[Paper Review] A Cross-Domain Graph Learning Protocol for Single-Step Molecular Geometry Refinement

Chengchun Liu, Wendi Cai+2 more|arXiv (Cornell University)|Jan 30, 2026

Machine Learning in Materials Science0 citations

TL;DR

GeoOpt-Net is a multi-branch SE(3)-equivariant geometry refinement network that produces DFT-quality geometries in a single forward pass (B3LYP/TZVP) from low-cost conformers, with a two-stage multi-fidelity training and FAFM calibration.

ABSTRACT

Accurate molecular geometries are a prerequisite for reliable quantum-chemical predictions, yet density functional theory (DFT) optimization remains a major bottleneck for high-throughput molecular screening. Here we present GeoOpt-Net, a multi-branch SE(3)-equivariant geometry refinement network that predicts DFT-quality structures at the B3LYP/TZVP level of theory in a single forward pass starting from inexpensive initial conformers generated at a low-cost force-field level. GeoOpt-Net is trained using a two-stage strategy in which a broadly pretrained geometric representation is subsequently fine-tuned to approach B3LYP/TZVP-level accuracy, with theory- and basis-set-aware calibration enabled by a fidelity-aware feature modulation (FAFM) mechanism. Benchmarking against representative approaches spanning classical conformer generation (RDKit), semiempirical quantum methods (xTB), data-driven geometry refinement pipelines (Auto3D), and machine-learning interatomic potentials (UMA) on external drug-like molecules demonstrates that GeoOpt-Net achieves sub-milli-Å all-atom RMSD with near-zero B3LYP/TZVP single-point energy deviations, indicating DFT-ready geometries that closely reproduce both structural and energetic references. Beyond geometric metrics, GeoOpt-Net generates initial guesses intrinsically compatible with DFT convergence criteria, yielding nonzero ``All-YES'' convergence rates (65.0\% under loose and 33.4\% under default thresholds), and substantially reducing re-optimization steps and wall-clock time. GeoOpt-Net further exhibits smooth and predictable energy scaling with molecular complexity while preserving key electronic observables such as dipole moments. Collectively, these results establish GeoOpt-Net as a scalable, physically consistent geometry refinement framework that enables efficient acceleration of DFT-based quantum-chemical workflows.

Motivation & Objective

• Bridge inexpensive initial conformers to high-accuracy DFT geometries (B3LYP/TZVP) in one forward pass.
• Develop a multi-branch SE(3)-equivariant architecture that decouples bond lengths, angles, and dihedrals for robust refinement.
• Leverage a two-stage, multi-fidelity training strategy with fidelity-aware feature modulation to calibrate geometry across theory levels.
• Demonstrate improved DFT convergence likelihood and reduced wall-clock time for large-scale, drug-like molecules.

Proposed method

• Use a three-stream SE(3)-equivariant graph to encode pairwise distances, angles, and dihedrals as invariant and directional features.
• Decode with a Transformer to produce SE(3)-equivariant coordinate updates in a single pass.
• Train in two stages: pre-train on B3LYP/6-31G(2df,p) and fine-tune on B3LYP/TZVP with fidelity-aware feature modulation (FAFM).
• Employ a composite loss combining global Cartesian RMSD and bond length/angle/dihedral errors plus a bond-range constraint.
• Validate equivariance by rotate-then-predict vs predict-then-rotate tests and confirm numerical precision within 1e-5 Å.

Experimental results

Research questions

• RQ1 Can a single-pass, SE(3)-equivariant model refine arbitrary initial conformers to B3LYP/TZVP-quality geometries?
• RQ2 Does a two-stage, multi-fidelity training with FAFM enable transferable, theory-aware calibration across different electronic structure levels?
• RQ3 Do the geometry refinements translate into improved DFT convergence rates and preserved electronic observables for large, drug-like molecules?
• RQ4 How does GeoOpt-Net compare to force-field, semiempirical, and other ML-refinement baselines in geometric and energetic fidelity?
• RQ5 Is the method robust beyond its training distribution in terms of molecular size and complexity?

Key findings

• GeoOpt-Net achieves sub-milli-Å all-atom RMSD relative to B3LYP/TZVP references.
• Single-pass refinements yield near-zero ΔE deviations at B3LYP/TZVP, indicating accurate geometries.
• Initial geometries from GeoOpt-Net have higher all-YES DFT convergence rates (65.0% loose, 33.4% default) than baselines (0%).
• GeoOpt-Net shows substantial reductions in required optimization steps and wall-clock time for DFT re-optimizations.
• Dihedral (torsional) errors are reduced by 1–2 orders of magnitude, driving major gains in conformational accuracy.
• Dipole moments computed from GeoOpt-Net geometries match DFT references within 0.002 Debye, outperforming baselines (−0.369 to −0.498 Debye deviations).
• Energy deviations ΔE remain below 0.1 kcal/mol for most molecules across increasing molecular complexity, with smooth scaling.