论文标题
基于约束的波形和频率依赖性交换相关核的均匀电子气体的内核
Constraint-based Wavevector- and Frequency-dependent Exchange-Correlation Kernel of the Uniform Electron Gas
论文作者
论文摘要
According to time-dependent density functional theory, the exact exchange-correlation kernel f$_{xc}$(n, q, $ω$) 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/(4$π$r$^3_s$).在这里，我们根据确切约束的满意度提出了此功能的参数化。对于静态（$ω$ = 0）的限制，我们在小波动Q处修改君士坦丁和皮塔尔克的模型，以恢复已知的二阶梯度扩展以及其他更改。对于所有频率$ω$在Q $ = $ 0时，我们使用Gross，Kohn和Iwamoto的型号。 Cauchy的积分将此模型扩展到复杂的$ω$，并暗示了标准的Kramers-Kronig关系。缩放关系允许不仅为假想的封闭表格，而且允许F $ _ {XC} $的实际部分，用于真实的$ω$。然后，我们通过以大Q的方式抑制$ω$依赖性来结合这些成分，就像Q依赖性受阻一样。从Q $ = $ 0和$ω$ = $ 0的Q $ = $ = $ 0之外，对内核的相关性贡献在交换中占主导地位，即使在r $ _s $ = $ = $ 4，金属钠的价电子密度也是如此。基本上是精确的$ω$集成所产生的相关能量。密度响应函数的等离子极是通过分析延续f $ _ {xc} $到$ω$低于实际轴的$ω$的，而由此产生的等离子体寿命首先从无穷大降低，然后随着Q从0增长到电子孔连续体时增加。对于R $ _s $ $> $ 69，发现了一个静态电荷密度波，并证明与等离子模式的软化有关。我们静态内核的仅交换版本证实了Overhauser的1968年预测，即相关性增强了电荷密度波。
According to time-dependent density functional theory, the exact exchange-correlation kernel f$_{xc}$(n, q, $ω$) 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/(4$π$r$^3_s$). 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 at small wavevector q to recover the known second-order gradient expansion, plus other changes. For all frequencies $ω$ at q $=$ 0, we use the model of Gross, Kohn, and Iwamoto. A Cauchy integral extends this model to complex $ω$ and implies the standard Kramers-Kronig relations. A scaling relation permits closed forms for not only the imaginary but also the real part of f$_{xc}$ for real $ω$. We then combine these ingredients by damping out the $ω$ dependence at large q in the same way that the q dependence is damped. Away from q $=$ 0 and $ω$ $=$ 0, the correlation contribution to the kernel becomes dominant over exchange, even at r$_s$ $=$ 4, the valence electron density of metallic sodium. The resulting correlation energy from integration over imaginary $ω$ is 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 first decreases from infinity and then increases as q grows from 0 toward the electron-hole continuum. A static charge-density wave is found for r$_s$ $>$ 69, and shown to be associated with softening of the plasmon mode. The exchange-only version of our static kernel confirms Overhauser's 1968 prediction that correlation enhances the charge-density wave.
