雪莉插值-详细布里渊区积分的最佳基组
Shirley Interpolation - Optimal basis sets for detailed Brillouin zone integrations revisited
摘要：
本文给出了E. L. Shirley，Phys.Rev.B54，16464（1996）.该方法允许一个紧凑的k-依赖的哈密顿量的建设使用的数值优化的基础来自一个粗粒度的有效的单粒子电子结构计算（基于密度泛函理论在这项工作中）。我们提供了一些概括的初始方法，减少了所需的初始电子结构计算的数量，使准确的插值在整个布里渊区的基础上计算的区域中心，只有大型系统。我们还概括了非本地哈密顿的表示，从而导致一个更有效的实施，允许使用两个范数守恒和超软赝势的输入计算。数值内插的电子本征值的精度是在0.01 eV之内，可以产生在非常小的计算成本。此外，准确的本征函数-表示在最佳的基础上-提供了方便的访问有用的矩阵元素模拟光谱，我们提供的细节计算光学跃迁振幅。该方法也适用于其他理论框架，如准粒子激发的戴森方程或光学响应的Bethe-Salpeter方程。
英文摘要：
We present a new implementation of the k-space interpolation scheme for electronic structure presented by E. L. Shirley, Phys. Rev. B 54, 16464 (1996). The method permits the construction of a compact k-dependent Hamiltonian using a numerically optimal basis derived from a coarse-grained set of effective single-particle electronic structure calculations (based on density functional theory in this work). We provide some generalizations of the initial approach which reduce the number of required initial electronic structure calculations, enabling accurate interpolation over the entire Brillouin zone based on calculations at the zone-center only for large systems. We also generalize the representation of non-local Hamiltonians, leading to a more efficient implementation which permits the use of both norm-conserving and ultrasoft pseudopotentials in the input calculations. Numerically interpolated electronic eigenvalues with accuracy that is within 0.01 eV can be produced at very little computational cost. Furthermore, accurate eigenfunctions - expressed in the optimal basis - provide easy access to useful matrix elements for simulating spectroscopy and we provide details for computing optical transition amplitudes. The approach is also applicable to other theoretical frameworks such as the Dyson equation for quasiparticle excitations or the Bethe-Salpeter equation for optical responses.
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