CSC-IT Center for Science Ltd., Espoo, Finland.
J Phys Condens Matter. 2010 Jun 30;22(25):253202. doi: 10.1088/0953-8984/22/25/253202. Epub 2010 Jun 10.
Electronic structure calculations have become an indispensable tool in many areas of materials science and quantum chemistry. Even though the Kohn-Sham formulation of the density-functional theory (DFT) simplifies the many-body problem significantly, one is still confronted with several numerical challenges. In this article we present the projector augmented-wave (PAW) method as implemented in the GPAW program package (https://wiki.fysik.dtu.dk/gpaw) using a uniform real-space grid representation of the electronic wavefunctions. Compared to more traditional plane wave or localized basis set approaches, real-space grids offer several advantages, most notably good computational scalability and systematic convergence properties. However, as a unique feature GPAW also facilitates a localized atomic-orbital basis set in addition to the grid. The efficient atomic basis set is complementary to the more accurate grid, and the possibility to seamlessly switch between the two representations provides great flexibility. While DFT allows one to study ground state properties, time-dependent density-functional theory (TDDFT) provides access to the excited states. We have implemented the two common formulations of TDDFT, namely the linear-response and the time propagation schemes. Electron transport calculations under finite-bias conditions can be performed with GPAW using non-equilibrium Green functions and the localized basis set. In addition to the basic features of the real-space PAW method, we also describe the implementation of selected exchange-correlation functionals, parallelization schemes, ΔSCF-method, x-ray absorption spectra, and maximally localized Wannier orbitals.
电子结构计算已成为材料科学和量子化学许多领域不可或缺的工具。尽管密度泛函理论（DFT）的 Kohn-Sham 公式大大简化了多体问题，但仍面临着几个数值挑战。本文介绍了 GPAW 程序包中实现的投影原子波方法（PAW）（https://wiki.fysik.dtu.dk/gpaw），该方法使用电子波函数的均匀实空间网格表示。与更传统的平面波或局域基组方法相比，实空间网格具有几个优势，最重要的是良好的计算可扩展性和系统收敛性。然而，作为一个独特的特点，GPAW 还除了网格之外，还方便了局域原子轨道基组。高效的原子基组与更准确的网格互补，并且能够在两种表示之间无缝切换，提供了很大的灵活性。虽然 DFT 允许研究基态性质，但时间相关的密度泛函理论（TDDFT）则提供了对激发态的访问。我们实现了 TDDFT 的两种常见形式，即线性响应和时间传播方案。使用非平衡格林函数和局域基组，可以在 GPAW 中进行有限偏压条件下的电子输运计算。除了实空间 PAW 方法的基本功能外，我们还描述了所选交换相关泛函、并行化方案、ΔSCF 方法、X 射线吸收光谱和最大局域化 Wanier 轨道的实现。
