The Sternheimer approach to time-dependent density functional theory in the linear response regime is attractive because of its computational efficiency. The latter results from avoiding the explicit calculation of unoccupied orbitals and from the basic structure of the Sternheimer equations, which naturally lend themselves to far-reaching parallelization. In this article, we take a fresh look at the frequency-dependent Sternheimer equations. We first give a complete, self-contained derivation of the equations that complements previous derivations. We then discuss several aspects of an efficient numerical realization. As a worked example, we compute the photoabsorption spectra of small hydrogenated silicon clusters and confirm that for these the quality of the Kohn-Sham eigenvalues is more important than the effects of the exchange-correlation kernel. Finally, we demonstrate how triplet excitations can readily be computed from the Sternheimer approach.

中文翻译：

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没有空状态的线性响应时间相关的密度泛函理论：重新讨论了Kohn-Sham-Sternheimer方案

Sternheimer的方法在线性响应机制中依赖于时间的密度泛函理论是吸引人的，因为它的计算效率很高。后者是由于避免了对未占用轨道的显式计算以及Sternheimer方程的基本结构而产生的，而Sternheimer方程则自然而然地适用于深远的并行化。在本文中，我们将重新研究与频率相关的Sternheimer方程。我们首先给出方程的完整，自包含的推导，以补充先前的推导。然后，我们讨论有效数值实现的几个方面。作为一个可行的例子，我们计算了小的氢化硅团簇的光吸收光谱，并确认对于这些，Kohn-Sham特征值的质量比交换相关核的影响更重要。最后，我们演示了如何从Sternheimer方法轻松计算出三重态激发。