arXiv:2604.27256physics.chem-phcs.AI2026-04

用物理约束模型直接预测分子密度矩阵,大幅加速自洽场计算。

Towards Accelerated SCF Workflows with Equivariant Density-Matrix Learning and Analytic Refinement

论文配图:Towards Accelerated SCF Workflows with Equivariant Density-Matrix Learning and Analytic Refinement
图 1 · 摘自论文原文
  • 基于等变神经网络直接从几何结构预测单电子密度矩阵。
  • 六种分子的初始猜测使迭代次数减少49%至81%。
  • 无需力监督即可获得准确能量和原子力,适合量子化学初值生成。

我们提出 extsc{dm-PhiSNet},一种基于 extsc{PhiSNet} 的等变模型,可直接从分子几何结构(在原子轨道基下)预测一电子约化密度矩阵(1-RDM),以加速自洽场(SCF)流程。训练采用两阶段策略,逐步引入物理驱动目标,结果通过轻量级解析模块进行精修:该模块强制电子数守恒,推动1-RDM在原子轨道度量下趋于广义幂等性,并正则化 Löwdin 正交化密度的占据谱。在六种闭壳层体系(H$_2$O、CH$_4$、NH$_3$、HF、乙醇、NO$_3^-$)上,精修后的1-RDM作为初始猜测,相较标准初始化显著减少49%–81%的迭代步数。此外,学习得到的1-RDM可直接给出高精度的一次性总能与 Hellmann--Feynman 原子力,无需力监督,表明模型已捕捉到化学上合理的电子结构。结果表明,结合等变学习与解析约束强制,是一种简单通用的求解器就绪密度矩阵初值生成路径,可有效加速SCF流程。

原文摘要 · Abstract (English)

We present \textsc{dm-PhiSNet}, a physically constrained \textsc{PhiSNet}-based equivariant model that predicts one-electron reduced density matrices (1-RDMs) directly from molecular geometries in an atomic-orbital (AO) basis for accelerated self-consistent field (SCF) workflows. Training follows a two-stage schedule with progressively introduced physically motivated objectives, and the resulting predictions are refined by a lightweight analytic block. This block enforces electron-number conservation, drives the 1-RDM toward generalized idempotency in the AO metric, and regularizes the occupation spectrum of the Löwdin-orthogonalized density. Across six closed-shell systems -- H$_2$O, CH$_4$, NH$_3$, HF, ethanol, and NO$_3^-$ -- the refined 1-RDMs provide SCF initial guesses that substantially reduce iteration steps by 49--81\% relative to standard initializations. Beyond SCF acceleration, the learned 1-RDMs yield accurate one-shot total energies and Hellmann--Feynman atomic forces without force supervision, indicating that the model captures chemically meaningful electronic structure. These results demonstrate that combining equivariant learning with analytic constraint enforcement provides a simple, general route to solver-ready density-matrix initializations and accelerated SCF workflows.

SCF加速密度矩阵等变神经网络

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