Decoding local framework dynamics in the ultra-small pore MOF MIL-120(Al) CO_2 adsorbent using machine-learning potential

Domain: chemistry
Published: 2026-02-26
Editorial outcome: major_revision

Abstract
Metal–organic frameworks (MOFs) with ultra-small pores offer an optimal environment to effectively capture guest molecules such as CO . Subtle local dynamics of their frameworks, either throughout reorientation of functional groups grafted to the organic linkers or those present in their inorganic nodes, is expected to play a major role in their sorption behaviours. Herein, we investigated the local dynamics of bridging hydroxyl group (μ -OH) in the ultra-small pore MOF MIL-120(Al) using DFT combined with a purpose-trained machine-learning potential (MLP). Six distinct μ -OH configurations were identified with low interconversion barriers (0.07–0.19 eV), indicating significant dynamic behaviour at room temperature. Grand canonical Monte Carlo and hybrid GCMC–MD simulations driven by the MLP demonstrate that adsorption isotherms and low-pressure behaviour are sensitive to μ -OH ordering and whether framework and cell relaxation are considered. While standard rigid force-field simulations overestimated the heat of adsorption, MLP-driven GCMC-MD simulations successfully captured framework relaxation and dynamic μ -OH reorientation under CO loading. This work establishes that a reliable description of the local structure, such as reorientation/flipping of bridging hydroxyl groups, is a key feature to gain an accurate description of the guest locations and energetics in ultra-small pore MOFs.

Introduction
Metal–organic frameworks (MOFs) are crystalline coordination polymers constructed from metal ions or clusters connected by organic linkers, forming highly ordered nanoporous structures1–6. Owing to the unique tunability of their pore size, shape and chemical functionality, MOFs have emerged as promising materials for diverse applications including CO capture7–12. In particular, MOFs with ultra-small pores/channels combined potentially with polar groups decorating the pore walls offer a unique confined environment to favour an effective packing of CO in their pores13. This confers to this sub-class of MOFs attractive CO sorption performance even in the presence of co-adsorbed species such as N or CH of key importance in the context of CO capture in post- and pre-combustion conditions14–17. Notably, it has been documented that a very tiny change of the pore size of isoreticular ultra-small pore MOFs by modulating the nature of the metal sites as for example in the KAUST-8 series (Al, Fe, Ga) can fine-tune their CO sorption properties18–20. Local flexibility of such a sub-class of MOFs that can arise either from the dynamics of the functional groups of the organic linkers or the orientation of chemical functions present in the inorganic nodes can also play a key role in the CO sorption mechanism15,21,22. This structural dynamics is often overlooked, although decisive in controlling the CO /MOF interactions by modulating slightly the MOF pore confinement. This is especially true for ultra-small pore MOFs containing bridging hydroxyl functions, namely, μ -OH groups, with a notable experimental limitation lying in determining hydrogen atom positions since H atoms scatter X-rays only weakly and their locations cannot be detected by X-ray diffraction technique. As a result, hydrogen atoms are typically added post-hoc based on standard bond lengths and geometries criteria23. Such empirical treatments assume that μ -OH orientations exert only a minor influence on MOF framework properties, which might be only valid for medium- to large-pore MOFs. MIL-120(Al), first reported in 2009 by Férey and co-workers, is one representative ultra-small pore MOF24. This aluminum MOF is built from the assembly of tetratopic linker 1,2,4,5-benzenetetracarboxylate and infinite chains of edge-sharing AlO octahedra forming a three-dimensional network with one-dimensional ultra-small pores (~5.4 × 4.7 Å) aligned along the c-axis. This sustainable, easily scaled-up and low-cost MOF combines excellent thermal and hydrolytic stability with CO adsorption performance as attractive as the best MOFs reported so far for CO capture under flue-gas conditions (see Supplementary Table 1). This makes this MOF a promising candidate for further integration into large-scale industrial processes25,26. Our preliminary findings suggested that the orientation of the μ -OH groups present in this MOF affects the CO location in the pores and their associated energetics25. Nevertheless, a systematic exploration of the role played by the local dynamics of these μ -OH groups on the CO sorption properties of MIL-120(Al) and beyond other related-MOFs, is yet to be realized.

To address this gap, the present work employs a combination of DFT calculations and a MLP approach to systematically map the configurational landscape of μ -OH groups in MIL-120(Al). By quantifying the electronic stability of representative configurations, their structure interconversion pathways and their impact on CO adsorption thermodynamics, this study uncovers a previously overlooked structural degree of freedom in MIL-120(Al), and establishes a transferable computational framework to capture the impact of functional groups orientations on MOFs properties more broadly.

Results
Exploration of the local structural features of MIL-120(Al). The structure of MIL-120(Al) comprises edge-sharing AlO octahedra linked by bridging hydroxyl (μ -OH) groups forming one-dimensional chain motifs (cf. Fig. 1a). Among several possible μ -OH groups orientations, we constructed six representative structure models of MIL-120(Al) that differ exclusively in the orientation of the four μ -OH groups present in the unit cell, namely MIL-120(Al)-A, MIL-120(Al)-B, MIL-120(Al)-C, MIL-120(Al)-D, MIL-120(Al)-E and MIL-120(Al)-F (cf. Figs. 1b) while the MOF skeleton remains the same as shown in Fig. 1c with identical simulated X-ray diffraction patterns for all structure models in line with the corresponding experimental data25. Notably, because X-ray diffraction cannot resolve the positions of hydrogen atoms, previous studies have adopted MIL-120(Al)-F as a single representative structure model24,25. DFT geometry optimizations with full relaxation of atomic positions and cell parameters for the six structure models revealed clear differences in total electronic energy. MIL-120(Al)-A is the most stable configuration, while MIL-120(Al)-F has the highest energy, with a energy difference of ~0.59 eV per unit cell. Interestingly, the MIL-120(Al)-F configuration, reported in the literature for this MOF24, corresponds to a μ -OH group orientation that is not energetically favorable. In the lowest-energy MIL-120(Al)-A configuration, the μ -OH groups form an interlocking hydrogen-bond network linking adjacent Al(OH) O octahedral chains, as shown in Supplementary Fig. 1. The μ -OH groups orientate towards the neighbouring Al(OH) O chain on one side, establishing directional hydrogen bonds formed between the hydroxyl hydrogen atom of the μ -OH groups and the nearby Al–O framework oxygen of the adjacent polyhedral chains, while on the opposite side, they are pointing towards the channel. This cooperatively interlocking motif stabilises the MIL-120(Al)-A configuration. In contrast, the other five variants lack such motif, with more disordered μ -OH orientations that result in weaker cooperative intramolecular hydrogen-bond interactions. These six structure models exhibit only minor variations in their lattice parameters: the relative changes in a, b, c, α, β and γ remain within ±1.4%, and the cell volumes within ±3.5%, as shown in Fig. 1d and Supplementary Table 2. Despite these similar crystallographic features, their pore size distributions (PSDs) deviate with the main peak contribution distributed between ~3.8 and 4.2 Å, depending on the orientations of the μ -OH groups towards the MOF channel (cf. Fig. 1e). Owing to the ultra-small pores of this 1D MOCF channel, such sub-angstrom fluctuations in aperture can markedly impact guest accessibility and modulate MOF/guest interactions. Therefore μ -OH orientation represents a ‘hidden’ structural degree of freedom not detectable by standard X-ray diffraction techniques yet capable of influencing functional pore dimensions and energetics.

Machine-learning potential development and exploration of the stability of the different MIL-120(Al) configurations. To efficiently probe the full configurational ensemble and to enable in-depth exploration of the possible structure interconversion pathways between all these structure models, we developed a robust MLP, trained on a comprehensive MIL-120(Al)-specific DFT dataset, as shown in Supplementary Fig. 2. The dataset includes a wide range of DFT-optimised MOF structures, static single-point DFT calculations, MOF structures loaded with different CO uptakes, intermediate/transition structures obtained via climbing-image nudged elastic band (CI-NEB)27, and Ab Initio Molecular Dynamics (AIMD) snapshots under diverse NVT/NPT conditions (details of the collection, training, validation, and testing of the entire dataset can be found in Supplementary Note1 and Supplementary Figs. 3-4). We then trained a DeePMD potential28 and evaluated its coverage with the t-distributed stochastic neighbor embedding (t-SNE) method. As shown in Fig. 2a, distinct datasets occupy different regions of the descriptor space, allowing for a clear view of the occupation of each component in the entire dataset. This plot enables to confirm that there is an effective sampling of the configurational space throughout the MLP training. Fig. 2b shows a comparison between the MLP-and DFT-derived energies for the empty and CO -loaded (one CO per unit-cell, ~ 2.02 mmol g-1) MIL-120(Al) structures with root mean square error (RMSE) values of 0.217 meV/atom and 0.268 meV/atom (cf. Supplementary Table 3), respectively. Notably, these deviations are significantly lower than the values generally obtained for a standard MLP29,30, demonstrating the high accuracy and effectiveness of the MLP training process. The energy–volume curves derived from DFT optimization, MLP single-point evaluation based on DFT-optimized geometries, and fully MLP-relaxed structures show very good agreement, as shown in Fig. 2c in terms of both minima and overall curvatures of the plot. Phonon spectra predicted by MLP also show no imaginary modes at the whole Brillouin-zone path for all MIL-120(Al) variations, confirming the dynamical stability of all these configurations (cf. Fig. 2d). These results demonstrate that the trained MLP achieves near-DFT-level accuracy in describing the energetics, vibrational properties, and optimized geometries across the MIL-120(Al) configurations.

We then assessed the elasticity and failure responses of all six MIL-120(Al) variants by calculating the linear compressibility, Young's modulus, shear modulus, and Poisson's ratio (see Fig. 2e and Supplementary Table 4). These calculations revealed that local μ -OH ordering systematically affects the directional mechanical properties of MIL-120(Al). MIL-120(Al)-A in which μ -OH groups form cooperative inter-chain hydrogen bonding, exhibits stiffer coupling and reduced compressibility perpendicular to the chain axis. In contrast, variants with more disordered or pore-facing OH orientations (e.g. MIL-120(Al)-B and MIL-120(Al)-F) demonstrate softer inter-chain contacts and significantly higher compressibility in these directions. This is quantified by the maximum-to-minimum compressibility ratio, which reaches 3.6 for MIL-120(Al)-B in line with a substantial mechanical heterogeneity driven by the μ -OH groups arrangement.

Calculated stress-strain curves further confirm that μ -OH orientation controls failure behaviour. The chain direction ([010]) is the stiffest and most ductile axis in all variants, due to the rigid AlO octahedral backbone. Consequently, ultimate tensile strains along [100] exceed 50% across the series. However, the detailed shape of the stress–strain curve and the onset of strain softening vary systematically with μ -OH groups ordering (cf. Supplementary Figs. 5-8). This mechanical behaviour originates from the anisotropic topology of the 1D rigid AlO octahedra chains coupled with flexible hydrogen-bonded interchain contacts. Therefore, although the six MOF configurations exhibit comparable volumetric averages of the elastic modulus, their anisotropic mechanical responses differ significantly.

Structure interconversions and associated local μ -OH reorientations between MIL-120(Al) configurations predicted by DFT and MLP calculations. Quantitative characterisation of the kinetics of μ -OH orientations is essential for determining whether the identified polymorphs correspond to kinetically trapped states or whether they remain dynamically accessible under experimental conditions. For this purpose, we calculated the minimum-energy pathways between the different polymorphic states of MIL-120(Al)s using the climbing image nudged elastic band (CI-NEB) method27,31 interfaced with the DFT and MLP levels of theory. Representative CI-NEB profiles obtained from DFT (Fig. 3a) and MLP (Fig. 3b) revealed relatively moderate energy barriers of 0.07–0.19 eV per unit cell for the interconversion between the empty configurations. Importantly, the MLP-predicted pathways quantitatively reproduced the DFT-derived energy barriers and transition-state geometries across all computed systems. The energy profiles and the intermediate images are highly consistent, with almost complete overlap observed between the MLP and DFT curves (cf. Supplementary Figs. 9-26 for the complete curves). This quantitative agreement is particularly notable because CI-NEB probes transition-state regions of the potential-energy surface, where interpolation errors often compromise the accuracy of predicted energy. Thus, the MLP performance confirms that the training set adequately sampled both equilibrium configurations and critical transition configurations.

The presence of CO in the MOF pores is shown to only slightly affect these energy barriers. For some pathways, CO marginally reduces the energy barrier (~ 3–8%), indicating that guest-mediated stabilisation of specific transition states occurs through directional host–guest interactions. Analysis of CI-NEB snapshots for the empty MIL-120(Al) structures (Fig. 3c) shows that the structure interconversions imply a dynamic reorientation of the μ -OH groups, the H-atom temporarily forming and breaking hydrogen bonds with neighbouring oxygens, primarily with the carboxylate oxygens of the pyromellitate linker, while maintaining its covalent bond with the original μ -O. A synchronous H-atom displacement and transient hydrogen-bond rearrangement account for the relatively moderate energy barriers involved, highlighting the high degree of freedom of this μ -OH group and how it can easily reorient, thereby affecting the features of the accessible MOF pores.

In-depth microscopic understanding of CO adsorption in MIL-120(Al)s by DFT and MLP calculations. Next, we assessed how spatial distribution of μ -OH groups in MIL-120(Al)s modulates the adsorption geometries and energetics of CO within the MOF channels. To avoid bias towards local minima, the adsorption site locator protocol employed a random insertion approach, followed by MLP-based relaxation and subsequent DFT refinement of the lowest-energy candidates. MLP- (Fig. 4a) and DFT- (Supplementary Fig. 27)-optimized geometries for the six MOF variants loaded by 1 CO molecule per unit cell, show extremely similar guest locations and orientations, confirming that the MLP captures the local host–guest interactions accurately. Detailed analysis of the adsorbed CO₂ orientations uncovers a direct correlation with the μ -OH group arrangement. In most cases, the CO molecular axis is aligned nearly perpendicular to the pore axis. This maximises directional interactions with μ -OH groups pointing towards the channel. Both our DFT- and MLP-optimized geometries show that the O(CO )···H(μ -OH) separating distances are in the range of 2.17~2.74 Å, with both MLP and DFT optimized geometries giving consistent distances and geometries (cf. Fig. 4a). By contrast, in MIL-120(Al)-C and MIL-120(Al)-D, the local μ -OH distribution differs: the bridging hydroxyl groups adopt orientations more axial to the channel, which in turn sterically favour a parallel CO alignment along the channel. Notably, the presence of CO produces only minor adjustments of μ -OH orientations relative to the empty frameworks, consistent with the earlier finding that CO does not substantially alter the structure interconversion energy barriers.

In terms of CO interaction energy at 0 K, the MLP predictions deviate from DFT by at most 2.3 kJ mol-1 across all examined configurations (cf. Fig. 4b). Interestingly, our MLP performs better than other universal MLPs reported in the literature, such as MACE-MP-0 and fine-tuned MACE-DAC models32,33 leading to a systematic over- and under-estimation of the interaction energies, respectively (Fig. 4b). This strongly suggests that universal MLPs are poorly suited for MOFs with polar functionalities and local structural flexibility, especially when μ -OH group dynamics dominate host–guest interactions. Furthermore, the Widom insertion calculations performed using our trained MLP led to isosteric heats (Q ) which closely match the experimental values for MIL-120(Al)-A, MIL-120(Al)-B and MIL-120(Al)-C, as shown in Fig. 4c, compared to typical universal MLPs that show substantial deviations. Overall, the highest Q value is obtained for MIL-120(Al)-F, in line with a more confined pore environment of this configuration characterised by the highly ordered orientation of μ -OH groups towards the pore channels. The use of UFF leads to a substantial overestimation of Q for all configurations as compared to the corresponding experimental data supporting the need for an empirical tuning of the force-field parameters to obtain a better agreement with experimental data (Supplementary Fig. 28).

The small interconversion energy barriers between the different MIL-120(Al) structure models suggest that CO adsorption can readily trigger structural transitions. Each MIL-120(Al) configuration is therefore expected to contribute individually to the experimentally observed CO uptake across the full pressure range. However, conventional GCMC approaches typically treat the MOF framework as rigid and rely on empirical force fields such as UFF36. Such simulations cannot capture local, dynamical rearrangements of framework motifs, e.g. μ -OH reorientations, that we demonstrated to be important in the ultra-small-pore MIL-120(Al). Moreover, the UFF parametrization is poorly suited to describe the interactions between highly polar and sterically constrained environments with guest molecules as shown in Supplementary Fig. 30 with a deviation between the corresponding GCMC simulated adsorption isotherms for all configurations and the experimental data. Taken together, these effects lead to a systematic overestimation of the simulated Q and CO adsorption uptake compared to experimental data as already reported for such families of MOFs25,37,38. Empirical reparameterization of UFF can be used to align with specific experiments (see Supplementary Figs. 31-33), however this approach lacks transferability and predictive ability. To evaluate the impact of the μ -OH orientation associated with these distinct configurations on the overall CO sorption isotherms, we performed MLP-based GCMC simulations using three distinct approaches (cf. Supplementary Figs. 34-51): i) fully rigid MIL-120(Al) framework, where both atomic positions and unit cell were fixed, ii) hybrid GCMC- (NVT) MD scheme, coupling MC steps with molecular dynamics (MD) steps in the NVT ensemble (relaxed atomic positions, fixed unit cell parameter), and iii) hybrid GCMC- (NPT) MD scheme coupling MC steps with MD steps in the NPT ensemble (full relaxation of both atomic positions and unit cell parameters). The rigid-framework MLP-GCMC simulations were found to describe the experimental isotherm in the low-pressure region more faithfully than UFF-GCMC simulations as shown in Supplementary Fig. 52. The MLP-GCMC-(NPT) MD calculations performed starting with the different structure models converge towards similar adsorption isotherms closely matching those obtained by MLP-GCMC-(NVT) MD calculations for the MIL-120(Al)-A to MIL-120(Al)-D models (cf. Supplementary Fig. 53). This observation is consistent with the relative low energy between all these structures models, suggesting a structure relaxation towards the most stable MIL-120(Al) structures, i.e. MIL-120(Al)-A to MIL-120(Al)-D (cf. Fig. 3) upon adsorption. The MLP-based GCMC–(NPT) adsorption isotherms (Figs. 4d-4e) show an overall good agreement with two independent experimental datasets25,26 in the 0-1 bar region, and Supplementary Figs. 54-55 (273-313 K) further confirming the reliability of our MLP to capture the CO adsorption behaviour in the overall range of investigated temperature range. The MLP-MD derived Radial Distribution Functions (RDFs) computed for the predominant MOF/CO atom pair at a given CO loading of 2.02 mmol g⁻¹ and 300 K is in very good agreement with that obtained by AIMD in the same conditions (Fig. 4f). This comparison supports that the MLP captures well μ -OH position and orientation changes upon CO adsorption. As shown in Figs. 4g-4h, Supplementary Figs. 56-58, and Supplementary Movies 1-4, the μ -OH groups in the MIL-120(Al)-F model undergo pronounced rotations on ps time scales in the MLP-MD-derived trajectories at 300 K, and this behaviour appears both in the presence and absence of CO . At a low CO loading of 2.02 mmol g⁻1, analysis of the MLP-MD trajectories show that MIL-120(Al)-F structure reaches equilibrium after ~ 200 ps. The same structure loaded by 4.05 mmol g⁻1 of CO attains an equilibrium faster (~ 95 ps). This indicates that the phase/ordering transition depends on the guest loading: a critical CO density promotes cooperative reorientation and shortens the transition time. This interpretation is consistent with the relatively low CI-NEB energy barriers, which place μ -OH rotations within the range of thermal accessibility and allow guest-driven kinetics to control the observed timescales. Further examination of the adsorbate orientation indicates that the majority of the molecules are predominantly aligned in orientations axial to the channel, analogous to the low-energy structures of CO @MIL-120(Al)-C and CO @MIL-120(Al)-D (Fig. 4a). These findings reveal a complex interplay between the intrinsic conformational energetics of the MOF framework, governed by the local μ -OH dynamics, and the stabilization energy provided by the host-guest interactions. Notably in the case of the GCMC-(NVT) MD simulations (Supplementary Fig. 59), there is an overall reduction in CO sorption uptake compared to the GCMC simulations, a phenomenon attributed to the local dynamics of the μ -OH groups. Nevertheless, the overall trend in sorption uptakes from MIL-120(Al)-F to MIL-120(Al)-A is preserved, particularly at higher pressures. This suggests that even with the dominance of the local μ -OH dynamics, the global relaxation of the MOF structure is required to accurately capture the overall adsorption phenomena.

Methods
DFT calculations
All DFT calculations were carried out using the Vienna Ab-initio Simulation Package (VASP) code (Version: 5.4.4)39. The projector augmented wave (PAW) potential and the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional was adopted40,41. An energy cutoff of 650 eV and the Monkhorst-Pack 5 × 5 × 6 k-point grid42 was chosen to ensure convergence of total energy. These parameters yielded converged total energies and atomic forces within thresholds of 10-5 eV and 0.01 eV Å−1, respectively. All geometry optimizations were performed using the VASP code with the conjugate gradient (CG) algorithm. Dispersion interactions were accounted for using the DFT-D3 van der Waals (vdW) correction scheme43. The elastic constants were calculated using DFT-based static stress-strain calculations in VASP, where both lattice parameters and atomic positions were fully relaxed under small deformations to obtain the elastic tensor directly from energy-minimized structures. Finite-temperature AIMD simulations were carried out in 2 × 2 × 2 supercells to better capture local dynamics and hydrogen-bond rearrangements. AIMD runs used the canonical (NVT) ensemble with a Nosé–Hoover thermostat and a time step of 0.5 fs44. The AIMD trajectories were collected at 300, 500 and 800 K for durations exceeding 5 ps. Symmetry constraints were removed in all AIMD simulations to allow unrestricted sampling of local reorientation modes. CI-NEB27 calculations for transition-state pathways were performed within VASP using standard settings described in the Supplementary Note 1.

Dataset preparation for MLP training
To build a representative training dataset for the MIL-120(Al)s family, we combined configurations from multiple sampling protocols: DFT geometry optimizations, static single-point calculations, random Widom-insertions of CO at various loadings, structure optimizations under different strains and pressures, CI-NEB intermediate images sampled along μ -OH reorientation paths, and AIMD snapshots from both NVT and NPT ensembles. The dataset includes both empty and CO -loaded MIL-120(Al) configurations in unit-cell and supercell representations. In total 183,061 snapshots were collected. Further details are provided in Supplementary Notes 1-2.

MLP development
We trained a deep neural network potential using the DeePMD-kit (v2.0.1) implementation of the DeepPot-SE framework28. The embedding network sizes were set to {25, 50, 100} for successive embedding layers, while the fitting network used three hidden layers of sizes {240, 240, 240}. A radial cutoff of 7.8 Å and a smoothing-length of 1.2 Å were adopted to capture sufficient many-body information while maintaining computational efficiency for the MIL-120(Al)s environments. Training proceeded for 1,000,000 steps with an initial learning rate of 1×10-3 that decayed every 5,000 steps; other hyperparameters (batching and loss weightings) follow the protocol summarized in Supplementary Note 2. The choice of cutoff and network depth was validated by convergence tests to ensure robust reproduction of DFT energies and forces for both empty and CO -loaded configurations.

MLP-based molecular dynamics and property calculations
The trained DeePMD potential was also deployed for large-scale molecular dynamics via the DeepMD-LAMMPS interface, using the model as a LAMMPS pair style for energy and force evaluations45. Phonon calculations were performed using Phonopy and the phonoLAMMPS toolchain on 2×2×2 supercells along a consistent Brillouin zone path46,47. CI-NEB pathways were recomputed using the ASE-Python library48 and the trained MLP, with each intermediate structure optimized using the FIRE (Fast Inertial Relaxation Engine) algorithm, enabling extensive transition-state sampling at lower computational cost. The MLP was also used for exhaustive CO adsorption site discovery via Widom-insertion sampling and adsorption energy scans.

MLP-based hybrid GCMC simulations
To incorporate the framework dynamics and simulations with the trained MLP, we developed custom code to perform GCMC simulations based on MLP energies. The code performs insertion, deletion, rotation, and translation moves on the adsorbed molecule based on the Metropolis algorithm,49 with acceptance criteria calculated according to

βfV
P (O → N) = min{1, exp(−βΔU)} (1)
INSERTION
N+1
N
P (O → N) = min{1, exp(−βΔU)} (2)
DELETION
βfV
N
P (O → N) = min{1,exp(−βΔU)} (3)
ROTATION
P (O → N) = min{1,exp(−βΔU)} (4)
TRANSLATION

where β is the reciprocal thermodynamic temperature, 1/k T, with k being the Boltzmann constant, B B
U represents the potential energy of interaction, N the number of adsorbate molecules in the simulation box, V the volume of the simulation box, and f the fugacity of the adsorbing species. The fugacity was calculated as f = φP, with P being the pressure on the ideal reservoir and φ the fugacity coefficient, calculated by the Peng-Robinson equation of state50.

The code is based on the ASE-Python library48, with the energy evaluations being performed by the DeePMD-ASE calculator interface. The molecular dynamics (MD) simulations on the NVT ensemble were performed with the Berendsen thermostat, and on the NPT ensemble with the Berendsen thermostat and barostat51. For all simulations, a quasi-cubic unit cell with cell parameters larger than 25 Å was created. To sample the configurational space at each point, we implemented a hybrid MD+GCMC protocol consisting of 10 primary cycles. Each cycle was partitioned in 20,000 GCMC steps followed by 20,000 MD steps with a time step of 0.5 fs. Convergence was further refined through an additional 500,000 GCMC steps to obtain the equilibrated averages. Statistical analysis of the equilibrated averages was performed using pyMSER52.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript entitled \"Decoding local framework dynamics in the ultra-small pore MOF MIL-120(Al) CO2 sorbent\" by Maurin et al. reports an interesting aspect on the guest-induced local dynamics of ultra-small pore MOFs. This is really an intriguing property of this family of porous materials that calls for an in-depth microscopic exploration hardly achieved using even advanced experimental characterization tools. Therefore, the power of molecular simulations combined with accurate force field is to deliver unprecedented key insights into such complex guest-induced structural behavior.\nMajor results of this paper is the demonstration of the high quality trained MLP combined with the development of a novel hybrid MD-GCMC software for capturing this complex adsorption behavior leading to a highly accurate prediction of the low-pressure CO2 adsorption isotherm of MIL-120(Al). An important aspect of this contribution is to reveal the main role of μ2-OH groups reorientations/dynamics on the CO2 pore filling, conclusion that can be translated to any ultra-small pore MOFs for gas sorption. This point is very rarely discussed in a systematic way, most of the time even neglected in molecular simulation studies on this class of materials. I do believe the manuscript is well-prepared and suitable for publication in Nat Commun very useful for the MOF community and beyond for many responsive porous materials upon gas sorption. I recommend the following minor revision as listed below:\n1) A proper justification regarding the statement that Rigid UFF-based GCMC overestimates the experimental heat of adsorption and uptake for this class of MOF.\n2) In this study, MOF structures loaded with different CO2 uptakes, intermediate/transition structures obtained via climbing-image nudged elastic band (CI-NEB), and Ab Initio Molecular Dynamics (AIMD) snapshots under diverse NVT/NPT conditions have been included in the training dataset. The authors should discuss this choice of dataset and why they ruled out the possibility of having defective structure models?\n3) The authors show in Fig 4h the time it requires to observe the phase change upon CO2 loading of 4.05mmol/g (95 ps). the author may check how long does it take for the low adsorption uptake and discuss the correlation between time required for the transition and the CO2 loading.\n4) It is reported that the energy–volume curves derived from DFT optimization, MLP single-point evaluation based on DFT-optimized geometries, and fully MLP-relaxed structures show very good agreement, as shown in Fig. 2c in terms of both minima and overall curvatures of the plot, however there is no mention of the minimization method adopted for this work. In the case of VASP calculations also not reported the minimizer used for the geometry optimizations.\n5) How did the authors calculate the mechanical properties? Two methods are widely reported in the litterature, one is through energy minimizations and other one via MD simulations.\n6) In the case of Fig 4, the figure caption is bit confusing, “(a) Overlaid lowest-energy CO2 adsorption (2.02 mm?l g-1 CO2 loading, see Supplementary Fig. 27 for 4.05 mmol g-1 loading) sites obtained by MLP and DFT calculations for the different MIL-120(Al) structures.” it should be rephrased properly.\n7) The authors should compare the Qst,0 values they obtain with their own MLP with some current u-MLPs to justify the real need to train another MLP model for this MOF.\n8) The authors should report the simulated MD-GCMC isotherm in the range 0-0.2 bar since this is really the region of interest for a MOF for CO2 capture under post combustion working conditions. I would recommend the authors to reconsider all the simulated isotherms reported and make also a rigorous comparison with the data obtained using UFF-based GCMC simulations\n9) The MD-GCMC code developed in this work should be properly described. The authors are encouraged to share the code in a github environment with corresponding input files.", "reviewer_2": "In this manuscript, the authors employs a combination of density-functional theory calculations and a machine-learned potential approach to systematically map the configurational landscape of μ2-OH groups in MIL-120(Al). The study shows MLP-based GCMC–MD strategy is reliable for capturing accurately the host–guest interactions coupled with local structural dynamics, which cannot be achieved by applying a rigid framework UFF-based GCMC approach. More generally, these results also emphasize the necessity of system-specific, high-quality MLP for reliably predicting the adsorption behaviors of guest molecules in ultra-small pore MOFs. The paper is well written, with a clear introduction, results presentation and discussion. I would recommend this paper for publication once the authors address the following comments:\n(1) In these six representative structure models, what factors influence the orientation of the four μ2–OH groups? Is the structure randomly distributed? How can the desired ideal structure be obtained experimentally?\n(2) In Figure 4g, the three RDF curves show clear differences — the peak intensities vary, and the corresponding peak positions also differ. How did the authors conclude that the three RDF curves exhibit high consistency?\n(3) What is the simulated pressure in Figure 4h? From Figure 4(f), it can be seen that at high pressure, the CO₂ adsorption obtained by the MLP-MD method deviates significantly from the experimental results. Therefore, the MLP-MD method may not be suitable at higher pressures. How did the authors account for the discrepancies at high pressure?", "reviewer_3": "This is a great work that presents a novel application of MLP for CO2 capture in MIL-120(Al).\nThe authors explains the local framework dynamics through detailed atomistic and electronic-level calculations. The work meets the expected standards in our MOF community.\nI have minor comments before publication:\n1) Is it possible to perform flexible GCMC simulations with MLP for MIL-120(Al) instead of a hybrid approach? Why did the authors use snapshot method instead of this? Could you please comment on this?\n2) Please also comment on the potential of this MOF in terms of its commercial usage. Please include a table of CO2 uptake capacities of commercial MOFs to benchmark the current results."}, "author_response": "We would like to thank all three reviewers for their positive comments and valuable feedback on our paper. We are particularly encouraged by their recognition of the novelty of our findings. Below are our responses (in blue) to the reviewers' comments (in black italics).\nReviewer #1\nGeneral comment: The manuscript entitled \"Decoding local framework dynamics in the ultra-small pore MOF MIL-120(Al) CO2 sorbent\" by Maurin et al. reports an interesting aspect on the guest-induced local dynamics of ultra-small pore MOFs. This is really an intriguing property of this family of porous materials that calls for an in-depth microscopic exploration hardly achieved using even advanced experimental characterization tools. Therefore, the power of molecular simulations combined with accurate force field is to deliver unprecedented key insights into such complex guest-induced structural behavior. Major results of this paper is the demonstration of the high quality trained MLP combined with the development of a novel hybrid MD-GCMC software for capturing this complex adsorption behavior leading to a highly accurate prediction of the low-pressure CO2 adsorption isotherm of MIL-120(Al). An important aspect of this contribution is to reveal the main role of μ2-OH groups reorientations/dynamics on the CO2 pore filling, conclusion that can be translated to any ultra-small pore MOFs for gas sorption. This point is very rarely discussed in a systematic way, most of the time even neglected in molecular simulation studies on this class of materials. I do believe the manuscript is well-prepared and suitable for publication in Nat Commun very useful for the MOF community and beyond for many responsive porous materials upon gas sorption. I recommend the following minor revision as listed below:\nGeneral reply: We sincerely thank the reviewer for the insightful and positive assessment of our work. We are particularly grateful for the recognition of the methodological advances (MLP development and hybrid MD-GCMC implementation) and the fundamental insights into the role of μ -OH dynamics in ultra-small pore MOFs.\n2\nmachine-learning potential”. This slight change would enable to clarify the critical need to develop an accurate MLP to unravel the local framework dynamics in ultra-small pore MOFs and (ii) highlight the novelty and general applicability of the computational methodology to address flexibility of ultra-small pore MOFs.\nComment 1: A proper justification regarding the statement that Rigid UFF-based GCMC overestimates the experimental heat of adsorption and uptake for this class of MOF.\nReply 1: We appreciate the reviewer’s request for a rigorous justification of the observed overestimation of the isosteric heat of adsorption (Q ) when utilizing the st\nUniversal Force Field (UFF) within a rigid framework for MIL-120(Al) and related MOFs. Below we provide a detailed justification for MIL-120(Al) system.\nIn our study, the force field used to describe the host/guest interactions needs to account for (1) a high degree of confinement felt by CO in the small pore MIL-120(Al), 2\nand (2) the presence of specific adsorption sites, i.e. μ -OH that establish strong 2\ninteractions and associated short contacts with CO . It has been reported previously that 2\nin such a scenario the consideration of UFF LJ parameters for the MOF framework atoms fail to accurately capture the host/guest interactions and therefore leads to an overestimation of both heats and uptakes further requiring the refinement of the UFF parameters for a better agreement with experimental data. [Nature 2019, 576, 253-256; J. Chem. Theory Comput. 2024, 20, 23, 10540–10552；Adv. Sci. 2024, 11, 2401070]\nWe have added the following statement to the manuscript to highlight this limitation (Page 14 of the main text):\n“The small interconversion energy barriers between the different MIL-120(Al) structure models suggest that CO adsorption can readily trigger structural transitions. 2\nEach MIL-120(Al) configuration is therefore expected to contribute individually to the experimentally observed CO uptake across the full pressure range. However, 2\nconventional GCMC approaches typically treat the MOF framework as rigid and rely on empirical force fields such as UFF. 36 Such simulations cannot capture local, dynamical rearrangements of framework motifs, e.g. μ -OH reorientations, that we 2\ndemonstrated to be important in the ultra-small-pore MIL-120(Al). Moreover, the UFF parametrization is poorly suited to describe the interactions between highly polar and sterically constrained environments with guest molecules as shown in Fig. 4d and Supplementary Fig. 30 with a deviation between the corresponding GCMC simulated adsorption isotherms for all configurations and the experimental data. Taken together, these effects lead to a systematic overestimation of the simulated Qₛₜ and CO 2\nadsorption uptake compared to experimental data as already reported for such families of MOFs.25,37,38”\nComment 2: In this study, MOF structures loaded with different CO2 uptakes, intermediate/transition structures obtained via climbing-image nudged elastic band (CI-NEB), and Ab Initio Molecular Dynamics (AIMD) snapshots under diverse NVT/NPT conditions have been included in the training dataset. The authors should discuss this choice of dataset and why they ruled out the possibility of having defective structure models?\nReply 2: We thank the reviewer for raising this important methodological consideration.\nFirst, regarding the consideration of CO -loaded structures with different loading, the 2\nchoice of including CI-NEB transition paths, and AIMD snapshots (NVT/NPT, 100– 500 K) in the MLP training dataset in addition to DFT configurations was driven by the need to comprehensively capture dynamic host-guest behaviours: (1) DFT-derived CO -loaded configurations explicitly sample the adsorption-sites of CO (e.g., CO 2 2 2\npreferentially interacting with μ -OH vs. carboxylate groups) and the resulting CO 2 2\ngeometries in the pores of the different MIL-120(Al) variates as a function of the guest loading (as shown in Figure 4 of the main text); (2) CI-NEB transition structures map μ -OH reorientation pathways and associated energy barriers and (3) AIMD snapshots 2\nincorporate finite-temperature fluctuations (e.g., H-bond reforming/revolving) critical for entropy-driven processes in the following MLP-MD simulations. Such a hybrid approach for the dataset preparation enabled the training of a robust MLP that was successfully used to describe the MIL-120(Al)/CO system under different CO loading 2 2\nand temperature conditions.\nSecond, the exclusion of defective structures in our MLP training dataset is justified by two key factors:\n1. Material-specific evidence: Al-carboxylate MOFs (especially the MIL-53 structural platform including MIL-120) exhibits high crystallinity with minimal defects due to strong Al-O bond strength and kinetic inertness of Al3+ coordination, as demonstrated by previous in situ XRD/NMR characterizations of MIL-120 (Al) [Cell Reports Phys. Sci. 2023, 4.7] and corroborated in our recent studies (Adv. Sci. 2024, 11, 2401070). Typically, this behaviour contrasts sharply with defect-prone MOFs like Zr-UiO series where missing-linker defects exceed 20% [Nat. Chem. 2019, 11.7, 622-628].\n2. Research scope focus: Our study targets intrinsic μ -OH dynamics governed by 2\npristine framework topology. Introducing defects would add uncontrolled variables (e.g., missing linkers distorting local μ -OH environments) that would obscure the 2\nstructure-property relationships central to this work.\nNevertheless, the MLP training workflow and dataset construction are fully extensible: representative defective motifs and statistically sampled defect concentrations can be incorporated in future work to quantify defect effects on adsorption thermodynamics and local dynamics\nWe have rewritten Supplementary Note 1 (Pages 65-66 of the Supplementary Materials) adding the following content:\nMachine-learning potential (MLP) training and validation for MIL-120(Al) structures\nTo enable exhaustive exploration of the configurational and kinetic landscape of MIL-120(Al)s, in particular the μ -OH ordering, interconversion pathways and host– 2\nguest energetics, we developed a purpose-trained MLP within the DeePMD framework.6 The training dataset was constructed to sample the physically relevant regions of phase space (static minima, finite-temperature fluctuations, reaction/CI- NEB intermediates, strained and distorted lattices, and host–guest configurations). A summary schematic of dataset construction and workflow is provided in Supplementary Fig. 2.\nThe dataset intentionally spans five complementary classes of configurations:\n1. Static sampling: DFT single-point energies and forces for pristine and CO -loaded 2\ncells, including random Widom-style insertions and systematically varied CO loadings 2\n(unit cell and supercell representations).\n2. Ground states: DFT-optimized geometries for empty and CO -loaded MIL-120 2\nvariants (primitive cell and supercell).\n3. Dynamic sampling: AIMD snapshots collected under NVT/NPT conditions at multiple temperatures and CO loadings to capture thermal fluctuations and H-bond 2\ndynamics. All AIMD runs used 2×2×2 supercells.\n4. Reaction pathways: CI-NEB intermediates and single-point energies sampled along μ -OH reorientation paths, both for empty frameworks and CO -containing 2 2\nchannels.\n5. Mechanical/lattice distortions: Configurations sampled under controlled lattice expansion/scaling, applied strains, and selected high-stress failure points from stress– strain scans.\nWe did not include explicit defective-framework models (e.g., missing-linker or under-coordinated metal motifs) in the training set. This choice was motivated by two considerations: (i) material-specific evidence indicates that Al-carboxylate MOFs of the MIL-53/MIL-120 family generally exhibit high crystallinity and low intrinsic defect concentrations under standard synthesis and activation procedures, as supported by in-situ XRD/NMR characterizations and our experimental observations1; (ii) the present study focuses on elucidating intrinsic μ -OH ordering and cooperative local 2\ndynamics in the pristine topology, and the deliberate exclusion of defects avoids introducing heterogeneous, sample-dependent local environments (e.g., missing linkers, exposed metal sites, or adsorbed residuals) that would complicate mechanistic interpretation. Nevertheless, the MLP training workflow and dataset construction are fully extensible: representative defective motifs and statistically sampled defect concentrations can be incorporated in future work to quantify defect effects on adsorption thermodynamics and local dynamics.\nComment 3: The authors show in Fig 4h the time it requires to observe the phase change upon CO2 loading of 4.05mmol/g (95 ps). the author may check how long does it take for the low adsorption uptake and discuss the correlation between time required for the transition and the CO2 loading.\nReply 3: We appreciate the reviewer insightful suggestion. In response, we have performed additional simulations with a lower CO loading (1 molecule per unit cell 2\ncorresponding to an uptake of 2.02 mmol g⁻¹). The representative snapshots and the corresponding energy evolution curves are now provided in Figs. 4g-4h and in the Supplementary Figs. 54-56. At this low loading, local dynamical motions of the μ -OH 2\ngroups and their transient hydrogen-bonding interactions with adsorbed CO₂ molecules are still observed. The total potential energy displays only small fluctuations and the structure converges towards equilibrium more slowly (~ 200 ps). By contrast, at the higher loading (2 molecules per unit cell corresponding to an uptake of 4.05 mmol g⁻¹) we observe a pronounced energy drop and equilibration is attained much faster (~ 95 ps), confirming that reaching a critical CO density accelerates the large-scale 2\ncooperative transition.\nThe relevant figure (Figs. 4g-4h) and captions have been revised in the main text, and corresponding discussions have been added (as shown below):\nWe have included the relevant discussion in the main text on pages 15–16:\n“As shown in Figs. 4g-4h, Supplementary Fig. 54-56, and Supplementary Movies 1-4, the μ -OH groups in the MIL-120(Al)-F model undergo pronounced rotations on ps 2\ntime scales in the MLP-MD-derived trajectories at 300 K, and this behaviour appears both in the presence and absence of CO . At a low CO loading of 2.02 mmol g⁻1, 2 2\nanalysis of the MLP-MD trajectories show that MIL-120(Al)-F structure reaches equilibrium after ~ 200 ps. The same structure loaded by 4.05 mmol g⁻1 of CO attains 2\nan equilibrium faster (~ 95 ps). This indicates that the phase/ordering transition depends on the guest loading: a critical CO density promotes cooperative 2\nreorientation and shortens the transition time. This interpretation is consistent with the relatively low CI-NEB energy barriers, which place μ -OH rotations within the range 2\nof thermal accessibility and allow guest-driven kinetics to control the observed timescales.”\nComment 4: It is reported that the energy–volume curves derived from DFT optimization, MLP single-point evaluation based on DFT-optimized geometries, and fully MLP-relaxed structures show very good agreement, as shown in Fig. 2c in terms of both minima and overall curvatures of the plot, however there is no mention of the minimization method adopted for this work. In the case of VASP calculations also not reported the minimizer used for the geometry optimizations.\nReply 4: We thank the reviewer for noting this omission. For the DFT calculations, all geometry optimizations were performed using the VASP code with the conjugate gradient (CG) algorithm until the forces on all atoms were below 0.01 eV Å-1, and the total energy was converged within 10-5 eV. For the MLP-based relaxations, the energy minimization was carried out using the FIRE (Fast Inertial Relaxation Engine) algorithm as implemented in ASE, with identical convergence thresholds for energy and forces to ensure consistency with the DFT results. The manuscript has been revised to include a clear description of the minimization procedures used.\nThe following content has been added in the method section (Page 17-19 of the main text):\n“These parameters yielded converged total energies and atomic forces within thresholds of 10-5 eV and 0.01 eV Å−1, respectively. All geometry optimizations were performed using the VASP code with the conjugate gradient (CG) algorithm.”\n“CI-NEB pathways were recomputed using the ASE-Python library43 and the trained MLP, with each intermediate structure optimized using the FIRE (Fast Inertial Relaxation Engine) algorithm, enabling extensive transition-state sampling at negligible computational cost.”\nComment 5: How did the authors calculate the mechanical properties? Two methods are widely reported in the literature, one is through energy minimizations and other one via MD simulations.\nReply 5: We thank the reviewer for this comment. The mechanical properties in this work were calculated using DFT-based static stress-strain calculations. Specifically, we employed IBRION=6, NFREE=4, and ISIF=3 in VASP, which corresponds to the finite-difference method for obtaining elastic constants from energy-minimized structures. In this approach, the lattice parameters and atomic positions are fully relaxed under small deformations, providing the elastic tensor directly from DFT without using MD simulations. The following content has been added in the method section (Page 17 of the main text) to clarify this point:\n“The elastic constants were calculated using DFT-based static stress-strain calculations in VASP, where both lattice parameters and atomic positions were fully relaxed under small deformations to obtain the elastic tensor directly from energy- minimized structures.”\nComment 6: In the case of Fig 4, the figure caption is bit confusing, “(a) Overlaid lowest-energy CO2 adsorption (2.02 mmol g-1 CO2 loading, see Supplementary Fig. 27 for 4.05 mmol g-1 loading) sites obtained by MLP and DFT calculations for the different MIL-120(Al) structures.” it should be rephrased properly.\nReply 6: We thank the reviewers for highlighting this ambiguity. The content of the figure caption has been modified in the revised version to make clear that this figure contains the MLP-derived geometries and we included one more figure in the ESI for the DFT-derived geometries (Supplementary Figure S27). The modifications are as follows:\nFig. 4 | In-depth microscopic understanding of the CO adsorption in the diverse 2\nMIL-120(Al) configurations. (a) MLP-derived lowest-energy CO adsorption sites in 2\nthe different MIL-120(Al) structures for a loading of 1 molecule of CO per unit cell (~ 2\n2.02 mmol g⁻¹ at 298 K). The corresponding data for a loading of 2 molecules of CO 2\nper unit cell (4.05 mmol g⁻¹ corresponding to the experimental uptake at 1 bar) are shown in Supplementary Fig. 29.The green dashed line represents the shortest distance between CO₂ and the μ -OH groups of MIL-120(Al) (unit: Å). (b) CO interaction 2 2\nenergies computed by DFT, our MLP model, and other MLPs including MACE-MPA- 0 and MACE-DAC,32,33 respectively. These interaction energies ( ) were computed as using the optimized CO molecule, the Eint2\noptim Eii nzted\n= E\nemCOp2ty MMOFIL\n-\n-1\n(\n0M(OAFl)\n+\nE\naCnOd2\n)\nthe optimized CO 2\n@MIL-120(Al)s at each theoretical level (MLP/DFT). (c) Widom-insertion derived isosteric heats (Q ) at st\n298.15 K using our MLP, universal MLPs (including MACE-DAC,33 MACE-r2SCAN,34 UMA-m35), and classical UFF36 force field, respectively. The dashed line represents the experimental Q value reported earlier.25 (d) GCMC-simulated adsorption st\nisotherms for CO in MIL-120(Al)s at 298.15 K using classical UFF force field. (e) 2\nGCMC simulated adsorption isotherms for CO in MIL-120(Al)s at 298.15 K using 2\nMLP-based GCMC-MD (NPT). Error bars represent the standard deviation calculated over the equilibrated part of the simulation. (f) Radial distribution functions (RDF) for atom pairs at 300 K computed via AIMD and MLP-MD\nO\napCpOr2o\n∙\na\n∙∙\nc\nH\nhμe2s- OH[M I L- 120(A l)-VF T] ensemble for a CO 2\nloading of 2.02 mmol g⁻¹. (g) Representative MLP-MD snapshots for MIL-120-F loaded with 2.02 mmol g⁻¹ of CO , 2\nshowing configurations at 0 ps (top) and 200 ps (bottom). (h) Representative MLP-MD snapshots for MIL-120-F loaded with 4.05 mmol g⁻¹ of CO , showing configurations at 2\n0 ps (top) and 95 ps (bottom). The snapshots illustrate the rapid reorientation of pore-exposed μ –OH groups and the consequent reorganization of adsorbed CO₂ molecules. 2\nColour code for snapshots: Al, blue; O, red; C, grey; H, pink; CO , black and magenta 2\nfor C and O respectively.\nWe have included one more figure in the Supplementary Materials:\nSupplementary Fig. 27 | DFT-derived lowest-energy CO adsorption sites in the MIL- 2\n120(Al) structures loaded of 2.02 mmol g⁻¹ of CO .\nMLP- (Fig. 4a) and DFT- (Supplementary Fig. 27)-optimized geometries for the six MOF variants loaded by 1 CO molecule per unit cell, show extremely similar guest 2\nlocations and orientations, confirming that the MLP captures the local host–guest interactions accurately.\nComment 7: The authors should compare the Qst,0 values they obtain with their own MLP with some current u-MLPs to justify the real need to train another MLP model for this MOF.\nReply 7: We thank the reviewer for this insightful suggestion. To address this, we have included the Q results calculated using two additional universal MLPs, specifically st\nMACE-r2SCAN and UMA-m, in the revised Fig. 4c. The results clearly demonstrate that our purpose-trained MLP accurately reproduces the experimental benchmark value. In contrast, all tested universal MLPs lead to deviation in the predicted Q . This result st\ntherefore justifies our choice to train a dedicated MLP for MIL-120(Al). Alternative solution would be to (a) retrain u-MLPs with additional key configurations for the MOFs/guest system of interest or (b) adopt active-learning workflows that iteratively sample and add problematic adsorption configurations. These points were addressed as follows:\nFig. 4 | In-depth microscopic understanding of the CO adsorption in the diverse 2\nMIL-120(Al) configurations. (a) MLP-derived lowest-energy CO adsorption sites in 2\nthe different MIL-120(Al) structures for a loading of 1 molecule of CO per unit cell (~ 2\n2.02 mmol g⁻¹ at 298 K). The corresponding data for a loading of 2 molecules of CO 2\nper unit cell (4.05 mmol g⁻¹ corresponding to the experimental uptake at 1 bar) are shown in Supplementary Fig. 29. The green dashed line represents the shortest distance between CO₂ and the μ -OH groups of MIL-120(Al) (unit: Å). (b) CO interaction 2 2\nenergies computed by DFT, our MLP model, and other MLPs including MACE-MPA- 0 and MACE-DAC,32,33 respectively. These interaction energies ( ) were computed as using the optimized CO molecule, the Eint2\noptim Eii nzted\n= E\nemCOp2ty MMOFIL\n-\n-1\n(\n0M(OAFl)\n+\nE\naCnOd2\n)\nthe optimized CO 2\n@MIL-120(Al)s at each theoretical level (MLP/DFT). (c) Widom-insertion derived isosteric heats (Q ) at st\n298.15 K using our MLP, universal MLPs (including MACE-DAC,33 MACE-r2SCAN,34 UMA-m35), and classical UFF36 force field, respectively. The dashed line represents the experimental Q value reported earlier.25 (d) GCMC-simulated adsorption st\nisotherms for CO in MIL-120(Al)s at 298.15 K using classical UFF force field. (e) 2\nGCMC simulated adsorption isotherms for CO in MIL-120(Al)s at 298.15 K using 2\nMLP-based GCMC-MD (NPT). Error bars represent the standard deviation calculated over the equilibrated part of the simulation. (f) Radial distribution functions (RDF) for atom pairs at 300 K computed via AIMD and MLP-MD\nO\napCpOr2o\n∙\na\n∙∙\nc\nH\nhμe2s- OH[M I L- 120(A l)-VF T] ensemble for a CO 2\nloading of 2.02 mmol g⁻¹. (g) Representative MLP-MD snapshots for MIL-120-F loaded with 2.02 mmol g⁻¹ of CO , 2\nshowing configurations at 0 ps (top) and 200 ps (bottom). (h) Representative MLP-MD snapshots for MIL-120-F loaded with 4.05 mmol g⁻¹ of CO , showing configurations at 2\n0 ps (top) and 95 ps (bottom). The snapshots illustrate the rapid reorientation of pore-exposed μ –OH groups and the consequent reorganization of adsorbed CO₂ molecules. 2\nColour code for snapshots: Al, blue; O, red; C, grey; H, pink; CO , black and magenta 2\nfor C and O respectively.\nWe have included the following discussion in the main text (Page 12):\nThe Widom insertion calculations performed using our trained MLP led to isosteric heats (Q ) which closely match the experimental values for MIL-120(Al)-A, MIL- st\n120(Al)-B and MIL-120(Al)-C, as shown in Fig. 4c, compared to typical universal MLPs that show substantial deviations. Overall, the highest Q value is obtained for st\nMIL-120(Al)-F, in line with a more confined pore environment of this configuration characterised by the highly ordered orientation of μ -OH groups towards the pore 2\nchannels.\nComment 8: The authors should report the simulated MD-GCMC isotherm in the range 0-0.2 bar since this is really the region of interest for a MOF for CO2 capture under post combustion working conditions. I would recommend the authors to reconsider all the simulated isotherms reported and make also a rigorous comparison with the data obtained using UFF-based GCMC simulations\nReply 8: We thank the reviewer for this important suggestion. The 0-0.2 bar region is indeed the most relevant pressure window for post-combustion CO capture (typical 2\nflue-gas CO partial pressures are on the order of ~0.10-0.15 bar, i.e., 10~15% CO ). In 2 2\nthe revised manuscript, we zoom-in the isotherms for 0-0.2 bar into the main text (Fig. 4 d and Fig. 4e) and place the full 0-1.0 bar data in the Supplementary Figs. 30 and 52- 53. The MLP-based GCMC-MD(NVT) isotherms show very good agreement with experimental data in the low-pressure domain (see Fig. 4e).\nThe following 0–1 bar adsorption isotherm data have been added to the Supplementary Materials:\nSupplementary Fig. 30 | GCMC-simulated CO adsorption isotherms (0-1 bar, 298.15 2\nK) for MIL-120(Al)- A to F configurations using UFF force field.\nSupplementary Fig. 52 | Simulated CO adsorption isotherms (0-1 bar, 298.15 K) for 2\nMIL-120(Al)- A to F configurations using rigid MLP-GCMC simulations.\nSupplementary Fig. 53 | Simulated CO adsorption isotherms (0-1 bar, 298.15 K) for 2\nMIL-120(Al)- A to F configurations using NPT MLP-GCMC simulation.\nHere are the following sentences added to the main text on page 15:\n“This observation is consistent with the relative low energy between all these structures models, suggesting a structure relaxation towards the most stable MIL-120(Al) structures, i.e. MIL-120(Al)-A to MIL-120(Al)-D (cf. Fig. 3) upon adsorption. Interestingly, the MLP-based GCMC-(NPT) MD derived adsorption isotherms show a very good agreement with the corresponding experimental data in the 0-0.2 bar pressure region most relevant for the post-combustion CO capture condition (typical 2\nflue-gas CO partial pressures are on the order of ~0.10-0.15 bar, i.e., 10~15% CO ).” 2 2\nComment 9: The MD-GCMC code developed in this work should be properly described. The authors are encouraged to share the code in a github environment with corresponding input files.\nReply 9: We thank the reviewer for this valuable suggestion. All codes developed in this work have been uploaded to a public GitHub repository, https://github.com/lipelopesoliveira/flames, together with example scripts and input files. For the MIL-120(Al) case discussed in this study, we also included a complete set of input files to facilitate reproducibility and further testing by the community (https://github.com/lipelopesoliveira/flames/tree/main/examples/Calculators/DeepMD ).\nThe relevant source documents have been added to the \"Data Availability\" section of the revised manuscript.\nData availability\nThe data used in this study are available in the Zenodo database in ref.53 Source data are also provided in this paper.\nReviewer #2\nGeneral comment:In this manuscript, the authors employ a combination of density- functional theory calculations and a machine-learned potential approach to systematically map the configurational landscape of μ2-OH groups in MIL-120(Al).\nThe study shows MLP-based GCMC–MD strategy is reliable for capturing accurately the host–guest interactions coupled with local structural dynamics, which cannot be achieved by applying a rigid framework UFF-based GCMC approach. More generally, these results also emphasize the necessity of system-specific, high-quality MLP for reliably predicting the adsorption behaviors of guest molecules in ultra-small pore MOFs. The paper is well written, with a clear introduction, results presentation and discussion. I would recommend this paper for publication once the authors address the following comments:\nGeneral Reply: We would like to thank the reviewer for the positive assessment of our work and the precise summary of our key findings in this manuscript. We appreciate the recognition that a high-quality, system-specific MLP coupled with a hybrid MD– GCMC protocol is necessary to capture coupled host–guest thermodynamics and local structural dynamics in ultra-small-pore MOFs. These are phenomena that rigid UFF- based GCMC cannot describe. The following are the point-to-point responses:\nComment 1: In these six representative structure models, what factors influence the orientation of the four μ2–OH groups? Is the structure randomly distributed? How can the desired ideal structure be obtained experimentally?\nReply 1: We thank the reviewer for pointing out this question. We are pleased to clarify these key points regarding the μ -OH group orientations in MIL-120(Al).\n2\n1. On the factors influencing μ -OH group orientation: We found that the 2\norientation of the μ -OH groups is primarily governed by the intra-framework 2\nhydrogen-bond network formed between adjacent AlO octahedral chains (as 6\nshown in Supplementary Fig. 1). These hydrogen bonds are formed between the hydroxyl hydrogen atom of the μ -OH groups and the nearby Al–O framework 2\noxygen of the adjacent polyhedral chains. The lowest-energy configuration, MIL-120(Al)-A, features a cooperative interlocking hydrogen-bond network that links these adjacent chains. This specific arrangement effectively stabilizes this configuration. In contrast, the other five variants MIL-120(Al) models lack this strong cooperative motif. Their more disordered μ -OH orientations result 2\nin weaker intra-framework hydrogen-bond interactions and are therefore energetically less favourable. In fact, our calculations also show that MIL- 120(Al)-F is the highest-energy configuration among the variants we studied.\n2. On whether the structures are randomly distributed: Our calculations show that the interconversion barriers between the six MIL-120(Al) configurations are low (≈0.07–0.19 eV per unit cell), indicating that these states are dynamically accessible at room temperature and that μ₂-OH reorientations occur rapidly in our MLP-MD simulations (Fig. 4). Consequently, MIL-120(Al) is better described as a dynamic configurational ensemble rather than a single fixed structure. The six configurations we report are representative motifs sampling the dominant μ -OH ordering patterns. Therefore, under experimental 2\nconditions, many combinations of these local motifs are expected to coexist. Importantly, the MLP reproduces DFT energetics and yields adsorption isotherms in very good agreement with experiment at low pressures, providing confidence in this ensemble picture.\n3. On how to obtain the desired ideal structure experimentally: Our work suggests that isolating a single \"ideal\" configuration (such as the lowest-energy MIL- 120(Al)-A model) is likely not feasible experimentally for two main reasons:\nFirst, the μ -OH orientation represents a \"hidden\" structural degree of freedom. 2\nBecause hydrogen atoms scatter X-rays weakly, their exact positions cannot be resolved by standard X-ray diffraction (XRD) techniques. This is precisely why previous studies assumed the MIL-120(Al)-F configuration based on empirical, post-hoc H-atom placement. Secondly, the low interconversion barriers mean that the system will dynamically sample all accessible configurations at standard experimental temperatures. Attempting to \"freeze\" the structure into a given configuration is indeed not realistic.\nTherefore, the conclusion of our paper is “that experimental sample of MIL-120(Al) likely behaves as a dynamic average or mixture of these configurations. This local-dynamics of the μ -OH groups is further demonstrated to be essential for accurately 2\ndescribing the CO adsorption properties.”\nReply 2: We thank the reviewer for this observation and for pointing out this imprecision in our manuscript. We apologize for the confusion and have revised this section. A direct comparison of all three curves is indeed not appropriate, as they are derived from different simulation protocols. The primary difference lies in the MLP- GCMC curve. This RDF is generated during the MLP-based GCMC process, where the number of CO molecules in the system is fluctuating as it samples different pressure. 2\nIn contrast, the AIMD and MLP-MD (NVT) simulations were run with a fixed CO 2\nloading. Therefore, the GCMC-MD curve represents an average over a range of CO 2\noccupancies, which naturally leads to different peak/position characteristics. The more meaningful comparison for validating our MLP accuracy is between the AIMD and the NVT MLP-MD simulations, as both are run in the NVT ensemble and with the same CO loading. When comparing these two, the minor difference in peak intensity is 2\nexpected and arises from differences in the simulation parameters. The AIMD simulations were run on a 2×2×2 supercell for a limited duration (5 ps), while the MLP- MD simulations could be run on larger systems for much longer timescales (500 ps), leading to more robust statistical sampling.\nIn response to this comment, we have revised the relevant part of the paragraph and the figure as following and corresponding discussions have been added (as shown below):\nFig. 4 | In-depth microscopic understanding of the CO adsorption in the diverse 2\nMIL-120(Al) configurations. (a) MLP-derived lowest-energy CO adsorption sites in 2\nthe different MIL-120(Al) structures for a loading of 1 molecule of CO per unit cell (~ 2\n2.02 mmol g⁻¹ at 298 K). The corresponding data for a loading of 2 molecules of CO 2\nper unit cell (4.05 mmol g⁻¹ corresponding to the experimental uptake at 1 bar) are shown in Supplementary Fig. 29. The green dashed line highlights the shortest distance between CO₂ and μ -OH groups in MIL-120(Al) variant structures (unit: Å). (b) CO 2 2\ninteraction energies computed by DFT, our MLP model, and other MLPs including MACE-MPA-0 and MACE-DAC,32,33 respectively. These interaction energies ( ) 2\nwere computed as using the optimized CO\nEint2\nmolecule, the optimize\nE\nd i n e t m\n=\npty\nE\nCO2@M-120(\n-\nAl\n(\n)\nE\ns,M an\n+\nthe\nE\nCop2t\n)\nimized CO\n2\n@MIL-120(Al)s at\neach theoretical level (MLP/DFT). (c) Widom-insertion derived isosteric heats (Q ) at st\n298.15 K from our MLP, typical universal MLPs (including MACE-DAC,33 MACE- r2SCAN,34 UMA-m35), and classical UFF36 force field, respectively. The dashed line represents the experimental Q value reported earlier.25 GCMC-simulated adsorption st\nisotherms for CO in MIL-120(Al)s at 298.15 K using (d) classical UFF force field 2\nGCMC simulated adsorption isotherms for CO in MIL-120(Al)s at 298.15 K (e) MLP- 2\nbased GCMC-MD simulated adsorption isotherms for CO in MIL-120(Al)s at 298.15 2\nK. Error bars represent the standard deviation calculated over the equilibrated part of the simulation. (f) Radial distribution functions (RDF) for\natom pairs at 298.15 K computed via AIMD and ML\nO\nP-CO2\n∙\nD\n∙∙\nH\napμp2-roOaHc[M I L- 120(A l)-VF T] ensemble for a CO 2\nloading of 2.02 mmol g⁻¹. (g) Representative\nMLP-MD snapshots for MIL-120-F loaded with 2.02 mmol g⁻¹ of CO , showing 2\nconfigurations at 0 ps (top) and 200 ps (bottom). (h) Representative MLP-MD snapshots for MIL-120-F loaded with 4.05 mmol g⁻¹ of CO , showing configurations at 2\n0 ps (top) and 95 ps (bottom). The snapshots illustrate the rapid reorientation of pore- exposed μ –OH groups and the consequent reorganization of adsorbed CO₂ molecules. 2\nColour code for snapshots: Al, blue; O, red; C, grey; H, pink; CO , magenta and black. 2\nComment 3:What is the simulated pressure in Figure 4h? From Figure 4(f), it can be seen that at high pressure, the CO₂ adsorption obtained by the MLP-MD method deviates significantly from the experimental results. Therefore, the MLP-MD method may not be suitable at higher pressures. How did the authors account for the discrepancies at high pressure?\nReply 3: We thank the reviewer for raising this important question. Fig. 4h corresponds to experimental uptakes at 1 bar, with a CO loading of 4.05 mmol g⁻¹ [≈ 2 CO per 2 2\nunit-cell of MIL-120(Al)]. We agree that the MLP-based GCMC simulations show deviations from experiment in the high-pressure regime (as shown in Fig. 4e and Supplementary Fig. 53). Diverse factors likely contribute to this deviation: (i) the inherent difficulty for MLP, which are primarily trained on short-range descriptors, to fully capture long-range electrostatics and many-body dispersion effects at high loadings; and (ii) possible approximations in the treatment of long-range interactions over GCMC simulations (e.g., finite cutoffs or incomplete coupling between ML potentials and electrostatic terms).\nWe clarified the pressure and loading reported in Fig. 4. Fig. 4g now corresponds to the low-loading snapshots (2.02 mmol g⁻¹) and Fig. 4h to the high-loading snapshots (4.05 mmol g⁻¹). We have also added Supplementary Fig. 55 showing the total potential-energy vs. time traces for both the low- and high-loading trajectories to make the different equilibration behaviours explicit. Below is the discussion we inserted in the main text (Page 15):\nAs shown in Figs. 4g-4h, Supplementary Fig. 54-56, and Supplementary Movies 1- 4, the μ -OH groups in the MIL-120(Al)-F model undergo pronounced rotations on sub- 2\n100 ps time scales in our trajectories at 300K MLP-MD simulations, and this behaviour appears both in the presence and absence of CO . At a low CO loading of 2.02 mmol 2 2\ng⁻1, the MIL-120(Al)-F structure reached equilibrium in ~ 200 ps from MLP-MD trajectories. This was slower than the equilibration of the same structure at a high loading of 4.05 mmol g⁻1, which occurred in ~ 95 ps. This indicates that the phase/ordering transition is dependent on the loading: a critical CO density promotes 2\ncooperative reorientation and shortens the transition time. This interpretation is consistent with the modest CI-NEB barriers reported here, which place μ -OH rotations 2\nwithin the range of thermal accessibility and allow guest-driven kinetics to control the observed timescales.\nWe equally added the following sentence in the manuscript on page 15:\nHere are the following sentences equally added to the main text on page 15:\n“This observation is consistent with the relative low energy between all these structures models, suggesting a structure relaxation towards the most stable MIL-120(Al) structures, i.e. MIL-120(Al)-A to MIL-120(Al)-D (cf. Fig. 3) upon adsorption. Interestingly, the MLP-based GCMC-(NPT) MD derived adsorption isotherms show a very good agreement with the corresponding experimental data in the 0-0.2 bar pressure region most relevant for the post-combustion CO capture condition (typical 2\nflue-gas CO partial pressures are on the order of ~0.10-0.15 bar, i.e., 10~15% CO ). 2 2\nThe observed deviation between the simulated and experimental adsorption isotherms at higher pressures is likely due to the under-representation of long-range interactions at high loading caused by finite interaction cutoffs (R ) and finite simulation cell sizes.” cut\nFig. 4 | In-depth microscopic understanding of the CO2 adsorption in the diverse MIL-120(Al) configurations. (a) MLP-derived lowest-energy CO adsorption sites in 2\nthe different MIL-120(Al) structures for a loading of 1 molecule of CO per unit cell (~ 2\n2.02 mmol g⁻¹ at 298 K). The corresponding data for a loading of 2 molecules of CO2 per unit cell (4.05 mmol g⁻¹ corresponding to the experimental uptake at 1 bar) are shown in Supplementary Fig. 29. The green dashed line highlights the shortest distance between CO₂ and μ -OH groups in MIL-120(Al) variant structures (unit: Å). (b) CO 2 2\ninteraction energies computed by DFT, our MLP model, and other MLPs including MACE-MPA-0 and MACE-DAC,32,33 respectively. These interaction energies ( ) 2\nwere computed as using the optimized CO\nEint2\nmolecule, the optimiz\nE\ned i n e\n=\nmp\nE\ntyC O2@ML-120(\n-\n0(A\n(\nE\nl)s,M an\n+\nd\nE\nCop2tim\n)\nized CO\n2\n@MIL-120(Al)s at\neach theoretical level (MLP/DFT). (c) Widom-insertion derived isosteric heats (Q ) st\nfrom our MLP, typical universal MLPs (including MACE-DAC,33 MACE- r2SCAN,34 UMA-m35), and classical UFF36 force field, respectively. The dashed line represents the experimental Q value reported earlier.25 GCMC-simulated adsorption isotherms st\nfor CO in MIL-120(Al)s at 298.15 K using (d) the classical UFF force field and (e) 2\nMLP-based GCMC-MD simulated adsorption isotherms for CO in MIL-120(Al)s at 2\n298.15 K. Error bars represent the standard deviation calculated over the equilibrated part of the simulation. (f) Radial distribution functions (RDF) for\natom pairs at 300 K computed via AIMD and ML\nO\nP-CO2\n∙\nD\n∙∙\nH\napμp2-roOaHc[M I L- 120(A l)-VF T] ensemble. (g) Representative MLP-MD snapshots for MIL-120- F at a CO loading of 2.02 mmol g⁻¹, showing configurations at 0 ps (top) and 200 ps 2\n(bottom). (h) Representative MLP-MD snapshots for MIL-120-F at a CO loading of 2\n4.05 mmol g⁻¹, showing configurations at 0 ps (top) and 95 ps (bottom). The snapshots illustrate the rapid reorientation of pore-exposed μ –OH groups and the consequent 2\nreorganization of adsorbed CO₂ molecules. Colour code for snapshots: Al, blue; O, red; C, grey; H, pink; CO , magenta and black 2\nReviewer #3\nGeneral comment:This is a great work that presents a novel application of MLP for CO2 capture in MIL-120(Al). The authors explains the local framework dynamics through detailed atomistic and electronic-level calculations. The work meets the expected standards in our MOF community. I have minor comments before publication:\nGeneral reply: We sincerely thank the reviewer for the positive and encouraging comments on our work. Our study provides mechanistic insights into μ -OH-driven 2\nlocal dynamics and advances simulation methodology for ultra-small-pore MOFs. We have addressed the reviewer minor points in the revised manuscript, providing a point- by-point response below.\nComment 1: 1) Is it possible to perform flexible GCMC simulations with MLP for MIL-120(Al) instead of a hybrid approach? Why did the authors use snapshot method instead of this? Could you please comment on this?\nReply 1: We thank the reviewer for this insightful question. In simulating CO 2\nadsorption isotherms, there are generally two approaches: the most standard one assumes a rigid MOF framework during CO adsorption (rigid GCMC), while others 2\nmethods including the hybrid MD/MC steps explicitly considers framework flexibility. In our work, the classical UFF-based GCMC simulations were performed with a fixed framework, whereas all MLP-based simulations were conducted with a flexible framework. Specifically, we performed both MLP-GCMC MD (NVT), which includes framework flexibility at constant volume, and MLP-GCMC MD (NPT), which also accounts for pressure-induced variations in the lattice parameters. The corresponding results are provided in the Supplementary Figs. 52-53 and Figure 4e in the revised version.\nIn addition, to provide direct insight into local structural dynamics, we analysed MLP-MD snapshots at representative loadings (2.02 and 4.05 mmol g⁻¹) and temperatures. The snapshot method allows us to visualize the rapid reorientation of μ - 2\nOH groups and the reorganization of adsorbed CO molecules, which are impossible to 2\nextract directly from rigid GCMC simulations.\nTherefore, we combined MLP-GCMC simulations at representative pressures with MLP-MD snapshots to achieve both accurate thermodynamic sampling and detailed mechanistic interpretation. Our MLP-GCMC–MD approach can be seen as the “flexible” GCMC scheme; the “hybrid” term we employ in the manuscript refers to the necessary coupling of MC and MD steps to ensure complete framework and μ -OH 2\nrelaxation and dynamic sampling during the adsorption process.\nComment 2: Please also comment on the potential of this MOF in terms of its commercial usage. Please include a table of CO2 uptake capacities of commercial MOFs to benchmark the current results.\nReply 2: We thank the reviewer for this valuable suggestion. MIL-120(Al) is an aluminum-based carboxylate MOF composed of inexpensive, non-toxic, and earth- abundant elements, which makes it highly attractive for potential large-scale and commercial applications. Its framework exhibits excellent thermal and chemical stability, particularly in humid environments, which is a key advantage over many open-metal-site MOFs that often suffer from hydrolysis. In our previous work (Adv. Sci. 2024, 11, 2401070), we revealed that MIL-120(Al) achieves a good trade-off between CO uptake capacity, heat of adsorption, stability, and cost-effectiveness, positioning it 2\nas one of the most promising MOFs for industrial post-combustion CO capture. Our 2\ncomputational work, by elucidating the critical role of μ -OH local dynamics, provides 2\nthe atomic-level understanding necessary to accurately predict and further optimize its performance toward commercial deployment.\nTo address the comment, we have made the following modifications to the Inline routing section of the manuscript (Page 3 of the main text).\n“This sustainable, easily scaled-up and low-cost MOF combines excellent thermal and hydrolytic stability with CO adsorption performance as attractive as the best MOFs 2\nreported so far for CO capture under flue-gas conditions (see Supplementary Table 1). 2\nThis makes this MOF a promising candidate for further integration into large-scale industrial processes.”\nThe table of CO uptake capacities of some typical benchmark MOFs has been added 2\nin the Supplementary Material (Page 2):\nSupplementary Table 1 | Comparison of volumetric and gravimetric CO uptakes at 2\n0.1, 1 bar, at 298 K between MIL-120(Al) and some typical benchmark adsorbents of MOFs.\nAdsorbed\nAdsorbed Amount Pressure\nMOFs Amount Ref.\n(mmol g−1) (bar)\n(cm3 cm−3)\nMIL-120(Al) 1.9/3.87 73.1/148.8 0.1/1 1\nCALF-20 2.5/3.8 107.1/161.6 0.1/1 1\nUTSA-16 1.6/3.8 64.2/152.0 0.1/1 1\nSIFSIX-3-Cu 2.1/2.2 83.6/84.4 0.1/1 1\nKAUST-7 2.14 / 1 2\nWe would like to thank the reviewers again for their careful reading of the manuscript and their insightful comments, which have helped to improve the manuscript significantly. We believe that these revisions have made the manuscript much more scientifically rigorous and clear.\nResponses to Reviewers\nWe would like to thank the reviewers for taking the time to provide valuable and insightful comments, which have helped us to significantly improve the quality of our study. Our responses to the reviewers’ comments are provided below (in blue).\nReviewer #1\nGeneral comment: As mentioned previously, this manuscript reports a very interesting and relevant aspect concerning the guest-induced local dynamics of ultra-small pore MOFs. Therefore, a comprehensive molecular simulation methodology is essential to reveal the unprecedented, complex, guest-induced structural behavior of porous materials such as ultra-pore MOFs, which is hardly achieved using even advanced experimental characterization tools. Interestingly, this paper demonstrates a high- quality, trained MLP combined with the development of a novel hybrid MD-GCMC software for capturing the complex adsorption behavior. This approach leads to a highly accurate prediction of the low-pressure CO2 adsorption isotherm of MIL- 120(Al). Another major aspect is the role of μ2-OH group dynamics on the CO2 pore filling of ultra-pore MOFs, which is rarely discussed in most molecular simulation studies on this class of materials. I do believe this revised manuscript is suitable for publication in Nat Commun since it has carefully addressed all of my queries with relevant additional data and thoughtful discussions.\nReply: We thank the reviewer again for the constructive and encouraging comments and for recommending the manuscript for publication in Nature Communications.\nReviewer #2\nGeneral comment: The manuscript still requires further improvement. I noticed that, in response to my third comment, the authors re-plotted the figure and removed the data in the 0.2–1 bar range, but did not further refine the high-pressure region, where the errors remain large. However, some of the conclusions are based on simulation results at high pressures; are these conclusions reliable? I suggest that the authors further optimize the simulation methodology.\nReply: We thank the reviewer for valuable comment to substantially improve the quality of the paper. Below, we summarise the improvements we have integrated to the simulation methodology and the additional data we have supplemented following carefully the suggestions.\nFirstly, we would like to emphasise that the trained MLP has undergone extensive validation with an accurate reproduction of (1) DFT-derived energetics of a large set of MIL-120(Al) configurations, (2) DFT-simulated mechanical properties of MIL-120(Al) configurations, (3) DFT-derived CI-NEB interconversion energy barriers between structure conformations, (4) DFT-calculated CO /MOF framework interaction 2\ngeometries and (5) DFT-predicted adsorption CO geometries in the MOF pores. This 2\nexcellent agreement between MLP and DFT results provides us with confidence that the local adsorption physics and dynamical mechanisms (μ -OH reorientations and 2\nlocal host–guest interactions) are accurately captured by the trained MLP.\nIn response to the reviewer’s comment regarding the CO adsorption data in the high- 2\npressure region of the adsorption isotherm, we have first refined our MLP-based GCMC methodology including the following aspects:\n1. Unwrap adsorbed molecules positions before applying rotations;\n2. Change the random rotation algorithm for a more efficient implementation;\n3. Restrict the random rotation to a max rotation of 90° around a random vector, instead of complete 360° rotations;\n4. Restrict the random translation vector to a maximum of 1.5 Å;\n5. Improved the hyperparameters of the MD simulations to increase its stability.\nThese improvements, implemented in FLAMES v0.4.4 [https://github.com/lipelopesoliveira/flames/tree/main], have increased the efficiency of Monte Carlo (MC) simulations by refining movement acceptance rates and enabling more stable MD simulations. Consequently, the equilibration statistics have improved.\nSecond, we have also revisited the simulation parameters used in the GCMC calculations. To ensure rigorous convergence we doubled the number of GCMC-MD cycles from 5 to 10 and increased the final number of equilibrated GCMC steps from 200,000 to 500,000. All the data in the main text and the ESI are based now on this new calculation parameters.\nThird, we have performed additional simulations at different temperatures (273 K, 293 K, 298 K, 303 K, 308 K, 313 K, and 318K) to provide a more comprehensive overview of the current performance of our MLP-based GCMC calculations and compared our simulations to two experimental adsorption data reported in two independent papers [Adv. Sci. 2024, 11.21, 2401070; Cell Reports Phys. Sci. 2023, 4.7,101470]. Supplementary Fig. 54 shows a comparison between the experimental data taken from [Cell Reports Phys. Sci. 2023, 4.7,101470] and the MLIP simulated isotherms at four different temperatures: 273, 293, 303, and 313 K. Supplementary Fig. 55 shows the comparison with experimental data taken from [Adv. Sci. 2024, 11.21, 2401070] at three different temperatures: 298, 308, and 318 K. Overall, these additional comparisons demonstrate that the MLP-GCMC simulated adsorption isotherms accurately reflect the experimental trends across the investigated temperature range providing good quantitative agreement even in the higher pressure range. We need also to keep in mind that the experimental adsorption data vary from one sample to another depending on their synthetic conditions for MIL-120(Al) that differ in the two reported papers ([Adv. Sci. 2024, 11.21, 2401070; Cell Reports Phys. Sci. 2023, 4.7,101470]). It is established that experimental adsorption measurements typically carry uncertainties of order 10–15% arising from synthesis, activation and measurement procedures, and this should be borne in mind when comparing simulations to laboratory data [Chem. Mater. 2017, 29, 10487-10495; Adv. Mater. 2022, 34, 2201502]. Decisively, these MLP results substantially outperform rigid, empirical UFF-based GCMC predictions that dramatically overpredict the experimental CO adsorption isotherms as reminded in 2\nSupplementary Fig. 30. Finally, the rather small high-pressure adsorption uptake deviation does not affect our principal mechanistic conclusions, which are supported by DFT validation and by the excellent agreement with experiments within the relevant application window of 0~0.2 bar.\nWe have updated the corresponding text in the main manuscript to reflect these comparisons (cf. Figs. 4d-4e, Page 13 of the main text).\nThe MLP-GCMC-(NPT) MD calculations performed starting with the different structure models converge towards similar adsorption isotherms closely matching those obtained by MLP-GCMC-(NVT) MD calculations for the MIL-120(Al)-A to MIL- 120(Al)-D models (cf. Supplementary Fig. 53). This observation is consistent with the relative low energy between all these structures models, suggesting a structure relaxation towards the most stable MIL-120(Al) structures, i.e. MIL-120(Al)-A to MIL- 120(Al)-D (cf. Fig. 3) upon adsorption. The MLP-based GCMC–(NPT) adsorption isotherms (Figs. 4d-4e) show an overall good agreement with two independent experimental datasets25,26 in the 0-1 bar region, and Supplementary Figs. 54-55 (273- 313 K) further confirming the reliability of our MLP to capture the CO adsorption 2\nbehaviour in the overall range of investigated temperature range.\nWe have also updated the text relating to the calculation method (Page 20 of the main text):\nTo sample the configurational space at each point, we implemented a hybrid MD+GCMC protocol consisting of 10 primary cycles. Each cycle was partitioned in 20,000 GCMC steps followed by 20,000 MD steps with a time step of 0.5 fs. Convergence was further refined through an additional 500,000 GCMC steps to obtain the equilibrated averages. Statistical analysis of the equilibrated averages was performed using pyMSER.52\nFig. 4 | In-depth microscopic understanding of the CO adsorption in the diverse 2\nMIL-120(Al) configurations. (a) MLP-derived lowest-energy CO adsorption sites in 2\nthe different MIL-120(Al) structures for a loading of 1 molecule of CO per unit cell (~ 2\n2.02 mmol g⁻¹ at 298 K). The corresponding data for a loading of 2 molecules of CO 2\nper unit cell (4.05 mmol g⁻¹ corresponding to the experimental uptake at 1 bar) are shown in Supplementary Fig. 29. The green dashed line represents the shortest distance between CO₂ and the μ -OH groups of MIL-120(Al) (unit: Å). (b) CO interaction 2 2\nenergies computed by DFT, our MLP model, and other MLPs including MACE-MPA- 0 and MACE-DAC,32,33 respectively. These interaction energies (E ) were computed !"}, {"round": 2, "reviewer_comments": {"reviewer_1": "As mentioned previously, this manuscript reports a very interesting and relevant aspect concerning the guest-induced local dynamics of ultra-small pore MOFs. Therefore, a comprehensive molecular simulation methodology is essential to reveal the unprecedented, complex, guest-induced structural behavior of porous materials such as ultra-pore MOFs, which is hardly achieved using even advanced experimental characterization tools. Interestingly, this paper demonstrates a high-quality, trained MLP combined with the development of a novel hybrid MD-GCMC software for capturing the complex adsorption behavior. This approach leads to a highly accurate prediction of the low-pressure CO2​ adsorption isotherm of MIL-120(Al). Another major aspect is the role of μ2​-OH group dynamics on the CO2​ pore filling of ultra-pore MOFs, which is rarely discussed in most molecular simulation studies on this class of materials. I do believe this revised manuscript is suitable for publication in Nat Commun since it has carefully addressed all of my queries with relevant additional data and thoughtful discussions.", "reviewer_2": "The manuscript still requires further improvement. I noticed that, in response to my third comment, the authors re-plotted the figure and removed the data in the 0.2–1 bar range, but did not further refine the high-pressure region, where the errors remain large. However, some of the conclusions are based on simulation results at high pressures; are these conclusions reliable? I suggest that the authors further optimize the simulation methodology.", "reviewer_3": "The authors did all the queries raised by reviewers."}, "author_response": "Responses to Reviewers\nWe would like to thank the reviewers for taking the time to provide valuable and insightful comments, which have helped us to significantly improve the quality of our study. Our responses to the reviewers’ comments are provided below (in blue).\nReviewer #1\nGeneral comment: As mentioned previously, this manuscript reports a very interesting and relevant aspect concerning the guest-induced local dynamics of ultra-small pore MOFs. Therefore, a comprehensive molecular simulation methodology is essential to reveal the unprecedented, complex, guest-induced structural behavior of porous materials such as ultra-pore MOFs, which is hardly achieved using even advanced experimental characterization tools. Interestingly, this paper demonstrates a high- quality, trained MLP combined with the development of a novel hybrid MD-GCMC software for capturing the complex adsorption behavior. This approach leads to a highly accurate prediction of the low-pressure CO2 adsorption isotherm of MIL- 120(Al). Another major aspect is the role of μ2-OH group dynamics on the CO2 pore filling of ultra-pore MOFs, which is rarely discussed in most molecular simulation studies on this class of materials. I do believe this revised manuscript is suitable for publication in Nat Commun since it has carefully addressed all of my queries with relevant additional data and thoughtful discussions.\nReply: We thank the reviewer again for the constructive and encouraging comments and for recommending the manuscript for publication in Nature Communications.\nReviewer #2\nGeneral comment: The manuscript still requires further improvement. I noticed that, in response to my third comment, the authors re-plotted the figure and removed the data in the 0.2–1 bar range, but did not further refine the high-pressure region, where the errors remain large. However, some of the conclusions are based on simulation results at high pressures; are these conclusions reliable? I suggest that the authors further optimize the simulation methodology.\nReply: We thank the reviewer for valuable comment to substantially improve the quality of the paper. Below, we summarise the improvements we have integrated to the simulation methodology and the additional data we have supplemented following carefully the suggestions.\nFirstly, we would like to emphasise that the trained MLP has undergone extensive validation with an accurate reproduction of (1) DFT-derived energetics of a large set of MIL-120(Al) configurations, (2) DFT-simulated mechanical properties of MIL-120(Al) configurations, (3) DFT-derived CI-NEB interconversion energy barriers between structure conformations, (4) DFT-calculated CO /MOF framework interaction 2\ngeometries and (5) DFT-predicted adsorption CO geometries in the MOF pores. This 2\nexcellent agreement between MLP and DFT results provides us with confidence that the local adsorption physics and dynamical mechanisms (μ -OH reorientations and 2\nlocal host–guest interactions) are accurately captured by the trained MLP.\nIn response to the reviewer’s comment regarding the CO adsorption data in the high- 2\npressure region of the adsorption isotherm, we have first refined our MLP-based GCMC methodology including the following aspects:\n1. Unwrap adsorbed molecules positions before applying rotations;\n2. Change the random rotation algorithm for a more efficient implementation;\n3. Restrict the random rotation to a max rotation of 90° around a random vector, instead of complete 360° rotations;\n4. Restrict the random translation vector to a maximum of 1.5 Å;\n5. Improved the hyperparameters of the MD simulations to increase its stability.\nThese improvements, implemented in FLAMES v0.4.4 [https://github.com/lipelopesoliveira/flames/tree/main], have increased the efficiency of Monte Carlo (MC) simulations by refining movement acceptance rates and enabling more stable MD simulations. Consequently, the equilibration statistics have improved.\nSecond, we have also revisited the simulation parameters used in the GCMC calculations. To ensure rigorous convergence we doubled the number of GCMC-MD cycles from 5 to 10 and increased the final number of equilibrated GCMC steps from 200,000 to 500,000. All the data in the main text and the ESI are based now on this new calculation parameters.\nThird, we have performed additional simulations at different temperatures (273 K, 293 K, 298 K, 303 K, 308 K, 313 K, and 318K) to provide a more comprehensive overview of the current performance of our MLP-based GCMC calculations and compared our simulations to two experimental adsorption data reported in two independent papers [Adv. Sci. 2024, 11.21, 2401070; Cell Reports Phys. Sci. 2023, 4.7,101470]. Supplementary Fig. 54 shows a comparison between the experimental data taken from [Cell Reports Phys. Sci. 2023, 4.7,101470] and the MLIP simulated isotherms at four different temperatures: 273, 293, 303, and 313 K. Supplementary Fig. 55 shows the comparison with experimental data taken from [Adv. Sci. 2024, 11.21, 2401070] at three different temperatures: 298, 308, and 318 K. Overall, these additional comparisons demonstrate that the MLP-GCMC simulated adsorption isotherms accurately reflect the experimental trends across the investigated temperature range providing good quantitative agreement even in the higher pressure range. We need also to keep in mind that the experimental adsorption data vary from one sample to another depending on their synthetic conditions for MIL-120(Al) that differ in the two reported papers ([Adv. Sci. 2024, 11.21, 2401070; Cell Reports Phys. Sci. 2023, 4.7,101470]). It is established that experimental adsorption measurements typically carry uncertainties of order 10–15% arising from synthesis, activation and measurement procedures, and this should be borne in mind when comparing simulations to laboratory data [Chem. Mater. 2017, 29, 10487-10495; Adv. Mater. 2022, 34, 2201502]. Decisively, these MLP results substantially outperform rigid, empirical UFF-based GCMC predictions that dramatically overpredict the experimental CO adsorption isotherms as reminded in 2\nSupplementary Fig. 30. Finally, the rather small high-pressure adsorption uptake deviation does not affect our principal mechanistic conclusions, which are supported by DFT validation and by the excellent agreement with experiments within the relevant application window of 0~0.2 bar.\nWe have updated the corresponding text in the main manuscript to reflect these comparisons (cf. Figs. 4d-4e, Page 13 of the main text).\nThe MLP-GCMC-(NPT) MD calculations performed starting with the different structure models converge towards similar adsorption isotherms closely matching those obtained by MLP-GCMC-(NVT) MD calculations for the MIL-120(Al)-A to MIL- 120(Al)-D models (cf. Supplementary Fig. 53). This observation is consistent with the relative low energy between all these structures models, suggesting a structure relaxation towards the most stable MIL-120(Al) structures, i.e. MIL-120(Al)-A to MIL- 120(Al)-D (cf. Fig. 3) upon adsorption. The MLP-based GCMC–(NPT) adsorption isotherms (Figs. 4d-4e) show an overall good agreement with two independent experimental datasets25,26 in the 0-1 bar region, and Supplementary Figs. 54-55 (273- 313 K) further confirming the reliability of our MLP to capture the CO adsorption 2\nbehaviour in the overall range of investigated temperature range.\nWe have also updated the text relating to the calculation method (Page 20 of the main text):\nTo sample the configurational space at each point, we implemented a hybrid MD+GCMC protocol consisting of 10 primary cycles. Each cycle was partitioned in 20,000 GCMC steps followed by 20,000 MD steps with a time step of 0.5 fs. Convergence was further refined through an additional 500,000 GCMC steps to obtain the equilibrated averages. Statistical analysis of the equilibrated averages was performed using pyMSER.52\nFig. 4 | In-depth microscopic understanding of the CO adsorption in the diverse 2\nMIL-120(Al) configurations. (a) MLP-derived lowest-energy CO adsorption sites in 2\nthe different MIL-120(Al) structures for a loading of 1 molecule of CO per unit cell (~ 2\n2.02 mmol g⁻¹ at 298 K). The corresponding data for a loading of 2 molecules of CO 2\nper unit cell (4.05 mmol g⁻¹ corresponding to the experimental uptake at 1 bar) are shown in Supplementary Fig. 29. The green dashed line represents the shortest distance between CO₂ and the μ -OH groups of MIL-120(Al) (unit: Å). (b) CO interaction 2 2\nenergies computed by DFT, our MLP model, and other MLPs including MACE-MPA- 0 and MACE-DAC,32,33 respectively. These interaction energies (E ) were computed !"}, {"round": 3, "reviewer_comments": {"reviewer_2": "The auhors have improved the manuscript according to the the reviewer's comment."}, "author_response": "RESPONSE TO REVIEWERS’ COMMENTS\nReviewer #2\nGeneral comment: The auhors have improved the manuscript according to the the reviewer's comment.\nReply: We would like to thank the reviewer once again for the comment, and for recommending our manuscript for publication in Nature Communications."}]

Decision letter