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MOFjson: An Explicit Topological Representation of Metal-Organic Frameworks for Language Models

Anabel Yong, Matthew Hart, Philippe Schwaller

arXiv:2610.34549v1cs.LGcs.SE

TL;DR

Existing MOF inputs leave language models to infer periodic connectivity from atomic coordinates or rely on compact identifiers that do not expose a structural graph. MOFjson provides raw atomic data with explicit bond shifts and a derived building-block graph, and the benchmark finds its clearest advantage on structure-dependent questions.

  • Problem

    Existing MOF formats separate atomic geometry from topology, leaving periodic connectivity implicit or encoded in non-queryable identifiers.

    Source: §1 · p. 1, §1.1 · p. 2

  • Method

    MOFjson combines raw atomic data and periodic bond shifts with a derived building-block graph, and evaluates structural reading against crystal-derived benchmark answers.

    Source: §2 · p. 2, §2.1 · p. 3, §2.2 · p. 3

  • Results

    MOFjson’s advantage is strongest on Net path, reaching 95–100% for gpt-5.6-luna and gemini-3.7-flash versus 18–47% for every baseline, while results are mixed on other categories.

    Source: §4 · p. 5

  • Takeaways & Limitations

    Explicit periodic graphs provide a foundation for spatial reasoning and generative design.

    Source: §5 · p. 5

    The ablation tests one mechanism on one model, and the paper reports no chance-level baselines bounding structural reading versus recall.

    Source: §5 · p. 5

Abstract

from arXiv · show

Language models for metal-organic frameworks (MOFs) rely on formats that separate atomic geometry from structural topology, forcing models to choose between unstructured coordinate lists and non-spatial string identifiers[1]. We present MOFjson, the first representation separating structural data into a raw atomic layer with explicit bond shift vectors and a derived layer exposing secondary building units (metal nodes and organic linkers) and network topology. Additionally, we introduce a benchmark with crystal-derived ground truth across four question categories. Across four models, MOFjson beats all three baselines in every category: 100% vs. 18-47% on reaching a block's nearest periodic copy, 96% vs. 71% on crystal system characterisation, and 60% vs. 48% on metal node and organic linker coordination. Ablating shift labels drops accuracy to 12.7%, proving models read the periodic graph rather than the surface format. MOFjson gives language models structure to read rather than reconstruct, establishing a foundation for agentic tool workflows and constrained MOF generation.

1 Introduction

MOF representations give language models either atomic geometry without explicit connectivity or compact topology codes without a queryable structural graph. MOFjson combines explicit periodic bond labels with a building-block graph so models can read connectivity rather than reconstruct it.

1 Introduction

  • MOF function depends on both composition and connectivity, which can vary even when the same building blocks are used.The introduction motivates representations that convey both structural aspects for property prediction and design.Source: §1 · p. 1
  • MOF language-model performance depends on serialization, while crystals require integer edge labels to encode which periodic image each bond reaches [3, 4, 5].Existing MOF representations leave those labels implicit despite MOFid’s use as model input and evaluation criterion [6–12].Source: §1 · p. 1
  • MOFjson adds integer bond-shift vectors and a building-block graph that directly records metal-node and organic-linker assignments and net connectivity.These additions state periodic connectivity rather than requiring it to be inferred from coordinates.Source: §1 · p. 1
  • Block-level representations are also relevant to tasks beyond question answering, including crystal structure prediction [4, 13–15].Source: §1 · p. 2

1.1 Limitations of Existing MOF Representations

  • CIFs provide atomic geometry but omit connectivity, whereas MOFid and MOFkey compress topology into codes that leave no structural graph to query.MOFjson labels bond-cell closures and adds a building-block graph, allowing most queries to use that graph instead of the atom list.Source: §1.1 · p. 2

2 Methodology

MOFjson keeps a lossless atomic record alongside a derived graph of building blocks and their periodic connectivity. Its benchmark uses crystal-derived ground truth to test whether models read structural information from the supplied representation.

2 Methodology

  • MOFjson separates CIF-native raw data from derived building-block, net-edge, and topology fields; raw data determines the structure, and CIF round-tripping reproduces lattice and connectivity.Conversion uses pymatgen and ASE; derived fields are recomputable.Source: §2 · p. 2

2.1 Explicit Periodic Graphs in MOFjson

  • Each periodic bond stores an integer shift vector naming the repeat cell containing its second endpoint, distinguishing bonds within a cell from bonds closing into neighboring copies.This stores labels that are otherwise recomputed per query.Source: §2.1 · p. 2
  • Figure 1 maps a crystal fragment to a labelled quotient graph and then MOFjson, with building blocks as vertices and shift-labelled bonds as arcs.The dia example has A bonded to four copies of B in different cells; attachment points are omitted from the MOFjson view.Source: Figure 1 · p. 3
  • A closed walk’s cycle sum is the signed sum of its bond shifts; zero marks an intra-cell ring, while a nonzero sum marks a path displaced into another periodic image.At the building-block level, internal bonds are absorbed and inter-block bonds become arcs with shifts re-anchored to block frames; the offsets telescope so cycle sums agree across layers.Source: §2.1 · p. 3

2.2 Benchmark QnA

  • The benchmark computes ground truth from crystals rather than retrieving answers from curated text or metadata, so accuracy measures reading the input structure rather than recall.Every prompt requires an answer; categories cover symmetry, chemical identity, connectivity, and nonzero-translation net paths, with example prompts in Table 2.Source: §2.2 · pp. 3–4, Table 2 · p. 4

3 Experiments

Experiments test raw-layer fidelity through CIF round-trips and benchmark question answering across four representations and four models against precomputed ground truth.

3 Experiments

  • All 2,737 computation-ready CoRE MOF CIFs were recovered after MOFjson conversion and back-conversion, across cells ranging from under 50 to over 800 atoms.Only the raw layer was tested, with reconstruction compared against source structures using pymatgen’s StructureMatcher.Source: §3 · p. 4
  • Each QnA run sampled 50 random structures and rendered them in CIF, MOFid, MOFkey, and MOFjson; results average three independent runs.Performance is reported as mean ± standard deviation.Source: §3 · p. 4
  • Four models were graded against precomputed ground truth, with task-specific exact-match rules and paired Wilcoxon tests against each baseline.Cliff’s δ is reported, and p-values are Holm-Bonferroni corrected across category-baseline comparisons.Source: §3 · p. 4

4 Results

MOFjson performs best where questions require structural reasoning, while model-level exceptions and a shift-vector ablation qualify the results.

4 Results

  • 95–100% on Net path for gpt-5.6-luna and gemini-3.7-flash, versus 18–47% for every baseline; MOFjson leads on three structural-reasoning categories.The three categories are Symmetry, Net path, and Connectivity; Chemical identity is readable from atom labels in every representation.Source: Figure 2 · p. 4, §4 · p. 5
  • MOFjson’s ordering holds for gpt-5.6-luna and gemini-3.7-flash, but claude-haiku-4.5 prefers CIF on Symmetry and apertus-v1.5-70b falls below baselines on Net path.Connectivity is mixed, including a MOFkey advantage over MOFjson for claude-haiku-4.5.Source: §4 · p. 5
  • MOFjson is the best-performing representation–model pair in every category, though Chemical identity separates only for apertus-v1.5-70b.Table 3 reports the best pair for each question category.Source: Table 3 · p. 5, §4 · p. 5
  • 12.7% ± 6.4% on Net path after zeroing edge shift vectors, down from 100.0% for gemini-3.7-flash.The ablation is graded against the unablated graph and uses the model with maximum headroom for isolating the drop.Source: §4 · p. 5

5 Discussion, Conclusion, and Future Work

The discussion links MOFjson’s advantage to structural reasoning and periodic shifts, while noting capability and evaluation limits and pointing toward spatial reasoning and generative design.

5 Discussion, Conclusion, and Future Work

  • p < 0.001 in every category supports the representation ordering, with Cliff’s δ concentrated on Symmetry and Net path at 0.25–0.45.Because pairs are clustered by structure across models, effective sample size is below n and the p-values are indicative.Source: §5 · p. 5
  • 12.7% ± 6.4% after zeroing shifts, versus 100.0% with shifts, locates the Net path advantage in periodic-shift information for gemini-3.7-flash.The ablation isolates only Net path questions.Source: Figure 3 · p. 5, §5 · p. 5
  • Improvements depend on model capability: apertus-v1.5-70b falls below baselines on Net path, and the ablation covers one mechanism on one model.The paper reports no chance-level baseline to bound structural reading versus recall.Source: §5 · p. 5
  • Explicit periodic graphs are presented as a foundation for spatial reasoning and generative design, while MOFjson is described as a starting point.The authors frame the format as an alternative to representations built for database search.Source: §5 · p. 5

6 Code and Reproducibility

The paper reports fixed query settings, versioned model identifiers, and public code and data.

6 Code and Reproducibility

  • All models were queried at temperature 0 with a fixed maximum output length and short, fixed-shape answers, without chain-of-thought or extended reasoning.Models were accessed through provider APIs.Source: §6 · p. 6
  • Run-to-run variance reflects the structure sample rather than decoding noise under the stated query settings.Source: §6 · p. 6
  • Versioned model identifiers are listed in Section 3, and code and data are available at the cited repository.Source: §6 · p. 6

A.1 HKUST-1 MOF: Schema, Structure, and Existing Identifiers

Figure 4 contrasts MOFjson’s explicit structural layers for HKUST-1 with MOFid and MOFkey’s compressed codes. The identifiers encode the same tbo net symbol.

A.1 HKUST-1 MOF: Schema, Structure, and Existing Identifiers

  • MOFjson’s HKUST-1 record separates a raw layer from a derived layer.The raw layer contains the lattice, atoms, and bonds; the derived layer contains building_blocks, net_edges, and topology.Source: Figure 4 · p. 9
  • MOFid and MOFkey encode HKUST-1’s tbo net symbol as strings.The figure contrasts those codes with MOFjson’s explicit periodic graph.Source: Figure 4 · p. 9
  • The figure pairs the MOFjson representation and identifier strings with an iRASPA rendering of the same structure [40].Source: Figure 4 · p. 9

A.2 Structural Fidelity of CIF to MOFjson Conversion

The raw MOFjson layer reconstructs all tested CoRE MOF structures across the reported cell-size range. A separate table identifies the best-performing representation-category pair for each model.

A.2 Structural Fidelity of CIF to MOFjson Conversion

  • 2,737 of 2,737 CoRE MOF structures are recovered from the raw layer, across cells from under 50 to over 800 atoms.The test compares reconstructed structures with their sources using StructureMatcher; derived fields are not required for reconstruction.Source: Figure 5 · p. 9

A.3 Best Representation by Model

  • Table 4 reports the best-performing representation-category pair for each model, with accuracy as mean ± SD across three runs.Source: Table 4 · p. 10

A.4 Breakdown of Model Performance on the four Question categories

MOFjson’s performance varies by question category and model: it leads broadly on net path and often on symmetry, while connectivity and chemical identity show exceptions.

Symmetry

  • 96.0% vs. 68.7% for gemini-3.7-flash and 88.0% vs. 18.0% for gpt-5.6-luna show MOFjson outperforming CIF on symmetry.MOFjson statistically ties CIF for claude-haiku-4.5 (70.0% vs. 71.3%); apertus-v1.5-70b scores 22.7% vs. 20.0%.Source: Figure 6 · p. 10

Connectivity

  • MOFjson leads on connectivity for gpt-5.6-luna (60.0% vs. 32.7–40.0%) and gemini-3.7-flash (58.7% vs. 38.0–46.0%), but not across all models.MOFkey scores highest for claude-haiku-4.5 (48.0%), while all representations are within error for apertus-v1.5-70b (34.0–45.3%).Source: Figure 7 · p. 10

Chemical identity

  • Chemical identity is statistically indistinguishable across representations for three models, with scores clustered within 30–34%.Only apertus-v1.5-70b separates, scoring 65.3% for MOFjson against 24.0–30.7% for baselines; the paper treats this as a single-model observation.Source: Figure 8 · p. 11

Net path

  • 100.0% for gemini-3.7-flash and 95.3% for gpt-5.6-luna on net path exceed every baseline’s 33.3–46.7% in both cases.For apertus-v1.5-70b, MOFjson scores 8.7%, below all three baselines (20.0-25.3%).Source: Figure 9 · p. 11

A.5 Paired Wilcoxon signed rank test and Cliff’s Delta

Paired Wilcoxon tests compare MOFjson with each baseline by question category using matched structure-level observations. The reported advantage is significant against every baseline in every category.

A.5 Paired Wilcoxon signed rank test and Cliff’s Delta

  • MOFjson’s advantage is significant (p < 0.001) against every baseline in every category.The 12 tests use Holm-Bonferroni-corrected p-values.Source: Table 5 · p. 11
  • Each run draws 50 structures and renders each in all four representations, creating matched pairs for each MOFjson-baseline comparison.Across three independent runs, de-duplicated draws leave 145–148 distinct structures per category; each contributes one paired observation per model.Source: Table 5 · p. 11
  • Cliff’s δ ranges from −1 to 1, with positive values indicating that MOFjson scores higher on a structure more often than it scores lower.Source: Table 5 · p. 11

B Token Cost Analysis

MOFjson uses fewer input tokens than CIF for most question categories, but symmetry queries require a full per-atom coordinate list and exceed CIF’s token cost. Token costs were measured across the full benchmark question pool by category.

B Token Cost Analysis

  • Prompts were tokenized with cl100k_base, and mean input token counts were computed across the full question pool for each category.Error bars show one standard deviation across structures within each category.Source: B Token Cost Analysis · p. 12
  • For most queries except symmetry, MOFjson uses 6–58× fewer input tokens than CIF, approaching MOFid and MOFkey in compactness; for symmetry, it exceeds CIF’s token cost.Source: Figure 10 · p. 12
  • For symmetry queries, MOFjson exceeds CIF’s token cost because it requires the full per-atom coordinate list and uses verbose JSON atom encoding.CIF’s atom-site format is more compact and tabular.Source: Figure 10 · p. 12
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