NucleoNet: A Nuclear-Aware Determinant Ansatz for Multi-Geometry Neural Variational Monte Carlo

Abstract

Neural-network variational Monte Carlo provides an accurate route to solving the electronic Schrödinger equation, but many neural wavefunctions are optimized for a single nuclear geometry, requiring separate calculations to map out a potential energy surface. We introduce NucleoNet, a nuclear-aware determinant ansatz in which electrons and nuclei form a unified particle set propagated through a shared electron--nucleus backbone that jointly evolves one-particle and two-particle representations. Nuclei carry learned representations that evolve alongside the electronic representations and condition orbital construction, while antisymmetry is imposed only by electronic determinants. On equilibrium small-molecule benchmarks, NucleoNet achieves accuracy comparable to established neural-wavefunction baselines with substantially fewer parameters. For each molecular system, a single model optimized jointly across geometries describes the N₂ dissociation curve, Li displacement in LiCN, and the ethane and formamide minimum-energy paths for bond dissociation. Sparse-geometry training generalizes to unseen geometries for N₂ and LiCN without further optimization, and N₂ ablations show that nuclear streams substantially improve this interpolation. These results show that a compact wavefunction with jointly evolved nuclear representations can describe the geometries of a molecular system with a single set of parameters.

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BibTeX RIS

BibTeX

@misc{gao2026nucleonet,
  title = {{NucleoNet: A Nuclear-Aware Determinant Ansatz for Multi-Geometry Neural Variational Monte Carlo}},
  author = {Qiao Gao and Yang Huang and Enze Hou and Yuzhi Liu and Jingrun Chen and Han Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12985},
  eprint = {2610.12985},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12985},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - NucleoNet: A Nuclear-Aware Determinant Ansatz for Multi-Geometry Neural Variational Monte Carlo
AU  - Qiao Gao
AU  - Yang Huang
AU  - Enze Hou
AU  - Yuzhi Liu
AU  - Jingrun Chen
AU  - Han Wang
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.12985
UR  - https://arxiv.org/abs/2610.12985
AB  - Neural-network variational Monte Carlo provides an accurate route to solving the electronic Schrödinger equation, but many neural wavefunctions are optimized for a single nuclear geometry, requiring separate calculations to map out a potential energy surface. We introduce NucleoNet, a nuclear-aware determinant ansatz in which electrons and nuclei form a unified particle set propagated through a shared electron--nucleus backbone that jointly evolves one-particle and two-particle representations. Nuclei carry learned representations that evolve alongside the electronic representations and condition orbital construction, while antisymmetry is imposed only by electronic determinants. On equilibrium small-molecule benchmarks, NucleoNet achieves accuracy comparable to established neural-wavefunction baselines with substantially fewer parameters. For each molecular system, a single model optimized jointly across geometries describes the N_2 dissociation curve, Li displacement in LiCN, and the ethane and formamide minimum-energy paths for bond dissociation. Sparse-geometry training generalizes to unseen geometries for N_2 and LiCN without further optimization, and N_2 ablations show that nuclear streams substantially improve this interpolation. These results show that a compact wavefunction with jointly evolved nuclear representations can describe the geometries of a molecular system with a single set of parameters.
ER  -

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