In ref (1), a coding error led to inaccuracies in the calculation of GW quasiparticle (QP) energies evaluated beyond the random phase approximation (RPA). After correcting the implementation, the conclusions of our original contribution remain valid. Here we report updated Figures 5–7 and Tables 1 and 2. The major difference between the updated results and the original ones was found for the quasiparticle (QP) energies of molecules computed at the G₀W₀^f_xc level. In Figure 5 we show the mean deviation (MD) of G₀W₀^f_xc and G₀W₀Γ₀ results from G₀W₀^RPA results. The MD between G₀W₀^f_xc and G₀W₀^RPA is −0.15/-0.13/-0.24 eV for the vertical ionization potential (VIP) and 0.15/0.15/0.23 eV for the vertical electron affinity (VEA) with the LDA/PBE/DDH functional, respectively (in ref (1). the MD was 0.30/0.31/0.58 eV for VIP and −0.01/-0.01/0.01 eV for VEA). Although the updated MD values are different from those of ref (1), this difference does not affect our original conclusions, i.e., that the effect of vertex correction at the G₀W₀^f_xc level is less significant than that found at the G₀W₀Γ₀ level. We found that the MD between G₀W₀Γ₀ and G₀W₀^RPA results is −0.35/-0.56/-0.40 eV for VIP and −0.49/-0.59/-0.66 eV for VEA with the LDA/PBE/DDH functional, respectively (in ref (1). the MD was −0.74/-0.76/-1.25 eV for VIP and −0.26/-0.30/-0.32 eV). The trend that both VIP and VEA obtained at the G₀W₀Γ₀ level are lower than those obtained at the G₀W₀^RPA level is the same as that reported in ref (1). Figure 5. Difference (ΔE) between vertical ionization potential (VIP) and vertical electron affinity (VEA) of molecules in the GW100 set computed at the G₀W₀^f_xc/G₀W₀Γ₀ level and corresponding G₀W₀^RPA results. Mean deviations (MDs) in electronvolts are shown in brackets and represented with black dashed lines. Results are presented for three different functionals (LDA, PBE, and PBE0) in the top, middle, and bottom panel, respectively. Figure 6. Vertical ionization potential (VIP), vertical electron affinity (VEA) and electronic gap of molecules in the GW100 set computed at G₀W₀^RPA, G₀W₀^f_xc, and G₀W₀Γ₀ levels of theory, compared to experimental and CCSD(T) results (black dashed lines). Figure 7. GW quasiparticle corrections to the valence band maximum (VBM) and the conduction band minimum (CBM). Circles, squares, and triangles are G₀W₀^RPA, G₀W₀^f_xc, and G₀W₀Γ₀ results, respectively; red, blue, and green markers correspond to calculations with LDA, PBE, and DDH functionals. We report vertical ionization potentials (VIP), vertical electron affinities (VEA), and the fundamental electronic gaps. All values are given in electronvolts. All calculations are performed at the Γ-point of supercells with 64–96 atoms (see section 1 of the Supporting Information for details). For solids, the updated band gap values (Table 2) are similar to those in ref (1), with the mean absolute deviation (MAD) between current and previous results being 0.17 eV for G₀W₀^f_xc calculations (fifth column) and 0.06 eV for G₀W₀Γ₀ calculations (sixth column). The largest difference was found in the case of G₀W₀^f_xc calculations of WO₃ and Si₃N₄, where the updated results are ∼0.3 eV lower than previous ones. The conclusion that in solids the effect of vertex corrections is much smaller than in molecules remains the same. We emphasize that while the specific numbers reported in the updated tables and figures are different from the corresponding ones in ref (1), the trends observed here are the same as those reported previously and therefore the major conclusions of ref (1) remain unaltered. All of the equations in ref (1) remain unchanged. Finally, we note that the update discussed here does not involve changes to the implementation of the finite-field algorithm presented in ref (1) for the calculation of response functions and exchange–correlation kernels. Therefore subsequent works of ref (1) that deploy the finite-field algorithm and its original implementation (e.g., ref (2)) remain unaltered. This article references 2 other publications.

中文翻译：

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在随机相位近似之外，对GW计算的有限域方法进行了校正。

在参考文献（1）中，编码错误导致对GW准粒子（QP）能量的计算不准确，超出了随机相位近似（RPA）评估。在更正实施之后，我们原始贡献的结论仍然有效。在这里，我们报告更新的图5–7以及表1和2。发现了更新结果和原始结果之间的主要差异，这是在G ₀ W ₀ ^{f _xc}能级下计算的分子的准粒子（QP）能量。在图5中，我们显示的平均偏差（MD）ģ ₀ w ^ ₀ ^{˚F _XC}和G ^ ₀ w ^ ₀ Γ ₀从结果ģ ₀ w ^ ₀ ^RPA结果。G ₀ W ₀ ^{f _xc}和G ₀ W ₀ ^RPA之间的MD对于具有LDA / PBE / DDH功能的垂直电离电势（VIP）为-0.15 / -0.13 / -0.24 eV，对于垂直电子亲和力（VEA）为0.15 / 0.15 / 0.23 eV（参考文献（1）。 VIP的MD值为0.30 / 0.31 / 0.58 eV，VEA的MD为-0.01 / -0.01 / 0.01 eV）。尽管更新的MD值与参考（1）的值不同，但是这种差异不会影响我们的原始结论，即，在G ₀ W ₀ ^{f _xc}级别的顶点校正的影响不如在G处发现的显着。₀ w ^ ₀ Γ ₀电平。我们发现之间的MD g ^ ₀ w ^ ₀ Γ ₀和g ^₀ W ₀具有LDA / PBE / DDH功能的VIP的^RPA结果分别为VIP的-0.35 / -0.56 / -0.40 eV和VEA的-0.49 / -0.59 / -0.66 eV（在参考文献（1）中，MD为- VIP为0.74 / -0.76 / -1.25 eV，−0.26 / -0.30 / -0.32 eV）。这两个VIP和VEA在所获得的趋势ģ ₀ w ^ ₀ Γ ₀电平是比在获得的那些低ģ ₀ w ^ ₀ ^RPA级是相同的，在参考文献（1）的报道。图5.以G ₀ W ₀ ^{f _xc}计算的GW100集合中的分子的垂直电离电势（VIP）和垂直电子亲和力（VEA）之间的差异（ΔE）/ g ^ ₀ w ^ ₀ Γ ₀级和对应ģ ₀ w ^ ₀ ^RPA结果。电子伏特的平均偏差（MDs）显示在括号中，并用黑色虚线表示。顶部，中间和底部分别显示了三种不同功能（LDA，PBE和PBE0）的结果。图6.在G ₀ W ₀ ^RPA，G ₀ W ₀ ^{f _xc}和G ₀ W _0下计算的GW100集中的分子的垂直电离势（VIP），垂直电子亲和力（VEA）和电子间隙Γ ₀水平的理论，相对于实验和CCSD（T）的结果（黑虚线）。图7. GW对价带最大值（VBM）和导带最小值（CBM）的准粒子校正。圆形，正方形和三角形是G ^ ₀ w ^ ₀ ^RPA，G ^ ₀ w ^ ₀ ^{˚F _XC}，和G ^ ₀ w ^ ₀ Γ ₀结果分别；红色，蓝色和绿色标记对应于LDA，PBE和DDH功能的计算。我们报告了垂直电离势（VIP），垂直电子亲和力（VEA）和基本电子间隙。所有值均以电子伏特为单位。所有计算均在具有64–96个原子的超级电池的Γ点执行（有关详细信息，请参阅《支持信息》的第1节）。对于固体，更新的带隙值（表2）与参考文献（1）中的值类似，对于G ₀ W ₀ ^{f _xc}计算，当前结果与先前结果之间的平均绝对偏差（MAD）为0.17 eV （第五列）和0.06电子伏特为G ^ ₀ w ^ ₀ Γ ₀计算（第六列）。在计算WO ₃和Si ₃ N ₄的G ₀ W ₀ ^{f _xc时}，发现最大的差异，其中更新的结果比以前的结果低约0.3 eV。在固体中，顶点校正的效果远小于在分子中的校正的结论保持不变。我们强调，虽然更新后的表格和图中报告的具体数字与参考文献（1）中的相应数字不同，但此处观察到的趋势与先前报告的趋势相同，因此参考文献（1）的主要结论保持不变。参考文献（1）中的所有方程式均保持不变。最后，我们注意到这里讨论的更新不涉及对参考函数（1）中介绍的用于计算响应函数和交换相关内核的有限域算法的实现的更改。因此，参考文献（1）的后续工作采用了有限域算法及其原始实现（例如，ref（2））保持不变。本文引用了其他2个出版物。