Predicting electronic screening for fast Koopmans spectral functional calculations

Koopmans spectral functionals are a powerful extension of Kohn-Sham density-functional theory (DFT) that enable the prediction of spectral properties with state-of-the-art accuracy. The success of these functionals relies on capturing the effects of electronic screening through scalar, orbital-dependent parameters. These parameters have to be computed for every calculation, making Koopmans spectral functionals more expensive than their DFT counterparts. In this work, we present a machine-learning model that — with minimal training — can predict these screening parameters directly from orbital densities calculated at the DFT level. We show on two prototypical use cases that using the screening parameters predicted by this model, instead of those calculated from linear response, leads to orbital energies that differ by less than 20 meV on average. Since this approach dramatically reduces run-times with minimal loss of accuracy, it will enable the application of Koopmans spectral functionals to classes of problems that previously would have been prohibitively expensive, such as the prediction of temperature-dependent spectral properties. More broadly, this work demonstrates that measuring violations of piecewise linearity (i.e. curvature in total energies with respect to occupancies) can be done efficiently by combining frozen-orbital approximations and machine learning.

库普曼斯谱函数泛函是对科恩-肖密特密度泛函理论（Kohn-Sham DFT）的强大扩展，能够以最先进的精度预测光谱性质。这些泛函的成功依赖于通过标量、轨道相关的参数捕捉电子屏蔽效应。这些参数必须针对每次计算进行计算，使得库普曼斯谱函数的成本高于其DFT等价物。在本研究中，我们提出了一种机器学习模型，通过最小化训练，可以直接从DFT级别的轨道密度预测这些屏蔽参数。我们通过两个典型用例展示，使用该模型预测的屏蔽参数而非通过线性响应计算得到的参数，平均轨道能量差异小于20毫电子伏特。由于这种方法显著减少了运行时间，同时最小化了精度损失，它将使库普曼斯谱函数的应用扩展到之前因成本过高而无法触及的领域，例如预测温度依赖性光谱性质。更广泛地说，这项工作证明了通过结合冻结轨道近似和机器学习，可以高效地测量分段线性（即总能量相对于占据度的曲率）的违反情况。