Kohn-Sham density functional theory (DFT) is a standard tool in most branches of chemistry, but accuracies for many molecules are limited to 2-3 kcal ⋅ mol⁻¹ with presently-available functionals. Ab initio methods, such as coupled-cluster, routinely produce much higher accuracy, but computational costs limit their application to small molecules. In this paper, we leverage machine learning to calculate coupled-cluster energies from DFT densities, reaching quantum chemical accuracy (errors below 1 kcal ⋅ mol⁻¹) on test data. Moreover, density-based Δ-learning (learning only the correction to a standard DFT calculation, termed Δ-DFT ) significantly reduces the amount of training data required, particularly when molecular symmetries are included. The robustness of Δ-DFT is highlighted by correcting “on the fly” DFT-based molecular dynamics (MD) simulations of resorcinol (C₆H₄(OH)₂) to obtain MD trajectories with coupled-cluster accuracy. We conclude, therefore, that Δ-DFT facilitates running gas-phase MD simulations with quantum chemical accuracy, even for strained geometries and conformer changes where standard DFT fails.

科恩深水密度泛函理论（DFT）是在化学的大多数分支的标准工具，但对于许多分子精度被限制在2-3千卡⋅摩尔^-1与目前可用的泛函。从头开始，例如耦合簇，通常会产生更高的准确性，但是计算成本限制了它们在小分子上的应用。在本文中，我们利用机器学习来计算从DFT密度耦合簇能量，达到量子化学精度（低于1千卡错误⋅摩尔^-1上的测试数据）。此外，基于密度的Δ学习（仅学习对标准DFT计算的校正，称为Δ-DFT）大大减少了所需的训练数据量，尤其是当包括分子对称性时。通过校正“动态”间苯二酚（C ₆ H ₄（OH）₂）的基于DFT的分子动力学（MD）模拟来获得具有耦合簇精度的MD轨迹，可以突出Δ -DFT的鲁棒性。因此，我们得出的结论是，即使对于标准DFT失效的应变几何形状和构象异构体变化，Δ -DFT仍有助于以量子化学精度运行气相MD模拟。