Smart Machine Learning for Solving the Full Electron-Nuclear Schrödinger Equation with a Quantum-Chemically Inspired Wavefunction Ansatz
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Zhang, Yaolong, Jiang, Bin, Guo, Hua
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7215088685