论文标题
用固定数量的电子计算基本差距的确切交换相关电位
Exact exchange-correlation potentials for calculating the fundamental gap with a fixed number of electrons
论文作者
论文摘要
从kohn-sham（ks）Gap，$ \ varepsilon_ \ varrepsilon_ \ varremrm {gsrm {gsrm {gs d f fartive ks ks d f fartive of Kohn-sham（ks）gap（kohn-sham（ks）gap，$ e_ \ mathrm {g} $，捕获确切交换相关（XC）潜在的不连续转移是计算基本差距的标准建议，$ e_ \ mathrm {g} $，$ \ \\ varepsilon_ $ e_ \ mathrm {g} = \ varepsilon_ \ mathrm {g} +δ$，但是现有近似值不存在这种不连续性。合奏DFT的“ $ n $中心”配方人为地维护了总的电子编号，$ n $，以产生$ e_ \ mathrm {g} $，而不是通过XC潜力的不连续转移而不是通过XC能量的集合派生衍生物来产生。在以$ n $中为中心的方法中，我们计算了一维有限系统的精确XC潜力，并在分析上表明，实际上可以将$δ$解释为不连续的$ n $以$ n $中心的集合XC电位的不连续转移，从而扩展到充电的激发型具有未充电的兴奋性。我们表明，在这种情况下，应用Levy-Zahariev“偏移率”程序将不连续的转移转移到系统的不重要的外围，因此实际上有效的XC电位没有不连续性，因此无法捕获不连续的行为的局部功能是不连续的。
Capturing the discontinuous shift by $Δ$ in the exact exchange-correlation (xc) potential is the standard proposal for calculating the fundamental gap, $E_\mathrm{g}$, from the Kohn-Sham (KS) gap, $\varepsilon_\mathrm{g}$, within KS density functional theory (DFT), as $E_\mathrm{g} = \varepsilon_\mathrm{g} + Δ$, yet this discontinuity is absent from existing approximations. The '$N$-centered' formulation of ensemble DFT artificially maintains a total electron number, $N$, in order to yield $E_\mathrm{g}$ not through a discontinuous shift in the xc potential but via the ensemble-weight derivative of the xc energy. Within the $N$-centered approach we calculate exact xc potentials for a one-dimensional finite system and show analytically that $Δ$ can in fact be interpreted as a discontinuous shift in the exact $N$-centered ensemble xc potential, thereby extending to charged excitations an exact property of uncharged excitations. We show that applying the Levy-Zahariev 'shift-in-potential' procedure in this context relocates the discontinuous shift to the unimportant periphery of the system, so that the exact xc potential in effect is free of discontinuities and thus the inability of a local functional to capture discontinuous behavior is inconsequential.
