Intermolecular Interactions in Direct Air Capture Materials: Insights from Charge Density Analysis

Abstract

Direct air capture (DAC) materials enable the removal of CO₂ from the atmosphere, but improving their efficiency requires a detailed understanding of the intermolecular interactions that govern CO₂ sorption and release. Here, we present an experimental electron density study of methylglyoxal-bis­(iminoguanidine) (MGBIG), a promising DAC material, using high-resolution X-ray and neutron diffraction data combined with quantum crystallographic analysis. This approach bridges theoretical and experimental data by quantifying electron density distributions and revealing how hydrogen bonds stabilize CO₂-derived carbonate phases and may influence the desorption behavior. We identify distinct hydrogen-bonding environments in two crystalline carbonate phases: P1, a transient kinetic product, and P3, a thermodynamically stable phase. Multipolar refinement and electrostatic potential and multipole moment calculations precisely map electron density distributions, revealing key hydrogen bonds involved in CO₂ capture. Topological analysis of electron density highlights a cooperative hydrogen-bonding network in the thermodynamically favored P3 phase, where enhanced electron density delocalization and water-mediated interactions contribute to a more stable lattice. Energetic analyses confirm that stronger hydrogen bonding networks enhance the stability of P3 with a binding energy of −607.0 kJ/mol and greater lattice stability (−847.3 kJ/mol) compared to P1 (−302.5 and −571.0 kJ/mol, respectively). Electrostatic potential maps further illustrate polarization patterns that may influence the stability of the binding of CO₂ and release conditions. These findings establish a direct experimental framework for linking electron density distributions to intermolecular interactions in DAC materials, providing a rational design strategy for optimizing sorbents with improved CO₂ capture efficiency and reduced energy demands.

1. Introduction

The accumulation of atmospheric carbon dioxide (CO₂) from human activities poses severe environmental challenges, including climate change, sea-level rise, and biodiversity loss. To mitigate these effects, both mitigation and adaptation strategies have been developed, including renewable energy adoption and carbon capture technologies. − Among these, direct air capture (DAC) stands out as a transformative approach capable of removing CO₂ directly from ambient air. − Despite its potential, DAC faces considerable hurdles. Current DAC processes tend to have excessively high energy requirements primarily due to the energy-intensive process of sorbent regeneration. These substantial energy requirements, coupled with economic constraints, highlight the urgent need for innovative approaches to improve the efficiency and scalability of DAC systems. An essential step in addressing these challenges is developing a molecular-level understanding of CO₂ capture and release processes, which can directly inform material design and process optimization.

Hydrogen bonding and intermolecular interactions, alongside proton transfer, have been identified by theoretical approaches as fundamental drivers of CO₂ capture mechanisms. ,− Computational methods, such as static density functional theory (DFT), have illuminated the stabilizing roles of these interactions within CO₂-capture materials, offering valuable insights into their sorption capabilities. However, theoretical models often rely on idealized assumptions, involving only a few molecules in the gas phase and/or an implicit solvent model, and thus struggle to fully capture the complexity of real systems, particularly in describing the dynamism of CO₂ capture/release. To address these limitations, explicit ab initio molecular dynamics (AIMD) , simulations have recently been proposed, offering a more dynamic perspective of CO₂ release processes. However, experimental validation is paramount to capture their dynamic behavior and refine these theoretical predictions. ,−

Crystallographic techniques, particularly high-resolution X-ray and neutron diffraction, offer a unique experimental pathway for probing the molecular-level mechanisms underlying CO₂ capture and release. , These methods enable precise quantification of electron density distribution , and hydrogen bonding, , and other intermolecular interactions, − shedding light on structural and energetic aspects and structural stability. − Advanced analytical approaches, such as quantum crystallography, further enhance these analyses, facilitating precise calculations of interaction energies and mapping the electron density features associated with material behavior. − Together, these experimental approaches bridge the gap between theory and application − and have the potential to provide critical insights into the chemical and energetic landscapes , by directly observing changes in atomic displacement parameters (ADPs), hydrogen bond geometry, and electron density distribution under extreme conditions, offering unique information on CO₂ binding and release processes.

A detailed understanding of the thermodynamic and mechanistic factors governing the CO₂-separation cycle is crucial for designing next-generation carbon capture systems with enhanced separation efficiencies and reduced energy demands. In this study, we established the workflow to investigate crystalline materials for DAC and apply it to the methylglyoxal-bis­(iminoguanidine) (MGBIG) compound, a material forming two distinct crystalline carbonate phases (P1 and P3) in the presence of atmospheric CO₂. These phases exhibit differing stability and CO₂ binding characteristics. Phase P1 is characterized by monoprotonated MGBIG molecules, while phase P3 consists of diprotonated MGBIG molecules. The crystallization of these phases depends on solution concentration: P1 forms typically from more concentrated solutions (>0.75 M), whereas P3 crystallizes from more dilute solutions (<0.3 M). The carbonate anions in both phases are stabilized by bidentate guanidinium hydrogen bonds, but P3 features additional hydrogen bonding from water molecules included in its crystal structure, which enhances its stability. By combining high-resolution X-ray and neutron diffraction techniques with advanced quantum crystallography methodologies via multipolar refinement, we explore how hydrogen-bonding networks and charge redistribution influence carbonate stabilization and may contribute to conditions conductive to proton delocalization or incipient transfer, which could play a role in the CO₂ release process (Scheme ). While Scheme outlines the overall chemical transformations, it is important to note that the release of CO₂ and H₂O from the carbonate phases is not spontaneous under ambient conditions and typically requires external stimuli, such as heating or exposure to low-humidity environments, as demonstrated in prior studies.

1. Reaction Scheme Showing the Overall Chemical Reactions Involved in the CO₂ and H₂O Release from P1 and P3 Phases .

^a The transformations require external stimuli such as heating or low pressure (e.g. vacuum) to proceed, consistent with previously reported experimental investigations.

A comparative analysis of electron density distributions and intermolecular interactions in the P1 and P3 phases reveals significant differences in hydrogen bonding networks, particularly those involving guanidinium and carbonate groups. By elucidating how hydrogen-bonding networks and proton dynamics influence CO₂ binding and release of CO₂ species, we contribute to the foundational knowledge that can inform the rational design of efficient DAC materials.

2. Experimental Section

2.1. X-ray Data Collection and Processing

High-resolution single-crystal X-ray diffraction data for P1 and P3 were collected at 100 K, extending to a resolution of 0.45 Å, to enable detailed electron density measurements. Data for P1 were collected using a Bruker APEX3 diffractometer, while for P3, an XtaLAB Synergy DW system with a rotating anode X-ray source (MoKα radiation, λ = 0.71073 Å) was utilized. Both instruments were equipped with mirror optics and Oxford Cryosystems nitrogen gas-flow apparatus, and they were controlled by the Bruker APEX3 and the Rigaku CrysAlisPro software, respectively. Block-shaped single crystals were mounted with Paratone-N oil on MiTeGen micromounts, with dimensions of 0.082 × 0.182 × 0.263 mm³ for P1 and 0.153 × 0.186 × 0.298 mm³ for P3. For the P1 system, data collection spanned a total exposure time of 28.23 h. The crystal was positioned at 50 mm from the CCD camera, and 1726 frames were measured at 2.0° intervals with detector counting times ranging from 10 to 80 s, depending on the 2θ angle. For the P3 system, the data were collected over 18.23 h. The crystal was positioned 60 mm from the HyPix detector, and 10,144 frames were recorded at 0.5° intervals with detector counting times ranging from 0.97 to 7.88 s. The frames for the P1 system were integrated using the APEX3, while for the P3 system, CrysAlisPro , software was used. Face-indexing analytical absorption correction was applied for the P1 system, while Gaussian absorption correction was used for the P3 system. No evidence of crystal damage was observed during or after the experiments. The crystal structures were refined using the independent atom model (IAM) within the graphical interface of Olex2, and the data sets were merged using SORTAV. Details of the data collection and refinement statistics are presented in Tables , , S1, and S2. Figures and graphical materials were prepared using Mercury and Corel software.

1. Crystal Data and Structure Refinement for P1.

	IAM	MM
data/restraints/parameters	12,692/0/206	8666/3/296
goodness-of-fit on F 2	1.054	1.422
final R indices [all data]	R1 = 0.0689	R1 = 0.0441
	wR2 = 0.1248	wR2 = 0.0647
largest diff. peak/hole/eÅ–3	0.64/–0.44	0.32/ −0.27

2. Crystal Data and Structure Refinement for P3.

	IAM	MM
data/restraints/parameters	15,097/0/244	13,032/0/300
goodness-of-fit on F 2	1.060	1.736
final R indices [all data]	R1 = 0.0302	R1 = 0.028
	wR2 = 0. 0884	wR2 = 0.058
largest diff. peak/hole/eÅ–3	0.63/–0.29	0.32/–0.21

2.2. Neutron Data Collection and Processing

Neutron data were collected at 100 K, the same temperature as X-ray data, on the TOPAZ beamline at the SNS Spallation Neutron Source from Oak Ridge National Laboratory, using the neutron wavelength-resolved time-of-flight Laue diffraction method. Data normalization, including neutron time-of-flight spectrum, Lorentz, and detector efficiency corrections, was performed following the procedures reported previously. A spherical absorption correction with absorption coefficients of 0.16043 + 0.10766λ mm^–1 and 0.15931 + 0.10913λ mm^–1 was applied for P1 and P3, respectively. The reduced data were saved in SHELX HKLF2 format, recording the wavelength separately for each reflection, and were not merged. The statistical parameters for crystal data and structure refinement for both phases are presented in Tables S1 and S2.

2.3. Multipole Refinement

The electron density refinements were performed using the XD2016 program, applying the Hansen–Coppens pseudoatom formalism. The multipole pseudoatom model was used to describe the electron density distribution in detail, with atomic scattering factors sourced from the Su, Coppens, and Macchi (SCM) databank. Refinement followed a systematic strategy to ensure an accurate modeling of the electron density distribution. Initially, the scale factor was refined. Local coordinate systems were assigned to non-hydrogen atoms, and their thermal parameters were refined. All X–H bond distances and hydrogen atomic displacement parameters (H-ADPs) were fixed at values derived from a neutron diffraction study. Following the scale factor refinement and thermal parameters for non-H atoms, the monopole populations and κ parameters were refined. This was succeeded by the refinement of higher-order multipoles, including full refinement up to hexadecapoles for non-hydrogen atoms and dipoles for hydrogen atoms. More details can be found in the Supporting Information (II. Model quality, Figure S1). The molecular structures with the labeling scheme are presented in Figure .

1.

Molecular structures from multipolar refinement with atom labeling schemes for (a) P1 phase with guanidine nitrogen atoms N(6) protonated; (b) P3 phase with both guanidine nitrogen atoms N(6) and N(3) protonated. Atomic displacement parameters are drawn at the 50% probability level.

2.4. Theoretical Calculations

Geometry optimization of atomic positions with the fixed unit cell parameters of both, P1 and P3 phases, under periodic boundary conditions was performed using the CRYSTAL23 software. , The calculations were conducted at the B3LYP level of theory with the pob-TZVP basis set. To account for dispersion interactions and basis set superposition error (BSSE), Grimme’s DFT-D3 dispersion corrections and counterpoise methods , were included in the crystal lattice energy computations. The truncation criteria of Coulomb and Exchange sums (TOLINTEG) were set to 7 7 7 7 14, and the shrinking parameter in the reciprocal space (SHRINK) was set to 8 8.

3. Results and Discussion

3.1. Workflow Overview and Methodology

The electron density analysis is a well-established method for investigating intermolecular interactions, widely applied in areas such as polymorph studies and the investigation of active pharmaceutical ingredients (APIs). − In these contexts, electron density studies have been instrumental in elucidating the stability of different materials and their properties. Here, we extend this robust methodology to a new class of DAC materials to uncover the key hydrogen bonds that facilitate CO₂ release. To achieve this, we adopted a systematic workflow consisting of four interconnected stages:

• 1.Data collection: High-resolution single-crystal X-ray and neutron diffraction data were collected at low temperatures (100 K) to maximize data quality. High-resolution X-ray diffraction experiments were conducted to obtain detailed information about electron density distribution, while neutron diffraction was crucial for accurately locating hydrogen atom positions and refining their ADPs. This is especially important in the context of our study, which focuses heavily on hydrogen bonding and polarization effects, features that are highly sensitive to hydrogen atom placement. The use of neutron data allows for a more reliable starting geometry in multipolar refinement and ensures a more accurate deconvolution of thermal motion from electron density features. To accommodate the requirements of neutron diffraction, larger crystals were selected, and details of the neutron data collection and crystal dimensions have been added to the Supporting Information (Tables S1 and S2). Careful selection of suitable crystals was performed for both techniques to ensure optimal diffraction quality, including considerations of size, symmetry, and data completeness.
• 2.Data reduction: Raw diffraction images were processed using standard data reduction protocols. Intensity integration was performed with meticulous care, and the Ewald sphere was examined for each data set. Any outliers and spurious signals, such as those originating from ice, were identified and excluded. Additionally, corrections for absorption effects were applied. The integrated data were then scaled and merged to produce a data set with high redundancy and low R-factors. This step ensured the accuracy and reliability of the reflection intensities, which serve as the foundation for subsequent electron density studies.
• 3.
  Data modeling: Modeling of experimentally collected X-ray diffraction data was performed using the Hansen–Coppens multipolar formalism implemented in the software XD2016. This approach enables a precise representation of total electron density distribution in crystals, which serves as the basis for charge density analysis. By quantifying deviations from spherical atomic densities, the analysis reveals the nature of bonding and interactions relevant to the stabilization and potential mobility of protons in DAC materials. The atomic electron density was described as comprising three components: (1) the core electron density, ρ_core; (2) the spherical valence density, represented by the monopole population P _val and contraction/expansion parameter κ; and (3) the deformation valence density, which included a radial term (R _l) and a spherical harmonic (d _lm±) component with multipole populations P _lm± and parameter κ′:

  $$\rho (r)={\rho }_{\mathrm{core}}(r)+P_{\mathrm{val}}{\kappa }^3{\rho }_{\mathrm{val}}(\kappa r)+{\kappa }^{\prime 3}\sum _{l=0}^{l_{\max }}{R}_l({\kappa }^{\prime }r)\sum _{m=-l}^{+l}{P}_{lm\pm }{d}_{lm\pm }(\theta ,\varphi )$$

  Rigorous convergence criteria and refinement validation were employed to ensure the accuracy of the multipolar model (as described in the Supporting Information: II. Model quality). The resulting aspherical electron density features provided a foundation for in-depth analyses of bonding interactions, intermolecular forces, and hydrogen-bond networks.
• 4.Data analysis: Several advanced analyses were performed on the refined electron density model to gain a comprehensive understanding of intermolecular interactions and electron density redistribution phenomena that may be relevant to CO₂ release mechanisms in DAC materials:

3.1.1. Hirshfeld Surface Analysis

Hirshfeld surface analysis was employed to partition the molecular electron density into distinct regions, allowing the visualization and quantification of intermolecular interactions. This method partitions the crystal electron density into regions where a molecule’s contribution is greater than or equal to that of its neighbors. The resulting surfaces provide an intuitive representation of the spatial arrangement of intermolecular forces, highlighting interactions such as hydrogen bonding, van der Waals forces, and π–π stacking.

This analysis has been widely used in the study of polymorphs and APIs, where it has been instrumental in identifying and quantifying the stabilizing interactions responsible for the relative stability of various crystalline forms. In the context of DAC materials, Hirshfeld surface analysis enabled the identification of key intermolecular interactions that may facilitate hydrogen bonding environments favorable to CO₂ releases. The generated 2D fingerprint plots further allowed for a comparative assessment of interaction types and their relative contributions to the crystal packing.

3.1.2. QTAIM Analysis

The quantum theory of atoms in molecules (QTAIM) is a theoretical framework used to analyze chemical bonding and intermolecular interactions by examining the topology of the total electron density distribution, typically obtained from quantum mechanical calculations or from high-resolution X-ray diffraction, in charge density studies. QTAIM identifies bond critical points (BCPs) in the electron density: points where the gradient of the density equals zero. At each BCP, QTAIM evaluates properties like electron density, Laplacian of the electron density, and energy density components, which enables reflecting the strength and character of the interactions at BCP. We employed this analysis to compare the studied structures in terms of intermolecular interactions, linking the molecular structure to material functionality.

3.1.3. Source Function Analysis

To further elucidate electron delocalization effects and investigate the directional character of key hydrogen bonds, we applied source function (SF) analysis. This method decomposes the electron density at a given point, such as a bond critical point, into atomic contributions from all atoms in the system. The percentage source contributions S%(D), S%(H), and S%(A) from the donor, hydrogen, and acceptor atoms, respectively, provide insight into the bond polarity and covalency. By comparing these values, along with the total S%(D + H + A) and the extent of external contributions (from atoms outside the D–H···A triad), we can classify hydrogen bonds into four categories: isolated hydrogen bonds (IHB), polarization-assisted hydrogen bonds (PAHB), resonance-assisted hydrogen bonds (RAHB), and charge-assisted hydrogen bonds (CAHB). These distinctions allow for a refined assessment of hydrogen bond strength, electron density localization, and their possible roles in proton mobility within DAC materials.

3.1.4. Intermolecular Interaction Energies

Interaction energies between molecular units were analyzed using the electrostatic potential and multipole moment (EPMM) method, which is rooted in the partitioning of the electron density obtained from electron density refinement. EPMM calculates intermolecular energies by decomposing them into electrostatic, polarization, dispersion, and exchange-repulsion components. This approach allows for a detailed understanding of the forces governing the molecular packing and interaction stability. In the case of DAC materials, EPMM was instrumental in quantifying the energetics of hydrogen bonding and other key interactions, which were further corroborated by periodic DFT calculations.

The data analysis phase encompassed a combination of advanced computational and visualization techniques to unravel intermolecular interactions in the DAC materials.

3.2. Structural Analysis of Hydrogen-Bond Networks

The crystal structures of P1 and P3 reveal distinct hydrogen-bonding environments that are crucial for phase stability and the retention of CO₂. To facilitate discussion, we introduce the abbreviations H₂O _H7 and H₂O _H2 to distinguish the crystallographically distinct water molecules in P3, while P1 contains only one crystallographically independent water molecule (Figures , S2, and S4).

In P1, the carbonate anion occupies a special position where atoms C6 and O3 lie on a 2-fold axis, resulting in a symmetrical arrangement of the oxygen atoms (Figures and S2). This symmetry leads to an equivalence in hydrogen bonding, meaning that while the full structure exhibits four guanidinium-carbonate interactions, only two unique interactions need to be reported due to the symmetry. The single water molecule in P1 is not directly coordinated to the carbonate anion but participates in separate hydrogen bonding, stabilizing the crystal packing without directly influencing carbonate interactions (Figures S2 and S3).

The P3 phase, in contrast, exhibits a more extended hydrogen-bonding network with two distinct water molecules (H₂O _H7 and H₂O _H2) interacting directly with the carbonate anion. This structural arrangement introduces additional hydrogen bonds that link the carbonate anion to three separate MGBIG cations, contributing to a more complex and interconnected hydrogen-bond network compared with P1 (Figures S4 and S5). The presence of direct carbonate-water interactions in P3 strengthens its structural integrity and could play a role in stabilizing carbonate within the solid phase.

These differences between P1 and P3 illustrate how changes in hydrogen bonding topology influence phase stability and CO₂ retention, with P3 exhibiting a more cooperative hydrogen-bonding network that facilitates a greater degree of structural stabilization. Importantly, neither phase displays channels or accessible voids in the packing arrangement (with packing indices of 69.2% for P1 and 69.1% for P3), suggesting that the diffusion of CO₂ and H₂O is limited to solid–liquid and solid–gas interfaces, during the CO₂ absorption and desorption, respectively, with the latter further requiring external stimuli such as heating or pressure changes. While this tight molecular packing contributes to thermodynamic stability, it may also limit the reversibility and kinetics of CO₂ uptake and release under ambient conditions. These structural constraints underscore the importance of considering both interaction energies and diffusion pathways in the design of next-generation DAC materials. Because the full crystal structures and hydrogen bonding patterns of P1 and P3 have already been published, we have included crystal packing diagrams in the Supporting Information (Figures S2–S5) to aid in visualizing the described interactions. These diagrams provide a clear representation of the distinct hydrogen-bonding networks observed in each phase.

3.3. Hirshfeld Surface Analysis

The Hirshfeld surface fingerprint plots clearly demonstrate the dominance of hydrogen bonding interactions in both P1 and P3 phases, while highlighting distinct differences in their bonding patterns (Figure ). These differences are consistent with the transient, metastable nature of P1, characterized by fewer structured hydrogen bonding interactions compared to the stable and cohesive network observed in P3.

2.

2D fingerprint plots for the molecules in (a) P1 and (b) P3 phases. Each point represents a bin (0.01 Å width) for the two distances, with color indicating the relative frequency of contacts (blue = few, red = many). Characteristic regions for H···H, C···H, and O···H interactions are marked for MGBIG and water molecules; these are not shown for the carbonate anion, which primarily forms O···H contacts. Water molecules in P3 are labeled as H₂O_H7 and H₂O_H2 to distinguish crystallographically distinct species.

Strong intermolecular interactions, such as hydrogen bonds, are reflected in the fingerprint plots by short d _i and d _e values (e.g., region of O···H contacts is marked on Figure as a red circle). Here, d _i represents the distance from the surface to the nearest atom inside (internal) the surface and d _e corresponds to the distance to the nearest atom outside (external) the surface, highlighting regions of close contact between interacting species.

In both phases, the carbonate fingerprint plots (Figure ) show sharp spikes at low d _i and d _e, which correspond to strong hydrogen bonds, reflecting significant intermolecular interactions. Differences between the two phases in the distribution of these spikes suggest variations in the strength and the chemical environment of the hydrogen bonds, including features that may influence the CO₂ release mechanism. The P3 phase appears to have more defined contributions in the plot for the carbonate anion, indicating a more ordered interaction environment, which may contribute to its greater stability. In contrast, the plots for the P1 exhibit broader distributions in its fingerprint plots, indicative of more diverse and flexible hydrogen bond interactions. This pattern aligns with the transient nature of P1, reflecting structural disorder or increased thermal motion. In contrast, the P3 phase shows narrower and more defined features in the plots, particularly for carbonate anion and water molecule contributions. This suggests more specific and directional hydrogen bond interactions, resulting in greater stability of this phase compared to that of P1. Both phases exhibit significant contributions from weak H···H interactions (above 40% of all contacts, Figure S6), which are visible as broader, diffuse regions in the full fingerprint plots of MGBIG cations and water molecules (Figure , purple circles). The P1 phase shows a more pronounced contribution from these weak interactions, as evidenced by the larger distribution in the middle and upper regions of the fingerprint. This indicates that H···H contacts play a larger role in stabilizing the P1 phase. The P3 phase, while still exhibiting H···H interactions, appears to have a lower overall contribution from these weak contacts with a greater focus on strong, directional hydrogen bonding. Both phases display strong interactions between the MGBIG cation and the carbonate anion, with sharp features in the carbonate plots indicative of robust hydrogen bonds. These interactions are crucial for stabilizing the crystal structure in both cases.

Water molecules also play a significant role in both phases, with distinct features corresponding to hydrogen bonding involving water molecules. For P1, the fingerprint plot for water molecules shows broader and less distinct features, indicating a wider range of hydrogen bonding interactions. The d _i and d _e values associated with water interactions in P1 exhibit significant variability, suggesting a more disordered or flexible hydrogen bonding network. This variability is consistent with the structural characteristics of the P1 phase, where water molecules are isolated from carbonate anions and primarily interact with the guanidine groups of the MGBIG cations. The broader distribution of features in the plots suggests that water contributes to a less structured hydrogen bond network, possibly reflecting thermal motion or weaker directional bonding.

In contrast, the P3 phase fingerprint plot for water molecules displays sharper, more defined features, particularly at lower d _i and d _e values. These features correspond to strong and specific hydrogen bonding interactions involving water and carbonate/MGBIG ions, which form extended hydrogen-bonding chains in this phase.

The well-defined contributions indicate a more ordered hydrogen bonding environment, which aligns with the structural stability and extended interaction network observed in P3. A key structural distinction contributing to the greater stability of P3 is the protonation state of the guanidine units. In P1, only one of the two guanidine moieties is protonated, resulting in an asymmetrical hydrogen-bonding network. Conversely, in P3, both guanidine units are protonated, forming a symmetrical and cohesive hydrogen-bonding framework. These features are reflected in the sharper fingerprint plot features for P3, consistent with a more ordered interaction network that likely enhances its structural robustness.

The two crystallographically distinct water molecules in P3, H₂O_H2 and H₂O_H7, exhibit subtle but reproducible differences in their fingerprint plots and hydrogen bonding environments. H₂O_H2 is involved in forming two extended hydrogen-bonded chains: one with carbonate anions and another with neighboring water molecules. This connectivity is evident in the fingerprint plot as sharp spikes at low d _i and d _e values, reflecting strong directional hydrogen bonds. These features are consistent with a highly ordered environment, where H₂O_H2 likely acts as a structural link within the extended hydrogen-bonded network.

In contrast, H₂O_H7 appears to participate in more localized interactions. Its fingerprint plot shows broader and less defined features, suggesting weaker or more variable hydrogen bonding. This behavior may be attributed to the positional context of H₂O_H7 within the lattice, where its interactions are less constrained by symmetry or extended connectivity. While we acknowledge that the differences are relatively nuanced, the combination of crystallographic environment, interaction topology, and fingerprint plot features supports a distinction in their roles. Specifically, H₂O_H2 may act as a backbone contributor to extended hydrogen bonding, whereas H₂O_H7 likely plays a secondary role in local stabilization.

The distinction between H₂O_H2 and H₂O_H7 in P3 reflects the hierarchical nature of the hydrogen bond network. H₂O molecules form the backbone of the extended chains, providing structural integrity, while H₂O_H7 molecules contribute to local stability and fill specific spatial roles within the lattice. While H₂O_H2 interactions suggest rigidity and stability in the hydrogen bond network, the presence of H₂O_H7 introduces a degree of flexibility or adaptability in the lattice, potentially allowing the system to accommodate external changes, such as temperature variations or mechanical stress.

3.4. Topological Analysis of Electron Density Distribution

The topological analysis of electron density provides valuable insights into the intermolecular interactions within the investigated systems, particularly focusing on hydrogen bonding involving the carbonate anion (Tables and ). Distinct hydrogen bonds with varying strengths are observed, playing integral roles in the guanidinium–carbonate and water–carbonate networks. For example, in P3, hydrogen bonds with a higher electron density (e.g., ρ­(r) = 0.39 eÅ^–3) coexist with weaker bonds (e.g., ρ­(r) = 0.22 eÅ^–3), illustrating a cooperative interaction network that enhances the overall stability of the system. However, in P1, guanidinium–carbonate interactions exhibit a wider range of electron density values (e.g., ρ­(r) = 0.19–0.41 eÅ^–3), suggesting greater variability and potential instability in its bonding network. This variability supports the interpretation of P1 as a less stable and potentially metastable form of P3. Differences in electron density between guanidinium–carbonate interactions in P1 and P3 further underscore the influence of local structural and environmental factors on bond strength and network organization.

3. Topological Properties at the Bond Critical Points for P1 for the Selected Hydrogen Bonds .

	pair of molecules/ions	H-bond	ρ(r) eÅ–3	Δρ(r) eÅ–5	Hr a.u.	Hr/ρ(r) a.u.	|V r|/G a.u.
1	guanidinium–carbonate	(N6–H6···O11)	0.41	4.06	–0.08	–1.317	1.22
	guanidinium–carbonate	(N8–H8B···O3)	0.40	4.07	–0.08	–1.350	1.22
2	guanidinium–carbonate	(N1–H1B2···O11)	0.19	2.31	0.00	0.000	1.00
	guanidinium–carbonate	(N2–H2B2···O1)	0.23	2.74	–0.01	–0.293	1.05
3	water–guanidinium	(O3–H3B···N4)	0.24	2.49	–0.02	–0.562	1.11

^aSuperscripts in the hydrogen bond notation indicate symmetry codes: ¹(0.5 – x, y, 1.5 – z), ²(−0.5 + x, 2 – y, 0.5 + z).

4. Topological Properties at the Bond Critical Points for P3 for Selected Hydrogen Bonds .

	pair of molecules/ions	H-bond	ρ(r) eÅ–3	Δρ(r) eÅ–5	Hr a.u.	Hr/ρ(r) a.u.	|V r|/G a.u.
1	guanidinium–carbonate	(N6–H6···O1)	0.32	3.41	–0.04	–0.844	1.14
		(N8–H8B···O2)	0.39	3.97	–0.07	–1.211	1.20
2	guanidinium–carbonate	(N2–H1D11···O1)	0.24	2.79	–0.01	–0.281	1.05
		(N1–H1A1···O2)	0.34	3.73	–0.05	–0.992	1.16
3	guanidinium–carbonate	(N3–H32···O2)	0.22	2.61	0.00	0.000	1.00
		(N1–H1B2···O3)	0.33	3.59	–0.04	–0.818	1.14
4	water–carbonate	(O4–H2···O3)	0.33	3.58	–0.04	–0.818	1.14
	water–carbonate	(O4–H13···O2)	0.32	3.52	–0.04	–0.844	1.14
5	water–carbonate	(O5–H7···O1)	0.22	2.58	–0.01	–0.307	1.06

^aSuperscripts in the hydrogen bond notation indicate symmetry codes: ¹(2 – x, −y, 1 – z), ²(x, 0.5 – y, −0.5 + z), ³(1 – x, −0.5 + y, 0.5 – z).

The energy density terms corroborate this cooperative nature. The values of H _r (total energy density) and H _r/ρ­(r) (total energy density normalized by electron density) are largely similar across interactions, reflecting comparable strengths. For instance, in P1, H _r is −0.08 au for guanidinium–carbonate interactions, indicating shared contributions to the network’s structural integrity despite the observed electron density discrepancies. Additionally, the ratio of potential to kinetic energy, |V _r|/G, consistently exceeds 1.0, signifying a weakly covalent character with a dominant electrostatic component. The similarity of |V _r|/G values highlights the complementary roles of different interactions in maintaining the system’s robustness.

The Laplacian of the electron density, Δρ­(r), provides further insight into these interactions. Positive Δρ­(r) values across all bonds confirm their closed-shell nature, which is characteristic for hydrogen bonding and ionic interactions. For example, in P3, carbonate-centered hydrogen bonds exhibit Δρ­(r) values ranging from 2.58 to 3.97 eÅ^–5, with corresponding electron densities between 0.22 and 0.39 eÅ^–3. These variations emphasize the significance of guanidinium–carbonate and water–carbonate interactions, which collectively stabilize the system while allowing for functional adaptability.

The interplay of different hydrogen bonds introduces flexibility into the bonding network, particularly under environmental changes such as pressure, temperature, or pH. Guanidinium–carbonate interactions in both P1 and P3 act as “anchors,” stabilizing the system under ambient conditions. In P1, the broader range of interaction strengths and less cohesive bonding network suggest that it may be more susceptible to external perturbations, reinforcing its identification as a metastable form. In contrast, P3’s tighter and more consistent bonding network supports its role as the thermodynamically stable phase.

The role of water in P3 further enhances the system’s behavior. Water–carbonate interactions span a range of strengths, with electron density values comparable to those of guanidinium–carbonate interactions. These interactions introduce additional hydrogen bonding pathways, increasing the system’s capacity to mediate dynamic rearrangements while maintaining structural integrity. Although proton transfer phenomena may contribute to carbonate release mechanisms, this analysis does not conclusively establish this role. Instead, the data suggest that the cooperative hydrogen bonding network, supported by water, ensures stability while enabling adaptability to environmental changes.

By examining the electron density ρ­(r), its Laplacian Δρ­(r), and energy density terms at bond critical points, this study highlights the diversity and cooperative nature of hydrogen bonding networks in these systems. These findings underscore the pivotal role of carbonate-centered interactions in maintaining stability and provide evidence for P1 as a metastable form of P3, which is influenced by local structural and environmental variations.

The deformation density maps presented in Figure provide valuable insights into electron density redistribution within the guanidinium–carbonate interactions. The blue regions, representing electron density accumulation, and the red regions, corresponding to electron depletion, highlight the localization of bonding interactions. Notably, the H6···O1 interaction exhibits a stronger deformation density feature than H8B···O2/O3, indicating a greater degree of electron density polarization along the hydrogen bond. This suggests that the H6···O1 hydrogen bond is more polarized and asymmetrically distributed compared to H8B···O2/O3.

3.

Deformation density maps [interval ± 0.01 eÅ^–3] for the experimental multipolar model of P1 (a) and P3 (b). Positive (electron accumulation) and negative (electron depletion) contours are represented by blue and red shades, respectively, according to the scale. The chosen plane highlights differences in electron density deformation between P1 and P3, focusing on hydrogen bonds: H6···O1 and H8B···O2/O3. The electron density distribution around H6 is more extended toward the acceptor atom (O1), indicating greater polarization and a stronger hydrogen bond compared to H8B···O2/O3, where the electron density is more localized. These differences reflect variations in the hydrogen-bonding environments between the two phases.

In the context of CO₂ capture and release, the polarization of H6···O1 may play a significant role in stabilizing carbonate in the solid phase. In P1, the pronounced electron accumulation along this bond suggests strong localization, possibly preparing it for electron density redistribution. As the system transitions to P3, the deformation density features become less pronounced, indicating that the electron density has been redistributed. This weakening of the electron density localization could be associated with hydrogen bond destabilization. The observed changes in deformation density suggest that the electron density redistribution at H6···O1 might contribute to the onset of carbonate mobility, potentially essential step in the CO₂ release process.

The Laplacian maps (Figures S8 and S9) further reinforce the trends observed in the deformation density analysis, illustrating the regions of electron concentration (blue contours) and depletion (red contours) around hydrogen bonds. As we mentioned, the ∇²ρ­(r) provides insight into bond strength and electron density distribution. In P1, the H6···O1 interaction is characterized by a high Laplacian value of 4.06 eÅ^–5, indicating a significant electron density localization. As the system transitions to P3, this value decreases to 3.41 eÅ^–5, suggesting a redistribution of the electron density and a weakening of the bond.

The reduction in Laplacian values between P1 and P3 suggests that electron density is becoming more diffuse, leading to a less covalent and more electrostatic interaction. This is consistent with a hydrogen bond that undergoes structural rearrangement. The comparison with H8B···O2/O3 further highlights the specificity of this change, as the Laplacian values for this interaction remain relatively stable, decreasing only slightly from 4.07 eÅ^–5 in P1 to 3.97 eÅ^–5 in P3. This lack of significant change suggests that while H8B···O3 remains largely unaffected by the phase transition, H6···O1 is undergoing electron density redistribution, reinforcing the idea that it is a key site for proton mobility.

Bader charge analysis provides a quantitative measure of the distribution of electron density across atomic basins and can serve as a useful indicator of charge redistribution between P1 and P3 phases. The Bader charge on H6 in P1 is 0.4554e, which decreases to 0.4138e in P3, indicating a reduced electron density at this site. Simultaneously, the charge on O1 becomes more negative, shifting from −0.9144e in P1 to −0.9988e in P3. This concurrent shift, decreasing positive character at H6 and increasing negative character at O1, suggests that a proton is being partially transferred or delocalized in the P3 phase.

The comparison with H8B···O2/O3 further supports this conclusion. The Bader charge on H8B in P1 is 0.4244e, decreasing only slightly to 0.3785e in P3, while the charge on O3 shifts from −1.0477e to −0.9100e. These relatively minor changes suggest that the H8B···O2/O3 hydrogen bond remains largely unaltered during the phase transition, in contrast to H6···O1, which exhibits more pronounced redistribution in electron density.

This shift in the electron density associated with the H6···O1 interaction is consistent with trends observed in the Laplacian maps and the deformation density analysis. The reduced positive Bader charge at H6 and more negative charge at O1 indicate increased ionic character and possible proton delocalization in P3, leading to weakening of the H6···O1 hydrogen bond. Such a change could act as an early stage mechanism for carbonate destabilization, ultimately facilitating CO₂ release.

To gain even more insight into proton polarization and interaction strength, we also employed SF analysis to evaluate atomic contributions to the electron density at selected bond critical points (BCPs). The analysis included hydrogen bonds relevant to potential CO₂ release, including N6–H6···O1 and N8–H8B···O2/O3 in both P1 and P3, as well as water-involved interactions in both phases (Tables and ).

5. Source Function Contributions for the Selected Hydrogen Bonds in P1.

interaction	S%(D)	S%(H)	S%(A)	S%(D + H)	S%(A + H)	S%(D + A + H)	Δ(S%(A) – S%(D))
N6–H6···O1	14.83%	14.47%	32.12%	29.30%	46.59%	61.42%	17.29%
N8–H8B···O2	22.63%	11.95%	33.26%	34.58%	45.21%	67.84%	10.63%
O3–H3B···N4	41.61%	–6.17%	0.92%	35.44%	–5.25%	36.36%	–40.69%

6. Source Function Contributions for Selected Hydrogen Bonds in P3.

interaction	S%(D)	S%(H)	S%(A)	S%(D + H)	S%(A + H)	S%(D + A + H)	Δ(S%(A) – S%(D))
N6–H6···O1	15.85%	6.39%	25.87%	22.24%	32.26%	48.11%	10.02%
N8–H8B···O3	21.48%	12.31%	35.18%	33.79%	47.49%	68.97%	13.70%
O4–H2···O3	34.55%	7.59%	30.36%	42.14%	37.95%	72.50%	–4.19%
O5–H7···O1	44.63%	–2.82%	23.42%	41.81%	20.60%	65.23%	–21.21%

In both P1 and P3 phases, the guanidinium-carbonate hydrogen bonds N6–H6···O1 and N8–H8B···O2/O3 fall under the category of polarization-assisted hydrogen bonds (PAHBs). These interactions exhibit moderate polarization toward the acceptor, characterized by S%(A) exceeding S%(D) by 10–17% (see Tables and ). Notably, while both remain PAHBs across phases, the polarization strength changes upon P1 to P3 transition: the N6–H6···O1 bond exhibits reduced polarization in P3 (Δ = 10.02%) compared to P1 (Δ = 17.29%), whereas N8–H8B···O2/O3 displays increased polarization in P3 (Δ = 13.70%) relative to P1 (Δ = 10.63%). These variations suggest that structural reorganization affects the electron density distribution differently across hydrogen bonds, possibly tuning their capacity for interaction or polarization.

Water-mediated hydrogen bonding interactions further diversify the bonding landscape. In P1, the contact of the O3–H3B···N4 shows features of an isolated hydrogen bond (IHB). The very high donor contribution and negligible acceptor input (Δ = −40.69%, Table ) combined with a negative hydrogen contribution imply weak directionality and a dominant electrostatic nature. This interaction appears to be electrostatically stabilized but structurally marginal.

In contrast, the P3 phase reveals water-mediated interactions that may contribute significantly to the cooperative bonding network. The O4–H2···O3 hydrogen bond, with nearly equal donor and acceptor contributions (Δ = −4.19%, Table ), and moderate hydrogen involvement, aligns with features typical of a RAHB analogue. Though it lacks π-delocalization, its symmetrical D–A source balance and role in a hydrogen-bonded chain suggest partial delocalization and network enhancement.

A distinct interaction in P3 and O5–H7···O1, presents signs of bond weakening or disruption. With a strong donor bias (Δ = −21.21%, Table ) and slightly negative hydrogen contribution, this water-mediated bond may be susceptible to dissociation. Its destabilization could permit water release and facilitate the subsequent hydrogen rearrangement from H6 to O1, potentially initiating carbonate destabilization and CO₂ release.

In P1, the N6–H6···O1 interaction shows nearly equal contributions from the donor (S%(D) = 14.83%) and hydrogen (S%(H) = 14.47%), with a larger contribution from the acceptor (S%(A) = 32.12%). The total contribution from the D–H–A triad is 61.42%, suggesting moderate localization and polarization toward the acceptor and indicating a significant but not extreme degree of delocalization. For N8–H8B···O3, the values are S%(D) = 22.63%, S%(H) = 11.95%, and S%(A) = 33.26%, with a D+H+A contribution of 67.84%, again showing polarization toward the acceptor and slightly stronger localization.

In P3, the corresponding H6···O1 interaction exhibits a lower hydrogen contribution (S%(H) = 6.39%) but comparable donor (15.85%) and acceptor (25.87%) values, with D+H+A = 48.11%. This marks a shift toward weaker hydrogen involvement and more delocalization. H8B···O3 in P3 is similar to P1 (S%(D) = 21.48%, S%(H) = 12.31%, S%(A) = 35.18%; D + H + A = 68.97%), indicating a stable interaction preserved across both phases.

Additional interactions in P3 show interesting behavior. The water–carbonate H-bond of the O4–H2···O3 shows S%(D) = 34.55%, S%(H) = 7.59%, and S%(A) = 30.36% (D + H + A = 72.50%), indicating a highly localized, balanced, and strongly polarized interaction, possibly acting as a proton reservoir. In contrast, the O5–H7···O1 bond shows an S%(D) = 44.63%, S%(H) = −2.82%, and S%(A) = 23.42% (D + H + A = 65.23%). The negative contribution from hydrogen suggests an unstable interaction, possibly facilitating water release and hydrogen bond rearrangement.

SF analysis supports a mechanism in which water dissociation via the H7···O1 bond may initiate a chain of polarization-driven events, including the migration of a proton from H6 toward an O1. This path is consistent with prior observations from deformation density, Laplacian, and Bader charge analyses, reinforcing the critical role of the H6···O1 interaction in polarization dynamics and highlighting its potential function as an early stage trigger for CO₂ release.

3.5. Electrostatic Potential Map Analysis

Figures and depict electrostatic potential maps for the P1 and P3 systems, visualized on an electron-density isosurface at a contour level of 0.1 eÅ^–3. These maps provide a detailed representation of a spatial representation of the electrostatic potential resulting from the electron density distribution and nuclear charges. The electrostatic potential is color-coded, with violet indicating regions of positive potential (electron-deficient areas) and red representing negative potential (electron-rich regions), highlighting areas likely involved in intermolecular interactions such as hydrogen bonding.

4.

Electrostatic potential (eÅ^–1) mapped onto the 0.1 eÅ^–3 electron-density isosurface for P1. The potential is drawn separately for each molecule, where the violet color denotes a positive value and the red color is related to the negative value.

5.

Electrostatic potential (eÅ^–1) mapped onto the 0.1 eÅ^–3 electron-density isosurface for P3. The potential is drawn separately for each molecule, where the violet color denotes a positive value, and the red color is related to the negative value.

In the P1 system (Figure ), the electrostatic potential map highlights distinct regions of positive and negative charges across the molecules, indicating areas likely to participate in intermolecular interactions. Yellow dashed lines represent hydrogen bonds, which are critical structural elements but do not definitively confirm proton transfer. For example, regions of positive potential on one molecule align with regions of negative potential on another, consistent with the formation of hydrogen bonds that could facilitate proton transfer under suitable conditions, especially between H6 and O1, and H3b and N4 pairs of atoms. The range of electrostatic potentials, from −0.129 to 0.417 eÅ^–1 for components such as MGBIG, carbonate, and water, reflects significant polarization. This polarization is most pronounced near hydrogen-bonded oxygen atoms, where negative potential dominates, suggesting a local environment conducive to proton redistribution. However, the narrower potential range in P1 compared to P3 may indicate lower overall polarization and, consequently, a less robust stabilization of the hydrogen-bonding network. This observation supports the classification of P1 as a metastable phase that may convert to P3 under favorable conditions.

In the P3 system (Figure ), the electrostatic potential map reveals a broader potential range (−0.199 to 0.435 eÅ^–1) indicating a higher degree of polarization than in P1. This enhanced polarization likely results from the more extensive and directional hydrogen-bonding network in P3, particularly involving both guanidinium units and water molecules. Such an environment may facilitate greater charge separation and more favorable conditions, contributing to the increased structural stability and thermodynamic preference of P3.

The yellow dashed lines connecting regions of high positive electrostatic potential on hydrogen atoms to regions of negative potential on oxygen atoms further emphasize the cooperative bonding network. Notably, the two water and MGBIG molecules exhibit spatially distinct regions of positive potential around hydrogen atoms and negative and less positive potential around oxygen and nitrogen atoms, respectively. These features indicate a system with greater stability, where enhanced polarization strengthens intermolecular interactions and reduces the likelihood of structural rearrangements.

The differing electrostatic potential ranges and polarization profiles between P1 and P3 highlight their relative stabilities with P3 appearing as the thermodynamically more stable form. The pronounced polarization within the hydrogen-bonding interactions in P3 could also serve as a starting point for proton transfer under specific conditions, contributing to its functional flexibility and adaptability. By contrast, P1’s lower polarization and narrower potential range suggest it may represent a less stable, intermediate form, potentially transitioning to P3 over time or under environmental changes.

3.6. Energy of the Intermolecular Interactions

Figure illustrates the intermolecular interaction energies between molecular fragments for the P1 and P3 crystal systems calculated using the EPMM hybrid method based on high-resolution single-crystal X-ray and neutron diffraction data. These interactions reveal significant differences in the stabilization of molecular fragments within the two systems.

6.

Intermolecular energies between molecular fragments for the P1 and P3 systems. Energies were computed by using Exact Potential and Multipole Moments (EPMM) hybrid method (kJ/mol) from high-resolution single crystal X-ray and neutron diffraction data. In P3, water molecules stabilize the carbonate anion, an effect absent in P1. Additionally, differences in MGBIG cation protonation between the phases lead to distinct MGBIG environments in both phases.

In the P1 system, the strongest stabilizing interaction occurs between two MGBIG cations and carbonate anion (the purple and red fragments due to N–H···O strong hydrogen bonds), with an energy of −82.32 and −145.77 kJ/mol (Figure ). The other interactions between carbonate anion and MGBIG cations show moderate stabilizing contributions, such as the light blue fragment (−40.50 and −33.89 kJ/mol). The overall network of interactions in P1 appears less cohesive compared to P3 due to weaker interactions between certain fragments, specifically between water molecule and MGBIG cations (−33.58, −22.02, and −41.22 kJ/mol). In contrast, the P3 system shows a more robust stabilizing network. The strongest interaction is observed between the MGBIG cations and carbonate anion, marked as purple and red fragments, with a highly stabilizing energy of −164.42 and −139.01 kJ/mol, respectively. Another interaction between MGBIG and carbonate ions, marked as light blue fragment, also exhibit a strong stabilizing interaction (−127.29 kJ/mol), further reinforcing the molecular assembly. The interactions involving other fragments between MGBIG cations and water molecules, as well as between carbonate anion and water molecules, show that the P3 system benefits from a more balanced distribution of stabilizing forces. The purple fragment in P3, with its exceptionally strong interaction with the red fragment, highlights a distinct feature of this system. This strong interaction likely stems from specific structural factors, such as enhanced electrostatic or dispersion forces, which differentiate it from the P1 system. Overall, the interplay of fragment-specific interactions in P3 leads to a more stable and cohesive crystal lattice compared to P1.

The disparity in carbonate binding energies and lattice stabilities between the two systems reflects the differences in their intermolecular interaction network. In particular, the guanidinium-carbonate interactions are notably stronger in P3 (−164.42 and −139.01 kJ/mol) compared with their P1 counterparts (−145.77 and −82.32 kJ/mol), indicating an enhanced charge-assisted hydrogen bonding framework in P3. Furthermore, additional stabilization arises from the stronger MGBIG-carbonate interaction in P3 (light blue fragment: −127.29 kJ/mol), whereas the same interaction in P1 is significantly weaker (−40.50 and −33.89 kJ/mol).

Another critical contributor to the increased stability of P3 is the direct involvement of water molecules in hydrogen bonding with the carbonate anion, which is absent in P1. In P1, water contributes only modestly to lattice stabilization through interactions with guanidinium (−33.58 to −22.02 kJ/mol), whereas in P3, carbonate-water interactions (−33.00 to −40.00 kJ/mol, depending on the specific pair) significantly reinforce the hydrogen-bonding network.

These fragment-specific differences are also reflected in the total EPMM-derived carbonate binding energy, which is nearly twice as negative in P3 (−591.4 kJ/mol) compared to that in P1 (−302.5 kJ/mol). Similarly, the crystal lattice energy of P3 (−847.3 kJ/mol) is much more favorable than that of P1 (−571.0 kJ/mol), and the reaction free energy is also more exergonic (−30.6 vs. −17.8 kJ/mol). Together, these data clearly demonstrate that P3 is stabilized by a more cooperative and synergistic hydrogen-bonding network with stronger, more directional, and more numerous interactions compared to P1. This directly supports the conclusion that cooperative hydrogen bonding is the primary energetic factor underpinning the thermodynamic stability of the P3 phase (Table S3).

4. Conclusions

In this study, we provide a detailed analysis of the intermolecular interactions in DAC, focusing on the role of hydrogen bonds and interaction energies in stabilizing CO₂ within two crystalline phases of MGBIG. Using high-resolution crystallographic data and advanced electron density analysis, we explored how hydrogen bonding networks contribute to both the structural stability and functional adaptability of the P1 and P3 phases. In both systems, intermolecular interactions play a dual role, offering stability while enabling the flexibility essential for dynamic CO₂ capture and release cycles.

Topological and electrostatic analyses, such as deformation electron density features, Laplacian maps, Bader charge distribution, and electrostatic potential isosurfaces, highlight key differences in the hydrogen bonding environments between P1 and P3. These features suggest an electron density redistribution in the hydrogen bonding network involving guanidinium, water, and carbonate anions, which may create conditions favorable for proton mobility, a potential early step in the CO₂ release process. Electrostatic potential maps reveal distinct regions of positive and negative charge aligned with hydrogen bonding interactions, further indicating possible electron density redistribution. The stronger electrostatic interactions in P3, attributed to its higher charge state (+2 vs. + 1 in P1), enhance carbonate stabilization, further supporting its thermodynamic stability. The enhanced polarization in P3 highlights its superior potential to stabilize charged intermediates, driven by greater charge separation and stronger hydrogen bonding networks compared to those of P1.

Notably, visual inspection of electrostatic potential maps suggested that the H6···O1 interaction in P3 appeared more polarized than that in H8B···O3, with greater surface-level charge contrast. However, source function analysis revealed a higher directional polarization for H8B···O2/O3 based on atomic contributions at the bond critical point. This apparent discrepancy underscores the complementary nature of ESP and SF analyses: while ESP maps visualize polarization at the molecular surface, SF provides a localized decomposition at the electron density level. Together, these tools provide a nuanced understanding of polarization, reinforcing the functional roles of both hydrogen bonds in enabling proton mobility and structural responsiveness.

Our SF analysis confirms that guanidinium–carbonate hydrogen bonds in both phases fall into the category of polarization-assisted hydrogen bonds (PAHBs). Notably, the degree of polarization changes upon phase transition: while the N6–H6···O1 bond becomes less polarized in P3, the N8–H8B···O3 interaction becomes more polarized. These asymmetrical trends indicate a redistribution of the electron density and responsiveness to structural reorganization. By combining global electrostatic visualization with localized source function decomposition, we provide a robust and multifaceted understanding of polarization and proton dynamics, enhancing the reliability of our conclusions on hydrogen bonding and CO₂ release mechanisms.

Water-mediated hydrogen bonding interactions further diversify the bonding landscape. In P1, the O3–H3B···N4 contact behaves as an IHB, electrostatically stabilized but weakly directional. In contrast, the P3 phase exhibits a more complex bonding network. The O4–H2···O3 hydrogen bond shows near-symmetric donor and acceptor source contributions and participates in a chain-like motif, classifying it as a RAHB analogue. Meanwhile, the O5–H7···O1 interaction shows signs of weakening and disruption, which could lead to water release and potentially initiate proton migration from nearby sites such as H6 toward the O1, triggering electron density redistribution across the network. This mechanism may underline the early stages of carbonate destabilization and CO₂ release.

Energetic analysis in Figure further underscores the advantages of P3 over P1. P3 exhibits stronger carbonate binding energies (−607.0 kJ/mol vs −302.5 kJ/mol), higher lattice stability (−847.3 kJ/mol vs −571.0 kJ/mol), and more favorable reaction free energies (−30.6 kJ/mol vs −17.8 kJ/mol). These energetic metrics reflect a more cohesive interaction network in P3, facilitating electron density rearrangements and the overall structural integrity.

The differences in the electron density and bonding interactions between P1 and P3 highlight the critical role of intermolecular interactions as a driving force in CO₂ capture. The greater stability of the P3 phase is driven by the dual protonation of both guanidine units. This symmetrical protonation creates a cohesive hydrogen-bonding network. This structural uniformity is consistent with the more ordered characteristics observed through Hirshfeld surface analyses, fingerprint plots, and electrostatic potential maps. The cohesive hydrogen-bonding network in P3 supports charge stabilization. In contrast, P1 features only one protonated guanidine, resulting in asymmetry and variability. These findings offer key insights into designing advanced DAC materials.

While direct evidence of proton transfer is not accessible under the current conditions, these observations identify candidate protons and interactions that are likely involved in this process at elevated temperatures. To validate these findings and explore dynamic material behavior, multitemperature X-ray and neutron diffraction experiments and molecular dynamics simulations are proposed as future directions. These approaches will help elucidate temperature-dependent structural flexibility, interaction dynamics, and their implications for CO₂ binding and release under operational conditions.

These results emphasize the importance of a balanced interaction framework in the DAC material design. The enhanced stability and adaptability of P3 provide a model for the development of next-generation materials with improved efficiency under varying environmental conditions, such as fluctuating humidity or CO₂ concentrations.

Glossary

Abbreviations

MGBIG

methylglyoxal-bis­(iminoguanidine)

P1

phase 1 of the MGBIG

P3

phase 3 of the MGBIG

DAC

direct air capture

ADP

atomic displacement parameter

EPMM

electrostatic potential and multipole moments

IAM

independent atom model

QTAIM

quantum theory of atoms in molecule

BCP

bond critical point

DFT

density functional theory

SCM

sourced from the Su, Coppens, and Macchi databank of atomic scattering factors

AIMD

explicit ab initio molecular dynamics

SNS

Spallation Neutron Source

BSSE

basis set superposition error

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacs.5c01946.

• X-ray diffraction data, model quality assessment via refinement parameters and residual electron density analysis, and charge density validation through fractal dimension and normal probability plots. Topological analysis provides molecular graphs of bond paths and critical points, while deformation density maps illustrate charge distribution differences. Multipole refinement details include local coordinate systems and refined parameters. Energetic and electrostatic properties, such as binding energies and electrostatic potential maps (PDF)

All authors have given approval to the final version of the manuscript.

DOE DE-AC05-00OR22725.

The authors declare no competing financial interest.