Screening 39 billion protostructures for materials discovery

TL;DR

This work tackles the vast combinatorial space of inorganic crystal structures by a two-stage strategy: coarse-grained protostructure enumeration constrained by Wyckoff complexity, followed by fine-grained symmetry-aware relaxation using MLIPs. By exhaustively enumerating ~ $39$ billion protostructures and prescreening to ~ $15$ million candidates with a Wren-based convex hull, the authors realize $81$ million relaxed crystal structures across $4495$ phase diagrams, uncovering $88{,}498$ novel prototypes. Validation on well-studied systems (Hf-Zn-N, Ti-Zn-N, Zr-Zn-N) and broader comparison against the Alexandria dataset demonstrate robust recovery rates and reasonable DFT-consistency, with a mean absolute error of $~33$ meV/atom between MLIP and DFT results. The resulting large, structured dataset and scalable workflow offer a practical path to systematic materials discovery and expansion of structural diversity beyond existing databases, enabling rapid downstream property evaluation and design.

Abstract

Large-scale computational surveys are increasingly used to map the landscape of stable crystalline materials. We report a high-throughput energy screening of inorganic crystals that enumerates binary and ternary compositions up to a specified unit-cell complexity, yielding 39 billion protostructures. Candidates predicted to lie on or near the convex hull are retained, and their degrees of freedom are explored via Latin hypercube sampling followed by relaxation with machine-learned interatomic potentials. The resulting dataset contains 81 million locally relaxed crystal structures spanning 4495 ternary phase diagrams constructed from elements ranging from lithium to bromine and contains 88,498 crystal prototypes not present in existing crystal-structure databases. The methods are validated both for three well-explored materials systems, Zr-Zn-N, Ti-Zn-N, and Hf-Zn-N, and by comparing with known data for structures resulting from the larger screening. The work provides a systematic map of low-energy compositional-structural space and a large, structured pool of candidates for downstream property evaluation and materials design.

Figures (7)

• Figure 1: Illustrated workflow: (a) We systematically enumerate over 39 billion protostructures for binary and ternary compounds with elements from lithium to bromine; (b) Using an updated version of Wren, an ML model trained on the Alexandria database, we construct a prescreen-level convex hull of thermodynamical stability which allows us to identify 0.04% of the protostructures as relevant for the next screening stage; (c) Each of the remaining protostructures are concretized as multiple crystal structures, and the MACE and ORB MLIPs are used to identify local minima, producing 81 million optimized structures; (d) From these structures a cumulated "web" of 4495 ternary phase diagrams is constructed. Each yellow star in the phase diagrams represents a structure whose protostructure label is not part of the Alexandria dataset, but is predicted to be stable by our workflow; (e) The phase diagrams allow the identification of 456,110 structures with a decomposition enthalpy below 100 meV/atom of the convex hull of thermodynamical stability and spans 88,498 new prototypes not in Alexandria or the GNoME data set Merchant2023. The Venn diagrams show the number of prototypes in the different sets within the same structural limits, 5 atoms in the asymmetric unit and 64 atoms in the unit cell, to show the large structural diversity resulting from our screening.
• Figure 2: Distribution of ordered crystal structures with space group $> 2$ in the ICSD over structural complexity (the number of atoms in the asymmetric unit). A log-log plot is used to show the long tail nature of the distribution. If these structures, sourced from publications, are representative of the space of discoverable crystal structures, it appears complexities up to just five cover more than half of the complete relevant structural space, i.e., the level exhaustively explored in this work. Extending our approach within reasonable levels of computational expense should allow reaching at least $80-90\%$.
• Figure 3: Validation for the materials systems Hf-Zn-N, Ti-Zn-N, Zr-Zn-N with columns: Prescreening for phase diagrams from enumeration and prescreening-level ML formation energy predictions; Standard for the standard level of our second stage of concretization and MLIP-relaxation; Refined for extended concretization beyond 5000 structures per phase diagram; Alexandria for the well-explored diagrams from structures known before this work. Phases in Alexandria not found by our workflow are shown as black x and a phase in Alexandria offset by the changes in thermodynamical stability due to our new phases is shown as a black dot. New phases not in Alexandria are shown as yellow stars.
• Figure 4: Large-scale screening outcome and error analysis: (a) Comparison of the number of unique structures discovered in our screening (red squares) out of all we identified (green circles) vs. the number of structures known in Alexandria within the screened chemical space, but with no other limits on complexity or number of atoms (gray triangles). The graphs show the cumulative count of structures with a decomposition enthalpy $H_d$below the value shown on the x-axis. It is common to consider structures with a $H_d$ below $50-100\ \mathrm{meV/atom}$ as relevant, to accommodate the accuracy of the underlying DFT computations and the possibility for metastability Bartel2019.Unique structures are structures whose protostructures are not in Alexandria, and for which $H_d \leq 100\ \mathrm{meV/atom}$ relative to the convex hull of stability of the union of our structures and Alexandria. For the full range up to $100\ \mathrm{meV/atom}$, we discovered 456,110 materials spanning 91,295 new prototypes; (b) An error analysis for the predicted materials also present in Alexandria.
• Figure S1: Recovery of stable phases from the Alexandria dataset using Wren screening. The plots show the cumulative fraction of Alexandria-stable phases (with complexity $\leq 5$ and $\leq 64$ atoms per cell) recovered as a function of the number of Wren-predicted candidates screened per system, ranked by energy above the Wren convex hull. With a screening budget of 5,000 candidates per system, 83.6% of the restricted-Alexandria stable phases are recovered.