论文标题
一单电子系统的地面和激发态的最近密度函数的良好功能如何？
How good are recent density functionals for ground and excited states of one-electron systems?
论文作者
论文摘要
Sun等。 [J。化学物理。 144，191101（2016）]提出，作为轨道淋巴结的必要结果，普通密度函数近似（DFA）应显示激发态的较大能量误差。由自我交织校正的密度功能计算在许多电子系统上的动机，我们继续他们的研究，以$ 1S $，$ 2p $和36美元的36个氢一个单电子离子（H-kr $^{35+} $）的$ 3D $状态进行研究，并以$ ovt的$ the $ updect $ $ 2的$ 2 $ 2 $ 2的$ 2。我们考虑在局部密度近似（LDA），广义梯度近似（GGA）以及元GGGA水平的56个功能，还包括几种混合功能，例如最近提出的机器学习的DM21局部杂交功能。 $ 1S $地面状态的最佳非混合功能是RevTPSS。 $ 2p $和$ 3D $兴奋的状态对于DFA来说更加困难，因为Sun等人。预测的，LDA功能证明在非杂交功能中为这些状态产生了最系统的准确性。总体上观察到这三个州的最佳性能是通过Bhandh全球混合型GGA功能，其中包含50％的Hartree-fock Exchange和50％的LDA交换。发现DM21的性能是不一致的，对于某些州和系统而言，准确性良好，而其他国家的准确性则差。基于这些结果，我们建议在未来的机器学习密度功能的培训中包括各种单电子阳离子。
Sun et al. [J. Chem. Phys. 144, 191101 (2016)] suggested that common density functional approximations (DFAs) should exhibit large energy errors for excited states as a necessary consequence of orbital nodality. Motivated by self-interaction corrected density functional calculations on many-electron systems, we continue their study with the exactly solvable $1s$, $2p$, and $3d$ states of 36 hydrogenic one-electron ions (H-Kr$^{35+}$) and demonstrate with self-consistent calculations that state-of-the-art DFAs indeed exhibit large errors for the $2p$ and $3d$ excited states. We consider 56 functionals at the local density approximation (LDA), generalized gradient approximation (GGA) as well as meta-GGA levels, also including several hybrid functionals like the recently proposed machine-learned DM21 local hybrid functional. The best non-hybrid functional for the $1s$ ground state is revTPSS. The $2p$ and $3d$ excited states are more difficult for DFAs as Sun et al. predicted, and LDA functionals turn out to yield the most systematic accuracy for these states amongst non-hybrid functionals. The best performance for the three states overall is observed with the BHandH global hybrid GGA functional, which contains 50% Hartree-Fock exchange and 50% LDA exchange. The performance of DM21 is found to be inconsistent, yielding good accuracy for some states and systems and poor accuracy for others. Based on these results, we recommend including a variety of one-electron cations in future training of machine-learned density functionals.
