$Δ$-Machine Learning for Potential Energy Surfaces: A PIP approach to bring a DFT-based PES to CCSD(T) Level of Theory
Emory University（埃默里大学）；University of Maryland, College Park（马里兰大学帕克分校）；Cornell University（康奈尔大学）；Georgia Institute of Technology（佐治亚理工学院）；Università Degli Studi di Milano（米兰大学）
Apurba Nandi, Chen Qu, Paul Houston, Riccardo Conte, Joel M. Bowman
``$Δ$-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 to 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 $V_{LL{\rightarrow}CC}=V_{LL}+Δ{V_{CC-LL}}$, and demonstrated for \ce{CH4}, \ce{H3O+}, and $trans$ and $cis$-$N$-methyl acetamide (NMA), \ce{CH3CONHCH3}. For these molecules, the LL PES, $V_{LL}$, is a PIP fit to DFT/B3LYP/6-31+G(d) energies and gradients, and $Δ{V_{CC-LL}}$ 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 \ce{CH4} these are new calculations adopting an aug-cc-pVDZ basis, for \ce{H3O+} 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.
N$_3^+$: Full-Dimensional Potential Energy Surface, Vibrational Energy Levels and Ground State Dynamics
在CCSD（T）-F_（12）和MRCI+Q水平上，通过三维势能面的量子束缚态计算，确定了N $_3^+$离子的电子基态的基本态和高振动激发态.在质量较高的CCSD（T）-F12表面上，振动基频位于1130 cm $^{-1}$（$ν_1$，对称拉伸）、807 cm $^{-1}$（$ν_3$，不对称拉伸）和406 cm $^{-1}$（$ν_2$，弯曲）。对于$ν_1$，计算结果接近于实验（1170 cm $^{-1}$）和先前计算\cite{rosmus.n3:1994}（发现其在1190 cm $^{-1}$）的估计频率。在MRCI+Q PES上对振动态的计算与CCSD（T）-F12 PES上的计算定性一致。MRCI+Q计算的参考CASSCF波函数的分析提供了进一步的了解PES的形状，并支持Hartree-Fock作为耦合簇计算的参考波函数的可靠性。据此，N-$_3^+$在其电子基态（$^3$ A-$''$）3d PES的所有低能区主要具有单参考特征.
Clarifying NH2 + O(3P) Reaction Dynamics: A Full-Dimensional MRCI, Machine-Learned PES Unravels High-Temperature Kinetics
MIIT Key Laboratory of Semiconductor Microstructure and Quantum Sensing, Department of Applied Physics, School of Physics, Nanjing University of Science and Technology（南京理工大学应用物理学院）
Permutationally invariant polynomial regression for energies and gradients, using reverse differentiation, achieves orders of magnitude speed-up with high precision compared to other machine learning methods
ExoMol line lists -- XL. Ro-vibrational molecular line list for the hydronium ion (H$_3$O$^+$)
计算水合氢（H $_3$ $^{16}$ O $^+$）的新的线列表。该谱线是基于一个新的从头计算偶极矩曲面（CCSD（T）/aug-cc-pVQZ）和一个新的经验势能面（PES）。H $_3$ O $^+$的经验PES是通过对从文献中收集的实验确定的振转能量进行全局拟合来精炼从头算表面而获得的，所述文献包括地面、$ν_1^{\pm}$、$ν_2^{\pm}$、$2ν_2^{\pm}$、$ν_3^{\pm}$和$ν_4^{\pm}$振动态。该线路表涵盖了高达10 000 cm $^{-1}$（波长$>1 μ$ m）的波数范围，并应在高达$T=1500$ K的温度下完成。这是H $_3$ O $^+$的第一个全面的线列表，具有广泛的波数覆盖范围和准确的过渡概率。讨论了太阳系巨行星和系外行星光谱中水合氢离子探测的前景。eXeL细胞系列表可从ExoMol和CDS数据库公开获得。
