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. 2026 Oct 13. Online ahead of print. doi: 10.1039/d6sc04283j

Accelerating the discovery of nanoporous gas separation materials via Coulomb-enhanced classical density functional theory

Yong Qiu a, Yu Liu b, Weiqiang Tang a, Zhen Zhou a,c,✉, Yun Tian a,✉
PMCID: PMC13673237  PMID: 42890474

Abstract

The design of advanced nanoporous materials for gas separations, such as carbon capture and alkyne purification, is increasingly driven by high-throughput screening. However, the accurate description of electrostatic interactions in porous frameworks remains challenging and can introduce sizable deviations between predicted and experimental performance, thereby hindering rational materials design. To address this gap, we present a computational framework, compatible with standard force fields under appropriate charge assignments, that explicitly incorporates a point-charge model to capture adsorbate–framework long-range Coulomb interactions via the Ewald summation technique within the external potential of classical density functional theory (cDFT), enabling adsorption prediction for common polar or quadrupolar gas molecules. The resulting Coulomb-enhanced cDFT (QcDFT) shows closer agreement with GCMC and experimental adsorption data than existing cDFT variants, and was applied to 689 CO2/MOF adsorption cases and nearly 10 000 CoRE MOF 2019 structures for C2H2/CO2 screening. By further integrating the string method, QcDFT allows for efficient prediction of adsorption selectivity and rapid estimation of self-diffusion coefficients, achieving up to three orders of magnitude acceleration relative to conventional molecular dynamics simulations. This combination of speed and accuracy makes QcDFT well suited to large-scale nanoporous materials screening, bridging atomic-scale adsorption mechanisms with separation-relevant candidate selection.

Here, we introduce QcDFT, a computational framework that explicitly accounts for Coulomb interactions in gas separation systems, demonstrating an excellent compromise between computational efficiency and predictive accuracy.graphic file with name d6sc04283j-ga.webp

Introduction

Efficient and green gas separation technologies have become essential for applications ranging from toxic gas capture to greenhouse gas mitigation.1,2 In parallel, industrial gases play a pivotal role in petrochemicals,3 energy conservation, environmental protection, food preservation, and high-precision electronic components,4,5 representing a substantial and growing market. For instance, the acetylene market in China alone was valued at approximately RMB 22.7 billion in 2024.6

Common non-polar gases such as CO2, C2H2, C2H4 and polar gases like NH3, SO2, CO, H2S,7 possess significant electrostatic multipole moments, leading to non-negligible coulombic interactions with separation materials.8,9 Precisely resolving and replicating these complex electrostatic matching behaviors in experiments remains highly challenging, often diverting materials discovery from rational molecular engineering toward trial-and-error screening. Even widely used simulation techniques, including Grand Canonical Monte Carlo (GCMC) and Molecular Dynamics (MD),10 face substantial computational costs when explicitly treating coulombic interactions, which may challenge their direct deployment in automated screening and design workflows.11,12 By circumventing stochastic sampling processes, classical density functional theory (cDFT) solves a deterministic functional minimization for density fields, providing molecular-level adsorption predictions at substantially lower computational cost, offering a favorable balance of accuracy and efficiency for gas adsorption and separation predictions in porous materials.13 However, the explicit treatment of long-range coulombic interactions in cDFT frameworks for gas (especially for neutral but polar/quadrupolar gas molecules) adsorption and separation in porous materials remains limited, which severely restricts predictive accuracy for most industry-relevant systems where electrostatics play a critical role.9,12,14–20

Standard Poisson-based cDFT formulations were originally developed for ionic systems, where the source term of the Poisson equation is the net charge density, effectively encoding only the zeroth moment of the charge distribution. For gas-phase molecules that are overall charge-neutral yet possess significant permanent multipole moments, such as the large quadrupole moment of CO2 (which is critical for its preferential adsorption over N2 in porous frameworks) and the notable quadrupole of C2H2, this zeroth-moment representation is fundamentally insufficient to capture the electrostatic potential landscape arising from higher-order charge anisotropy. Consequently, conventional Poisson-based cDFT treatments are inherently inadequate for predicting gas-phase separation performance in nanoporous materials, where subtle differences in electrostatic multipole interactions govern adsorption selectivity and can also influence molecular permeation in membrane systems.19,21–25

Machine-learning-augmented approaches, which attempt to approximate long-range electrostatic interactions through data-driven surrogates, remain in early development and often lack the accuracy, physical interpretability, or transferability required for reliable high-throughput screening across diverse porous framework topologies and gas mixtures. Poisson electrostatics is not intrinsically restricted to the net molecular charge; when its source retains a spatially resolved site-charge density, it can represent dipolar and quadrupolar fields. Electrostatic cDFT describes ionic fluids through spatial charge densities and electrostatic correlation functionals, whereas polar-fluid DFT introduces multipolar contributions and molecular DFT retains position-and-orientation densities. These approaches provide greater molecular resolution but require additional coupled fields or higher-dimensional distributions. In adsorption applications, computationally efficient cDFT formulations have therefore commonly represented adsorbates using spherical or coarse-grained molecular densities, often without a site-resolved framework–adsorbate electrostatic field. This trade-off motivates an intermediate-resolution formulation that improves the external-potential description while retaining a tractable coarse-grained excess functional.26–31 In recent studies, cDFT still exhibits significant discrepancies in predicting isotherms for quadrupolar systems such as CO2, precisely because they fail to self-consistently incorporate the full long-range coulombic interaction arising from distributed partial charges on molecular frameworks and adsorbates.32

To bridge this critical methodological gap, we present QcDFT, a cDFT framework that incorporates long-range framework–adsorbate coulombic interactions into the external potential via Ewald summation under periodic boundary conditions,33 coupled with discrete orientational sampling and Boltzmann averaging, thereby extending practical 3D cDFT predictions from spherical or nonpolar adsorbates to neutral but polar/quadrupolar gas molecules in charged frameworks while preserving the computational efficiency for high-throughput screening (Scheme 1). With rigorous yet computationally tractable electrostatic evaluations, the proposed method shows systematically improved agreement with experimental/molecular simulation data compared with existing 3D cDFT models under equivalent conditions. After comprehensive assessment of the efficiency–accuracy trade-off across diverse operational scenarios to establish robust protocols for subsequent high-throughput screening in realistic three-dimensional adsorption systems, our method enables the evaluation of nearly 10 000 metal–organic framework (MOF) structures when applied to C2H2/CO2 separation. Compared with thermodynamic properties, diffusion-related properties are far more sensitive to electrostatic interactions, which further supports our workflow for high-throughput screening of nanoporous materials for gas separation and mechanistic analysis of separation-relevant properties. New insight into the underlying separation mechanisms is also revealed with QcDFT, as the adsorption configuration of both C2H2 and CO2 induced by hydrogen bonding and strong electrostatic interactions are fully captured. Notably, QcDFT yields predictions more comparable with molecular-simulation benchmarks than other cDFT variants while requiring less than 1% of the molecular-simulation computational cost. This work establishes a scalable and reliable computational framework for high-throughput screening of separation materials, offering a practical computational tool for the rational design of separation-relevant porous materials and facilitating future integration with automated discovery workflows and experimental validation.

Scheme 1. Workflow for high-throughput screening of nanoporous materials for gas separation using QcDFT.

Scheme 1

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Results

Benchmarking QcDFT for gas adsorption in porous frameworks

An accurate representation of the external potential field is essential for the predictive capability of cDFT in determining thermodynamic properties. We first performed a direct comparison of Coulomb interactions computed using identical parameters with reference GCMC data, as summarized in Table S1, which shows excellent agreement.

To ensure fair evaluation, all computational parameters (force fields, charges, cutoffs) were kept consistent across methods. Among the cDFT variants, the widely used spherical cDFT16 is most efficient but limited to fluids without configurational effect nor appreciable electrostatic multipole moments (e.g., CH4, Xe, Kr); dual-model cDFT17 (DM-cDFT) represents a state-of-the-art extension to multi-site LJ description to include configurational effect but neglects Coulomb interactions; while QcDFT is built upon previous versions and further incorporates fixed-charge framework–adsorbate Coulomb interactions in the external potential, as shown in Table 1. The performance of QcDFT was then systematically investigated via the predicted adsorption isotherms of several industrially relevant gases (CO2, CO, NH3, H2S, and SO2) in porous materials (Fig. 1). Comparison with experiment shows system-dependent performance (Fig. 1 and Table S5). Across the eight gas/material systems, QcDFT gave lower MAE than GCMC in five systems, GCMC gave lower errors in three systems. For NH3 adsorption in MOF-5, QcDFT more closely reproduced the step-like uptake and high-pressure (QcDFT high-pressure error: 2.66 mol kg−1) plateau than GCMC, although the predicted transition pressure remained shifted to higher pressure. Although a slight deviation between QcDFT and experimental data is observed for CO (Fig. 1h) likely attributable to limitations in the underlying force field or experimental/structural uncertainties, the QcDFT predictions overall remain more accurate than those obtained from the other cDFT methods under the same force-field and charge settings. Therefore, GCMC comparisons under identical model settings are used to assess the numerical performance of QcDFT, while deviations from experiment may also reflect force-field, charge-assignment, structural, and experimental uncertainties.

Table 1. Comparison of different cDFT variants.

cDFT method Configurational effect Coulomb interactions
Spherical cDFT ✗ ✗
DM-cDFT ✓ ✗
QcDFT ✓ ✓
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Fig. 1. Comparison of adsorption isotherms among DM-cDFT, spherical cDFT, GCMC, QcDFT and experiments (solid, dotted, and dashed lines denote QcDFT, DM-cDFT, and spherical cDFT(cDFT)), respectively. Open triangles denote GCMC data,17,34 crosses denote literature simulation data,35,36 and filled circles denote experimental data.34–41.

Fig. 1

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We further observe that adsorption isotherms predicted by QcDFT generally align more closely with GCMC reference results than those from DM-cDFT. This improvement can be attributed to the explicit treatment of coulombic interactions in QcDFT. For example, as shown in Fig. 1c–f, QcDFT effectively mitigates the overestimation commonly observed in DM-cDFT, while also alleviating the underestimation of adsorption capacity in the case of H2S. In COF structures, where frameworks are predominantly held together by covalent bonds and coulombic interactions are relatively weak, both cDFT variants yield comparable predictions. In contrast, the influence of electrostatic interactions becomes markedly more pronounced in MOFs containing metal nodes. QcDFT deterministically reproduces step-like adsorption behavior without extensive stochastic sampling, although the predicted transition pressure can remain shifted, as observed for NH3 adsorption. We also computed the adsorption of C2H2, C2H4, and C2H6 (molecules with quadrupole moments) in porous frameworks. The comparable performance between QcDFT and DM-cDFT in these cases indicates that adding electrostatic contributions moderately improves prediction accuracy, even though the adsorption of these gases remains primarily governed by van der Waals interactions (Fig. S1).

Computational efficiency is a key advantage of the cDFT framework. However, incorporating explicit long-range Coulomb interactions between gas molecules and framework materials within QcDFT leads to a substantial increase in computational cost, typically several times higher than that of DM-cDFT. Given that long-range electrostatics is not always the dominant contribution in gas separation processes, we systematically evaluated the accuracy and efficiency of QcDFT by benchmarking adsorption uptake predictions against varying numerical precisions and cutoff radii.

As shown in Fig. 2, grid resolution has considerable influence on adsorption predictions. Coarser grids may fail to resolve key adsorption sites or inaccurately estimate average energy barriers. In contrast, within the tested range, the real-space cutoff radius in the Ewald treatment has a much smaller influence on the results, as illustrated by the efficiency comparison in Fig. S2. These findings are consistent with local molecular field (LMF) theory, indicating that extending the cutoff model reveals long-range forces to converge to a weak, mean-field-like contribution.42 As demonstrated in Fig. 2c, a real-space-only Coulomb cutoff approximation substantially improves computational efficiency, almost comparable with DM-cDFT, and retains reasonable agreement in this representative case. But this agreement should be interpreted cautiously, as it may partially arise from error cancellation rather than from a physically superior electrostatic approximation. Although the long-range electrostatic interactions are non-negligible, it might support a hierarchical screening strategy: a simple and fast cutoff approximation can be used for preliminary screening of weakly multipolar molecules in large-scale databases, followed by more rigorous and computationally more expensive long-range electrostatic calculations for complex cases and final evaluation, thereby balancing overall efficiency and accuracy.

Fig. 2. Accuracy-efficiency trade-off in QcDFT using the representative MOF in Fig. 1g as a model system. (a) Effect of the real-space truncation radius, r_c, in the Ewald-based electrostatic treatment. (b) Effect of grid spacing (Δx) on adsorption uptake. (c) Adsorption isotherms predicted using only real-space Coulomb interactions compared with cDFT, DM-cDFT, GCMC, QcDFT, and experiment. (d) Comparison of adsorption behavior predicted by the real-space Coulomb model versus the full point-charge interaction scheme.

Fig. 2

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High-throughput performance evaluation of QcDFT

To validate the efficacy of QcDFT, we performed high-throughput computations of adsorption isotherms for 689 MOFs, generating nearly 7000 data points for comparison against DM-cDFT and GCMC benchmarks, which is quantitatively evaluated in Table S6. As shown in Fig. 3a, the DM-cDFT method underestimates the adsorption uptake in several MOFs, which we attribute to its neglect of explicit electrostatic interactions between the framework's metal sites and CO2 molecules. Fig. 3b and c present the comparison of adsorption uptake between QcDFT and GCMC using charges derived from the PACMOF and DDEC methods, respectively. In contrast to DM-cDFT, these results underscore that electrostatic interactions are critical for accurately modeling molecules with significant quadrupole moments. Using each MOF isotherm as the statistical unit (as shown in Fig. S3, S4 and Table S7), QcDFT yielded a lower MARD than DM-cDFT for 633 of 689 MOFs (91.9%; 95% MOF-level bootstrap confidence interval, 89.7–93.9%). The median QcDFT MARD was 17.2% (interquartile range, 10.3–28.1%), indicating a broad improvement over DM-cDFT within this CO2/MOF benchmark. QcDFT yielded a higher full-range MARD for a small minority of MOFs (∼8%). In the representative NUCREJ case, this difference arose mainly from low-pressure overestimation, although QcDFT gave loadings closer to GCMC at intermediate and high pressures. Discrepancies between the adsorption uptakes predicted by GCMC and QcDFT are subject to differences in their inherent algorithms and numerical issues. To evaluate the sensitivity of the predictions to charge assignment, we systematically compared the effects of two machine-learning derived charge methods, PACMAN43 and PACMOF,44 as shown in Fig. 3d. The results indicate that the charges predicted by the PACMAN method yield closer agreement with the DDEC charges, used here as a quantum-derived reference. To better assess charge-assignment sensitivity in electrostatically sensitive systems, we examined the target C2H2/CO2 mixture using two QMOF datasets: approximately 100 open-metal-site MOFs with available DDEC charges and a second representative set of 100 MOFs selected by stratified max–min diversity sampling across the screening-selectivity range. PACMAN and PACMOF charges were generated for the same structures, and Henry constants, finite-loading adsorption, selectivity, and screening rankings were recalculated using the same QcDFT workflow. As summarized in Fig. S5 and S6, PACMAN shows consistently smaller deviations from DDEC and better preserves the DDEC-referenced rankings than PACMOF in both datasets, supporting its use for high-throughput QcDFT screening. This result is consistent with recent benchmark studies on partial charge methods for porous materials.43,45 DDEC serves as the quantum-derived reference for evaluating the relative consistency of PACMAN and PACMOF, rather than as an exact standard for adsorption performance.

Fig. 3. High-throughput prediction of CO2 adsorption uptake across different computational models. (a) Correlation between adsorption uptakes predicted by GCMC and DM-cDFT. (b) Correlation between GCMC and QcDFT using PACMOF-derived atomic charges. (c) Correlation between GCMC and QcDFT using DDEC-derived atomic charges. (d) Comparison of QcDFT-predicted adsorption uptakes employing two machine-learning charge assignment methods relative to the quantum-derived DDEC reference charge model. Grey dashed lines denote parity lines.

Fig. 3

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Mechanistic insights into C2H2/CO2 separation: a case study by QcDFT

The industrial separation of gas mixtures, particularly the purification of C2H2 by removing trace CO2, presents a pressing challenge due to their similar physical properties. A data-driven understanding of the underlying separation mechanism is essential for the rational design of advanced materials. The equimolar C2H2/CO2 mixture at 298 K and 1 bar was selected as the thermodynamic condition for material screening, as it is a standard experimental condition relevant to industrial separation scenarios.7 In this work, we perform a computational analysis of the CoreMOF2019 database, conducting high-throughput screening of nearly 10 000 MOFs with pore limiting diameters exceeding 3.3 Å (the kinetic diameter of CO2), detailed filtering statistics are summarized in Table S8, with the top 10C2H2/CO2 adsorption-selective candidates listed in Table S9, and the distributions of selectivity and physical features are presented in Fig. S7. Through DFT calculations, we provide multi-scale mechanistic insights into C2H2/CO2 separation. As shown in Fig. 4a and b, we compare the correlation of Henry's constants with both ideal and actual adsorption selectivity. The actual selectivity, which accounts for competitive adsorption under realistic thermodynamic conditions, exhibits a weaker correlation with Henry's constants than the ideal selectivity does.

Fig. 4. Database analysis and adsorption separation mechanism for C2H2/CO2. (a) Correlation between actual adsorption selectivity and Henry's constants. (b) Relationship between ideal adsorption selectivity and Henry's constants. Adsorption density distributions of (c) C2H2 and (d) CO2 in the prototypical MOF-5 framework.

Fig. 4

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To further evaluate the reliability of these binary-mixture screening results, we compared QcDFT predictions with controlled binary GCMC simulations. The validation set comprised 18 frameworks, including 10 Top-100 candidates (55.6%), four Top-10 candidates, OMS and non-OMS structures, and PLDs of 3.31–22.85 Å. QcDFT and GCMC used identical structures, force-field parameters, charges, molecular definitions, and fugacity mappings. Three expe33rimentally relevant C2H2/CO2 feeds (1 : 1, industrially motivated 2 : 1, and trace-level 1 : 99) were evaluated at 298 K over 0.01–10 bar.46–48 As shown in Fig. S8–S11, the Spearman correlation was 0.76–0.98 and the median rank displacement was 0–2 positions, typically only one to two positions. Median per-isotherm MARDs were 11.7–18.5% for C2H2 and 13.2–21.1% for CO2. Several narrow-pore frameworks showed larger high-pressure deviations. This behavior likely reflects the coarse-grained excess functional, which does not explicitly resolve dense molecular packing or intermolecular orientational correlations. Nevertheless, QcDFT preserved the overall material ordering across mixture compositions and pressures, thereby supporting its use for efficient high-throughput material prioritization.

Distinct from prior analyses of Xe/Kr and CH4/H2 separation systems,9,49 our machine-learning analysis, which included both a full-feature model and a model excluding the two Henry-constant features (Fig. S12), identifies increased importance of atomic descriptors associated with nitrogen, hydrogen, and metal-coordination sites. This shift may partly reflect the partial-charge characteristics of these sites, which can enhance electrostatic interactions with adsorbate molecules and contribute to a distinct adsorption regime. The resulting differences are reflected in comparative interpretability analyses, including SHAP and Pearson correlation patterns distinct from those observed for the previously studied gas pairs (Fig. S13 and S14).

To elucidate the mechanistic underpinnings of C2H2/CO2 separation, we conducted a comprehensive analysis of the prototypical MOF-5 framework, as shown in Fig. S15, which exhibits a selectivity of approximately 3. Analysis of the adsorption density distributions (Fig. 4c for C2H2; Fig. 4d for CO2) reveals that while both gases occupy two primary adsorption sites (A and B, as shown in Fig. 4c), their binding modes differ significantly. C2H2 molecules localize near organic linker oxygen atoms, engaging in cooperative C–H⋯O hydrogen bonding and electrostatic interactions. In regions adjacent to linker hydrogen atoms, the carbon atom of C2H2 also exhibits attractive interactions with framework H atoms. By contrast, CO2 adsorption is dominated by the stronger electrostatic attraction between its negatively charged oxygen atoms and linker hydrogens, with a secondary contribution from coordination to metal sites.

Ab initio DFT and Atoms in Molecules (AIM)50 analyses were used as local microscopic probes of the interaction motifs suggested by QcDFT, serving as a complementary proof of the overall separation mechanism. C2H2 exhibits a stronger binding energy than CO2 at equivalent sites (C2H2: −17.37 kJ mol; CO2: −16.40 kJ mol−1), and this energetic preference appears to stem from the greater strength of the C–H⋯O_(Zn) hydrogen bonding formed by C2H2 compared with the C–O⋯H_(linker) interaction favored by CO2, a finding corroborated also by calculated electron density difference maps, as shown in Fig. S16. Furthermore, we quantitatively assessed the strength of hydrogen bonds through AIM topological analysis with Multiwfn.51,52 The calculated hydrogen bonding energy is −0.707 kcal mol−1 for C2H2 and −0.286 kcal mol−1 for CO2, as shown in Fig. S17. Although hydrogen bonding represents a relatively weak interaction, it effectively pre-organizes the molecule at the optimal adsorption site, thereby enabling synergistic engagement with multiple weak interaction sites (such as attraction to linker hydrogen atoms). This cooperation leads to the formation of a stable adsorption state with considerable cumulative binding energy manifested by the hydrogen bonding network. To understand the competitive adsorption mechanism, we performed a global potential energy surface (PES) analysis, as shown in Fig. S18. This reveals that C2H2 (∼4 Å in length) interacts more strongly near metal-cluster oxygen terminals, and its longer molecular length, compared with CO2 (3.3 Å), promotes a pronounced pore-sieving effect. The adsorption sites identified by the PES show excellent agreement with those observed in the adsorption density plots.

To provide more comprehensive mechanistic insight, we further analyzed top-ranked C2H2/CO2 candidates from the screening set (Fig. S19), besides the prototypical MOF-5. The paired external-potential analysis shows that C2H2 density is preferentially localized in lower C2H2 potential regions than CO2, while high-selectivity candidates exhibit O/acceptor-containing low-potential basins and a relatively narrow PLD window. These results suggest that C2H2/CO2 selectivity arises from combined effects of C2H2-favorable potential wells, weak directional framework-adsorbate contacts, and pore-aperture matching. In addition, we systematically analyzed ISISUZ_clean, a high-performing representative with a C2H2/CO2 selectivity of approximately 49, and the DFT/AIM results provide consistent microscopic evidence for C2H2-favorable potential wells and weak directional framework-adsorbate interactions, as shown in Fig. S20 and S21.

Probing diffusion properties via QcDFT

Beyond thermodynamic adsorption performance, diffusion properties provide useful supporting information for evaluating separation-relevant nanoporous materials. In our previous work,9,53 we employed string method rooted in transition state theory (TST) to estimate the self-diffusion coefficients of gas molecules such as CH4/H2 in porous frameworks, where explicit electrostatic interactions play a negligible role. However, this approach is not directly applicable to the current system due to the significant influence of coulombic interactions. Our results indicate that variations in the external potential exert a more pronounced influence on diffusion properties than on adsorption equilibria.

Reported CO2 diffusion data in MOFs remain scarce. The available literature values include direct self-diffusion data from PFG-NMR, quasi-elastic neutron scattering, and equilibrium MD, together with approximate intracrystalline diffusivities from low-loading uptake and frequency-response measurements; membrane-permeation values are treated only as transport-related references. As shown in Fig. 5a (Table S10), including framework–adsorbate electrostatics generally shifts the predicted CO2 diffusivities toward the literature-reported range, whereas neglecting these interactions tends to overestimate diffusivity. A notable exception is Mg-MOF-74, where the QcDFT prediction underestimates the experimental value by an order of magnitude, which we attribute to framework flexibility. This observation aligns with prior reports that rigid framework models can underestimate diffusivity by an order of magnitude compared with flexible simulations.54 Given the differences in diffusion definitions and measurement conditions, Fig. 5a is interpreted semiquantitatively at the order-of-magnitude level rather than as a strict same-condition benchmark.

Fig. 5. Prediction of CO2 diffusion coefficients in MOFs. (a) Comparison of CO2 diffusion coefficients predicted by the string method using external potentials from DM-cDFT and QcDFT against experimental data, detailed in Table S10. (b) Effect of electrostatic interactions on the diffusion energy barrier profile in MOF-5. CO2 adsorption density distributions in MOF-5 derived from (c) QcDFT and (d) DM-cDFT calculations.

Fig. 5

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Fig. 5b illustrates the energy barriers along the diffusion pathway in MOF-5 with and without electrostatic interactions. The inclusion of electrostatics introduces deeper potential wells that enhance adsorption but also require molecules to overcome higher energy barriers, thereby moderately suppressing diffusion rates. This effect is further corroborated by the adsorption density distributions shown in Fig. 5c (with charge) and Fig. 5d (without charge), where a more localized, condensed adsorbate configuration is evident in the former. To further validate the QcDFT approach, we compared the String/TST migration barriers with Arrhenius activation energies obtained from three independently equilibrated 10 ns MD trajectories at 250, 298, 350, and 400 K, using identical rigid framework structures, UFF Lennard-Jones parameters, DDEC charges, and the same charged three-site CO2 model (Fig. S22, S23 and Tables S11, S12). The agreement in the activation barriers and temperature-dependent trends supports the use of the QcDFT-derived external potential for dilute-limit migration-barrier and qualitative trend analysis.

Computational cost comparison

In the context of automated design for materials, which includes both forward and inverse design approaches, the generation and validation of large-scale datasets are essential components. The computational cost of property evaluation serves as a critical determinant of the overall discovery throughput. Our high-throughput benchmarking demonstrates that QcDFT achieves average computation time of approximately 8 minutes for single-component CO2 systems and 31 minutes for binary gas mixtures using a nominal target grid spacing of 0.5 Å subject to a 60 × 60 × 60 grid cap, as shown in Fig. 6, with all computations performed on a single core of an AMD EPYC 9654 processor. This represents nearly a hundredfold efficiency improvement vs. the 2-days requirement for single-gas adsorption using GCMC simulations.12 Furthermore, when combined with TST, the string method provides a 2–3 order of magnitude acceleration over MD for diffusion coefficient estimation, with all computations executed on an NVIDIA GeForce RTX 4090 where a single task completes in approximately 5 minutes.

Fig. 6. Relationship between QcDFT computational efficiency and system size for single-component and binary gas mixtures.

Fig. 6

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Notably, the computational expense of QcDFT shows a super-linear correlation with materials system size, contrasting with conventional computational scaling expectations.12 This distinction can be attributed to two main factors. Firstly, materials dimensions do not directly correlate with system density, and increased framework atom counts require more extensive computation of framework–gas interactions; second, materials with complex chemical environments, particularly those containing multiple elements, produce intricate variations in the external potential that significantly increase the iterative computational workload during the optimization of grand potential. Finally, the smoothing effect of Ewald's Fourier-space representation guides iterations more directly toward the true solution, reducing convergence steps.

Discussion

This work presents a reliable and efficient computational framework for assessing materials performance in gas separation by incorporating Coulomb interactions into cDFT. The developed approach, termed QcDFT, enables high-throughput prediction of key thermodynamic properties, including adsorption selectivity and Henry coefficients, while its derived external potential, combined with the string method, facilitates the determination of diffusion coefficients for gases exhibiting pronounced electrostatic interactions. The method achieves a thousandfold acceleration in computational efficiency relative to conventional molecular simulations, while improving agreement with molecular-simulation results relative to previous cDFT variants in the present benchmark. Moreover, QcDFT is compatible with standard force field and point charge model. Notably, the weaker sensitivity of weakly multipolar adsorption to long-range interactions compared with diffusion permits the decoupling of initial screening from computationally demanding long-range calculations, significantly reducing overall computational cost.

The controlled binary comparisons further establish QcDFT as a high-throughput method for electrostatics-sensitive mixture screening. Across three experimentally relevant compositions and nine pressures, QcDFT preserved the broad GCMC material ordering (Spearman ρ = 0.76–0.98), with typical rank differences of only one to two positions. Larger high-pressure deviations in narrow pores reflect the coarse-grained excess treatment, but these localized deviations did not obscure the broader ranking trends. QcDFT therefore occupies a practical intermediate position between lower-resolution cDFT and fully molecular GCMC/MDFT, retaining site-resolved framework–adsorbate electrostatics at substantially lower computational cost. This combination enables rapid prioritization of rigid porous materials across diverse chemistries and pore sizes.

Despite these advantages, QcDFT shares a common limitation with many molecular simulation techniques in that accounting for framework flexibility remains computationally challenging, especially for high-throughput screening where multiple flexible conformations (e.g., pore breathing, hinge bending) cannot be easily sampled. Therefore, the present high-throughput results should be interpreted as rigid-framework screening predictions, with materials of known or suspected flexibility should be flagged for follow-up flexible-framework simulations or experimental validation, as exemplified by the literature-identified subset of guest-responsive CoRE MOF 2019-ASR frameworks summarized in Table S13. While general solutions for incorporating flexibility remain challenging within classical frameworks, recent advances in machine-learned force fields offer a promising direction. Specifically, for promising candidate materials or those where framework flexibility is expected to significantly affect adsorption, integrating QcDFT with structural snapshots derived from molecular dynamics simulations using machine-learned potentials may provide an effective strategy to mitigate this limitation.54 Notwithstanding current constraints, QcDFT establishes itself as a promising theoretical framework for the rapid assessment of gas separation performance. With its demonstrated computational efficiency and improved agreement relative to previous cDFT variants, QcDFT is well suited for integration into automated materials-discovery workflows as a rapid screening and mechanistic-analysis tool. This integration holds the potential to accelerate materials discovery, deepen mechanistic understanding, and enable the rational design of next-generation separation materials.

Author contributions

Yong Qiu: conceptualization, methodology, software, investigation, formal analysis, writing – original draft. Yu Liu: writing – review & editing, software. Weiqiang Tang: writing – review & editing. Zhen Zhou: funding acquisition, supervision. Yun Tian: conceptualization, methodology, supervision, writing – review & editing, funding acquisition. All authors discussed the results and approved the final manuscript.

Conflicts of interest

There are no conflicts to declare.

Supplementary Material

SC-OLF-D6SC04283J-s001

Acknowledgments

This work was supported by National Natural Science Foundation of China (No. 22478361) and Natural Science Foundation of Henan Province (No. 252300421176). The computations were performed at National Supercomputing Center in Zhengzhou, China. We extend our sincere appreciation to Dr Zhao Li (Purdue University) for constructive discussion on encoding electrostatic interactions into current cDFT framework, to Dr Vincent Dufour-Décieux for their insights into cDFT methodology development.

Data availability

The details of the computational methods used in this study are described in the supplementary information (SI). The Zenodo archives contain QcDFT source code, example input files, screened MOF identifiers, GCMC reference data, database-level QcDFT performance tables, trained machine-learning models, and source files used for figure generation and mechanistic analyses. The archives are available at https://doi.org/10.5281/zenodo.20027280. Supplementary information is available. See DOI: https://doi.org/10.1039/d6sc04283j.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

SC-OLF-D6SC04283J-s001
SC-OLF-D6SC04283J-s001.pdf (6.3MB, pdf)

Data Availability Statement

The details of the computational methods used in this study are described in the supplementary information (SI). The Zenodo archives contain QcDFT source code, example input files, screened MOF identifiers, GCMC reference data, database-level QcDFT performance tables, trained machine-learning models, and source files used for figure generation and mechanistic analyses. The archives are available at https://doi.org/10.5281/zenodo.20027280. Supplementary information is available. See DOI: https://doi.org/10.1039/d6sc04283j.

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