密度泛函理论中带隙的分数电荷观点
Fractional charge perspective on the band-gap in density-functional theory
摘要：
通过考虑能量随电子数的变化关系，研究了用密度泛函理论（DFT）方法计算带隙的方法。研究发现，用最近似泛函对带隙的预测不正确，主要是由于描述分数电荷系统时的错误。相对于电子数的能量导数的公式推导出澄清的作用，在预测的带隙优化的有效电位。计算与最近的功能，有很大的改善行为的分数电荷给出了一个很好的预测的能隙，也$ε_{\rm homo}\simeq-I$有限系统。我们的研究结果表明，在DFT中，有可能有一个功能，其特征值或衍生物准确地预测带隙。
英文摘要：
The calculation of the band-gap by density-functional theory (DFT) methods is examined by considering the behavior of the energy as a function of number of electrons. It is found that the incorrect band-gap prediction with most approximate functionals originates mainly from errors in describing systems with fractional charges. Formulas for the energy derivatives with respect to number of electrons are derived which clarify the role of optimized effective potentials in prediction of the band-gap. Calculations with a recent functional that has much improved behavior for fractional charges give a good prediction of the energy gap and also $ε_{\rm homo}\simeq-I$ for finite systems. Our results indicate it is possible, within DFT, to have a functional whose eigenvalues or derivatives accurately predict the band-gap.
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