Metal-organic frameworks (MOFs) are a class of porous hybrid materials with diverse applications in catalysis, gas storage, separation, electronic devices, and drug delivery. The vast number of possible MOF structures and the challenges in experimental characterization necessitate accurate and efficient computational methods. Ab-initio methods like density functional theory (DFT) are often too computationally expensive, especially for dynamic properties. Classical force field potentials (FFPs) offer speed but lack accuracy. Transferable force fields like Dreiding and UFF4MOF, while easy to use, show significant errors in predicting dynamic properties. More advanced potentials, such as GAFF, COMPASS, and MOF-FF, provide improved accuracy for specific materials classes but still struggle with vibrational properties and require extensive, often cumbersome, system-specific parametrization. ReaxFF offers flexibility but often compromises on accuracy. Machine-learned potentials (MLPs) have emerged as a promising alternative, offering accuracy comparable to DFT while improving computational efficiency, however, their application to MOFs has been limited and often requires extensive DFT reference data. This study aims to address the efficient use of MLPs for MOF modeling, focusing on VASP MLPs and MTPs, to improve the computational modeling of structural and dynamic MOF properties.

The literature review extensively examines existing force field potentials used for MOF simulations. It highlights the limitations of transferable force fields like Dreiding and UFF4MOF, which, despite their ease of use, often produce significant errors in predicting dynamic properties. More advanced potentials, such as GAFF, COMPASS, and MOF-FF, provide improved accuracy but lack transferability and require considerable effort for system-specific parameterization. The review then transitions to machine-learned potentials (MLPs), showcasing their potential for achieving DFT-level accuracy with enhanced efficiency. However, the review notes that the application of MLPs to MOFs has been limited and often requires a large number of DFT reference data for training. The need for efficient sampling techniques and optimized parametrization strategies is emphasized.

The proposed approach employs active learning strategies to generate reference configurations for training the machine-learned potentials. The VASP code's active learning approach dynamically expands the basis set during molecular dynamics (MD) simulations. When the Bayesian error of the forces exceeds a threshold, DFT calculations are performed to update the reference data and refine the potential. The threshold is adjusted dynamically to account for temperature variations. Moment tensor potentials (MTPs) are used in conjunction with the VASP MLPs. MTPs, implemented in MLIP, use a fixed basis set and are readily parameterized. The study utilizes DFT (PBE functional with D3 correction) to generate reference data. The MOFs studied include MOF-5, UiO-66, MOF-74, and both the large and narrow pore phases of MIL-53. Both the number of atom types (full separation vs. single type per element) and the size of the reference data sets were investigated to assess the trade-off between accuracy and computational cost. For MTPs, the level and radial basis set size were varied to explore the accuracy-speed relationship. Benchmarking included unit cell parameters, energies, forces, stresses, elastic constants, thermal expansion coefficients, and thermal conductivities. Phonon band structures and densities of states were calculated to assess vibrational properties. Non-equilibrium molecular dynamics (NEMD) and approach-to-equilibrium molecular dynamics (AEMD) were used to calculate thermal conductivity, and finite size effects were addressed through extrapolation techniques. A comparison with UFF4MOF and MOF-FF served as a baseline.

The developed MLFFs (MTPs and VASP MLPs) demonstrated exceptional accuracy in predicting various properties of the studied MOFs. Unit cell volumes showed deviations of less than 0.2% from DFT for isotropic systems, significantly outperforming UFF4MOF. Even for anisotropic systems, the deviations remained small (around 0.3%). Excellent agreement was observed for energies, forces, and stresses in validation sets, with errors for MLFFs being two orders of magnitude lower than those obtained from UFF4MOF. Phonon band structures and densities of states were accurately reproduced, showcasing the MLFFs ability to capture vibrational properties that are crucial for various material characteristics. Elastic constants were also predicted with high accuracy, showing significant improvement over UFF4MOF. Importantly, the thermal conductivity of MOF-5, calculated using the MTPs, was found to be in full quantitative agreement with experimental data (0.32 W(mK)⁻¹), substantially better than results from UFF4MOF and MOF-FF. Thermal expansion coefficients showed more variability, with improved agreement for MOF-5 but larger deviations for MOF-74 compared to experimental results. The MTPs exhibited a good accuracy-to-cost ratio, with higher levels offering superior accuracy but slower speeds. VASP MLPs showed similar accuracy to high-level MTPs but were generally slower. The study explores the effect of the number of atom types in the parametrization and reveals that including the separation of atom types in chemically different environments improves the accuracy of the MTPs more significantly than that of VASP MLPs.

The findings demonstrate the superiority of the developed MLFFs (MTPs and VASP MLPs) over traditional force fields in accurately predicting various properties of MOFs. The near-DFT accuracy achieved, particularly in predicting dynamic properties such as phonon band structures and thermal conductivity, highlights the potential of MLFFs for investigating complex MOF behaviors. The exceptional agreement with experimental thermal conductivity data for MOF-5 validates the approach's reliability. The observed discrepancies in thermal expansion coefficients suggest a potential limitation, possibly related to the accuracy of the DFT methodology used to generate reference data or inherent to the MOF system itself. The relatively good performance of MTPs and their tunable accuracy-speed trade-off makes them a valuable tool for large-scale simulations. The higher computational cost associated with VASP MLPs needs to be considered, particularly for large systems. Overall, these results significantly advance computational MOF modeling, particularly concerning dynamical properties that are challenging for conventional DFT-based techniques.

This study presents a highly effective approach for generating accurate and efficient machine-learned force fields for MOFs, combining the VASP active learning strategy with the flexible MTPs and VASP MLPs. The exceptional accuracy and efficiency of the resulting MLFFs significantly improve the computational modeling of MOFs, especially for dynamic properties. Future research can focus on refining the training procedures to improve the description of thermal expansion and further enhance the long-term stability of the MTPs, potentially by exploring different data sampling strategies or adding specific potential terms. The development of enhanced parallelization techniques for the VASP MLPs could also boost their efficiency and competitiveness with MTPs.

The study primarily focuses on chemically stable and homogeneous MOFs, excluding phenomena like chemical reactions or the diffusion of guest molecules. The comparison of thermal expansion coefficients with experimental data is hindered by uncertainties in both experimental and DFT-calculated values. Some challenges in obtaining thermally stable MTPs for certain systems were also encountered, which were addressed through dedicated high-temperature training runs. The computational efficiency analysis is limited to the specific force field implementations and hardware used in the study, and might not represent all possibilities.