We review the theory and application of adiabatic exchange–correlation (xc)-kernels for ab initio calculations of ground state energies and quasiparticle excitations within the frameworks of the adiabatic connection fluctuation dissipation theorem and Hedin’s equations, respectively. Various different xc-kernels, which are all rooted in the homogeneous electron gas, are introduced but hereafter we focus on the specific class of renormalized adiabatic kernels, in particular the rALDA and rAPBE. The kernels drastically improve the description of short-range correlations as compared to the random phase approximation (RPA), resulting in significantly better correlation energies. This effect greatly reduces the reliance on error cancellations, which is essential in RPA, and systematically improves covalent bond energies while preserving the good performance of the RPA for dispersive interactions. For quasiparticle energies, the xc-kernels account for vertex corrections that are missing in the GW self-energy. In this context, we show that the short-range correlations mainly correct the absolute band positions while the band gap is less affected in agreement with the known good performance of GW for the latter. The renormalized xc-kernels offer a rigorous extension of the RPA and GW methods with clear improvements in terms of accuracy at little extra computational cost.

我们回顾了绝热交换相关（xc）核在绝热连接波动耗散定理和Hedin方程框架内从头计算基态能量和准粒子激发的理论和应用。介绍了各种均基于均质电子气的不同xc内核，但此后我们将重点关注特定种类的重新归一化绝热内核，特别是rALDA和rAPBE。与随机相位近似（RPA）相比，内核极大地改善了对短程相关性的描述，从而显着改善了相关能量。这种效果大大减少了对误差消除的依赖，这在RPA中至关重要，并系统地提高了共价键能，同时保留了RPA在分散相互作用中的良好性能。对于准粒子能量，xc内核说明了GW自能量中缺少的顶点校正。在这种情况下，我们表明，短程相关性主要是校正绝对带位置，而与GW已知的良好性能相一致，带隙受到的影响较小。重新标准化的xc内核对RPA和GW方法进行了严格的扩展，在准确性方面有明显的改进，而几乎没有额外的计算成本。我们表明，短程相关性主要校正绝对带位置，而带隙的影响较小，这与GW已知的良好性能相一致。重新标准化的xc内核对RPA和GW方法进行了严格的扩展，在准确性方面有明显的改进，而几乎没有额外的计算成本。我们表明，短程相关性主要校正绝对带位置，而带隙的影响较小，这与GW已知的良好性能相一致。重新标准化的xc内核对RPA和GW方法进行了严格的扩展，在准确性方面有明显的改进，而几乎没有额外的计算成本。