用精确数据训练神经网络，提升量子化学计算精度。
Learning local and semi-local density functionals from exact exchange-correlation potentials and energies
- 基于精确密度、能量和势能，用神经网络学习交换关联泛函。
- 仅用五种原子和两种分子训练，对数百种分子预测更准。
- 用势能信息建模，效果媲美高阶泛函，适合量子化学研究者。
寻找准确的交换关联（XC）泛函仍是密度泛函理论（DFT）的核心挑战。尽管经过40年发展，现有泛函仍未达到化学精度。本文提出一种数据驱动方法，利用精确的电子密度、XC能量和XC势能来学习XC泛函。精确密度来自高精度组态相互作用（CI），而精确的XC能量与势能则通过逆DFT计算得到。我们展示了仅用五个原子和两个分子训练的神经网络局部密度近似（LDA）和广义梯度近似（GGA），即可显著提升数百种未见分子的总能量、电子密度、原子化能和能垒高度预测精度。特别是，基于神经网络的GGA泛函精度接近更高层级的SCAN元泛函，凸显了使用XC势能在构建泛函中的潜力。该方法有望为系统性学习更精确、更复杂的XC泛函铺平道路。
原文摘要 · Abstract (English)
Finding accurate exchange-correlation (XC) functionals remains the defining challenge in density functional theory (DFT). Despite 40 years of active development, the desired chemical accuracy is still elusive with existing functionals. We present a data-driven pathway to learn the XC functionals by utilizing the exact density, XC energy, and XC potential. While the exact densities are obtained from accurate configuration interaction (CI), the exact XC energies and XC potentials are obtained via inverse DFT calculations on the CI densities. We demonstrate how simple neural network (NN) based local density approximation (LDA) and generalized gradient approximation (GGA), trained on just five atoms and two molecules, provide remarkable improvement in total energies, densities, atomization energies, and barrier heights for hundreds of molecules outside the training set. Particularly, the NN-based GGA functional attains similar accuracy as the higher rung SCAN meta-GGA, highlighting the promise of using the XC potential in modeling XC functionals. We expect this approach to pave the way for systematic learning of increasingly accurate and sophisticated XC functionals.
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