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Crystal-structure design by agentic AI in a language of motifs

Dinh-Khiet Le, Minh-Quyet Ha, Hong-Phuc Vu-Dinh, Takashi Miyake, Hiori Kino, Hieu-Chi Dam

arXiv:2608.15900v1cond-mat.mtrl-scics.LG

TL;DR

Materials discovery remains slow and costly, while computational approaches often struggle to reach new crystal structure types. MatEvolve evolves interpretable motif profiles, edits them to generate crystals, and validates candidates from first principles. On rare-earth-lean permanent magnets, it matched a generative model on the target property while reaching new structural prototypes far more often.

  • Problem

    Materials discovery remains slow and costly because candidate structures are vast and experimentally expensive to synthesize and characterize.

  • Method

    MatEvolve evolves human-readable motif profiles, edits them to generate offspring crystals, and validates top-ranked candidates using first-principles calculations.

  • Results

    On rare-earth-lean permanent magnets, MatEvolve matched a magnetization-conditioned generative model on the target property and reached new structural prototypes far more often.

  • Takeaways & Limitations

    The motif-editing loop offers an interpretable and transferable complement to task-trained generators for designs that must be understood, checked, or reused.

  • Takeaways & Limitations

    The computational demonstration evaluates stability and saturation magnetization but not anisotropy, Curie temperature, synthesizability, or eventual usability.

Abstract

from arXiv · show

Data-driven materials discovery interpolates more reliably than it extrapolates and seldom reaches new structure types. We present MatEvolve, an agentic-AI framework designing crystals, proposing each candidate with a stated rationale and testing it. The agent reasons in an interpretable \emph{language of motifs}, writing each crystal as a \emph{motif profile} that describes the recurring geometric patterns---the \emph{motifs}---composing it. The motif profile serves not merely as a description of a material but as the medium for material design: the agent edits the profile and constructs a crystal from the modified one, and the most promising candidates are validated by first-principles calculation. Applied to the design of rare-earth-lean permanent magnets, MatEvolve---built on the state-of-the-art language model Claude Fable~5 without fine-tuning---reaches new structural prototypes more than three times as often as generative models under an equal validation budget, at a comparable on-target-magnet rate. Beyond design, analysing the discovered crystals' human-readable profiles reveals structure--property relationships.

1. Introduction · 2. Results

MatEvolve addresses poor extrapolation in materials discovery by evolving crystals through human-readable motif profiles, with agents proposing and testing edits. In rare-earth-lean magnet design, it reaches new structural prototypes substantially more often than generative models while maintaining comparable target-property performance.

  • 1. Introduction: Existing materials-discovery methods interpolate reliably but extrapolate poorly, while generators rarely reach genuinely new prototypes and provide little rationale for their proposals.Agent-based approaches instead verbalize reasoning, enabling reciprocal exchange between scientists and models.
  • 2.1. Framework overview: MatEvolve evolves crystals by recombining or mutating human-readable motif profiles, constructing candidates from edited profiles, and validating promising designs from first principles.The framework can be retargeted by restating the objective rather than re-engineering the pipeline.
  • 2.3. Structure reconstruction fidelity: 57% of 957 motif-profile reconstructions matched their original structures at conventional deep-learning evaluation tolerances.Profiles omit coordinates, lattice parameters, space groups, and structure-type labels, so reconstruction requires Text2CIF to place atoms.
  • 2.3. Structure reconstruction fidelity: 0.51 Å and 4.60 were the mean RMSD and CShM across all 957 reconstructions, remaining within notable distortion and below the breakdown boundary.Among matched reconstructions, nearly nine in ten showed no more than slight distortion.
  • 2.4. Benchmarking and discovery of new stable magnets: MatEvolve reached new structural prototypes more than three times as often as a purpose-trained generative model on an equal validation budget, without retraining its agents.Its target-magnet rate was comparable to that of a magnetization-conditioned generator.
  • 2.4. Benchmarking and discovery of new stable magnets: Of 300 validated candidates, 74 were stable or metastable, all were unique and novel against the reference set, and six lay on the convex hull with magnetization above 1 T.Among 72 property-targeted hits, 63 realized prototypes absent from both databases, while nine used known lattices with new chemistries.
  • 2.5. Structural insights into novelty and stability through motif analysis: Across 17 motif groups, stable-or-metastable fractions ranged from 57–70%, indicating that stability depended more on motif combinations than on individual geometries.Only ∼3% of observed binary and ∼2% of observed ternary combinations were unique to generated structures, so novelty mainly appeared at whole-structure level.
  • Discussion: MatEvolve’s motif-editing loop transferred to competitive magnet design using Claude Fable 5 without fine-tuning, requiring only a reset objective and revised task-specific components.The motif-editing loop itself was not tailored to magnetism.

1. Evolutionary search over motif profiles

MatEvolve performs an evolutionary search over motif profiles, iteratively translating, editing, realizing and ranking candidate crystal structures. The search begins from a seed set and proceeds for three generations.

  • Evolutionary search: The population is initialized from the seed set and evolved for three generations.Each generation selects parents from the current pool before producing and evaluating offspring.
  • Evolutionary search: Structure Translate writes selected parents as motif profiles, Structure Design edits those profiles into offspring, and the edited profiles are realized as candidate structures.The ERS then ranks the resulting candidates.

2. Structure Translate — forward translation with bidirectional-consistency enforcement

Structure Translate accepts a motif profile only when reconstructing the crystal passes bidirectional consistency checks for motif coverage and structural agreement. It iteratively revises failed translations, while rejecting profiles that cannot satisfy these checks within five rounds.

  • Structure Translate: Structure Translate maps a crystal S to a motif profile T, reconstructs S′ from T, and returns T only if the round trip validates.Otherwise, the procedure returns reject.
  • Structure Translate: Five rounds are attempted, with feedback identifying missing or spurious motifs and composition or symmetry mismatches before revision.Each round applies CIF2TEXT, TEXT2CIF, and a second CIF2TEXT pass.
  • Acceptance — round-trip fidelity: Acceptance requires both motif coverage and STRUCTUREMATCHER agreement, ensuring that the same building blocks are retained and assembled into the same structure.The checks are complementary: correct motifs can be arranged incorrectly, or coordinates can match while motifs differ.
  • Acceptance — round-trip fidelity: Motif coverage requires recall r = 1 and permits precision p ≥ 0.7, treating extra detail as benign but missing motifs as lost information.Coverage is applied first because it tests the defining building blocks directly.
  • Reconstruction fidelity: TEXT2CIF outputs are pre-relaxed with M3GNet and reduced to primitive cells before re-entering the loop, but reported Section 2.3 fidelity measures use raw outputs.Shape fidelity uses CShM, where S = 0 denotes an identical match and larger values indicate greater distortion.

3. Structure Design — offspring proposal and realization

Structure Design generates offspring by editing motif profiles through crossover or mutation, then realizes each profile as a candidate crystal. Candidates are retained only when the realized crystal contains the designed motifs, using feedback-driven retries before downstream quality evaluation.

  • Offspring proposal: The design agent proposes offspring profiles by crossing over motifs from two parents or mutating a parent’s elements or geometries.TEXT2CIF then realizes the proposed profile as candidate structure S_off.
  • Realization consistency: A candidate passes realization consistency only when CIF2TEXT rederives every designed motif with few spurious motifs.The check compares the realized crystal’s motif profile with the target profile rather than with a reference structure.
  • Realization consistency: Five attempts are allowed to realize a proposed profile, with uncovered or spurious motifs returned as feedback after failed checks.If consistency is not achieved within the retry budget, the proposal is rejected.
  • Downstream evaluation: The consistency check certifies construction from the intended motifs, while stability, novelty, and magnetism are assessed downstream by ERS.Passing realization consistency does not establish that a candidate is a good magnet.

4. Motif clustering

Motif clustering uses an agentic K-means procedure in which language-model workers assign text-based motifs to prototype groups and iteratively update those prototypes. Group merging, splitting, and creation of new groups handle ambiguity and previously uncovered geometries, with stopping based on consensus and assignment stability.

  • Method: Agentic K-means clusters text-based motifs by worker votes, representing each group with a prototype paragraph that summarizes its members.The assignment step has language-model workers vote on each motif’s best-matching group, while the update step re-summarizes each prototype.
  • Convergence: Clustering stops when mean consensus s̄ ≥ 0.8 and ARI ≥ 0.95 for two rounds, or after eight rounds.Consensus measures worker agreement, while ARI measures agreement between assignments in successive rounds.
  • Adaptive group operations: Groups merge at confusion c_gh ≥ 0.5, split when contested fraction ρ_g > 0.3, or merge instead when disagreement concentrates on one rival group.Merging requires at least three motifs; splitting addresses groups whose members disagree.
  • Adaptive group operations: 15 motifs repeatedly voted “none” trigger analysis and summarization into one or more new groups, covering geometries absent from existing clusters.These new groups enter the next clustering round.

5. Evidence-based Recommender System (ERS)

The evidence-based recommender system (ERS) provides an inexpensive, uncertainty-aware prior for ordering candidates before costly first-principles validation. It learns motif-group plausibility and substitutability from observed structures, then fuses host-based evidence to rank candidates by target likelihood.

  • Candidate prioritization: The ERS orders each generation’s candidates so costly first-principles validation begins with the most promising structures.It supplies an inexpensive, uncertainty-aware prior rather than determining stability, which remains the role of DFT.
  • Motif-set representation: Each structure is represented as the set of motif groups it contains from a 17-group vocabulary.Multiplicity, connectivity, composition, and lattice information are omitted, so the output is a prior over motif-set plausibility rather than a thermodynamic prediction.
  • Substitutability evidence: The ERS infers substitutability by comparing observed structures that share motif groups and differ in their remaining combinations.Dempster–Shafer evidence theory combines these observations into a symmetric substitutability belief for motif-combination pairs.
  • Target scoring: For each candidate, the ERS applies nonzero-belief motif substitutions to observed host structures and transfers host labels with strength equal to the substitutability belief.The remaining mass represents ignorance.
  • Evidence fusion and ranking: Candidates are ranked by descending fused mass for meeting the target, using Dempster’s rule to combine evidence from all hosts.The discount parameter is selected by grid search at α=0.1 to maximize cross-validated reproduction of observed labels, with ranking largely insensitive to it.

6. Property evaluation and first-principles validation

Property evaluation combines spin-polarized DFT relaxation with thermodynamic-stability and magnetization analyses. The workflow records relaxed structures, energies, energy above hull, and target properties for database return.

  • DFT Relaxation: Final structural optimization uses spin-polarized VASP with PBE-GGA and PAW potentials for the rare-earth–transition-metal compounds studied.The calculations use Sm_3 and Fe_pv potentials, a 520 eV plane-wave cutoff, and Γ-centered k-point meshes with KSPACING = 0.25 Å−1.
  • DFT Relaxation: Full relaxation optimizes ionic positions, cell shape, and volume until electronic and ionic convergence criteria are reached.Relaxation uses EDIFF = 10−4 eV, ED-IFFG = −10−3 eV/Å, conjugate-gradient optimization, and up to 100 ionic steps.
  • Thermodynamic Stability: Formation energy per atom and energy above the convex hull quantify candidate stability relative to elemental references and competing Materials Project phases.Positive energy-above-hull values denote metastability, whereas the hull energy is obtained from proportion-weighted formation energies at the candidate composition.
  • Magnetization Calculation: Magnetization is recalculated by combining DFT moments of non-lanthanide atoms with analytically restored lanthanide 4f moments.The correction accounts for the open-core treatment of Sm 4f electrons and their coupling to the transition-metal sublattice.

Supplementary Information · S1 CIF2Text and the motif-profile representation

MatEvolve represents crystals as human-readable motif profiles that capture recurring geometric structures and support both crystal reconstruction and structure–property reasoning. CIF2Text extracts motifs from CIF files, then standardizes them into a geometry-only controlled vocabulary for matching, clustering, and downstream design.

  • Supplementary Information: The framework is driven by Claude Fable 5 without fine-tuning, with every agent queried at decoding temperature 0.5.This implementation detail applies to the agents used throughout the motif-profile workflow.
  • S1 CIF2Text and the motif-profile representation: CIF2Text converts a CIF into JSON containing global information, typically 5–10 model-selected genes, and a hard-magnet assessment.It uses neighbour lists within 3.5 Å under periodic boundary conditions and Voronoi coordination analysis before standardizing gene descriptions.
  • S1 CIF2Text and the motif-profile representation: Each gene description links geometry to function, mechanism, and property impact, including possible effects on exchange, anisotropy, stability, Tc, Ms, or K1.The requested analysis follows a structure → interaction → property narrative and includes geometry sufficient to reconstruct the CIF.
  • S1 CIF2Text and the motif-profile representation: A gene is a multi-atom structural motif with a specific function, and genes may overlap in atoms while representing distinct functional roles.Gene selection is structure-dependent, spans periodic cell boundaries when necessary, and is guided by reconstructable geometric information.
  • S1 CIF2Text and the motif-profile representation: MatEvolve uses a motif language to describe crystals through recurring local structures such as coordination polyhedra, cages, clusters, and their connections.The motif profile is intended to capture the structural features driving thermodynamic stability and magnetization rather than raw atomic coordinates.
  • S1 CIF2Text and the motif-profile representation: The motif profile serves as a design representation because downstream agents can reason over its textual form and use it to operate on crystal structures.Expressing motifs as text enables design and synthesis agents to work directly with the representation.
  • S1 CIF2Text and the motif-profile representation: The standardization pass rewrites motifs into square-bracketed geometry-only tags so entries from different structures can be matched and clustered.The vocabulary encodes shape, coordination, connectivity, and periodicity while excluding property, electronic-structure, and magnetic terms.
  • S1 CIF2Text and the motif-profile representation: Each standardized entry declares exactly one motif type and assigns geometric atom roles, fixed coordination categories, bond-regime labels, site symmetry, and optional connectivity context.Bond distances are normalized against the sum of covalent radii, so standardized descriptions contain no raw Å values.

S2 Text2CIF: prompts, validation and iteration budget

Text2CIF converts an integral composition and text-described target motifs into a CIF using a language-model agent as a crystallographic structure generator. It validates motif realization, composition, coordination geometry, and atomic separations, regenerating structures when issue feedback is received.

  • Text2CIF workflow: Text2CIF maps an integral composition and text description of target motifs to a CIF through a language-model agent.The agent treats the motif profile as a geometric specification that can be constructed without explicit coordinates.
  • Text2CIF workflow: The generator parses the design concept, identifies its composition and genes, selects a space group from gene symmetries, and writes integral-occupancy crystallographic data.The prescribed construction uses full occupancy (1.0) at all sites and integral atom counts only.
  • Validation: Validation checks that every designed gene appears, coordination geometries match specifications, no atomic overlap occurs below 1.5 A, and the composition matches the target formula.These checks constitute the gene-realization validation step for the generated structure.
  • Iteration: On receiving issue feedback, the agent analyzes the problem and regenerates the CIF.The output protocol returns only CIF file contents, without explanations.

S3 Evolutionary operator over motif profiles

MatEvolve generates crystal candidates by editing motif profiles with interpretable evolutionary moves, then ranks the resulting designs separately. The operator produces offspring through crossover, element mutation, or geometry mutation, with each design specified in a generator-ready format.

  • Evolutionary moves: Three moves generate offspring profiles: crossover combines motifs from two parents, element mutation substitutes species, and geometry mutation alters coordination or connectivity.The operator accepts one or two parent profiles, depending on the move.
  • Evolutionary moves: The operator is the only component that reasons about properties to propose motif-profile edits; ERS later ranks the resulting candidates.
  • Design-agent output: Each offspring design is returned as strict JSON containing its motif set, an integral composition, and a self-contained description that Text2CIF can realize without parent context.The description must connect the listed genes to sufficient structural detail for construction.

S4 Evaluation metrics

The evaluation scores DFT-relaxed candidate sets using common rate definitions and fixed stability, magnetization, and reference-database criteria. It organizes design quality through S.U.N. metrics and an AFLOW-based prototype label, while also comparing evidence-based recommender selection with unselected candidates.

  • Common scoring: All reported rates use the DFT-relaxed candidate set size N as their denominator, with 300 benchmark candidates selected by each method’s own ranking procedure.Baselines select the top 300 of 1,000 raw proposals using CHGNet-estimated formation energy and moment per atom; MatEvolve selects the top 100 of 200 per generation using ERS.
  • Thresholds and predicates: The evaluation fixes ε = 0.1 eV/atom for stability, τ = 1 T for target magnetization, and Materials Project ∪ Alexandria as the reference database.Stability, uniqueness, novelty, and the design-target property are defined as candidate-level predicates.
  • S.U.N. metrics: A candidate is S.U.N. only when it is simultaneously stable, unique, and novel, forming the base for increasingly stringent nested design metrics.The evaluation follows crystal-structure generation literature in defining S.U.N. and builds a ladder of increasingly stringent design metrics.
  • Prototype metric: Prototype identity is assigned by collapsing periodic-block elements, symmetrizing the resulting structure, and encoding it as an AFLOW prototype string.The procedure applies identically to candidates and reference entries, grouping structures such as SmFe12, SmFe11Co, and DyFe12 under one label.
  • ERS analysis: Table S2 compares ERS-selected and unselected halves of a 600-proposal benchmark pool across the three S.U.N. tiers, alongside the full-pool yield.Each half contains 300 DFT-relaxed candidates, and the comparison is post-hoc and descriptive rather than fully independent of earlier ranking.

S5 Structure map by motif-group substitutability

The structure map represents each crystal by its motif-group content and compares structures using both group overlap and motif-group substitutability. It embeds these distances with t-SNE, maps combination coverage, and identifies robustly supported stable group pairings.

  • Structure representation and distance: Each structure is represented by the set of 17 motif groups it contains, and pairwise distance combines set overlap with substitutability of differing groups.Substitutability distance is small when differing groups are readily interchangeable.
  • Structure representation and distance: Distances derived from the motif-group matrix are embedded using t-SNE to relate structures through their motif content.The evidence includes labelled seed structures and DFT-validated candidates added during generation, with uncertainty parameter α = 0.1.
  • Combination coverage: Combination coverage enumerates all possible motif-group combinations of orders k ∈{2, 3, 4} and labels each as observed in the seed set, generated set, both, or neither.This produces the combination-coverage analysis shown in Fig. 6b of the main text.
  • Pair stability: Pair stability rates measure the fraction of structures containing each group pair that lie within 0.1 eV/atom of the convex hull, highlighting pairs exceeding 0.8.Because support varies and can be small, the threshold identifies a robustly supported compatible-pair class rather than individually significance-tested pairs.

S6 Motif-group word clouds

Figure 5a represents each of 17 motif groups with a word cloud of recurring controlled-vocabulary geometry tags. This keeps the visualization within the motif representation’s interpretable grammar rather than free text.

  • Word-cloud construction: Figure 5a labels all 17 motif groups with word clouds of recurring controlled-vocabulary tags naming their motifs.The tags are bracketed geometry descriptors from the standardized motif descriptions, so each word cloud uses the representation’s own vocabulary.

S7 Relation to text-based crystal representations

The motif profile is a geometry-only, controlled-vocabulary representation that differs from descriptive and text-conditioned crystal representations. It is certified generative and functions as an editable design medium whose realization is part of a design loop.

  • Representation and generation: Unlike automated descriptions, the motif profile withholds coordinates, lattice parameters, space group, and structure-type labels while requiring successful reconstruction.A profile is accepted only if a matching structure can be rebuilt from it.
  • Representation and generation: Unlike text-conditioned generation, motif-profile realization starts from detailed motifs rather than a composition-and-symmetry prompt and serves as one leg of a design loop.Realization is not the final goal of the framework.
  • Vocabulary design: Semiglobal textual information—connectivity and structural arrangement—contributes most to property prediction beyond graph-encoded local structure, supporting the motif vocabulary’s design range.The vocabulary spans local coordination units, cages, nets, layers, chains, connectivity, and dimensionality.
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