Lewis Alan M, Berkelbach Timothy C
Department of Chemistry and James Franck Institute , University of Chicago , Chicago , Illinois 60637 , United States.
Department of Chemistry , Columbia University , New York , New York 10027 , United States.
J Chem Theory Comput. 2019 May 14;15(5):2925-2932. doi: 10.1021/acs.jctc.8b00995. Epub 2019 Apr 16.
The GW approximation is based on the neglect of vertex corrections, which appear in the exact self-energy and the exact polarizability. Here, we investigate the importance of vertex corrections in the polarizability only. We calculate the polarizability with equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD), which rigorously includes a large class of diagrammatically defined vertex corrections beyond the random phase approximation (RPA). As is well-known, the frequency-dependent polarizability predicted by EOM-CCSD is quite different and generally more accurate than that predicted by the RPA. We evaluate the effect of these vertex corrections on a test set of 20 atoms and molecules. When using a Hartree-Fock reference, ionization potentials predicted by the GW approximation with the RPA polarizability are typically overestimated with a mean absolute error of 0.3 eV. However, those predicted with a vertex-corrected polarizability are typically underestimated with an increased mean absolute error of 0.5 eV. This result suggests that vertex corrections in the self-energy cannot be neglected, at least for molecules. We also assess the behavior of eigenvalue self-consistency in vertex-corrected GW calculations, finding a further worsening of the predicted ionization potentials.
GW近似基于对顶点修正的忽略，顶点修正出现在精确的自能和精确的极化率中。在此，我们仅研究极化率中顶点修正的重要性。我们使用含单双激发的运动方程耦合簇理论（EOM - CCSD）来计算极化率，该理论严格包含了一大类超出随机相位近似（RPA）的、由图解定义的顶点修正。众所周知，EOM - CCSD预测的频率相关极化率与RPA预测的有很大不同，并且通常更准确。我们评估了这些顶点修正在20个原子和分子的测试集上的效果。当使用哈特里 - 福克参考时，采用RPA极化率的GW近似预测的电离势通常被高估，平均绝对误差为0.3电子伏特。然而，采用顶点修正极化率预测的电离势通常被低估，平均绝对误差增加到0.5电子伏特。这一结果表明，至少对于分子而言，自能中的顶点修正不能被忽略。我们还评估了顶点修正的GW计算中本征值自洽性的行为，发现预测的电离势进一步恶化。
