近幾十年來，密度泛函理論（DFT）一直是第一性原理材料科學的主力軍。改進的交換關聯（xc）泛函如今已有數百種不同類型，包括廣義梯度近似（GGA）、元GGA、（篩選的）混合函數、Hubbard修正的局部密度近似（LDA+U）/廣義梯度近似（GGA + U）和非局域范德華（vdW）密度泛函等。通常，這些泛函包含針對特定類型或特定材料類別對幾個參數所作的優化。此外，它們依賴於交換近似和關聯近似之間的誤差消除，限制了常用交換關聯泛函的通用性和預測能力，其準確性也常常高度依賴於系統。這種非通用性的特點不能令人滿意。
來自丹麥技術大學物理系計算原子尺度材料設計（CAMD）的Thomas Olsen教授帶領的團隊，重點綜述了含時密度泛函理論（TDDFT）中的靜態非局部交換關聯泛函所描述的RPA和GW方法中的物理理論、實現途徑和意義。作者並未詳述RPA和GW方法本身，該方法的綜述已在另一篇綜述中闡明。在「理論」一節中，他們分別介紹了基於絕熱連接漲落耗散定理和Hedin方程的基態和QP能量計算的基本理論。作者為HEG引入了幾個非局域的交換關聯泛函，並描述了從（半）局域交換關聯泛函構造非局域交換關聯泛函的重整化過程。
在「實現」一節中，作者描述了非局域交換關聯泛函的數值實現，包括將HEG泛函推廣到非均勻密度體系的不同策略、倒空間格點和基集收斂性等方面。在「結果」一節中，作者提供了一系列計算結果，用以說明交換關聯泛函對總能量和QP能帶結構的影響和重要性。具體而言，作者評估了重整化絕熱局域密度近似（rALDA）和重整化絕熱廣義梯度近似（rAPBE）在固體結構參數、共價固體和共價分子的原子化能、氧化物形成能、vdW鍵、靜態關聯的原子二聚體的解離、表面和化學吸附能、結構相變，以及塊體和二維半導體的QP能等方面的性能。最後，對全文進行了總結和展望。
該文近期發表於npj Computational Materials 5: 106 (2019)，英文標題與摘要如下，點擊https://www.nature.com/articles/s41524-019-0242-8可以自由獲取論文PDF。
Beyond the RPA and GW methods with adiabatic xc-kernels for accurate ground state and quasiparticle energies
Thomas Olsen, Christopher E. Patrick, Jefferson E. Bates, Adrienn Ruzsinszky & Kristian S. Thygesen
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 (renormalized adiabatic local density approximation) and rAPBE (renormalized adiabatic Perdew–Burke–Ernzerhof）. 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.