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Constraint-based wave vector and frequency dependent exchange-correlation kernel of the uniform electron gas

机译：基于约束的波矢量和均匀电子气体的频率相关交换核

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摘要

According to time-dependent density functional theory, the exact exchange-correlation kernel f_x(n, q, ω) for wave vector q and frequency ω determines not only the ground-state energy but also the excited-state energies/lifetimes and time-dependent linear density response of an electron gas of uniform density n = 3/(4πr_s~3). Here we propose a parametrization of this function based upon the satisfaction of exact constraints. For the static (ω = 0) limit, we modify the model of Constantin and Pitarke to recover at small q the known second-order gradient expansion, and to correct its approach to the large q limit. For all ω at q = 0, we use the model of Gross, Kohn, and Iwamoto. A Cauchy integral extends this model to complex ω. Scaling relations are identified. We then combine these ingredients, damping out the ω dependence at large q. Away from q = 0 and ω = 0, the correlation contribution to the kernel becomes dominant over exchange, even at r_s = 4. The resulting correlation energies for 1 ≤ r_s ≤ 10 from integration over imaginary ω are essentially exact. The plasmon pole of the density response function is found by analytic continuation of f_(xc) to ω just below the real axis, and the resulting plasmon lifetime at r_s = 4 is found for q ＜ k_F. A static charge-density wave is found for r_s ＞ 69, and shown to be associated with softening of the plasmon mode.
机译：根据时间依赖性密度泛函理论，波矢量Q和频率ω的精确交换相关性核F_x（n，q，ω）不仅确定地面能量，还决定了兴奋状态的能量/寿命和时间 - 均匀密度n = 3 /（4πr_s〜3）的电子气体的依赖性线性密度响应。在这里，我们提出了基于对确切约束的满足感的这种功能的参数化。对于静态（Ω= 0）限制，我们修改Constantin和Pitarke的模型，以便在Smally Q中恢复已知的二阶梯度扩展，并纠正其对大Q限制的方法。对于Q = 0的所有Ω，我们使用毛，Kohn和Iwamoto的模型。 Cauchy Integral将该模型扩展到复杂Ω。识别缩放关系。然后，我们结合了这些成分，抑制了大Q的ω依赖性。远离Q = 0和ω= 0，即使在R_S = 4中也会对内核的相关贡献变得优势。从虚拟ω的集成到1≤r_s≤10的结果相关性能基本上是精确的。密度响应函数的等离子体杆通过在实轴下的分析延续到Ω进行分析延续，并且在Q 69，并显示与等离子体模式的软化相关。

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  • 来源
    《Physical review》 |2020年第24期|245135.1-245135.9|共9页
  • 作者

    Adrienn Ruzsinszky; Niraj K. Nepal; J. M. Pitarke; John P. Perdew;

  • 作者单位

    Department of Physics Temple University Philadelphia Pennsylvania 19122 USA;

    Department of Physics Temple University Philadelphia Pennsylvania 19122 USA;

    CIC nanoGUNE BRTA and DIPC E-20018 Donostia Basque Country Spain Materia Kondentsatuaren Fisika Saila and Centro Fisica Materiales CSIC-UPV/EHU E-48080 Bilbao Basque Country Spain;

    Department of Chemistry Temple University Philadelphia Pennsylvania 19122 USA;

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