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

cond-mat.mtrl-sciAug 16, 2026

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

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

Organizations: Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan · Department of Physics, School of Science, Institute of Science Tokyo, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan · Research Center for Materials Informatics, Department of Advanced Data Science, The Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo 190-8562, Japan · International Center for Synchrotron Radiation Innovation Smart (SRIS), Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan

Abstract

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 language of motifs, writing each crystal as a motif profile that describes the recurring geometric patterns---the 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.

Figures & tables

Figure 1: Overview of MatEvolve. An interpretable, agent-based framework for crystal-structure design built on the motif profile —a human-readable text representation that describes a crystal in terms of the recurring geometric motifs from which it is constructed. One turn of the loop consists of three stages. Structure translate : an agent writes a parent structure as its motif profile. Structure design : an agent edits the parent’s profile—recombining and mutating motifs—to propose new candidate structures with a stated rationale, which a generator then realizes. Evaluation : an uncertainty-aware recommender prioritizes candidates for first-principles validation, which assesses and optimizes each candidate; every validated candidate returns to the pool from which the next parents are drawn.

Figure 2: Structure Translation and Structure Design loops. Blue boxes denote AI-reasoning (language-model) agents; green shapes represent deterministic Python tools. (a) Structure Translation converts a crystal into a validated motif profile, enforcing bidirectional consistency: the profile is accepted only if a structure rebuilt from it reproduces the original, in terms of both its motifs and geometry. (b) Structure Design edits parent profiles into new offspring structures through the evolutionary operator, retaining only candidates that realize the designed motifs.

Figure 3: Reconstruction fidelity of the motif profile (round-trip Structure Translate: CIF2Text

\rightarrow

Text2CIF). (a) Eight representative reconstructions spanning the range of outcomes. In each pair the left structure is the original Materials Project reference and the right structure is the one regenerated by Text2CIF from the motif profile; RMSD is the root-mean-square displacement between matched atomic positions in Ångstroms, and CShM the dimensionless continuous shape measure of the reconstruction relative to the original [ 49 , 50 ] . (b) Distribution of RMSD and (c) of CShM, in each case over the matched reconstructions.

Method	S.U.N.	Property-targeted S.U.N. ( $\mathcal{P}$ )	New-proto. S.U.N. ( $\mathcal{P}$ )
This work	25%	24%	21%
Chemeleon2, MP+Alexandria (unconditioned)	30%	1%	1%
MatterGen, MP+Alexandria (unconditioned)	40%	0%	0%
MatterGen, magnetization-conditioned	22%	20%	6%

Table 1: Benchmark of MatEvolve against generative models on magnetic-material design. Each method contributes 300 DFT-validated candidates, drawn from its own proposal pool by its own ranking procedure (baselines: top 300 of 1,000 ranked with CHGNet on formation energy and predicted magnetic moment; MatEvolve: top 100 of 200 per generation by the ERS). Three rates are reported (in %): the stable–unique–novel (S.U.N.) rate; the property-targeted rate (

\text{S.U.N.}_{\mathcal{P}}

, S.U.N. structures reaching

\mu_{0}M_{s}>1

T); and the new-prototype property-targeted rate (

\text{S.U.N.}_{\mathcal{P}}^{\text{proto}}

, property-targeted S.U.N. structures that additionally realize a structural prototype absent from the reference databases). Bold marks the highest rate in each column. All rates are conditional on each method’s own ranking—its intended mode of use; ranking method, sequential feedback, seed chemistry prior, and input representation are not separately controlled.

Figure 4: Stability and magnetization of the MatEvolve-generated magnets and the baseline sets. (a) Saturation magnetization $\mu_{0}M_{s}$ versus energy above the convex hull for each method’s 300 DFT-validated candidates: MatEvolve (blue), the seed set $\mathcal{D}_{\mathrm{seed}}$ (grey), and the generative baselines—unconditioned MatterGen (red), magnetization-conditioned MatterGen (orange), and Chemeleon2 (green)—; the horizontal dashed line marks the saturation magnetization of Nd 2 Fe 14 B. (b) The six on-hull property-targeted S.U.N. structures ( $E_{\mathrm{hull}}=0$ , $\mu_{0}M_{s}>1$ T), each absent from the Materials Project and Alexandria; each panel reports the formula, space group, and $\mu_{0}M_{s}$ . (c) Four representative new-prototype property-targeted S.U.N. structures ( $\text{S.U.N.}_{\mathcal{P}}^{\text{proto}}$ ; metastable, $0<E_{\mathrm{hull}}\leq 0.1$ eV/atom), each realizing a prototype absent from both databases.

Figure 5: Motif groups discovered from the seed and assigned across the study. The groups are discovered from the seed structures’ motifs, and the motifs of the generated structures are then assigned to them (10,096 motifs across all 1,557 structures). (a) Word clouds of the 17 motif groups; each group is summarized by its most representative keywords, ranked by TF–IDF over the group’s motif descriptions from candidate terms proposed by the language-model agents. (b) For each group, the fraction of contributing structures that are stable or metastable (blue) versus unstable (red). (c) For each group, the distribution of saturation magnetization $\mu_{0}M_{s}$ across the structures that contain a motif from that group; the dashed line marks the $1$ T design target. (d) For each group, the number of contributing structures from the Materials Project seed set ( $\mathcal{D}_{\mathrm{seed}}$ , grey) and from MatEvolve ( $\mathcal{D}_{\mathrm{MatEvolve}}$ , black).

Figure 6: Motif-group composition, combination coverage and pairwise stability across the 1,557 structures. (a) Structure map: each of the 1,557 structures is represented by the set of 17 motif groups it contains and embedded so that structures sharing groups—or built from mutually substitutable groups—lie close together (t-SNE on a substitutability-weighted set-overlap distance; axes are arbitrary embedding coordinates). Marker shape encodes origin—Materials Project seed structures (tripods) versus MatEvolve-generated structures (circles); the origin is denoted by marker shape, not by shade as in Fig. 5 d, and the colour encodes stability: blue for stable or metastable and red for unstable; grey contours are a kernel-density estimate of the seed structures’ distribution in the embedding. (b) Coverage of motif-group combinations by order: for the binary, ternary and quaternary combinations of the 17 groups, the fraction of all possible combinations observed only in the seed set ( $\mathcal{D}_{\mathrm{seed}}$ ), only among the generated structures ( $\mathcal{D}_{\mathrm{MatEvolve}}$ ), in both, or in neither (counts in parentheses). (c) Pairwise motif-group stability: for every pair of the 17 groups, a pie gives the fraction of the structures containing that pair that are stable or metastable (blue) versus unstable (red), and pie size is binned by the number of contributing structures (more than 50, 20–50, or fewer than 20).

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Tag	Condition	Meaning
[short bond]	$d<0.90\,r_{\mathrm{sum}}$	compressed, strong overlap
[typical bond]	$0.90\,r_{\mathrm{sum}}\leq d\leq 1.10\,r_{\mathrm{sum}}$	standard bonding
[long bond]	$1.10\,r_{\mathrm{sum}}<d\leq 1.30\,r_{\mathrm{sum}}$	stretched, weak
[non-bonded]	$d>1.30\,r_{\mathrm{sum}}$	no direct bond

Appendix

Table S1: Bond-distance regimes of the motif grammar.

	S.U.N.	S.U.N. P	S.U.N. ${}_{\mathcal{P}}^{\text{proto}}$
With ERS (selected 300)	74 (25%)	72 (24%)	63 (21%)
Without ERS (unselected 300)	53 (18%)	41 (14%)	23 (8%)
Full pool (600)	127 (21%)	113 (19%)	86 (14%)

Appendix

Table S2: Effect of the evidence-based recommender (ERS). The 600-proposal pool of the benchmark run, split into the ERS-selected half (the benchmark set of Table 1 of the main text) and the unselected half, each comprising 300 DFT-relaxed candidates; the full-pool row gives the run’s total yield. Rates are on the three S.U.N. tiers. The selected-versus-unselected comparison is post-hoc and descriptive, and the two halves are not fully independent of earlier ranking, as the parents of generations two and three were drawn from ERS-prioritized candidates.

Work	Direction	Purpose	Relation to MatEvolve
Robocrystallographer [ 10 ]	Crystal $\rightarrow$ text	Structure description	Direct precedent of CIF2Text; its text reports space group and prototype and is an end product, not an editable object
LLM-Prop [ 11 ]	Text $\rightarrow$ property	Property prediction	Establishes text as a machine-readable crystal representation
Lattice Lingo [ 12 ]	Crystal $\rightarrow$ text $\rightarrow$ property	Multimodal property prediction	Establishes the value of semiglobal textual information
Ozawa et al. [ 13 ]	Representation $\rightarrow$ property	Input-representation comparison	Establishes that representation design governs model performance
CrysText [ 14 ]	Text $\rightarrow$ crystal	Crystal generation	Direct analogue of Text2CIF, conditioned on composition and symmetry rather than a motif profile

Appendix

Table S3: Prior text-based treatments of crystals and their relation to MatEvolve.

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