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We propose a staggered mesh method for correlation energy calculations ofperiodic systems under the random phase approximation (RPA), which generalizesthe recently developed staggered mesh method for periodic second orderM{\o}ller-Plesset perturbation theory (MP2) calculations [Xing, Li, Lin, JCTC2021]. Compared to standard RPA calculations, the staggered mesh methodintroduces negligible additional computational cost. It avoids a significantportion of the finite-size error, and can be asymptotically advantageous forquasi-1D systems and certain quasi-2D and 3D systems with high symmetries. Wedemonstrate the applicability of the method using two different formalisms: thedirect ring coupled cluster doubles (drCCD) theory, and theadiabatic-connection (AC) fluctuation-dissipation theory. In the drCCDformalism, the second order screened exchange (SOSEX) correction can also bereadily obtained using the staggered mesh method. In the AC formalism, thestaggered mesh method naturally avoids the need of performing "head/wing"corrections to the dielectric operator. The effectiveness of the staggered meshmethod for insulating systems is theoretically justified by investigating thefinite-size error of each individual perturbative term in the RPA correlationenergy, expanded as an infinite series of terms associated with ring diagrams.As a side contribution, our analysis provides a proof that the finite-sizeerror of each perturbative term of standard RPA and SOSEX calculations scalesas $\mathcal{O}(N_{\mathbf{k}}^{-1})$, where $N_{\mathbf{k}}$ is the number ofgrid points in a Monkhorst-Pack mesh.

journal of chemical theory and computation

Staggered mesh method for correlation energy calculations of solids:  Random phase approximation in direct ring coupled cluster doubles and  adiabatic connection formalisms