LATHE writes seven crystallographic properties as differentiable objectives, enabling natural-language fine-grained crystal editing
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Synopsis
The authors present LATHE, a geometric toolkit that expresses seven classes of crystallographic properties, namely bond length, bond angle, dihedral angle, coordination environment, lattice parameters, cell volume, and space group, as differentiable objectives so that a given crystal structure can be edited directly; on single-property benchmarks all seven property types reach near-perfect constraint satisfaction while optimized structures stay close to local energy minima, the LATHE-equipped agent translates over 87.5% of natural-language prompts into valid executable configurations, and in a band-gap inverse-design case study nine of ten independent runs reach the target tolerance window at a typical cost of thirteen hypothesis-evaluation cycles.
Figure 1: Representative gradient-optimization trajectories. Each row shows four frames of a single optimization — the initial structure, frames at approximately 1/3 and 2/3 of the trajectory, and the final optimized structure, with the step index given in parentheses. In every panel, periodic-image partners that lie outside the primitive cell are indicated by a dashed black ring drawn around the atom. (a) Bond-length optimization of a CaCO 3 structure (mp-556235). Ten bonds are jointly driven to user-specified distances under a weak MLIP-energy co-objective ( w = 0.01 w=0.01 ). Each targeted ( i , j ) (i,j) pair is drawn as a uniform blue line connecting the two atoms (or atom i i and the nearest periodic image of atom j j when the bond wraps through the cell boundary). The first frame labels each bond with its starting distance (in Å); the final frame labels each bond with its target distance (in Å); intermediate frames show the bonds without numerical labels for clarity. (b) Space-group elevation of Al 2 O 3 (mp-638765) from P-1 (No. 2) to R-3m (No. 166). The 2 × 2 × 2 2\times 2\times 2 supercell of the structures are shown. The optimization is again regularized by the MLIP-energy co-objective. (c) Coordination-environment modification of an oxygen site in MgSiO 3 (mp-1180468). The goal is to raise the number of Mg neighbors of an Oxygen atom from one to three while maintaining the number of Si and O neighbors. The target oxygen atom is highlighted with a bold solid black ring, and its first-neighbor shell within the coordination-loss cutoff of 3.5 Å is drawn as colored lines from the target site to each neighbor, one line per (atom, periodic-image) contact and colored by the element of the neighbor (Mg in green, Si in blue; O in red). As the optimization progresses, the number and identity of neighbors inside the cutoff shell evolve toward the specified target coordination.
arXivInterpretation
LATHE unifies seven classes of crystallographic properties as differentiable objectives, so a given crystal structure can be edited geometrically rather than only generated from scratch. In existing frameworks, LLMs have poor spatial awareness and operate at coarse granularity in token space, while diffusion- and gradient-based structure generation generally produces complete structures de novo; LATHE addresses fine-grained editing of a given input under arbitrary constraints. The abstract reports that across single-property benchmarks all seven property types attain near-perfect constraint satisfaction while optimized structures remain close to local energy minima.
LATHE is exposed through a Model Context Protocol server and embedded in a closed-loop multi-agent system that translates hypotheses into geometric modifications in natural language. This connects natural-language hypothesis generation with physically grounded gradient-based structural editing, forming an interpretable closed-loop computational materials discovery workflow. The abstract reports that the LATHE-equipped agent translates over 87.5% of natural-language prompts into valid executable configurations and faithfully completes them.
In a band-gap inverse-design case study, the multi-agent loop reaches the target tolerance window. The case study demonstrates the full loop from a design objective, through natural-language hypotheses, to geometric editing for a concrete functional property. The abstract reports that nine of ten independent runs reach the target tolerance window at a typical cost of thirteen hypothesis-evaluation cycles.
Perspective
The work targets materials design settings that require geometric or symmetry constraints on a given crystal structure, for computational materials researchers doing inverse design of functional materials and for agent developers who want natural-language-driven structural editing. LATHE's scope is defined by seven property classes: bond length, bond angle, dihedral angle, coordination environment, lattice parameters, cell volume, and space group; the closed-loop demonstration addresses band-gap inverse design as a concrete objective. On this basis, additional design objectives could be connected to the same differentiable-objective and multi-agent framework, or the toolkit could be applied to other tasks requiring fine structural editing.
The abstract does not state the sample sizes of the single-property benchmarks, how the properties interact with one another, or the criterion for being close to a local energy minimum; the failure modes and error types in prompt-to-configuration translation are also not detailed. In the band-gap case, one of ten runs did not reach the tolerance window, and the reason and the distribution of cycle costs remain unclear. In addition, the reading scope here is the abstract only, without figures or experimental detail from the body, so the statistical uncertainty of these numbers and their generalization across material systems remain open questions.