Meta-Generalized Gradient Approximations (meta-GGAs) can, in principle, include spatial and temporal nonlocality in time-dependent density functional theory at a much lower computational cost than functionals that use exact exchange. We here test whether a meta-GGA that has recently been developed with a focus on capturing nonlocal response properties and the particle number discontinuity can realize such features in practice. To this end, we extended the frequency-dependent Sternheimer formalism to the meta-GGA case. Using the Krieger–Li–Iafrate (KLI) approximation, we calculate the optical response for the selected paradigm molecular systems and compare the meta-GGA Kohn–Sham response to the one found with exact exchange and conventional (semi-)local functionals. We find that the new meta-GGA captures important properties of the nonlocal exchange response. The KLI approximation, however, emerges as a limiting factor in the evaluation of charge-transfer excitations.

中文翻译：

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从Kohn-Sham方案的亚广义梯度近似获得分子激发。

从原则上讲，与时间依赖的密度泛函理论相比，亚广义梯度逼近（meta-GGAs）可以包含时空非局部性，而计算成本要比使用精确交换的泛函近似低得多。我们在这里测试最近开发的专注于捕获非局部响应特性和粒子数不连续性的meta-GGA在实践中是否可以实现这些功能。为此，我们将频率相关的Sternheimer形式主义扩展到了meta-GGA案例。使用Krieger–Li–Iafrate（KLI）近似，我们计算所选范式分子系统的光学响应，并将meta-GGA Kohn–Sham响应与具有精确交换和常规（半）局部功能的响应进行比较。我们发现新的meta-GGA捕获了非本地交换响应的重要属性。但是，在评估电荷转移激发时，KLI近似成为限制因素。