Smart Machine Learning for Solving the Full Electron-Nuclear Schrödinger Equation with a Quantum-Chemically Inspired Wavefunction Ansatz
Abstract
Directly solving the full electron-nuclear Schrödinger equation remains one of the grand challenges in quantum mechanics. Here, we propose a quantum-chemically motivated orbital-based neural network wavefunction ansatz with explicit many-body electron-electron correlation terms, with parameters depending on the entire electron-nuclear configuration, enabling an accurate description of strongly correlated and/or multi-reference electronic structures by a single Slater-determinant across a broad nuclear configuration space. To train this wavefunction, we further develop an efficient hybrid optimization strategy that combines the variational Monte Carlo technique with local-energy constraints, mitigating the intrinsic sampling bias of the former and considerably reducing the statistical error. These advances are embedded in a unified neural network framework, Schrödinger, enabling the determination of globally accurate potential energy surfaces with a single training for systems ranging from strongly correlated diatomic molecules, triatomic reactions containing conical intersections, to polyatomic multi-reference molecules. This work offers a practical machine-learning tool for solving the electron-nuclear Schrödinger equation and capturing full quantum effects beyond the Born-Oppenheimer approximation.
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BibTeX
@misc{zhang2026smart,
title = {{Smart Machine Learning for Solving the Full Electron-Nuclear Schrödinger Equation with a Quantum-Chemically Inspired Wavefunction Ansatz}},
author = {Yaolong Zhang and Bin Jiang and Hua Guo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.40112},
eprint = {2609.40112},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40112},
}
RIS
TY - UNPB
TI - Smart Machine Learning for Solving the Full Electron-Nuclear Schrödinger Equation with a Quantum-Chemically Inspired Wavefunction Ansatz
AU - Yaolong Zhang
AU - Bin Jiang
AU - Hua Guo
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.40112
UR - https://arxiv.org/abs/2609.40112
AB - Directly solving the full electron-nuclear Schrödinger equation remains one of the grand challenges in quantum mechanics. Here, we propose a quantum-chemically motivated orbital-based neural network wavefunction ansatz with explicit many-body electron-electron correlation terms, with parameters depending on the entire electron-nuclear configuration, enabling an accurate description of strongly correlated and/or multi-reference electronic structures by a single Slater-determinant across a broad nuclear configuration space. To train this wavefunction, we further develop an efficient hybrid optimization strategy that combines the variational Monte Carlo technique with local-energy constraints, mitigating the intrinsic sampling bias of the former and considerably reducing the statistical error. These advances are embedded in a unified neural network framework, Schrödinger, enabling the determination of globally accurate potential energy surfaces with a single training for systems ranging from strongly correlated diatomic molecules, triatomic reactions containing conical intersections, to polyatomic multi-reference molecules. This work offers a practical machine-learning tool for solving the electron-nuclear Schrödinger equation and capturing full quantum effects beyond the Born-Oppenheimer approximation.
ER -