We propose a staggered mesh method for correlation energy calculations of periodic systems under the random phase approximation (RPA), which generalizes the recently developed staggered mesh method for periodic second order M{\o}ller-Plesset perturbation theory (MP2) calculations [Xing, Li, Lin, JCTC 2021]. Compared to standard RPA calculations, the staggered mesh method introduces negligible additional computational cost. It avoids a significant portion of the finite-size error, and can be asymptotically advantageous for quasi-1D systems and certain quasi-2D and 3D systems with high symmetries. We demonstrate the applicability of the method using two different formalisms: the direct ring coupled cluster doubles (drCCD) theory, and the adiabatic-connection (AC) fluctuation-dissipation theory. In the drCCD formalism, the second order screened exchange (SOSEX) correction can also be readily obtained using the staggered mesh method. In the AC formalism, the staggered mesh method naturally avoids the need of performing "head/wing" corrections to the dielectric operator. The effectiveness of the staggered mesh method for insulating systems is theoretically justified by investigating the finite-size error of each individual perturbative term in the RPA correlation energy, expanded as an infinite series of terms associated with ring diagrams. As a side contribution, our analysis provides a proof that the finite-size error of each perturbative term of standard RPA and SOSEX calculations scales as $\mathcal{O}(N_{\mathbf{k}}^{-1})$, where $N_{\mathbf{k}}$ is the number of grid points in a Monkhorst-Pack mesh.

翻译：我们提出了一个用于在随机阶段近似(RPA)下对周期系统进行相关能量计算的错位网格方法{错位网格方法{在随机阶段近似(RPA)下对周期性系统进行相关能量计算,该方法概括了最近开发的周期性第二顺序M=o}的错位网格方法(MP2)计算[Xing,Li,Lin,JCT 2021]。与标准的RPA计算相比,错位网格方法引入了微不足道的额外计算成本。它避免了一定比例的错误,对于准-1D系统以及某些准-2D和3D系统来说,它可能具有同样优势。我们用两种不同的格式来展示该方法的可适用性:直接环联组双(MPA)计算 [Xing,LI,JCT 20211] 计算。在标准MERFS(SOS EX) 修正中,第二个顺序筛选交换(SOS-PO) 也很容易用错位数方法获得。在A-salental-al-late-lational-lational-al-lock ltal-leckal-lational-deal-deal-deal-deal-deal-deal real real real ex real ex ex exal exal ex ex ex ex ex ex exal ex ex ex ex exal ex ex ex ex ex exal ex ex ex 分析, 需要用每个算算法 方法来进行一个正常式的自动计算法性 方法, 方法来进行正常的精确的精确的精确性分析。