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.
翻译:对扩展系统的 MP2 相关能量的计算可被视为热力极限中一个多维的组成部分,而评估 MP2 能量的标准方法可被视为一种诱杀性分裂性二次曲线图案。 我们证明,现有的分析忽略了某些贡献,因为未切除未切除的正切度,而且可能大大低估了一定的误差。 我们提出了一个新的错开网格方法,即分别使用两个错开的Monkhorst-Pack-meshes来计算 MP2 能量。 错开网格方法绕过标准方法中的一个重要错误源, 即某些二次方位节点总是位于原点不连续的点上。 拟议方法的一个重大优点是没有金枪鱼参数, 所需要的额外数字努力与标准 MP2 计算相比可能是微不足道的。 Numical 结果表明, 错开网格方法对于准-1D 系统以及具有某些正弦的准-2D 和 3D 系统特别有利。