AI 中文总结
本文针对周期量子化学入门难问题，提供涵盖平均场与相关理论的教学教程，详述Ewald求和、基函数、k点采样等关键技术，给出多种周期量子化学方法的工作方程及相关理论，为该领域应用提供支持。
AI 中文摘要
高精度分子量子化学为凝聚相体系应用提供了极具前景的工具库，但由于该领域融合了分子量子化学、固态物理与数值方法等多主题，入门难度较大。为简化这一过渡过程，我们呈现了一份涵盖平均场与相关理论的全面、教学式周期量子化学计算教程。详细讨论了周期库仑相互作用的微妙之处，重点聚焦于Ewald求和方法；介绍了两种最常用的周期单电子基函数——平面波与原子轨道的周期线性组合，并给出了所有哈密顿积分的公式。接下来，解释了k点采样作为超胞基函数的对称性适配方法及其带来的计算成本节约，以及密度拟合与相关近似方法在进一步降低成本中的应用。给出了包括Hartree-Fock理论、微扰理论、耦合簇理论在内的几种典型周期量子化学方法的工作方程，讨论了它们的有限尺寸误差及向物理相关热力学极限的收敛性。最后，简要探讨了因晶格平移对称性而特别适用于周期体系的局域相关与量子嵌入理论。
英文摘要
High-accuracy molecular quantum chemistry offers a promising toolbox for applications to condensed-phase systems, but this field is difficult to enter due to its combination of topics from molecular quantum chemistry, solid-state physics, and numerical methods. Aiming to ease this transition, we present a comprehensive, pedagogical tutorial on periodic quantum chemistry calculations, using both mean-field and correlated theories. The subtleties of periodic Coulomb interactions are discussed in detail, focusing on the Ewald summation approach. We describe the two most popular periodic, one-electron basis functions---plane waves and periodic linear combinations of atomic orbitals---and we give formulas for all Hamiltonian integrals. Next, we explain the use of $k$-point sampling as a symmetry adaptation of supercell basis functions and the associated savings in computational costs as well as the use of density fitting and related approximations to further reduce costs. We present the working equations of a few example periodic quantum chemistry methods, including Hartree-Fock theory, perturbation theory, and coupled-cluster theory, and we discuss their finite-size errors and convergence to the physically relevant thermodynamic limit. Finally, we briefly discuss local correlation and quantum embedding theories, which are especially appropriate for periodic systems due to their lattice translational symmetries.
Comments22 pages, 6 figures
