具有近似密度泛函的基本能隙：从系综考虑揭示的导数不连续性
Fundamental gaps with approximate density functionals: the derivative discontinuity revealed from ensemble considerations
摘要：
基本能隙是物质电子结构中的一个中心量。不幸的是，即使在原则上，基本能隙也通常不等于密度泛函理论（DFT）的Kohn-Sham能隙。这两个差距的不同，正是由衍生物的不连续性，即，在斜率的交换相关（xc）能量作为电子数的函数，预计在一个整数电子点的突然变化。流行的近似泛函被认为是缺乏一个衍生物的不连续性，强烈损害其性能的光谱性质的预测。在这里，我们表明，事实上，所有的交换相关泛函具有衍生物的不连续性，这自然产生于DFT内的合奏考虑的应用程序，没有任何dichloricism。这种导数不连续性可以用封闭形式表示，只使用在中性系统的标准DFT计算过程中获得的量。对于小的，有限的系统，除了这个衍生物的不连续性确实导致在一个大大改善的预测的基本差距，即使是基于最简单的近似交换相关密度泛函-局域密度近似（LDA）。对于固体，同样的方案在原则上是精确的，但当应用于LDA时，它会导致导数不连续性校正消失。这种失败被证明是直接相关的LDA在预测的总能量差在扩展系统中的基本差距的失败。
英文摘要：
The fundamental gap is a central quantity in the electronic structure of matter. Unfortunately, the fundamental gap is not generally equal to the Kohn-Sham gap of density functional theory (DFT), even in principle. The two gaps differ precisely by the derivative discontinuity, namely, an abrupt change in slope of the exchange-correlation (xc) energy as a function of electron number, expected across an integer-electron point. Popular approximate functionals are thought to be devoid of a derivative discontinuity, strongly compromising their performance for prediction of spectroscopic properties. Here we show that, in fact, all exchange-correlation functionals possess a derivative discontinuity, which arises naturally from the application of ensemble considerations within DFT, without any empiricism. This derivative discontinuity can be expressed in closed form using only quantities obtained in the course of a standard DFT calculation of the neutral system. For small, finite systems, addition of this derivative discontinuity indeed results in a greatly improved prediction for the fundamental gap, even when based on the most simple approximate exchange-correlation density functional - the local density approximation (LDA). For solids, the same scheme is exact in principle, but when applied to LDA it results in a vanishing derivative discontinuity correction. This failure is shown to be directly related to the failure of LDA in predicting fundamental gaps from total energy differences in extended systems.
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