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This research introduces a novel machine learning framework, Schrödinger, designed to solve the full electron-nuclear Schrödinger equation by integrating quantum-chemical principles with neural networks. The approach utilizes a hybrid optimization strategy combining variational Monte Carlo with local-energy constraints to accurately model strongly correlated electronic structures across diverse molecular systems. This advancement represents a significant step toward practical tools for capturing full quantum effects beyond standard approximations in computational chemistry.
Smart Machine Learning for Solving the Full Electron-Nuclear Schr\"odinger Equation with a Quantum-Chemically Inspired Wavefunction Ansatz
arXiv:2609.40112v1 Announce Type: cross Abstract: Directly solving the full electron-nuclear Schr\"odinger 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, Schr\"odinger, 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 Schr\"odinger equation and capturing full quantum effects beyond the Born-Oppenheimer approximation.
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.
Chemical Physics (physics.chem-ph); Computational Physics (physics.comp-ph); Quantum Physics (quant-ph)
arXiv:2609.40112 [physics.chem-ph]
(or arXiv:2609.40112v1 [physics.chem-ph] for this version)
https://doi.org/10.48550/arXiv.2609.40112 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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