Keller Levi, Blum Volker, Rinke Patrick, Golze Dorothea
Department of Applied Physics, Aalto University, Otakaari 1, FI-02150 Espoo, Finland.
Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708, USA.
J Chem Phys. 2020 Sep 21;153(11):114110. doi: 10.1063/5.0018231.
We present a relativistic correction scheme to improve the accuracy of 1s core-level binding energies calculated from Green's function theory in the GW approximation, which does not add computational overhead. An element-specific corrective term is derived as the difference between the 1s eigenvalues obtained from the self-consistent solutions to the non- or scalar-relativistic Kohn-Sham equations and the four-component Dirac-Kohn-Sham equations for a free neutral atom. We examine the dependence of this corrective term on the molecular environment and the amount of exact exchange in hybrid exchange-correlation functionals. This corrective term is then added as a perturbation to the quasiparticle energies from partially self-consistent and single-shot GW calculations. We show that this element-specific relativistic correction, when applied to a previously reported benchmark set of 65 core-state excitations [D. Golze et al., J. Phys. Chem. Lett. 11, 1840-1847 (2020)], reduces the mean absolute error (MAE) with respect to the experiment from 0.55 eV to 0.30 eV and eliminates the species dependence of the MAE, which otherwise increases with the atomic number. The relativistic corrections also reduce the species dependence for the optimal amount of exact exchange in the hybrid functional used as a starting point for the single-shot GW calculations. Our correction scheme can be transferred to other methods, which we demonstrate for the delta self-consistent field (ΔSCF) approach based on density functional theory.
我们提出了一种相对论修正方案，以提高在GW近似下从格林函数理论计算得到的1s芯能级结合能的准确性，且该方案不会增加计算开销。通过自由中性原子的非相对论或标量相对论Kohn-Sham方程与四分量Dirac-Kohn-Sham方程的自洽解所得到的1s本征值之间的差值，推导出了一个元素特定的校正项。我们研究了该校正项对分子环境以及杂化交换相关泛函中精确交换量的依赖性。然后，将该校正项作为微扰添加到部分自洽和单次GW计算得到的准粒子能量中。我们表明，当将这种元素特定的相对论修正应用于先前报道的包含65个芯态激发的基准集[D. Golze等人，《物理化学快报》11, 1840 - 1847 (2020)]时，相对于实验的平均绝对误差(MAE)从0.55 eV降低到了0.30 eV，并且消除了MAE对物种的依赖性，否则MAE会随着原子序数的增加而增大。相对论修正还降低了作为单次GW计算起点的杂化泛函中精确交换最佳量对物种的依赖性。我们的修正方案可以转移到其他方法上，我们基于密度泛函理论的δ自洽场(ΔSCF)方法对此进行了演示。
