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 G₀W₀ 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.

中文翻译：

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GW的核心层结合能的相对论校正方案。

我们提出以提高1S核心级的结合从格林函数理论计算出的能量的准确性相对论修正方案GW近似，不增加计算开销。特定元素的校正项是从非相对论或标量相对论Kohn-Sham方程与四分量Dirac-Kohn-Sham方程的自洽解获得的1s特征值之间的差而得出的。我们研究了该校正术语对分子环境的依赖性以及杂化交换相关功能中精确交换的数量。然后将此校正项作为对部分自洽和单发GW的准粒子能量的扰动添加计算。我们表明，将这种特定于元素的相对论校正应用于先前报告的65个核心态激励的基准测试集[D. Golze等。，J。Phys。化学 来吧 11，1840年至1847年（2020年）]，降低了平均绝对误差（MAE）相对于在实验0.55电子伏特到0.30电子伏特，并消除了物种MAE，其以其它方式与原子序数增加的依赖性。相对论校正还减少了物种相关性，从而使混合功能中最佳精确交换的最佳量用作单次G ₀ W ₀的起点计算。我们的校正方案可以转移到其他方法，我们将基于密度泛函理论针对增量自洽场（ΔSCF）方法进行演示。