用于固体关联能计算的交错网格方法：直接环耦合簇二重态与绝热连接形式中的随机相近似
Staggered mesh method for correlation energy calculations of solids: Random phase approximation in direct ring coupled cluster doubles and adiabatic connection formalisms
AI总结：
本文提出一种用于周期系统随机相近似关联能计算的交错网格方法，该方法计算成本极低，能有效减少有限尺寸误差，并在drCCD和绝热连接两种形式下均表现出良好适用性。
摘要：
我们提出了一种交错网格方法，用于计算周期系统在随机相近似（RPA）下的关联能，该方法推广了最近开发的用于周期性二阶 Møller-Plesset 微扰理论（MP2）计算的交错网格方法 [Xing, Li, Lin, JCTC 2021]。与标准 RPA 计算相比，交错网格方法引入的额外计算成本可以忽略不计。它避免了相当一部分有限尺寸误差，并且对于准一维系统以及某些具有高对称性的准二维和三维系统具有渐近优势。我们使用两种不同的形式论证了该方法的适用性：直接环耦合簇二重态（drCCD）理论和绝热连接（AC）涨落耗散理论。在 drCCD 形式中，使用交错网格方法也可以很容易地获得二阶屏蔽交换（SOSEX）校正。在 AC 形式中，交错网格方法自然地避免了对介电算符进行“头/翼”校正的需要。通过研究 RPA 关联能中每个微扰项的有限尺寸误差（展开为与环图相关联的项的无穷级数），从理论上证明了交错网格方法对绝缘系统的有效性。作为附带贡献，我们的分析证明了标准 RPA 和 SOSEX 计算的每个微扰项的有限尺寸误差标度为 $\mathcal{O}(N_{\mathbf{k}}^{-1})$，其中 $N_{\mathbf{k}}$ 是 Monkhorst-Pack 网格中的网格点数。
英文摘要：
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 Møller-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.
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