Density-Based Basis-Set Incompleteness Correction for <i>GW</i> Methods

Similar to other electron correlation methods, many-body perturbation theory methods based on Green's functions, such as the so-called GW approximation, suffer from the usual slow convergence of energetic properties with respect to the size of the one-electron basis set. This displeasing feature is due to the lack of explicit electron–electron terms modeling the infamous Kato electron–electron cusp and the correlation Coulomb hole around it. Here, we propose a computationally efficient density-based basis-set correction based on short-range correlation density functionals which significantly speeds up the convergence of energetics toward the complete basis set limit. The performance of this density-based correction is illustrated by computing the ionization potentials of the 20 smallest atoms and molecules of the GW100 test set at the perturbative GW (or G0W0) level using increasingly large basis sets. We also compute the ionization potentials of the five canonical nucleobases (adenine, cytosine, thymine, guanine, and uracil) and show that, here again, a significant improvement is obtained.与其他电子关联方法类似，基于格林函数（Green's functions）的多体微扰理论方法——例如所谓的GW近似（GW approximation）——同样存在常见的性能缺陷：其能量性质随单电子基组尺寸增大的收敛速度偏慢。这一不尽如人意的特性源于现有方法未引入显式的电子-电子相互作用项，以刻画臭名昭著的Kato电子电子尖点及其周边的关联库仑空穴。本文提出一种基于短程关联密度泛函、计算效率优异的基组校正方法，可显著加速能量性质向完备基组极限的收敛过程。我们通过在微扰GW（即G0W0）理论级别下，使用尺寸逐步增大的基组，计算GW100测试集中前20个最小原子与分子的电离能，以此验证该密度基校正方法的性能。此外，我们还计算了五种经典核碱基——腺嘌呤（adenine）、胞嘧啶（cytosine）、胸腺嘧啶（thymine）、鸟嘌呤（guanine）与尿嘧啶（uracil）——的电离能，结果表明该方法同样能带来显著的性能提升。