Computational modeling of physical processes in metal-organic frameworks (MOFs) is highly challenging due to the presence of spatial heterogeneities and complex operating conditions which affect their behavior. Density functional theory (DFT) may describe interatomic interactions at the quantum mechanical level, but is computationally too expensive for systems beyond the nanometer and picosecond range. Herein, we propose an incremental learning scheme to construct accurate and data-efficient machine learning potentials for MOFs. The scheme builds on the power of equivariant neural network potentials in combination with parallelized enhanced sampling and on-the-fly training to simultaneously explore and learn the phase space in an iterative manner. With only a few hundred single-point DFT evaluations per material, accurate and transferable potentials are obtained, even for flexible frameworks with multiple structurally different phases. The incremental learning scheme is universally applicable and may pave the way to model framework materials in larger spatiotemporal windows with higher accuracy.

Metal-organic frameworks (MOFs) are hybrid materials constructed from metal clusters linked by organic linkers, which can be engineered for target functional applications in, for example, catalysis, sensing, and storage. The dynamic response of MOFs on external stimuli can be tuned by spatial heterogeneities such as defects and crystal size as well as by operating conditions such as temperature, pressure, moisture, and external fields. Modeling the spatiotemporal evolution of MOFs under operating conditions and at length and time scales comparable with experimental observations is extremely challenging. Herein, we give a status on modeling spatiotemporal processes in MOFs under working conditions and reflect on how modeling can be reconciled with in situ spectroscopy measurements. HighlightsMetal-organic frameworks (MOFs) can respond in an anomalous way to external stimuli, giving rise to dynamic bond rearrangement and/or large-amplitude structural transformations without breakage of the crystal.

While metal halide perovskites (MHPs) have shown great potential for various optoelectronic applications, their widespread adoption in commercial photovoltaic cells or photosensors is currently restricted, given that MHPs such as CsPbI3 and FAPbI3 spontaneously transition to an optically inactive nonperovskite phase at ambient conditions. Herein, we put forward an accurate first-principles procedure to obtain fundamental insight into this phase stability conundrum. To this end, we computationally predict the Helmholtz free energy, composed of the electronic ground state energy and thermal corrections, as this is the fundamental quantity describing the phase stability in polymorphic materials. By adopting the random phase approximation method as a wave function-based method that intrinsically accounts for many-body electron correlation effects as a benchmark for the ground state energy, we validate the performance of different exchange-correlation functionals and dispersion methods. The thermal corrections, accessed through the vibrational density of states, are accessed through molecular dynamics simulations, using a phase-transferable machine learning potential to accurately account for the MHPs’ anharmonicity and mitigate size effects. The here proposed procedure is critically validated on CsPbI3, which is a challenging material as its phase stability changes slowly with varying temperature. We demonstrate that our procedure is essential to reproduce the experimental transition temperature, as choosing an inadequate functional can easily miss the transition temperature by more than 100 K. These results demonstrate that the here validated methodology is ideally suited to understand how factors such as strain engineering, surface functionalization, or compositional engineering could help to phase-stabilize MHPs for targeted applications.

Soft porous crystals have the ability to undergo large structural transformations upon exposure to external stimuli while maintaining their long-range structural order, and the size of the crystal plays an important role in this flexible behavior. Computational modeling has the potential to unravel mechanistic details of these phase transitions, provided that the models are representative for experimental crystal sizes and allow for spatially disordered phenomena to occur. Here, we take a major step forward and enable simulations of metal-organic frameworks containing more than a million atoms. This is achieved by exploiting the massive parallelism of state-of-the-art GPUs using the OpenMM software package, for which we developed a new pressure control algorithm that allows for fully anisotropic unit cell fluctuations. As a proof of concept, we study the transition mechanism in MIL-53(Al) under various external pressures. In the lower pressure regime, a layer-by-layer mechanism is observed, while at higher pressures, the transition is initiated at discrete nucleation points and temporarily induces various domains in both the open and closed pore phases. The presented workflow opens the possibility to deduce transition mechanism diagrams for soft porous crystals in terms of the crystal size and the strength of the external stimulus.