Hardness of molecules and the band gap of solids within the Kohn-Sham formalism: A perturbation-scaling approach.
Hardness of molecules and the band gap of solids within the Kohn-Sham formalism: A perturbation-scaling approach.
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Kohn-Sham 形式主义中的分子硬度和固体带隙：一种微扰尺度方法。
DOI：
10.1103/physreva.52.4493
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发表时间：
1995
期刊：
影响因子：
--
通讯作者：
Lévy
中科院分区：
文献类型：
--
作者：
Görling;Lévy
原子和分子硬度的有限差分表达式，即根据 Parr 和 Pearson 的电离势和电子亲和势之差的一半 [J.是。化学。苏克。 105, 7512 (1983)]，在这里被表示为 Kohn-Sham 轨道、Kohn-Sham 特征值差、库仑势以及交换相关势的某些部分的显式函数。该泛函是通过利用电子密度的均匀坐标缩放与电子-电子相互作用的微扰理论之间的关系而导出的。硬度是作为扰动展开式获得的，该扰动展开式由每项与 ${\mathit{e}}^{2}$ 的特定阶相关联的项组成，其中 e 是电子电荷。原则上，这允许人们在 Kohn-Sham 方法中精确地确定硬度，或者在实际应用中，在 ${\mathit{e}}^{2}$ 中达到某种选定的顺序。实际的展开是通过二阶来显示的。在某种程度上，该结果对于固体带隙的情况也是有效的。
The finite difference expression for the hardness of atoms and molecules, i.e. half the difference between the ionization potential and the electron affinity according to Parr and Pearson [J. Am. Chem. Soc. 105, 7512 (1983)], is expressed here as an explicit functional of the Kohn-Sham orbitals, of the Kohn-Sham eigenvalue differences, of the Coulomb potential, and of certain parts of the exchange-correlation potential. The functional is derived by exploiting the relationship between uniform coordinate scaling of the electron density and a perturbation theory with respect to the electron-electron interaction. The hardness is obtained as a perturbation expansion consisting of terms which each are connected to a specific order of ${\mathit{e}}^{2}$ with e being the electronic charge. This allows one, in principle, to determine the hardness exactly within the Kohn-Sham method or, in actual applications, up to some chosen order in ${\mathit{e}}^{2}$. The actual expansion is displayed through second order. To some extent the results are also valid in the case of band gaps of solids.