Gradient expansion of the exchange energy from second-order density response theory.
Gradient expansion of the exchange energy from second-order density response theory.
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根据二阶密度响应理论交换能量的梯度展开。
DOI：
10.1103/physrevb.54.17402
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
U. Barth
中科院分区：
文献类型：
--
作者：
Per;U. Barth
本工作背后的基本思想是，原子不是电子气体的线性扰动。因此，我们分析了非均匀电子气体在偏离定密度时的三阶交换能。我们给出了相应的二阶响应函数Lx所遵循的对称性质，并演示了Lx如何引起交换能的梯度修正。在密度梯度中一直到六阶的展开，也包括密度的拉普拉斯函数。在静态屏蔽库仑相互作用的情况下，我们用解析和数值方法计算了二阶和四阶梯度项的系数。与线性响应理论的相应结果类似，当筛分消失时，显示出四阶系数发散。对于裸库仑相互作用，我们还没有成功地获得解析结果，并且，由于在小q矢量处的数值问题，我们的数值获得的系数估计不确定性为20%。(少)
The basic idea behind the present work is that an atom is not a linear perturbation of the electron gas. We have thus analyzed the exchange energy of the inhomogeneous electron gas to third order in the deviation from a constant density. We give the symmetry properties obeyed by the corresponding second-order response function Lx, and demonstrate how Lx gives rise to gradient corrections to the exchange energy. The expansion, which is taken up to sixth order in the density gradient, also includes the Laplacian of the density. In the case of a statically screened Coulomb interaction, we have calculated the coefficients of second- and fourth-order gradient terms both analytically and numerically. In analogy with the corresponding results from linear-response theory, the fourth-order coefficient is shown to diverge as the screening is made to vanish. For the bare Coulomb interaction we have not succeeded in obtaining analytical results, and, due to numerical problems at small-q vectors, our numerically obtained coefficients have an estimated uncertainty of 20%. (Less)