{
  "abstract": "Rigid-body factorization is an appealing route to molecular-crystal structure prediction: freezing each molecule’s conformer reduces a crystal to a lattice, a set of fractional centroids on the torus T3, and a per-molecule orientation on SO(3). Whether the orientation field is actually learnable on real molecular crystals has not been examined. We introduce SymMC-Flow, a space-groupconditioned rigid-body flow on lattice×T3×SO(3), used as a diagnostic study on 1,127 crystals from the Cambridge Structural Database. The lattice and centroid flows learn normally, but the absolute per-molecule orientation flow remains at its predict-zero floor. We trace this to a decomposition of the orientation target, Rm = rot(gm) · Rasym, into a space-group-determined relative rotation between symmetry copies and the asymmetric unit’s gauge-arbitrary free orientation, which is not learnable from composition and packing; the relative part is. Re-gauging to cancel the free part lifts held-out non-reference orientation loss by 27% (versus ∼0% for the absolute target) and reconstructs 13.7% (mean over three seeds) of held-out multi-copy packings exactly under StructureMatcher, against 0% for the predict-floor baseline. Conditioning on a discrete space-group coset identity raises the learnable signal to roughly 48% (three-seed mean), showing the residual ceiling is set by the difficulty of inferring the symmetry operation from packing rather than by network capacity. End-to-end joint generation does not yet reconstruct packings exactly, placing this as a characterization rather than a finished generator. The result maps what a rigid-body SO(3) flow can and cannot contribute to molecular-crystal generation, and suggests such generators should condition on crystal symmetry for the relative orientation and sample, rather than regress, the remaining free pose.",
  "abstract_shown": true,
  "affiliations": [
    "Purdue University"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Frank Cai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cqffqqkkchy9v.bib",
  "cited_by": 0,
  "doi": "10.26434/chemrxiv.15008279/v1",
  "fulltext_url": null,
  "id": "cqffqqkkchy9v",
  "issns": [],
  "landing_url": "https://chemrxiv.org/doi/full/10.26434/chemrxiv.15008279/v1",
  "language": null,
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2505|Machine Learning in Materials Science"
    ]
  ],
  "openalex": "W7208707923",
  "pdf_url": "https://chemrxiv.org/doi/pdf/10.26434/chemrxiv.15008279/v1",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": "American Chemical Society (ACS)",
  "ris": "https://research.draconitic.com/paper/cqffqqkkchy9v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:17Z",
      "native_id": "10.26434/chemrxiv.15008279",
      "source": "chemrxiv",
      "url": "https://chemrxiv.org/doi/full/10.26434/chemrxiv.15008279/v1"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "openalex:2505|Machine Learning in Materials Science",
      "subfield": "materials-polymers"
    }
  ],
  "title": "What an SO(3) orientation flow can and cannot learn in molecular-crystal structure prediction",
  "title_text": "What an SO(3) orientation flow can and cannot learn in molecular-crystal structure prediction",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:17Z",
  "url": "https://research.draconitic.com/paper/cqffqqkkchy9v",
  "venue": "ChemRxiv",
  "versions": []
}