Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA.
Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, USA.
J Chem Phys. 2021 Feb 7;154(5):051102. doi: 10.1063/5.0038301.
"Δ-machine learning" refers to a machine learning approach to bring a property such as a potential energy surface (PES) based on low-level (LL) density functional theory (DFT) energies and gradients close to a coupled cluster (CC) level of accuracy. Here, we present such an approach that uses the permutationally invariant polynomial (PIP) method to fit high-dimensional PESs. The approach is represented by a simple equation, in obvious notation V = V + ΔV, and demonstrated for CH, HO, and trans and cis-N-methyl acetamide (NMA), CHCONHCH. For these molecules, the LL PES, V, is a PIP fit to DFT/B3LYP/6-31+G(d) energies and gradients and ΔV is a precise PIP fit obtained using a low-order PIP basis set and based on a relatively small number of CCSD(T) energies. For CH, these are new calculations adopting an aug-cc-pVDZ basis, for HO, previous CCSD(T)-F12/aug-cc-pVQZ energies are used, while for NMA, new CCSD(T)-F12/aug-cc-pVDZ calculations are performed. With as few as 200 CCSD(T) energies, the new PESs are in excellent agreement with benchmark CCSD(T) results for the small molecules, and for 12-atom NMA, training is done with 4696 CCSD(T) energies.
“Δ-机器学习”是指一种机器学习方法，可以将势能面（PES）等性质逼近基于低水平（LL）密度泛函理论（DFT）能量和梯度的耦合簇（CC）精度。在这里，我们提出了一种使用置换不变多项式（PIP）方法拟合高维 PES 的方法。该方法用一个简单的方程表示，符号明显，V=V+ΔV，并对 CH、HO、反式和顺式-N-甲基乙酰胺（NMA）、CHCONHCH 进行了演示。对于这些分子，LL PES，V，是一个对 DFT/B3LYP/6-31+G(d)能量和梯度的 PIP 拟合，而 ΔV 是一个基于低阶 PIP 基集并使用相对较少的 CCSD(T)能量的精确 PIP 拟合。对于 CH，这些是采用 aug-cc-pVDZ 基的新计算，对于 HO，使用以前的 CCSD(T)-F12/aug-cc-pVQZ 能量，而对于 NMA，则进行新的 CCSD(T)-F12/aug-cc-pVDZ 计算。仅用 200 个 CCSD(T)能量，新的 PES 与小分子的基准 CCSD(T)结果非常吻合，而对于 12 原子 NMA，则使用 4696 个 CCSD(T)能量进行训练。
