弱非均匀电子气的精确动力学交换关联核
Exact dynamical exchange-correlation kernel of a weakly inhomogeneous electron gas
摘要：
非均匀电子气的动力学交换关联核$f_{xc}$是电子系统含时密度泛函理论的重要输入。已知该核的长波长行为具有$f_{xc}= α/q^2$的形式，其中$q$是波矢量，而$α$是频率相关系数。我们证明了在弱非均匀性的极限下，系数$α$与{ \it uniform}电子气的基态密度和平均密度下的频率相关核有一个简单而精确的表达式.我们提出了一个近似的评价，这个表达式的硅和讨论其影响的激子效应的理论。
英文摘要：
The dynamical exchange-correlation kernel $f_{xc}$ of a non-uniform electron gas is an essential input for the time-dependent density functional theory of electronic systems. The long-wavelength behavior of this kernel is known to be of the form $f_{xc}= α/q^2$ where $q$ is the wave vector and $α$ is a frequency-dependent coefficient. We show that in the limit of weak non-uniformity the coefficient $α$ has a simple and exact expression in terms of the ground-state density and the frequency-dependent kernel of a {\it uniform} electron gas at the average density. We present an approximate evaluation of this expression for Si and discuss its implications for the theory of excitonic effects.
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