Interaction topology theory deciphers multiscale codes of MOF-like materials

Impact of Metal Heterogeneity on Multivariate and High-Entropy MOF SBUs.

In chemically complex multimetal systems, how local coordination asymmetry emerges and propagates to define the bulk structural behavior remains fundamentally unresolved. In high-entropy metal-organic frameworks (MOFs), long-range crystallographic order coexists with intrinsic chemical disorder, yet a quantitative relationship among metal identity, local coordination geometry, and lattice-scale response has not been established. Here, we demonstrate that metal heterogeneity induces well-defined, composition-dependent distortions within trinuclear secondary building units (SBUs), which propagate coherently to produce measurable lattice-level structural changes. Using a porphyrinic TCPP framework with conserved topology, metal identity was varied across mono-, bi-, tri-, and five-metal compositions containing Fe, Co, Ni, Cu, and Zn. Nearly 20 compositions and ∼50 element-specific extended X-ray absorption fine structure (EXAFS) measurements provide metal-dependent bond-distance references across the full series. Single- and bimetallic references resolve M-O, M-C, and M-M distances, showing that heterometal substitution generates asymmetric, occupancy-dependent node distortions. In tri- and five-metal compositions, EXAFS signatures remain distributed rather than collapsing to a single averaged geometry, indicating persistent local heterogeneity within the conserved framework. These local distortions correlate with reproducible, composition-dependent lattice-parameter shifts while retaining long-range order. Time-resolved X-ray diffraction (XRD) and inductively coupled plasma mass spectrometry (ICP-MS) further reveal dynamic, metal-dependent incorporation during framework formation, while molecular dynamics (MD) simulations identify metal-nitrate binding and precursor lability as descriptors that rationalize early incorporation and late substitution trends. Together, these results provide an experimentally anchored framework for connecting metal identity, local coordination asymmetry, lattice response, and time-dependent incorporation in multivariate and high-entropy MOFs.

Building atomistic models of heterointerfaces with optimal transport

Heterogeneous interfaces underpin technologies from microelectronics to energy conversion and storage, but their configurational complexity precludes exhaustive first-principles screening of interface registries. Although data-driven approaches can alleviate this burden, they remain limited by sparse interface datasets. Here, we introduce an energy-independent workflow that represents coherent interfaces as attributed graphs, quantifies their similarity to parent bulk environments using the fused Gromov-Wasserstein (FGW) distance, and couples this metric with Bayesian optimization over the in-plane registry space. We assess the approach for KI/NaCl, GaP/GaAs and GaN/$\mathrm{Al_{2}O_{3}}$ interfaces spanning ionic, covalent and mixed-bonding regimes, using hierarchical validation with MACE and density functional theory (DFT). Comparison with single-point energy landscapes shows that the FGW distance captures registry-dependent periodicity, while interfaces exhibit deviations between structural and energetic extrema, reflecting additional chemistry-specific contributions. Furthermore, FGW distances show an overall association with relaxed energies. Under limited screening budgets, FGW-guided registry selection consistently outperforms random search and is more robust across interface systems than selection guided by pretrained MACE energies. The workflow converts the qualitative notion of bulk-like continuity into a quantitative prescreening criterion, enabling efficient registry exploration and providing physically informed candidate structures for materials discovery workflows.

Multiple-Kernel Ridge Regression for Learning the Structure-Electronic Property Relationships of Pyranoazacoronene COFs

Covalent organic frameworks (COFs) are highly ordered, porous organic materials whose reticular construction from tailored nodes and linkers enables atomic-level control over structure and function. The design space of COFs is vast with virtually unlimited combinations of nodes, linkers, and functional groups. Interpretable machine learning (ML) offers a pathway to navigate this complexity by identifying the structural features that govern materials performance, yet interpretability often comes at the cost of predictive accuracy. In this work, we introduce a novel multiple-kernel learning framework that achieves both accuracy and mechanistic insight. A multiple-kernel ridge regression (MKRR) model was trained on band gaps predicted from GFN1-xTB level theory for a data set of 232 theoretical pyranoazacoronene (PAC) COFs produced from eight different conjugated linkers and 29 functional groups. Modifying these building units alone produced a range of band gaps between 0.4–2 eV. Manual analysis of the theoretical band gaps versus the linker indicates that breaking the conjugation pathway by altering the bond angle or by introducing a σ-bond increases the band gap while increasing the length of the linker decreases the band gap. All functional groups appear to reduce the band gap with three specific electron withdrawing groups reducing the band gap near 0.4 eV. For the ML, the building units were represented with three independent kernels that encoded the local environments of each node, linker, and functional group calculated from the Smooth Overlap of Atomic Positions (SOAP). After decomposing each kernel’s contribution to the model’s global predictions, we found that the MKRR model successfully captures the underlying structure–property relationships that influence the band gap. These results demonstrate that MKRR is an effective and interpretable framework for understanding and designing functional COFs.

Interpretable Nanoporous Materials Design with Equivariant Networks

A new family of hollow Au60 cages: topological diversity and connectivity-driven stability.

Hollow gold nanoclusters are nanoscale systems in which relativistic effects, coordination, topology, and thermal fluctuations compete to determine structural stability. Here, we combine density functional theory, descriptor-based machine-learning-assisted analysis, and finite-temperature molecular dynamics to investigate Au60 hollow cages. We generate 30 new neutral Au60 hollow isomers from different topological seeds and analyze them together with the previously reported I-Au60 cage. Their energetics are assessed at the PBE, PBE + SOC, and PBE + SOC + D3 levels. Low-symmetry cages with compact coordination environments are found to be significantly more stable than the fullerene-like I structure, which lies in the high-energy tail of the hollow landscape. Dispersion corrections further penalize under-connected or perforated motifs, several of which undergo partial closure toward more locally packed and less porous arrangements. Descriptor-based analysis shows that stability correlates primarily with network connectivity and local coordination, rather than with spherical character, global symmetry, frontier electronic gaps, or chirality. In particular, leave-one-out regression identifies the average coordination number as the dominant descriptor of relative stability. Finite-temperature simulations reveal a clear hierarchy of thermal robustness: highly connected cages remain metastable up to, and in some cases above, room temperature, whereas the I cage and strongly perforated motifs reconstruct early. These results show that connectivity and mechanical adaptability, rather than maximal symmetry, are the key ingredients for stabilizing hollow Au60 cages.

Data-driven Design of Metal-Organic Frameworks with Tunable Negative Thermal Expansion

Materials with negative thermal expansion (NTE) are essential for applications requiring precise control of thermal expansion. Owing to their exceptional chemical tunability, flexible architectures, and low-energy lattice vibrations, metal-organic frameworks (MOFs) represent a rich platform for exploring NTE. However, uncovering the structural motifs that govern NTE across the enormous MOF design space remains experimentally challenging, and large-scale first-principles phonon calculations are computationally prohibitive. Here, we comprehensively evaluate the factors influencing NTE in MOFs by utilizing a high-throughput workflow based on MACE-MP-MOF0, a machine learning interatomic potential fine-tuned for MOFs with near-ab initio accuracy, to construct PhononMOFdb, a database of phonons, inelastic neutron scattering spectra, bulk moduli, and heat capacities for over 12,000 MOFs. High-throughput screening of this database reveals that highly porous cubic topology frameworks with heavier, lower-valent metal nodes favor strong NTE, while linker functionalization provides a practical handle for tuning NTE magnitude and sign without compromising mechanical stability. Experimental validation via high-resolution temperature-dependent synchrotron powder X-ray diffraction on the Ce-UiO-66 MOF and its brominated variants confirms the design recipe and yields volumetric NTE coefficients surpassing current records. This work establishes a data-driven strategy for engineering NTE in MOFs, showing how machine learning-accelerated discovery and targeted experimental validation together unlock predictive materials design.