Kohn-Sham密度泛函理论在不连续Galerkin框架中的自适应局部基组 I: 总能计算
Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework I: Total energy calculation
AI总结：
提出一种在不连续Galerkin框架中自适应构建局部基函数的方法，以高效高精度计算Kohn-Sham密度泛函理论的总能。
摘要：
Kohn-Sham密度泛函理论是最广泛使用的电子结构理论之一。在赝势框架下，Kohn-Sham哈密顿量的均匀离散化通常导致每个原子需要大量基函数，以解析Kohn-Sham轨道在原子核附近的快速振荡。先前减少每个原子基函数数量的尝试包括使用原子轨道和类似对象，但原子轨道通常需要精细调谐才能达到高精度。我们提出一种新的离散化方案，自适应且系统地将Kohn-Sham轨道在原子核附近的快速振荡以及环境效应构建到基函数中。得到的基函数在实空间中局域，并在全局域上不连续。连续Kohn-Sham轨道和电子密度从不连续基函数利用不连续Galerkin（DG）框架计算。我们的方法并行实现，当前实现能够处理至少数千个原子的系统。数值算例表明，我们的方法能以每个原子非常少的基函数（4~40个）达到非常高的精度（小于1meV）。
英文摘要：
Kohn-Sham density functional theory is one of the most widely used electronic structure theories. In the pseudopotential framework, uniform discretization of the Kohn-Sham Hamiltonian generally results in a large number of basis functions per atom in order to resolve the rapid oscillations of the Kohn-Sham orbitals around the nuclei. Previous attempts to reduce the number of basis functions per atom include the usage of atomic orbitals and similar objects, but the atomic orbitals generally require fine tuning in order to reach high accuracy. We present a novel discretization scheme that adaptively and systematically builds the rapid oscillations of the Kohn-Sham orbitals around the nuclei as well as environmental effects into the basis functions. The resulting basis functions are localized in the real space, and are discontinuous in the global domain. The continuous Kohn-Sham orbitals and the electron density are evaluated from the discontinuous basis functions using the discontinuous Galerkin (DG) framework. Our method is implemented in parallel and the current implementation is able to handle systems with at least thousands of atoms. Numerical examples indicate that our method can reach very high accuracy (less than 1meV) with a very small number ($4\sim 40$) of basis functions per atom.
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