用于固体相关能计算的交错网格方法：二阶Møller-Plesset微扰理论
Staggered mesh method for correlation energy calculations of solids: Second order Møller-Plesset perturbation theory
AI总结：
提出一种无参数的交错网格方法，通过分别为占据和虚轨道使用交错的Monkhorst-Pack网格计算MP2相关能，规避了标准梯形求积在不连续点处的误差源，对准1D及特定对称性的准2D/3D系统尤为有利。
摘要：
计算扩展系统的MP2相关能可视为热力学极限下的多维积分，而评估MP2能量的标准方法可视为梯形求积方案。我们证明现有分析由于被积函数的非光滑性忽略了某些贡献，可能显著低估有限尺寸误差。我们提出一种新的交错网格方法，分别使用两个交错的Monkhorst-Pack网格用于占据轨道和虚轨道来计算MP2能量。该方法规避了标准方法中某些求积节点总是位于被积函数不连续点处的显著误差源。该方法的一个显著优势是没有可调参数，且与标准MP2计算相比所需的额外数值开销可忽略不计。数值结果表明，交错网格方法对准1D系统以及具有特定对称性的准2D和3D系统尤为有利。
英文摘要：
The calculation of the MP2 correlation energy for extended systems can be viewed as a multi-dimensional integral in the thermodynamic limit, and the standard method for evaluating the MP2 energy can be viewed as a trapezoidal quadrature scheme. We demonstrate that existing analysis neglects certain contributions due to the non-smoothness of the integrand, and may significantly underestimate finite-size errors. We propose a new staggered mesh method, which uses two staggered Monkhorst-Pack meshes for occupied and virtual orbitals, respectively, to compute the MP2 energy. The staggered mesh method circumvents a significant error source in the standard method, in which certain quadrature nodes are always placed on points where the integrand is discontinuous. One significant advantage of the proposed method is that there are no tunable parameters, and the additional numerical effort needed can be negligible compared to the standard MP2 calculation. Numerical results indicate that the staggered mesh method can be particularly advantageous for quasi-1D systems, as well as quasi-2D and 3D systems with certain symmetries.
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