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Predictive molecular simulations require fast, accurate and reactive interatomic potentials. Machine learning offers a promising approach to construct such potentials by fitting energies and forces to high-level quantum-mechanical data, but doing so typically requires considerable human intervention and data volume. Here we show that, by leveraging hierarchical and active learning, accurate Gaussian Approximation Potential (GAP) models can be developed for diverse chemical systems in an autonomous manner, requiring only hundreds to a few thousand energy and gradient evaluations on a reference potential-energy surface. The approach uses separate intra- and inter-molecular fits and employs a prospective error metric to assess the accuracy of the potentials. We demonstrate applications to a range of molecular systems with relevance to computational organic chemistry: ranging from bulk solvents, a solvated metal ion and a metallocage onwards to chemical reactivity, including a bifurcating Diels–Alder reaction in the gas phase and non-equilibrium dynamics (a model SN2 reaction) in explicit solvent. The method provides a route to routinely generating machine-learned force fields for reactive molecular systems., An efficient strategy for training Gaussian Approximation Potential (GAP) models to study chemical reactions using hierarchical and active learning.

Two-dimensionally extended amorphous carbon ("amorphous graphene") is a prototype system for disorder in 2D, showing a rich and complex configurational space that is yet to be fully understood. Here we explore the nature of amorphous graphene with an atomistic machine-learning (ML) model. We create structural models by introducing defects into ordered graphene through Monte-Carlo bond switching, defining acceptance criteria using the machine-learned local, atomic energies associated with a defect, as well as the nearest-neighbor (NN) environments. We find that physically meaningful structural models arise from ML atomic energies in this way, ranging from continuous random networks to paracrystalline structures. Our results show that ML atomic energies can be used to guide Monte-Carlo structural searches in principle, and that their predictions of local stability can be linked to short- and medium-range order in amorphous graphene. We expect that the former point will be relevant more generally to the study of amorphous materials, and that the latter has wider implications for the interpretation of ML potential models.

Phosphide-based materials have been investigated as promising candidates for solid electrolytes, among which the recently reported Li9AlP4 displays an ionic conductivity of 3 mS cm-1. While the phases Li-Al-P and Li-Ga-P have already been investigated, no ternary indium-based phosphide has been reported up to now. Here, we describe the synthesis and characterization of the first lithium phosphidoindate Li3InP2, which is easily accessible via ball milling of the elements and subsequent annealing. Li3InP2 crystallizes in the tetragonal space group I41/acd with lattice parameters of a = 12.0007(2) and c = 23.917(5) A, featuring a supertetrahedral polyanionic framework of interconnected InP4 tetrahedra. All lithium atoms occupy tetrahedral voids with no partial occupation. Remarkably, Li3InP2 is not isotypic to the previously reported homologues Li3AlP2 and Li3GaP2, which both crystallize in the space group Cmce and feature 2D layers of connected tetrahedra but no supertetrahedral framework. DFT computations support the observed stability of Li3InP2. A detailed geometrical analysis leads to a more general insight into the structural factors governing lithium ion mobility in phosphide-based materials: in the non-ionic conducting Li3InP2 the Li ions exclusively occupy tetrahedral voids in the distorted close packing of P atoms, whereas partially filled octahedral voids are present in the moderate ionic conductors Li2SiP2 and Li2GeP2.

Phosphide-based materials have been investigated as promising candidates for solid electrolytes, among which the recently reported Li9AlP4 displays an ionic conductivity of 3 mS cm−1. While the phases Li–Al–P and Li–Ga–P have already been investigated, no ternary indium-based phosphide has been reported up to now. Here, we describe the synthesis and characterization of the first lithium phosphidoindate Li3InP2, which is easily accessible via ball milling of the elements and subsequent annealing. Li3InP2 crystallizes in the tetragonal space group I41/acd with lattice parameters of a = 12.0007(2) and c = 23.917(5) Å, featuring a supertetrahedral polyanionic framework of interconnected InP4 tetrahedra. All lithium atoms occupy tetrahedral voids with no partial occupation. Remarkably, Li3InP2 is not isotypic to the previously reported homologues Li3AlP2 and Li3GaP2, which both crystallize in the space group Cmce and feature 2D layers of connected tetrahedra but no supertetrahedral framework. DFT computations support the observed stability of Li3InP2. A detailed geometrical analysis leads to a more general insight into the structural factors governing lithium ion mobility in phosphide-based materials: in the non-ionic conducting Li3InP2 the Li ions exclusively occupy tetrahedral voids in the distorted close packing of P atoms, whereas partially filled octahedral voids are present in the moderate ionic conductors Li2SiP2 and Li2GeP2., Li3InP2 exhibits a polyanionic framework of corner-sharing InP4 tetrahedra and DFT computations reveal the stability trend for indium in the tetragonal structure compared to the orthorhombic structure of the lighter homologues.

Much of our understanding of complex structures is based on simplification: for example, metal–organic frameworks are often discussed in the context of “nodes” and “linkers”, allowing for a qualitative comparison with simpler inorganic structures. Here we show how such an understanding can be obtained in a systematic and quantitative framework, combining atom-density based similarity (kernel) functions and unsupervised machine learning with the long-standing idea of “coarse-graining” atomic structure. We demonstrate how the latter enables a comparison of vastly different chemical systems, and we use it to create a unified, two-dimensional structure map of experimentally known tetrahedral AB2 networks – including clathrate hydrates, zeolitic imidazolate frameworks (ZIFs), and diverse inorganic phases. The structural relationships that emerge can then be linked to microscopic properties of interest, which we exemplify for structural heterogeneity and tetrahedral density., A coarse-graining approach enables structural comparisons across vastly different chemical spaces, from inorganic polymorphs to hybrid framework materials.