Density Functional Theory (DFT) is a pivotal method within quantum chemistry and materials science, with its core involving the construction and solution of the Kohn-Sham Hamiltonian. Despite its importance, the application of DFT is frequently limited by the substantial computational resources required to construct the Kohn-Sham Hamiltonian. In response to these limitations, current research has employed deep-learning models to efficiently predict molecular and solid Hamiltonians, with roto-translational symmetries encoded in their neural networks. However, the scalability of prior models may be problematic when applied to large molecules, resulting in non-physical predictions of ground-state properties. In this study, we generate a substantially larger training set (PubChemQH) than used previously and use it to create a scalable model for DFT calculations with physical accuracy. For our model, we introduce a loss function derived from physical principles, which we call Wavefunction Alignment Loss (WALoss). WALoss involves performing a basis change on the predicted Hamiltonian to align it with the observed one; thus, the resulting differences can serve as a surrogate for orbital energy differences, allowing models to make better predictions for molecular orbitals and total energies than previously possible. WALoss also substantially accelerates self-consistent-field (SCF) DFT calculations. Here, we show it achieves a reduction in total energy prediction error by a factor of 1347 and an SCF calculation speed-up by a factor of 18%. These substantial improvements set new benchmarks for achieving accurate and applicable predictions in larger molecular systems.

翻译：密度泛函理论（DFT）是量子化学和材料科学中的关键方法，其核心在于构建并求解Kohn-Sham哈密顿量。尽管DFT至关重要，但其应用常受限于构建Kohn-Sham哈密顿量所需的大量计算资源。针对这些限制，当前研究已采用深度学习模型来高效预测分子与固体哈密顿量，并在神经网络中编码了旋转平移对称性。然而，现有模型的可扩展性在应用于大分子时可能存在问题，导致对基态性质的非物理预测。在本研究中，我们生成了一个比以往所用数据集大得多的训练集（PubChemQH），并利用它创建了一个具有物理精度的、可扩展的DFT计算模型。对于我们的模型，我们引入了一种基于物理原理推导的损失函数，称之为波函数对齐损失（WALoss）。WALoss涉及对预测的哈密顿量进行基变换以使其与观测值对齐；由此产生的差异可作为轨道能量差异的替代度量，使模型能够比以往更准确地预测分子轨道和总能量。WALoss还显著加速了自洽场（SCF）DFT计算。本文表明，该模型将总能量预测误差降低了1347倍，并将SCF计算速度提升了18%。这些显著改进为在更大分子系统中实现精确且适用的预测设立了新的基准。