发表机构
University of New Mexico; University of Science and Technology of China（新墨西哥大学; 中国科学技术大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种量子化学启发的神经网络波函数拟设，结合变分蒙特卡洛与局域能量约束的混合优化，在统一框架Schrödinger中一次训练即可准确求解电子-核薛定谔方程，获得全局势能面并捕捉超越玻恩-奥本海默近似的量子效应。
AI 中文摘要
直接求解完整的电子-核薛定谔方程仍是量子力学中的重大挑战之一。在此，我们提出一种受量子化学启发的基于轨道的神经网络波函数拟设，其中包含显式的多体电子-电子关联项，其参数依赖于整个电子-核构型，从而能够在广泛的核构型空间中，通过单个Slater行列式准确描述强关联和/或多参考电子结构。为了训练该波函数，我们进一步开发了一种高效的混合优化策略，该策略将变分蒙特卡洛技术与局域能量约束相结合，缓解了前者固有的采样偏差，并显著降低了统计误差。这些进展被整合到一个统一的神经网络框架Schrödinger中，使得仅通过一次训练即可为从强关联双原子分子、含圆锥交叉的三原子反应，到多原子多参考分子等系统确定全局准确的势能面。本工作为求解电子-核薛定谔方程并提供超越玻恩-奥本海默近似的全量子效应，提供了一种实用的机器学习工具。
英文摘要
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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