Koopmans-Compliant Functionals and Potentials and Their Application to the GW100 Test Set

Koopmans-compliant (KC) functionals have been shown to provide accurate spectral properties through a generalized condition of piecewise linearity of the total energy as a function of the fractional addition/removal of an electron to/from any orbital. We analyze the performance of different KC functionals on a large and standardized set of 100 molecules, the GW100 test set, comparing vertical ionization potentials (taken as opposite of the orbital energies) to those obtained from accurate quantum chemistry methods, and to experimental results. We find excellent agreement, with a mean absolute error of 0.20 eV for the KIPZ functional on the first ionization potential, which is state-of-the-art for both density functional theory (DFT)-based calculations and many-body perturbation theory. We highlight similarities and differences between KC functionals and other electronic-structure approaches, such as dielectric-dependent hybrid functionals and Green's function methods, both from a theoretical and from a practical point of view, arguing that KC potentials can be considered as local and orbital-dependent approximations to the electronic self-energy, already including approximate vertex corrections.

符合库普曼斯准则的泛函（Koopmans-compliant functionals，KC）已被证实可通过广义分段线性条件实现精准的光谱性质计算，该条件将总能量定义为向任意轨道进行分数级电子添加或移除的函数。本研究针对包含100个分子的大型标准化数据集GW100测试集（GW100 test set），分析了不同KC泛函的计算性能，将垂直电离势（即轨道能量的相反数）与高精度量子化学方法所得结果及实验结果进行对比。研究结果显示二者吻合度极佳：针对第一电离势，KIPZ泛函的平均绝对误差仅为0.20 eV，这一精度在基于密度泛函理论（DFT）的计算及多体微扰理论领域均处于当前顶尖水平。本研究从理论与实践双维度出发，对比分析了KC泛函与其他电子结构方法（如依赖介电常数的杂化泛函、格林函数方法）的异同，并提出：KC势能可被视为针对电子自能的局域性、轨道依赖性近似，且已包含近似顶点修正项。