties for DAC.

The CO₂ uptake performance for ILs and DESs/ESs has been previously studied using experimental and computational approaches.^11,36–46 For example, Lee et al. elucidated the different CO₂ binding pathways for an imidazolium [HBAc]⁺ and pyrrolide [HBAa]⁻ in the presence of ethylene glycol (EG), finding that CO₂ prefers to bind to the [HBAc]⁺.⁴⁷ Further advancements by Klemm et al. demonstrate how the CO₂ uptake capacity can be tuned by converting amino acid-based ILs to ESs through the addition of EG.¹⁴ Supplemental modeling insights demonstrate how the HBD alters the interactions within the solvent leading to a difference in uptake for the IL vs. the ES.

These studies motivate the need for research aimed at identifying the CO₂ complexation mechanisms associated with CO₂ uptake. Developing strategies to predict CO₂ uptake performance a priori is of critical importance due to the large experimental design space for these materials. There are multiple mechanisms for CO₂ complexation within an ES,^37,48 as defined by the CO₂ binding site (i.e., to the [HBAc]⁺, the [HBAa]⁻, and/or the HBD species). The simplest mechanism is complexation to the [HBAa]⁻, where CO₂ can bind directly to the species without the need for proton transfer to create the binding site. However, the [HBAc]⁺ and the HBD species can also accept CO₂ following proton transfer to create a site for complexation.^14,38,49,50 The thermodynamics and kinetics behind these different complexation pathways are influenced by several properties, including the chemical nature of the various components of the sorbent material. Ultimately, the goal is to understand how to tune CO₂ complexation in ILs/DESs/ESs via chemical functionality.

Along these lines, in this work we combine high-throughput screening and density functional theory (DFT) calculations to probe CO₂ complexation by identifying the CO₂ binding locations and thermodynamics for CO₂ binding and proton transfer reaction steps. Quantifying the complexation thermodynamics of the various species within ILs and DESs/ESs is fundamental for rationally designing tunable CO₂ sorbent materials. We specifically focus on ESs by computing the CO₂ complexation thermodynamics for ∼420 combinations of ESs (i.e., unique cations, anions, and HBDs species). A library of hypothetical ESs provides information into the CO₂ complexation thermodynamics associated with different complexation pathways and the intermolecular proton transfers. Additionally, [HBAa]⁻ functionalization is also systematically explored by varying the functional groups around the CO₂ binding site with electron-donating and electron-withdrawing groups. Overall, our work provides fundamental insights into the CO₂ sorption for ESs while laying the groundwork for rationally constructing solvents for CO₂ capture.

Methodology

The following sections discuss CO₂ complexation to the HBA and HBD components of ESs. For the HBA species, the cationic component is denoted as HBAc and the anionic component is denoted as HBAa. Charged species are denoted with brackets (i.e., [ ]), and positive and negative charges are indicated using [ ]⁺ for cationic and [ ]⁻ and anionic species, respectively. Species without brackets are neutral. This delineation is essential when defining the different fundamental reactions since these reactions can involve proton transfers, which alter the charges of the species. For example, a proton transfer from the [HBAc]⁺ or the HBD is needed before CO₂ complexation to those species. These proton transfers can neutralize or charge these species (i.e., [HBAc]⁺ → HBAcf + [H]⁺ or HBD → [HBD]⁻ + [H]⁺). Given the more favorable kinetics for intermolecular proton transfers over intramolecular proton transfers,^14,47,51 only intermolecular proton transfers are considered in this work. Protons that are transferred are hence transferred to the [HBAa]⁻ (i.e., [HBAa]⁻ + [H]⁺ → HBAa).

Structure library

A library of structures consisting of 5 [HBAc]⁺, 12 [HBAa]⁻, and 7 HBD species is investigated. Fig. 1 provides the full and abbreviated naming conventions and the structural representations for each species investigated, with the ball-and-stick representations for all species provided in ESI† Section S1. Hypothetical ESs are constructed by combining a single [HBAc]⁺, [HBAa]⁻, and HBD species, producing a total of 420 different hypothetical mixtures. However, the total number of structures considered is even larger due to the multiple binding sites for CO₂ sorption and proton binding. For example, on a [HBAa]⁻ comprising multiple N binding sites, CO₂ can bind to each N atom. All possible binding sites are considered to ensure the lowest energy conformer is found; the lowest energy conformers are reported in this manuscript. All structures are stored in an open, online repository.⁵²

Fig. 1 The (a) hydrogen bond acceptor cations ([HBAc]⁺), (b) hydrogen bond acceptor anions ([HBAa]⁻), and (c) hydrogen bond donors (HBD) considered in this work. Both the full- and abbreviated-naming conventions are provided; the cationic and anionic species are identified with brackets and charges, respectively.

A subset of the [HBAa]⁻ library (i.e., [Im]⁻ and [Pyr]⁻) comprises similar species with different functional groups to investigate how different functional groups influence complexation. The functional groups are selected based on their electron-donating (e.g., R–OH) and electron-withdrawing (e.g., R–CHO) capabilities to understand the influence on CO₂ binding. The different functional groups are attached adjacent to the N binding site on the [Im]⁻ and [Pyr]⁻ species (Fig. 2a) at ortho positions relative to the CO₂ binding site. Specifically for [Im]⁻, the functional group attachment occurs between the ring N atoms. These functionalized [HBAa]⁻ species are compared to the unfunctionalized [Im]⁻ and [Pyr]⁻ species (which have a hydrogen atom in the ortho position). The left column in Fig. 2b shows the electron-donating groups (i.e., R–Me, R–Et, R–OH, R–MeOH, and R–EtOH), and the right column in Fig. 2b shows the electron-withdrawing groups (R–F, R–CN, R–CHO, R–COCH₃, and R–COOCH₃) considered in this work.

Fig. 2 [Pyr–X]⁻ and [Im–X]⁻ (a) were investigated for the influence of functionalization with the ten different functional groups (X) shown in (b). In part (b), electron-donating groups are shown in the left column while electron-withdrawing groups are shown in the right column.

Fundamental reactions

For a given [HBAc]⁺[HBAa]⁻:HBD ES, the hypothetical reaction mechanisms for CO₂ complexation, consisting of CO₂ binding and proton transfer steps, are presented in Table 1. The proton transfer reactions are included to account for cases where a species must donate a proton for CO₂ complexation. The generic, hypothetical reaction mechanisms determine the individual thermodynamics of each step and, when combined, the subsequent CO₂ complexation pathway free energies (Fig. 3).

Table 1 Fundamental reactions in a [HBAc]⁺[HBAa]⁻:HBD ES

Reaction mechanism
All proton transfer reactions are written as affinity reactions for consistency.
	R1
	R2
	R3
	R4
	R5
	R6
	R7
	R8

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Fig. 3 The different CO₂ complexation pathways considered for a [HBAc]⁺[HBAa]⁻:HBD ES. Complexation occurs via the [HBAa]⁻ (pink), HBAc (mauve), [HBD]⁻ (purple), and HBD (blue) pathways. Reaction numbers are the same as in Table 1. Only the [HBAa]⁻ pathway does not require a proton transfer for CO₂ complexation. The other three pathways all involve an intermolecular proton transfer, which is modeled here as occurring to the [HBAa]⁻ species.

Hypothetical reaction pathways

There are four distinct CO₂ complexation pathways considered in this work, which are outlined in Fig. 3. We label these pathways as the ‘[HBAa]⁻’, ‘HBAc’, ‘[HBD]⁻’, and ‘HBD’ pathways. The pathways are defined by the species that CO₂ binds to (i.e., to the [HBAa]⁻, HBAc, [HBD]⁻, or HBD species). In the [HBAa]⁻ pathway, CO₂ complexes directly to the [HBAa]⁻ via reaction R2. CO₂ binding to the [HBAc]⁺ requires proton transfer via the reverse of reaction R3 (all proton transfer reactions in Table 1 are written as affinity reactions for consistency) prior to complexation via reaction R4. CO₂ can complex to the HBD via two pathways. In the [HBD]⁻ pathway, the HBD species first transfers a proton via the reverse of reaction R5. CO₂ then complexes to the deprotonated HBD species (i.e., [HBD]⁻) via reaction R6. An additional HBD pathway is considered where CO₂ first forms a weak complex with the neutral HBD molecule (reaction R7) prior to proton transfer via reaction R8. Theoretically, protons could be transferred to any negatively charged species in the solvent. We consider the case where they are transferred to the [HBAa]⁻, converting it to the HBAa via reaction R1. The total free energy of complexation is denoted ΔG^c and is the sum of all necessary reactions en route to CO₂ complexation. For example, considering the [HBAc]⁺ pathway (mauve color in Fig. 3), ΔG^c = −ΔG₃ + ΔG₁ + ΔG₄.

Quantum chemical (QM) calculations

The entire hypothetical reaction library is screened using the Gaussian16 Revision C.02 software,⁵³ with the structures, energies, and vibrational frequencies calculated at the B3LYP/6-311+G(d,p) level of theory. Test calculations performed at the ωB97XD/6-311+G(d,p) level of theory indicate a maximum 3.3 kJ mol⁻¹ difference in free energy. Dispersion corrections formulated by Grimme et al. with Becke–Johnson (BJ) damping are included.^54,55 Solvation is needed to stabilize the electronic and geometric structures of the ionic species. We use implicit solvation for simplicity. However, explicit intermolecular interactions could contribute to the reported free energies. To learn how this could influence the results, we investigated the influence of hydrogen bonded HBD species on the [HBAa]⁻ complexation pathway free energies. This analysis is summarized in ESI† Section S3. We find that, generally, explicit stabilization leads to a decrease in the CO₂ complexation free energies to the [HBAa]⁻ species (i.e., CO₂ complexation is more favorable). Exploring this further would be an excellent topic for future work. Our simulations utilize ethanol (ε = 24.8520) as the implicit solvent, since it is representative of the range of dielectric constants of the hypothetical ESs. Further rationale for this choice is provided in ESI† Section S2.

The computational workflow is fully automated, thus enabling the quick generation of Gaussian16 input files, the collection and analysis of the energies, and the creation of the pathway energies. The workflow, which heavily utilizes the atomic simulation environment (ASE),⁵⁶ ensures that all potential binding sites are explored for each structure. For every structure presented in Fig. 1, the necessary reactions for each component presented in Table 1 are calculated. Free energies are estimated by adding the vibrational free energy contributions from the harmonic oscillator approximation to the electronic energies. The vibrational contributions are calculated using the pMuTT⁵⁷ python package. All vibrational frequencies below 50 cm⁻¹ are set equal to 50 cm⁻¹ to avoid overestimating the entropic contribution of low-frequency modes, which is a limitation of the harmonic oscillator approximation.⁵⁸ The energy of [H]⁺ is calculated relative to H₃O⁺/H₂O, i.e., G_[H]⁺ = G_[H3O]⁺ − G_H2O, since it is not possible to compute the energy of an isolated proton (G_[H]⁺) in most electronic structure software. This is a modeling choice that does not impact the results, but enables the calculation of relative proton transfer reaction free energies.

Results

CO₂ complexation

CO₂ complexation to the [HBAa]⁻ species. The CO₂ binding free energies to the [HBAa]⁻ species (which are equal to the complexation pathway free energies, ΔG^c; see Fig. 3) are plotted in Fig. 4. These values range from −14.7 kJ mol⁻¹ to −94.9 kJ mol⁻¹. The species considered feature secondary amines and are organized by structural similarity in Fig. 4. For example, the different [Im]⁻ species feature different functional groups (i.e., R–H, R–CH₃, and R–CH₂CH₃) anchored to the ring C atom between the two ring secondary amines (NR₂), and [BIm]⁻ features a benzene ring anchored to the 5-membered ring. These functional groups induce minimal variations on the CO₂ complexation free energies, with values of ΔG^c ranging from −60 kJ mol⁻¹ to −70 kJ mol⁻¹. The same can be said for the [Trz]⁻ family as well as for [Pyz]⁻ and [Ind]⁻. In contrast, the [Pyr]⁻ family has drastically different CO₂ complexation energies. Despite the same ring N binding site, [Pyr]⁻ has a drastically different energy compared to [2-CNpyr]⁻. Structurally, the difference between [Pyr]⁻ and [2-CNpyr]⁻ is a change in the functional group (R–H to R–CN) at the adjacent ring C site. The presence of the cyano group (R–CN) weakens the binding energy by ∼45 kJ mol⁻¹.

Fig. 4 The [HBAa]⁻ CO₂ complexation free energies (in kJ mol⁻¹), where ΔG^c = ΔG₂. The figure is organized by structural similarity to compare how functionalization impacts CO₂ binding. Chemical structures are included to illustrate structural similarities and differences. Atom color key: gray = carbon, blue = nitrogen, red = oxygen, white = hydrogen. Different families of [HBAa]⁻ species are denoted with the purple, blue, teal, and orange brackets.

The influence of chemical functionality on CO₂ complexation is further investigated by systematically adding different functional groups around the CO₂ binding site on both the [Pyr]⁻ and [Im]⁻ species. The influence of different functional groups on CO₂ complexation free energies to [Pyr–X]⁻ and [Im–X]⁻ species, where X represents the different functional groups, is presented in Fig. 5. We find that alkyl functional groups (i.e., R–Et and R–Me), which are considered weakly electron-donating groups, exhibit similar free energies as the parent [Pyr]⁻ and [Im]⁻ structures. The main electron donating groups considered are R–OH, R–MeOH, and R–EtOH. For [Pyr–X]⁻, only R–OH results in stronger CO₂ complexation (by ∼15 kJ mol⁻¹). In contrast, R–MeOH leads to a similar complexation energy, and R–EtOH has a CO₂ complexation energy that is less favorable (more positive) by ∼11 kJ mol⁻¹. For [Im–X]⁻, the presence of all electron donating groups leads to more negative (stronger) CO₂ complexation energies, ranging from ∼12 to 20 kJ mol⁻¹ compared to [Im]⁻.

Fig. 5 The [HBAa]⁻ CO₂ complexation free energies (in kJ mol⁻¹), where ΔG^c = ΔG₂ for the (a) [Pyr–X]⁻ and (b) [Im–X]⁻ families with different functional groups (as shown in Fig. 2). The single hatch indicates electron-donating groups and the double hatch indicates electron-withdrawing groups. The naming conventions for structures appearing in Fig. 4 are modified according to the naming convention in Fig. 2 (i.e., [Pyr–CN]⁻ = [2–CNpyr]⁻, [Im–Me]⁻ = [MeIm]⁻, and [Im–Et]⁻ = [EtIm]⁻). Atom color key: gray = carbon, blue = nitrogen, red = oxygen, white = hydrogen.

Conversely, the presence of electron withdrawing groups leads to more positive (i.e., less thermodynamically favorable) CO₂ complexation energies compared to the parent species. Electron withdrawing groups remove electron density from the ring structure, resulting in a less nucleophilic N binding sites for CO₂ complexation. These results suggest that CO₂ complexation free energies to [HBAa]⁻ species may be tuned with careful selection of the functional groups adjacent to the N binding site. In general, the CO₂ complexation results for the [HBAa]⁻ species highlight the potential tunability of CO₂ complexation to the [HBAa]⁻ species.

CO₂ complexation to the [HBAc]⁺ species. Free energies involved in CO₂ complexation to the [HBAc]⁺ species are presented in Fig. 6. Unlike for the [HBAa]⁻ species, CO₂ complexation to the [HBAc]⁺ species requires an intermolecular proton transfer, forming the HBAc species. The proton transfer from the [HBAc]⁺ to the [HBAa]⁻ occurs via the reverse of reaction R3 plus reaction R1, with free energy equal to −ΔG₃ + ΔG₁. These quantities are plotted in Fig. 6 with the orange bars using [Im]⁻ as a reference. Selecting a different [HBAa]⁻ would simply shift these free energies. A more negative proton transfer energy indicates that the [HBAc]⁺ is more likely to donate a proton to [Im]⁻. Both [EMIM]⁺ and [Ch]⁺ exhibit positive proton transfer free energies (ΔG₃ < ΔG₁), meaning that they are less likely to donate a proton to the [Im]⁻ species. However, the sulfur-containing [HBAc]⁺ species (i.e., [EMMTH]⁺, [EHMTH]⁺, and [ETH]⁺) all exhibit negative proton transfer free energies (ΔG₃ > ΔG₁), meaning that they are more likely to donate a proton to the [Im]⁻ species. Furthermore, these species exhibit small deviations in proton transfer free energies (−5.1 kJ mol⁻¹ to −17.2 kJ mol⁻¹) as a function of the functional groups attached to the ring C atoms (i.e., R–H, R–CH₂OH, and R–CH₃).

Fig. 6 The HBAc pathway free energies (ΔG^c = −ΔG₃ + ΔG₁ + ΔG₄; mauve), the proton transfer free energies (−ΔG₃ + ΔG₁; orange), and the CO₂ binding free energies (ΔG₄; yellow). ΔG₁ is calculated using [Im]⁻ as the proton acceptor. The structure insets illustrate the CO₂ complexation final products. Atom color key: gray = carbon, blue = nitrogen, red = oxygen, white = hydrogen, yellow = sulfur.

The overall CO₂ complexation pathway free energies (ΔG^c) for the [HBAc]⁺ species are presented by the mauve bars in Fig. 6. The pathway free energies are obtained by summing the proton transfer free energies with the CO₂ binding energy, i.e., −ΔG₃ + ΔG₁ + ΔG₄. Overall, the CO₂ complexation pathway free energies range from −77.2 kJ mol⁻¹ to −89.4 kJ mol⁻¹. They are strongly negative due to the favorable/negative CO₂ binding free energies (i.e., ΔG₄), which span from −69.4 kJ mol⁻¹ to −96.2 kJ mol⁻¹ (yellow bars in Fig. 6). As previously mentioned, the sulfur-containing [HBAc]⁺ species exhibit deviations in proton transfer energies. However, these deviations are not observed in the ΔG^c free energies (−84.6 kJ mol⁻¹ to −89.4 kJ mol⁻¹). The CO₂ binding free energies (ΔG₄) compensate for the differences in proton transfer free energies for the [EMMTH]⁺, [EHMTH]⁺, and [ETH]⁺ species, such that the overall complexation free energies for all [HBAc]⁺ species are similar.

CO₂ complexation to the HBD species. The product for CO₂ complexation to the HBD species is [HBD–CO₂]⁻, which involves CO₂ complexation onto the –N site (e.g., PDA, TDA, and EDA) or the –OH site (e.g., EG, PG, GOL). Two pathways leading to the same [HBD–CO₂]⁻ products are considered. They are denoted by the initial step, which either forms a weakly complexed CO₂ (HBD–CO₂) or deprotonated HBD species ([HBD]⁻). In the weak CO₂ complexation HBD pathway, CO₂ initially weakly complexes to the HBD (reaction R7) before proton transfer to the [HBAa]⁻ (reverse of reaction R8 plus reaction R1). For the deprotonated HBD pathway, the proton transfer to the [HBAa]⁻ (reverse of reaction R5 plus reaction R1) occurs first, forming an [HBD]⁻ species. CO₂ then complexes to the [HBD]⁻ species (reaction R6). Both pathways are considered to investigate the differences in the thermodynamic landscape, even though the final values of ΔG^c are the same.

Free energies involved in CO₂ complexation to the different HBD species are reported in Fig. 7. Overall, the CO₂ complexation pathways for the different HBD species (green bars in Fig. 7) are thermodynamically similar, with ΔG^c of ∼−65 kJ mol⁻¹, despite variations in the chain length of the diamine species (increasing in length from EDA to TDA to PDA). The exception is GOL, which forms an intramolecular hydrogen bond between the complexed CO₂ and the adjacent –OH group and exhibits ΔG^c of −87.5 kJ mol⁻¹, but even this difference is minor. All HBDs considered in this work prefer the pathway where weak CO₂ complexation occurs initially. This is due to the proton transfer free energies being more favorable from the weakly complexed species than for the uncomplexed species (i.e., −ΔG₅ + ΔG₁ ≫ ΔG₇; more positive purple bars than blue bars in Fig. 7). This is particularly true for the HBDs with the –N site, where proton transfer from the HBD is significantly uphill (∼160 kJ mol⁻¹) compared to the free energy to form HBD–CO₂ species (∼−20 kJ mol⁻¹), and because the free energies of proton transfer from the weakly complexed HBD–CO₂ species (i.e., −ΔG₈ + ΔG₁) are negative for all HBD species.

Fig. 7 The HBD/[HBD]⁻ CO₂ complexation pathway free energies (ΔG^c = −ΔG₅ + ΔG₁ + ΔG₆ = ΔG₇ − ΔG₈ + ΔG₁; green), the free energies for transferring a proton from the HBD to [Im]⁻ (−ΔG₅ + ΔG₁; purple), the free energy of weak CO₂ complexation (ΔG₇; blue), and the free energies of proton transfer from HBD–CO₂ to [Im]⁻ (−ΔG₈ + ΔG₁; light blue). ΔG₁ is calculated using [Im]⁻ as the proton acceptor. The structure inserts demonstrate the different intermediates for the HBD and [HBD]⁻ complexation pathways. Atom color key: gray = carbon, blue = nitrogen, red = oxygen, white = hydrogen.

Comparing CO₂ complexation pathways. As previously discussed, the complexation pathways to the [HBAc]⁺ and HBD species involve multiple steps. To understand which species CO₂ is more likely to bind to, proton transfer free energies for the [HBAc]⁺ species are compared to weak CO₂ complexation of the HBD pathway in Fig. 8a. Additional comparisons between the proton transfer steps for the [HBD]⁻ and HBAc pathways are presented in Fig. S6.† Specifically, Fig. 8a plots the difference in the weak complexation CO₂ free energies (ΔG₇) and the proton transfer free energies (−ΔG₃ + ΔG₁), with values ranging from ∼0 kJ mol⁻¹ to −49.2 kJ mol⁻¹. All values are negative. For [Ch]⁺ and [EMIM]⁺, the free energy differences range from ∼−30 kJ mol⁻¹ to ∼−50 kJ mol⁻¹, demonstrating that weak CO₂ complexation to the HBD species is preferred. That said, [EHMTH]⁺ and [ETH]⁺ exhibit free energies that are ∼0 kJ mol⁻¹, suggesting that HBD–CO₂ and HBAc species are both likely to occur in solution.

Fig. 8 Heat maps comparing the free energies between the HBD and HBAc pathways: (a) difference between the weakly complexed CO₂ step (ΔG₇) and the proton transfer step (−ΔG₃ + ΔG₁) free energies and (b) difference between HBD (ΔG^c_HBD) and HBAc complexation pathway free energies. For the proton transfer steps, the energy (ΔG₁) is calculated using [Im]⁻ as the proton acceptor. The color bar indicates the more favorable pathway. For (a), purple indicates that weak complex is more favorable (ΔG₇ < −ΔG₃ + ΔG₁) and mauve indicates the proton transfer is more favorable (ΔG₇ > −ΔG₃ + ΔG₁). For (b), purple indicates that the HBD complexation is preferred (ΔG^c_HBD < ΔG^c_HBAc) and mauve indicates that the HBAc complexation pathway is preferred (ΔG^c_HBD > ΔG^c_HBAc).

The HBD vs. [HBAc]⁺ pathway complexation free energies are presented in Fig. 8b. Specifically, Fig. 8b plots the difference between the HBD complexation pathway (ΔG^c_HBD) and the HBAc complexation pathway (ΔG^c_HBAc) free energies. For all species except GOL, the reported free energies differences are positive (ΔG^c_HBD − ΔG^c_HBAc > 0), with free energies ranging from ∼11 kJ mol⁻¹ to ∼26 kJ mol⁻¹. These results indicate that for all HBD species except GOL, CO₂ complexation to the HBAc is favored (i.e., ΔG^c_HBAc < ΔG^c_HBD).

The free energies for the [HBAa]⁻ and HBD complexation pathways are compared in Fig. 9. Since the [HBAa]⁻ does not require proton transfer, the free energy of CO₂ binding to the [HBAa]⁻ species (ΔG₂) is compared to the free energy of weak CO₂ complexation to the HBD (ΔG₇) in Fig. 9a. The difference in free energies ranges from −18 kJ mol⁻¹ to +76 kJ mol⁻¹. These differences are strongly influenced by the [HBAa]⁻ species, which exhibits large variations in CO₂ complexation free energies (ΔG₂) as reported in Fig. 4. However, the overall complexation pathway free energies are presented in Fig. 9b and show a more neutral thermodynamic landscape for most [HBAa]⁻/HBD pairs with only GOL breaking this trend. Overall, this suggests that thermodynamically, these species are approximately equally likely to complex CO₂.

Fig. 9 Heat maps comparing the free energies between the HBD and [HBAa]⁻ pathways: (a) difference between the weak CO₂ complexation free energy (ΔG₇) and the [HBAa]⁻ CO₂ complexation free energy (ΔG₂) and (b) difference between HBD (ΔG^c_HBD) and [HBAa]⁻ complexation pathway free energies. For the proton transfer steps, the energy (ΔG₁) is calculated using the corresponding [HBAa]⁻ species as the proton acceptor. The color bar indicates the more favorable pathway. For (a), purple indicates that weak complexation to the HBD is more favorable (ΔG₇ < ΔG₂) and pink indicates that complexation to the [HBAa]⁻ is more favorable (ΔG₇ > ΔG₂). For (b), purple indicates that the HBD complexation pathway is preferred and pink indicates that the [HBAa]⁻ complexation pathway is preferred .

Discussion

The values of ΔG^c calculated in this work support that, with the exception of GOL, CO₂ complexation to the [HBAc]⁺ is favored, but that multiple complexation pathways are present within eutectic solvents, with CO₂ complexation occurring to the [HBAc]⁺, [HBAa]⁻, and HBD species. This suggests that multiple CO₂ sorption products could be present in IL/ES/DES solvents. This poses significant challenges when designing different sorbents with specific CO₂ uptake properties since identifying the mechanisms and thermodynamics for complexation is challenging. Although not explored here, understanding CO₂ complexation is also further complicated by a single species potentially complexing multiple CO₂. For example, while our structure library only considers a single CO₂ complexation for each HBD, experimentally, certain HBD species have been observed to complex multiple CO₂ molecules.^10,59 When rationalizing experimental uptake data, understanding the locations and potential for a single species that complexes multiple CO₂ molecules is important to identify the different mechanisms.

Furthermore, our findings demonstrate that functional groups around the complexation site result in large deviations (∼70 kJ mol⁻¹) of the CO₂ complexation energies. The electron-donating groups display more favorable (i.e., more negative values of ΔG^c); electron-withdrawing groups display less favorable (i.e., more positive values of ΔG^c). Generally, the species with more negative complexation free energies display intramolecular hydrogen bonds between the complexed CO₂ and adjacent ligands. As reported in Fig. S7,† these intramolecular hydrogen bonds lower the CO₂ complexation free energies by ∼30 kJ mol⁻¹ for the [IM–EtOH]⁻, [IM–MeOH]⁻, and [Pyr–OH]⁻ species. This observation supports the observation made by Klemm et al. that intramolecular hydrogen bond formation stabilizes complexed CO₂ reaction intermediates.¹⁴ Overall, these findings suggest that rationally selecting the functional groups around the CO₂ binding site provides significant opportunities for tuning CO₂ complexation.

Another potential mechanism for tuning CO₂ complexation is considering the nucleophilicity of a given molecule, which is well established for CO₂ complexation.⁶⁰ Most CO₂ sorption materials rely on nucleophiles (i.e., containing electron lone pairs) to capture CO₂. However, the same strong, electron-rich character also promotes proton transfer reactions. The relationship between nucleophilicity to both CO₂ binding and proton transfer reactions presents a challenge in designing solvents (Fig. S8 and S9†). For the [HBAa]⁻ species (Fig. S9a†), a more negative (i.e., stronger) proton transfer free energy indicates a more negative (i.e., stronger) CO₂ binding energy, and this is attributed to the increased nucleophilicity of the [HBAa]⁻. A similar observation is established for both [HBAc]⁺ (Fig. S9b†) and [HBD]⁻ species (Fig. S8†). However, since the HBAc and [HBD]⁻ rely on intermolecular proton transfers for CO₂ complexation, a stronger (more negative) proton transfer energy leads to unfavorable CO₂ binding thermodynamics as these species must donate a proton. These findings support the idea that there is a competitive process between CO₂ binding and proton affinity for an [HBAa]⁻ species, which can be attributed to the nucleophilicity of the species. The interplay between nucleophilicity and the CO₂ binding and proton transfer steps is fundamental to the CO₂ complexation process. A strong correlation between the CO₂ binding and proton transfer reactions for all [HBAc]⁺, [HBAa]⁻ and HBD species suggests that experimental parameters (i.e., proton affinity or pK_a)⁶¹ might be a reasonable descriptor for CO₂ binding.

Additionally, the hydrogen bond network^62–64 within ILs and DESs/ESs poses further challenges in understanding CO₂ complexation. In ILs, the hydrogen bond network is relatively simple, with hydrogen bonds forming between the [HBAc]⁺ and [HBAa]⁻.^65,66 The inclusion of the HBD complicates the hydrogen bond network by adding additional hydrogen bond interactions ([HBAc]⁺/[HBAa]⁻, [HBAa]⁻/HBD, and [HBAa]⁻/HBD).^67,68 The hydrogen bond network can have a significant influence on how and where CO₂ complexation occurs.^14,39,69,70 Tuning CO₂ complexation via the rational selection of HBDs is another potential ‘design’ variable outside the scope of this particular work.

Overall, our findings demonstrate a large range of complexation free energies to the different ILs/DESs/ESs components. Prior literature suggests reaction enthalpies ranging from ∼−50 kJ mol⁻¹ to −65 kJ mol⁻¹ for energy-efficient DAC.^71,72 Using this range of values as a guide, systems consisting of imidazolide (i.e., [Im]⁻, [MeIm]⁻, [EtIm]⁻, and [BIm]⁻) and 2-cyanopyrrolide ([2-CNpyr]⁻) as [HBAa]⁻ species and all HBD species considered exhibit complexation free energies within the target range. These findings are supported by experimental observations in reaction enthalpies for an [EMIM]⁺[2-CNpyr]⁻ IL⁷³ and potential production distribution for an [MEAH]⁺[Im]⁻:EG DES.⁷⁴ Elucidating the thermodynamic landscape by investigating the CO₂ complexation is a necessary first step towards designing DAC materials but cannot fully explain CO₂ sorption. Additional information about mass transfer⁷⁵ and reaction kinetics⁷⁶ and mechanisms would be needed to fully clarify CO₂ uptake. Such investigations would be good topics for future work.

Conclusion

DFT calculations provide insights into the thermodynamics for CO₂ complexation to hypothetical ESs ([HBAc]⁺[HBAa]⁻:HBD). A structure library, comprised of different [HBAc]⁺, [HBAa]⁻, and HBD species is used to model CO₂ binding and proton transfer reaction steps, given that these fundamental reactions are involved in CO₂ complexation. The [HBAa]⁻ complexation pathway is the simplest since no intermolecular proton transfer is required for CO₂ binding. However, both the [HBAc]⁺ and the HBD species require an intermolecular proton transfer for CO₂ complexation. The complexation thermodynamics behind these pathways are explored, with the HBAc pathway being slightly more thermodynamically favorable compared to the [HBAa]⁻ and HBD pathways. However, differences in the experimentally, observed product distributions could be influenced by free energy effects related to solvent structure that are beyond the scope of this work.

Furthermore, the functional groups surrounding the CO₂ binding site influence on complexation is also studied for the [HBAa]⁻ species and [HBAc]⁺ species. For [HBAa]⁻, the N binding site is ‘tuned’ by electron-withdrawing and electron-donating groups near the binding site. The findings demonstrate that electron-withdrawing groups lead to weaker (less favorable) complexation free energies, whereas electron-donating groups lead to stronger (more favorable) complexation free energies. For [HBAc]⁺, deviations for the [ETH]⁺-based species (i.e., different functional groups R–H, R–CH₂OH, and R–CH₃) is observed. Interestingly, these findings suggest that there might be differences in the functional groups that impact complexation to the [HBAc]⁺ and [HBAa]⁻ species. Our findings suggest that tuning CO₂ complexation via functionalization is possible.

Data availability

The data supporting this article have been included as part of the ESI.† Additionally, all structures are located on a GitHub repository.

Author contributions

SPV designed the study, performed the calculations, analyzed the data, wrote the initial manuscript draft, and reviewed and edited the manuscript. OI performed calculations and reviewed and edited the manuscript. RBG designed the study, supervised the work, reviewed and edited the manuscript, and provided financial support.

Conflicts of interest

The authors declare no competing interests.

Acknowledgements

This work is supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under award number DESC0022214. SPV was also supported by a GAANN Fellowship (Award Number: P200A180076) from the United States Department of Education. SPV and RBG would like to acknowledge the Clemson Computing and Information Technology (CITI) Advanced Computing and Data Science (ACDS) group for the generous allotment of compute time on the Palmetto cluster. OI and RBG would also like to thank the Ohio Supercomputer Center for its high-performance computing resources and expertise.

Notes and references

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5me00034c

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