AI 中文总结
本论文在前期解决非均匀电子气梯度展开近似系数历史争议的基础上，建立系统框架计算相关积分表达式，推导得到次领头阶项系数，为广义梯度近似泛函开发提供精确确定的约束。
AI 中文摘要
在我们近期发表的工作（参考文献1）中，我们重新研究了相互作用电子气的梯度展开近似（GEA），并在高密度缓变极限下，重新计算了电子密度梯度平方的系数$B_{xc}[n]$中相对于维格纳-塞茨半径$r_s$的领头阶贡献。该工作解决了关于这些系数的历史争议，表明严重的误解导致对广义梯度近似（GGA）中流行泛函施加了不正确的约束。在本论文中，我们将该计算扩展以得到次领头阶项的系数，其相对于领头阶的标度为$r_s \text{ln}(r_s)$。首先，我们建立了一个系统框架，用于计算长波极限（$q \to 0$）下密度-密度响应函数领头项（$\boldsymbol{\text{~}} q^2$）的$b_{xc}$系数的积分表达式——这是计算$B_{xc}[n]$的前提。该计算的重要性源于以下证明：$r_s \text{ln}(r_s)$项的系数不会受到高阶图表达式的修正。因此，我们推导得到的值可作为未来GGA泛函开发的精确、确定的约束；在高密度缓变极限下，任何有效泛函都必须复现我们前期工作和本论文中建立的精确约束。
英文摘要
In our recently published work (our Ref. 1) we revisited the gradient expansion approximation (GEA) of the interacting electron gas, and recalculated the leading-order contribution$-$with respect to the Wigner-Seitz radius $r_s$$-$to the coefficient $B_{xc}[n]$ of the square of the gradient of the electron density in the high-density and slowly varying limits. That work resolved historical controversies regarding these coefficients and demonstrated that serious misconceptions have led to incorrect constraints being imposed on popular functionals within the generalized gradient approximation (GGA). In the present paper, we extend this calculation to obtain the coefficient of the next-to-leading term, which scales as $r_s \ln(r_s)$ relative to the leading order. First, we establish a systematic framework to evaluate the integral expressions for the $b_{xc}$ coefficient of the leading term ($\sim q^2$) of the density-density response function in the long-wavelength limit ($q \to 0$)$-$a prerequisite for computing $B_{xc}[n]$. The significance of the calculation stems from the proof that the coefficient of this $r_s \ln(r_s)$ term receives no corrections from higher-order diagrammatic expressions. Consequently, our derived value serves as an exact, definitive constraint for future GGA functional development; in the high-density slowly-varying limit, any valid functional must reproduce the exact constraints established in both our previous work and the present paper.
Comments26 two-column pages, 7 figures
