QPLDA的简化：一种实用的修正LDA带隙问题的方法
Simplification of QPLDA: A practical method to the correction for the LDA band gap problem
摘要：
为了解决LDA中的带隙问题，必须采用准粒子计算。准粒子LDA（Quasi-Particle-LDA）是一种快速、可靠的大规模GWA算法，其总计算量与N成正比。历史上，Sham和Kohn引入了基于局部波数的局部质量算子的想法，类似于WKB，但没有执行实际的数值计算。他们只考虑了交换的相互作用，我们无论如何也不能指望精确的处理方法。后来，Pickett和Wang提出了一种更定性的方法，并在半导体的例子中显示了它的潜力，如硅，金刚石和GaP。他们使用了一个模型解析公式的辩证功能，并采用了一个模型的能量色散，这是自由电子一样，除了，伴随着一个人工带隙不连续性。后一种方法有两个缺点。首先，为了执行计算，需要几个参数，例如宏观介电常数和带隙，这些参数应该通过计算本身来评估，而不是准备作为参数。其次，在计算质量算符时，需要在直接空间网格的每个点上进行二维或三维数值积分，这在确定局部波数和准粒子能量的迭代过程中需要大量的计算成本。这可能是QPLDA直到现在还没有被广泛使用的原因。本文提出了一种不需要任何实验参数的QPLDA定性方法，比Picket和Wang的方法更快，比Sham和Kohn的方法更精确。本工作采用的计算方法是Sham和Kohn的原始建议的修改，而不是Picket和Wang的。
英文摘要：
It is necessary to employ quasi-particle calculations to correct band gap problems in LDA. As an expedient way for the reliable but massive GWA, Quasi-Particle-LDA (QPLDA) is proposed by several authors, where the total computational cost scales with N. Historically, Sham and Kohn introduced the idea of the local mass operator based on local wavenumber similar to WKB, but did not execute actual numerical calculations. They took into account exchange interaction only, from which we could not expect precise treatments anyway. Later, Pickett and Wang had proposed a more qualitative method and had shown its potentiality in examples of semiconductors, such as silicon, diamond and GaP. They used a model analytic formula for the dialectic function and adopted a model energy dispersion, which is free-electron like one, except that, being accompanied with an artificial band-gap discontinuity. The latter method has two shortcomings. First, to execute the calculation, several parameters are needed, such as the macroscopic dielectric constant and the band gap, which should be evaluated by the calculation itself, rather than being prepared as parameters. Second, in their computation of the mass operator, two or three dimensional numerical integrations are needed on each point of the direct space mesh, which demand large computational costs in iterative procedures in determining local wavenumbers and quasi-particle energies. This may be the reason why QPLDA has not been widely used until now. The present work proposes a qualitative way of QPLDA which does not need any experimental parameters, being much speedier than the formalism of Picket and Wang, and more precise than that of Sham and Kohn. The computational method adopted by the present work is a modification of the original proposal by Sham and Kohn, rather than that of Picket and Wang.
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