Introduction

With readily tunable structures and functionalities, metal–organic frameworks (MOFs) have received considerable attention for many potential applications. However, it is technically challenging to select promising MOFs as the chemical space is tremendously large. To date, over 100,000 MOFs have been experimentally synthesized, and in principle, infinite MOFs can be constructed by varying building blocks and topologies1. Experimentally identifying suitable candidates from the enormous number of MOFs for applications is economically inviable. In this context, high-throughput computational screening (HTCS) is a powerful technique to assist in establishing quantitative structure-property relationships and identifying top MOFs.

We have witnessed great success in using HTCS to identify top MOFs for different applications2,3,4, particularly CO2 capture5. For instance, the Computationally-Ready Experimental (CoRE) MOFs6 were screened for post-combustion CO2 capture and natural gas purification7. The separation of hexane and heptane isomers was simulated in CoRE MOFs, then one candidate was synthesized and characterized8. The latest version of the CoRE MOF database (2019)9 with over 10,000 structures was screened to isolate unique MOFs for paraffin/olefin separation10,11. The Cambridge Structural Database (CSD) MOFs12 were also screened for CO2 capture and H2 purification, and a handful of MOFs were identified to possess selective adsorption and molecular sieving capabilities13. The identified experimental MOFs by HTCS are synthesizable, regardless of possible difficulties that might be encountered, but crucial stability measures are scarcely considered in HTCS, which might lead to the utilization of unstable MOFs for applications.

Meanwhile, hypothetical MOFs (hMOFs) have also been widely examined by HTCS. The adsorption of CO2, N2 and CH4 in over 137,953 hMOFs was simulated, and the relationships between structural characteristics, as well as chemical functionality, with adsorbent evaluation criteria were proposed for CO2 separation14. Based on the adsorption, diffusion and permeation of CO2, N2 and CH4, 137,953 hMOFs were screened for a single-step membrane separation of CO2/N2/CH4 mixture15. Among over 300,000 hMOFs, different strong CO2-binding sites were classified, and hydrophobic MOFs with high CO2/N2 selectivity in wet flue gases were identified and further synthesized16. A database of ∼20,000 hMOFs with diverse metal nodes, organic linkers, functional groups and pore geometries was designed and assessed for post-combustion CO2 capture and H2 storage17. However, most HTCS studies of hMOFs were not accompanied or followed by experimental validation, hence the identified hMOFs might not be synthesizable and stable. Therefore, the synthetic likelihood and stability metrics must be incorporated in HTCS, along with performance metrics, to identify possible candidates that are potentially synthesizable and stable.

In this study, for the first time, we integrate crucial stability metrics with HTCS to screen hMOFs for CO2 capture. A collection of 15,219 hMOFs is obtained from the ARC-MOF database18, along with their computed adsorption data. As shown in Fig. 1, separation performance metrics are first used to shortlist top-performing hMOFs, and then four stability metrics (thermodynamic, mechanical, thermal, and activation) are integrated. Specifically, the thermodynamic stability (i.e., synthetic likelihood) is evaluated from free energies based on molecular dynamics (MD) simulations. The mechanical stability is calculated from elastic constants also obtained through MD simulations. Moreover, the activation and thermal stabilities are predicted using machine learning (ML) models. Finally, all the stability metrics are integrated to identify synthesizable, stable, and top-performing hMOFs for CO2 capture.

Fig. 1: High-throughput computational screening (HTCS) of hMOFs for CO2 capture.
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in which stability metrics (thermodynamic, mechanical, thermal, and activation) are integrated with separation performance metrics.

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Results and discussion

Separation performance

Different metrics can be used to evaluate the separation performance of a gas mixture in MOFs. Particularly, uptake and selectivity are widely used in HTCS studies, though there are other metrics such as working capacity19, purity, recovery, productivity20, and general evaluation metric21. For CO2 capture in this study, CO2 uptake (mmol/g) and CO2/N2 selectivity were chosen. As plotted in Fig. 2a, 148 out of 15,219 hMOFs in DB5 subset exhibit CO2 uptake ≥4 mmol/g and CO2/N2 selectivity ≥200, which were set as the thresholds. It is interesting to examine the metal node chemistry of the hMOFs. Figure 2b shows the percentages of five different metal node types among 15,219 hMOFs and among the 148 top-performing hMOFs for CO2 capture. Those with Zn4O metal node represent 33.5% in the entire DB5 subset, but this percentage drops to 0.7% among the 148 top-performing hMOFs. By contrast, V3O3 metal node is minority in DB5 (12.4%) but prevailing in the top-performing hMOFs (46.6%). This metal node, which resembles a one-dimensional rod, is able to promote CO2 adsorption as favorable adsorption sites exist near the bridging oxygen in V3O316. Indeed, higher CO2 uptake for V3O3 metal node is observed in Supplementary Fig. 1a, which shows the count of hMOFs for each metal node type versus CO2 uptake. The percentages of pillared Zn- and Cu-paddlewheel metal nodes are found to not be much different between DB5 and the top-performing hMOFs. Lastly, a few hMOFs with Zr6O6 metal node exist in DB5 (0.1%) but are not among the top-performing MOFs. Figure 2c shows ranked CO2 uptake in 148 top-performing hMOFs by different metal node types. There is no unique pattern to describe the distribution of metal nodes. This is because, aside from metal nodes, organic linkers also play an important role in CO2 adsorption. Among 148 top-performing hMOFs, the highest CO2 uptake (8.47 mmol/g) is found in a hMOF with V3O3 metal node. As shown in Fig. 2d, the notable CO2 uptake in this hMOF can be attributed to the presence of strong adsorbaphore16, which originated from parallel aromatic rings separated by a distance of 6.8 Å, in addition to the V3O3 metal node.

Fig. 2: Separation performance of hMOFs.
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a Top- and low-performing hMOFs for CO2 capture at 298 K, 0.9 bar and feed composition of 17%/83% in a CO2/N2 mixture, the data were taken from the ARC-MOF database18. b Percentages of five different metal node types among 15,219 hMOFs in DB5 subset and among 148 top-performing hMOFs for CO2 capture. Metal node labels: (i) Zn4O, (ii) pillared Zn-paddlewheel, (iii) pillared Cu-paddlewheel, (iv) V3O3, and (v) Zr6O6. c Ranked CO2 uptake in 148 top-performing hMOFs by different metal node types. d hMOF with the highest CO2 uptake, showing V3O3 metal node and parallel organic linkers composed of aromatic rings (adsorbaphore).

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Subsequently, the stabilities of 148 top-performing hMOFs are evaluated. We should note that the sequence of screening is not unique. One may first evaluate the stabilities, and for those deemed to be stable, then the separation performance can be determined. The order of these two screening steps depends on their computational cost. In the present study, the adsorption data are readily available in the ARC-MOF database and hence used at the first stage; consequently, there is no need to evaluate the stabilities of 15,219 hMOFs in the entire DB5 subset.

Thermodynamic stability

The thermodynamic stability is assessed by free energies (F) at ambient temperature, calculated using the FL method22,23,24. Figure 3a shows the free energies versus the percentage of metal atoms in 148 hMOFs. To judge the synthetic likelihood, we need to set a criterion and label those crossing the criterion as thermodynamically unstable. As such, the free energies of experimental MOFs were calculated and used for benchmarking. For this purpose, 79 CoRE MOFs with four different metal node types: pillared Cu-paddlewheel, pillared Zn-paddlewheel, Zn4O and V3O3 were considered. For each type, the CoRE MOFs were selected to have close similarity in metal nodes to the hMOFs using the revised autocorrelation functions (RACs)25,26. The calculated free energies of the hMOFs and selected CoRE MOFs are plotted in Fig. 3b. For each metal node type, the free energies of CoRE MOFs are fitted against the percentage of metal atoms, acting as a reference line24. By subtracting the corresponding value of the reference line (FLM) from the true F, the relative free energies ΔLMF are obtained. As presented in Fig. 3c, all the CoRE MOFs are capped within ΔLMF of ~4.2 kJ/mol, which is then taken as an upper bound for thermodynamic stability. This value is close to 4.4 kJ/mol reported by Anderson et al.24 Among 148 hMOFs, 41 have ΔLMF higher than the upper bound, thus considered thermodynamically unstable and not recommended for synthesis. We should note, practically, that kinetic factors (e.g., solvent, modulator, pH, and temperature) may affect the synthesis process27,28, which is not simply governed by thermodynamic stability.

Fig. 3: Free energies of MOFs.
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a Free energies of 148 hMOFs with all the five metal node types versus the percentage of metal atoms. b Free energies of hMOFs and experimental MOFs with various metal node types: pillared Cu-paddlewheel, pillared Zn-paddlewheel, Zn4O and V3O3. c Relative free energies of 148 hMOFs (o) and selected benchmarking experimental MOFs (✩). The hMOFs with ΔLMF > 4.2 kJ/mol are considered thermodynamically unstable (unsynthesizable).

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Mechanical stability

MOFs should retain integrity during synthesis, activation, pelletization, and gas adsorption. Typically, post-combustion CO2 capture is operated at low pressure (~1 bar), and hence no significant pressure on MOFs is expected to arise during CO2 capture. Nevertheless, stress is applied during pelletization to shape MOFs, which in many cases leads to a significant loss of surface area, and such structural collapse can be mitigated by loading solvents into MOFs and stabilizing frameworks29. Therefore, structural degradation by mechanical stress at this stage is a resolvable issue. Rather, we need to determine the intrinsic mechanical stability of unstressed MOFs. MD simulations were conducted at two different temperatures (0 and 298 K) to calculate elastic properties, including bulk (K), shear (G) and Young (E) moduli, which can be used to quantify the rigidity of MOFs.

Figure 4a shows the distributions of elastic moduli of 148 hMOFs at 0 K. Many hMOFs exhibit low moduli, which might be inappropriately classified as unstable (not robust) and lack of practical significance. A handful of experimentally synthesized MOFs have elastic moduli of even less than 5 GPa30,31. They are commonly known as flexible MOFs, and their flexibility may bring favorable adsorptive characteristics. These flexible MOFs cannot be simply discarded by labeling them as unstable; thus, the elastic moduli alone are not adequate to judge mechanical stability. Instead, the Born stability criterion32,33 can be used to more reliably determine mechanical stability. Based on this criterion, all the eigenvalues of elastic matrix must be positive to declare a structure as stable, and the smallest eigenvalue can differentiate stable and unstable structures34. As shown in Fig. 4b, at 0 K, only a few hMOFs do not satisfy the criterion and are marked as unstable. Nevertheless, several stable hMOFs show eigenvalues very close to zero, indicating these hMOFs possess a soft deformation mode35 and may become unstable under stress or at a higher temperature. As presented in Fig. 4c, at 298 K, the number of unstable hMOFs increases. Consequently, it is important to assess the mechanical stability at a relevant temperature, as the calculations at 0 K might be misleading.

Fig. 4: Mechanical properties of 148 hMOFs.
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a Distributions of bulk, shear, and Young moduli at 0 K. Distributions of the smallest eigenvalues at b 0 K and c 298 K.

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Activation stability

Removal of solvent, modulator and unreacted substance is a prerequisite to activate MOFs for applications. On many occasions of activation, MOFs collapse to a dense amorphous phase, as commonly attributed to capillary force arising from evaporation or evacuation of solvent36. But still, there is no coherent understanding of this phenomenon that would enable computational prediction of collapse events (for instance, using molecular simulation). Though there is a relation between collapse likelihood and mechanical properties, with the collapsed MOFs always showing low moduli for certain types of MOFs31, mechanical properties are insufficient to assess activation stability. This is because solvent characteristics and solvent-MOF interactions also affect the activation process.

As an alternative, ML models trained on experimental data can be used to predict activation stability. Using MOFSimplify37, we predicted the activation scores of 148 hMOFs. As presented in Fig. 5a, the activation scores range from 0 to 1.0, corresponding to unstable (collapsible) and stable (activatable) likelihoods, respectively. An activation score of 0.5 is used here to distinguish collapsible and activatable structures. Among 148 hMOFs, 43 have activation scores < 0.5, thus assigned as collapsible upon solvent removal. It is important to note that the employed ML models do not consider the actual activation method, which may affect the successfulness of activation. For instance, there are advanced activation methods, such as the supercritical CO2 approach, that can effectively remove solvents if other conventional activation methods fail. Moreover, solvent characteristics and activation conditions may have considerable influences but were not taken into consideration in MOFSimplify. Yet, the adopted ML models appear as a simple and fast method to provide a reasonable assessment of whether the hMOFs would survive in activation.

Fig. 5: Activation and thermal stabilities of 148 hMOFs.
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a Activation scores of 148 hMOFs, those with scores <0.5 are classified as collapsible. b Decomposition temperatures (Td) of 148 hMOFs, 300 °C is used as the threshold for thermal stability.

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Thermal stability

For high-temperature applications such as catalytic reactions, the thermal stability of MOFs is crucial. By contrast, post-combustion CO2 capture is conventionally performed near ambient temperature. Thus, the major concern here about the thermal stability is when synthesized MOFs need to be thermally activated by increasing temperature to remove entrapped solvent or unreacted substance. As such, the temperature required is highly dependent on the boiling point of the solvent or the thermal decomposition temperature (Td) of unreacted substance38. If the interaction between solvent and MOF is strong, a high temperature is required beyond the boiling point to completely remove the solvent. For instance, HKUST-1 contains open metal sites with strongly bounded water molecules, and the activation temperature can reach 200 °C39. Consequently, it is challenging to set a distinct limit to quantify the thermal stability of MOFs. Yet, those decomposing below 300 °C can be considered thermally unstable, similar to hybrid ultra-microporous materials40. Thus, 300 °C is set as the threshold for thermal stability. To predict the Td of hMOFs, we also used MOFSimplify37. As shown in Fig. 5b, among 148 hMOFs, 117 exhibit Td > 300 °C, which indicates that most of the 148 hMOFs have decent thermal stability. The remaining 31 hMOFs are considered thermally unstable, and the lowest predicted Td is ~199 °C.

Integration of stability metrics

Based on the above four stability metrics, Fig. 6a summarizes the percentages of stable and unstable structures among 148 hMOFs. The thermodynamic stable structures represent 72% of 148 hMOFs; thus, only 28% are unsynthesizable. Regarding mechanical stability, the percentage of stable structures at ambient temperature is 79%. The predicted activation and thermally stable structures, based on ML models, are 72% and 79%, respectively. However, these two stability metrics are subject to the accuracy of ML models and the designated boundaries to distinguish stable and unstable structures. Figure 6b shows the number of stable hMOFs based on the four stability metrics. Not surprisingly, some MOFs satisfy one metric but fail in the other. Although the four metrics are evaluated using different approaches, considerable overlaps are seen as there are conceptual links among them. Particularly, the thermodynamic and mechanical stabilities are correlated, to a certain extent, with the thermal stability (Supplementary Fig. 2). The intersection in Fig. 6b gives 51 hMOFs, as listed in Supplementary Table 1, representing the final top-performing hMOFs that meet the separation performance requirement for CO2 capture and also satisfy all the four stability requirements. The building blocks of these hMOFs are listed in Supplementary Table 2. Interestingly, a handful of top-performing hMOFs in Fig. 2c with the highest CO2 uptake are found unstable. Therefore, integrating stability metrics is important to discard unstable hMOFs. It is worthwhile to note that the stability metrics can only tell if the structures are stable, but not how to synthesize them. Yet, it is possible to obtain an initial guess for synthesis conditions and additives using ML models that were trained using experimental data of successfully synthesized MOFs41.

Fig. 6: Integration of stability metrics for 148 hMOFs.
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a Percentages of stable and unstable hMOFs based on four stability metrics. b Overlapping of stable hMOFs based on four stability metrics, the intersection among them gives the final top-performing, synthesizable, and stable hMOFs for CO2 capture.

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Performance of a top-performing stable hMOF

Finally, it is instructive to provide microscopic insight into the separation mechanism in the top-performing stable hMOFs. For this purpose, grand-canonical Monte Carlo (GCMC) simulations were carried out for the adsorption of a CO2/N2 mixture (17%/83%) in a hMOF with V3O3 metal node and methyl functionalized pyrene-2,7-dicarboxylic acid (PDC) linker. This hMOF exhibits the highest CO2 uptake among 51 stable candidates, along with high CO2/N2 selectivity. Figure 7a shows the adsorption isotherms of CO2 and N2 in this hMOF, which reveals far more significant adsorption of CO2 over N2 in the entire pressure range (0–1 bar). At 1 bar, CO2 uptake is 7.49 mmol/g, and CO2/N2 selectivity is 355, which surpasses many reported experimental MOFs. The high CO2 uptake in this hMOF is attributed to the presence of strong adsorbaphore16, which originated from parallel aromatic rings separated by a distance of 6.8 Å, as well as the favorable interaction sites in V3O3 metal node. The adsorption heats in Fig. 7b assert the preferential adsorption of CO2 over N2 at various pressures. Moreover, the separation performance of this hMOF is assessed with the presence of moisture in the CO2/N2 mixture. As shown in Fig. 7c, d, both CO2 uptake and CO2/N2 selectivity are marginally affected by the relative humidity (RH). Specifically, CO2 uptake remains nearly constant at low-to-moderate RH, though there is a slight decrease at a high RH; meanwhile, N2 uptake also decreases. Consequently, CO2/N2 selectivity increases slightly with RH. Overall, this hMOF is expected to separate CO2 efficiently from dry or wet flue gas.

Fig. 7: Separation performance of a top-performing stable hMOF.
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a Adsorption isotherms and b adsorption heats of CO2 and N2 for a CO2/N2 mixture (17%/83%) at 298 K. The insets illustrate CO2 adsorbaphore and simulation snapshot at 1.0 bar (CO2: purple, N2: blue). c CO2 uptake and d CO2/N2 selectivity versus relative humidity (RH).

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Conclusions

Computational screening of hMOFs often returns many top-performing candidates, yet there are large uncertainties in their synthetic likelihood and stabilities. In the present study, we integrate four stability metrics in the screening of hMOFs for CO2 capture. The stabilities are evaluated using different approaches, including MD simulations and ML models. The synthetic likelihood (thermodynamic stability) is assessed by free energies, while the mechanical stability is examined through the Born stability criterion at ambient temperature. Moreover, hMOFs that retain activation and thermal stabilities are predicted. Finally, we identify the top-performing hMOFs satisfying all these stability requirements. For future work, chemical stability should also be taken into consideration to examine possible structural degradation if MOFs are exposed to water, corrosive gases, and organic solvents.

Methods

MOF database

A subset of hMOFs (labeled as DB5) in the ARC-MOF database18 was considered in the present study. This subset was originally created by Wilmer et al.42 and refined by Chung et al.43 The adsorption data for post-combustion CO2 capture were also extracted from the ARC-MOF database, as calculated from Monte Carlo simulations. Specifically, CO2 uptake and CO2/N2 selectivity at 298 K and 0.9 bar at a feed composition of 17%/83% for a CO2/N2 mixture were used. Among 22,366 hMOFs with adsorption data in DB5, we investigated the non-interpenetrated (non-catenated) hMOFs by verifying the second integers of their 6-chromosome names (which encode actual interpenetration), resulting in 15,219 hMOFs. The selected dataset comprises five different metal node types: Zn4O, pillared Cu-paddlewheel, pillared Zn-paddlewheel, V3O3 and Zr6O6.

MD simulations

The thermodynamic and mechanical stabilities were evaluated using MD simulations. For a given MOF, the LAMMPS interface44 was used to prepare input files for bonded and non-bonded interaction potentials. It was found, for many of the hMOFs under study, that the implemented bonding algorithm in the LAMMPS interface led to incorrectly coordinated atoms or bonds, which subsequently caused the failure of MD simulations or inaccurate calculations of desired properties. To overcome this issue, the bonding information was precomputed and added to the Crystallographic Information Files (CIFs) prior to using the LAMMPS interface. As employed by Bruner et al.18, the IsayevNN45 algorithm in Pymatgen46 was used to generate the bonding information. This algorithm considers two atoms as neighbors (bonded) if they share a Voronoi facet and the separated distance is less than the sum of their covalent radii plus a tolerance. The default tolerance (0.25 Å) was used to detect bonding and found reliable to detect the Cu-Cu bond in pillared Cu-paddlewheel metal node present in the hMOFs. Yet, to identify the Zn-Zn bond in the pillared Zn-paddlewheel metal node, the tolerance was increased (0.5 Å) to search for neighboring Zn atoms. Computing the bonds based on the above algorithm resulted in fewer structures with incorrect bonds, which were manually corrected. The interactions between different atoms were described using the UFF4MOF force field47. For pillared Cu- and Zn-paddlewheel metal nodes, we assigned Cu4+2 and Zn4+2 metal types, respectively. It was revealed in the literature that the inclusion of electrostatic interactions with UFF4MOF would lead to inaccurate calculations of MOF properties such as elastic moduli and thermal expansion coefficients, and the optimized MOF structures would differ significantly from experimental measurements44. Thus, electrostatic interactions were not included here, as also in previous studies24,34. All the MD simulations were performed using the LAMMPS package48.

Thermodynamic stability

To determine thermodynamic stability (i.e., synthetic likelihood), the free energies of hMOFs were calculated using the Frenkel–Ladd (FL) thermodynamic integration method22,23. It has been proven that the FL method predicts the free energies of MOFs more accurately compared to other approaches24. The FL path is a thermodynamic integration between the ideal Einstein crystal and its actual representation described by a force field. MD simulations were performed at 298 K and zero pressure, repeated three times using different seeds for the initial velocity distributions, and the computed free energies were averaged. The fix ti/spring command was used to perform thermodynamic integration, with 400 ps switching time using 1 fs timestep. The free energies of hMOFs were computed per atom basis, with a maximum standard deviation of ± 0.29 kJ/mol. To benchmark the free energies of the hMOFs, a set of experimental MOFs was used as a reference. Specifically, the CoRE MOFs9, labeled as DB12 in the ARC-MOF database18 were used. As in the hMOFs, the non-interpenetrated (non-catenated) structures were detected using MOFid49 and considered. Given that free energy is sensitive to metal node type, only the CoRE MOFs possessing the same metal node as those in the hMOFs were selected. As such, the revised autocorrelations (RACs)25,26 for metal nodes were used to find the matching CoRE MOFs. First, the hMOFs were grouped based on their metal node types, and the centroid of each cluster of hMOFs was calculated using KMeans algorithm, as implemented in Scikit-learn. Then, the Nearest-Neighbors algorithm was used to locate the nearest 20 CoRE MOFs to each centroid calculated for hMOFs. Lastly, the final selected CoRE MOFs were manually examined to ensure matching with the designated metal node and free of any disorder. A handful of duplicate structures were found, especially those having V3O3 metal node.

Mechanical stability

To examine mechanical stability, the average elastic properties, including bulk (K), shear (G), and Young (E) moduli, as well as the Born stability criterion, were evaluated at both 0 K and 298 K. Derived from Hooke’s law that relates stress with strain, the elastic constants can be calculated through an explicit deformation approach. At 0 K, initially, a structure was optimized using two stages of energy minimization. The first stage was performed using the conjugate gradient algorithm, coupled with triclinic box relaxation at zero pressure, while in the second stage, the fire algorithm50 was used at a fixed volume. In each stage, the energy and force-stopping tolerance were set as 10−15 kcal mol−1 Å−1 with 105 maximum iterations or force evaluations. This scheme was repeated for 200 cycles, where atomic positions were slightly disturbed between cycles to achieve minimum energy configuration. At the end of structure relaxation, the pressures (stresses) were saved. Next, the structure was strained (1%) in various directions, followed by 10 cycles of energy minimization with the fire algorithm to optimize atomic positions at a fixed volume. The corresponding pressures (stresses) on the structure at each deformation were collected and used with the initial stresses to calculate elastic constants. To calculate the elastic constants at 298 K, the above explicit deformation method was used after replacing energy minimization with MD simulation, though this approach is computationally expensive as the structure must be strained in various directions and followed by long MD simulation. Moreover, a large simulation box (minimum length of 50 Å) was used to improve accuracy. First, the simulation box was relaxed at zero pressure in the NPT (triclinic) ensemble using the Nosé–Hoover thermostat and barostat to control temperature and pressure, respectively. The equilibration time was 4 ns, followed by 4 ns production, during which the cell parameters were sampled. Afterward, the simulation box was adjusted to the averaged cell parameters. Then, simulation was performed in the NVT ensemble (0.5 ns equilibration, 4 ns production), during which the pressures (stresses) acting on the simulation box were collected every timestep, averaged, and saved as the initial stresses for the non-deformed structure. Next, deformations were applied to various directions (1% strain). For each deformation, simulation was performed in the NVT ensemble (0.5 ns equilibration, 4 ns production), and the stresses during production were collected and averaged. Finally, from the collected stresses of the non-deformed and deformed structures, the elastic constants were calculated.

Activation and thermal stabilities

The activation and thermal stabilities were predicted using ML-based MOFSimplify37. This platform takes a CIF as an input and then internally conducts featurization and prediction. For activation stability, the implemented ML model was trained on thousands of experimental MOFs to predict the likelihood of removing solvents without structural collapse. For thermal stability, the ML model was trained on experimentally measured decomposition temperatures (Td) extracted from thermogravimetric analysis (TGA) data.

Monte Carlo simulations

After identifying top-performing synthesizable and stable hMOFs for CO2 capture, to provide in-depth insight into separation performance, grand-canonical Monte Carlo (GCMC) simulations were conducted for the adsorption of a CO2/N2 mixture (composition of 17%/83%) in a hMOF at 298 K. The force fields used were identical to those in the ARC-MOF database18. Specifically, the university force field (UFF)51 was used to describe the dispersion interactions of framework atoms, while the REPEAT atomic charges were included for electrostatic interactions. For CO2 and N2 adsorbates, the potential parameters were adopted from literature52,53. Furthermore, to examine the effect of moisture on separation, GCMC simulations were also performed at different relative humidities. H2O was represented by the TIP4P model54, which has a saturation pressure of 4365 Pa55. The Lorentz–Berthelot combining rules were used to calculate the cross interactions. The cutoff to evaluate dispersion intermolecular interactions was set to 12.8 Å, and the Ewald sum was used to calculate long-range electrostatic interactions. The number of cycles was 200,000, with the first half for equilibration and the second half for production. During GCMC simulations, the framework was held rigid. Five different trial moves were attempted for the adsorbate molecules, including translation, rotation, reinsertion, identity change and swap with probabilities of 16.7%, 16.7%, 16.7%, 16.7% and 33.2%, respectively. All the GCMC simulations were conducted using the RASPA56.