论文标题
变分投影仪增强波法：固态物理中电子结构计算的全电力方法
Variational projector-augmented wave method: a full-potential approach for electronic structure calculations in solid-state physics
论文作者
论文摘要
在固态物理学中，通常通过Kohn-Sham方程的平面波离散计算晶体的能量。但是，库仑奇异性的存在需要使用大型平面波截断来产生准确的数值结果。在本文中，提出了对使用变量投影仪 - 功率波（VPAW）方法的周期性线性汉顿量特征值（具有库仑电势）的平面波收敛的分析。在VPAW方法中，将可逆转换应用于原始特征值问题，该问题局部作用于以奇异性为中心的球。在这种情况下，需要使用平面波解决广义特征值问题。我们表明，在细胞核位置，VPAW特征值问题的特征函数的尖大大降低了。但是，这些特征函数在以核的为中心的球体上具有高阶导数不连续性。通过平衡两个误差源，我们表明VPAW方法可以通过较小的额外计算成本大大改善特征值的平面波收敛。提供了数值测试，以确认治疗库仑奇异性的方法的效率。
In solid-state physics, energies of crystals are usually computed with a plane-wave discretization of Kohn-Sham equations. However the presence of Coulomb singularities requires the use of large plane-wave cut-offs to produce accurate numerical results. In this paper, an analysis of the plane-wave convergence of the eigenvalues of periodic linear Hamiltonians with Coulomb potentials using the variational projector-augmented wave (VPAW) method is presented. In the VPAW method, an invertible transformation is applied to the original eigenvalue problem, acting locally in balls centered at the singularities. In this setting, a generalized eigenvalue problem needs to be solved using plane-waves. We show that cusps of the eigenfunctions of the VPAW eigenvalue problem at the positions of the nuclei are significantly reduced. These eigenfunctions have however a higher-order derivative discontinuity at the spheres centered at the nuclei. By balancing both sources of error, we show that the VPAW method can drastically improve the plane-wave convergence of the eigenvalues with a minor additional computational cost. Numerical tests are provided confirming the efficiency of the method to treat Coulomb singularities.
