无需梯度计算，直接预测分子力场的二阶导数
HIP: Hessian Interatomic Potentials without derivatives
- 用图神经网络提取对称性特征，直接输出哈密顿矩阵
- 速度提升10~100倍，精度更高且内存占用更低
- 适合需要高精度振动分析的分子模拟研究者
分子哈密顿矩阵（二阶导数）是计算化学中诸多流程的基础。传统方法依赖量子化学或机器学习势能模型，计算成本高且随体系规模增长迅速。本文提出哈密顿原子间势能（HIP），一种深度学习模型，直接预测哈密顿矩阵，不依赖自动微分或有限差分。通过图神经网络提取至$ l=2 $阶的不可约表示特征，构建具有SE(3)等变性和对称性的哈密顿矩阵。实验表明，HIP在计算速度上快1到2个数量级，精度更高、内存效率更优，且随系统规模增长更友好。在多种下游任务中验证：过渡态搜索、几何优化、零点能校正和振动分析均表现更优。代码与模型权重已开源。
原文摘要 · Abstract (English)
Molecular Hessians, the second derivatives of the potential energy, are fundamental to many workflows in computational chemistry. Usually, accurate Hessians are computationally expensive to calculate and scale poorly with system size, whether computed using quantum chemistry methods or machine-learning interatomic potentials (MLIPs). In this work, we introduce Hessian interatomic potentials (HIPs), a deep learning model that directly predicts Hessians without relying on automatic differentiation or finite differences. To do so, we construct SE(3)-equivariant, symmetric Hessians from irreducible representation (irrep) features up to degree $l$=2, computed by a graph neural network. HIP Hessians are one to two orders of magnitude faster, more accurate, more memory efficient, easier to train, and exhibit more favourable scaling with system size. We validate our predictions across a wide range of downstream tasks, demonstrating consistently superior performance in transition state search, geometry optimization, zero-point energy corrections, and vibrational analysis. We open-source the HIP code and model weights.
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