Staggered mesh method for correlation energy calculations of solids: Random phase approximation in direct ring coupled cluster doubles and adiabatic connection formalisms
Staggered mesh method for correlation energy calculations of solids: Random phase approximation in direct ring coupled cluster doubles and adiabatic connection formalisms
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DOI：
10.1021/acs.jctc.1c00985
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发表时间：
2021-09
影响因子：
5.5
通讯作者：
Xin Xing;Lin Lin-Lin
中科院分区：
文献类型：
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作者：
Xin Xing;Lin Lin-Lin
本文提出了一种在无规相近似（RPA）下计算周期体系相关能的交错网格方法，它推广了最近发展的用于周期性二阶Møller-Plesset微扰理论（MP2）计算的交错网格方法[Xing; Li; Lin J. Chem. Theory Comput. 2021年]。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。它避免了一个显着的部分有限尺寸的错误，可以是渐近的准一维系统和某些准二维和三维系统具有高对称性的优势。我们证明了该方法的适用性，使用两种不同的形式主义：直接环耦合集群双打（drCCD）理论，绝热连接（AC）波动耗散理论。在drCCD形式主义，二阶屏蔽交换（SOSEX）校正也可以很容易地获得使用交错网格方法。在AC形式主义中，交错网格方法自然避免了对介电算子执行“头/翼”校正的需要。交错网格方法的绝缘系统的有效性从理论上证明了通过调查的RPA相关能量，扩展为一个无限系列的项与环形图中的每个单独的微扰项的有限大小的错误。作为一个侧面的贡献，我们的分析提供了证据，标准RPA和SOSEX计算规模为O（Nk-1），其中Nk是网格点的数量在Monkhorst-Pack网格的每个微扰项的有限大小的错误。
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 J. Chem. Theory Comput. 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 proof that the finite-size error of each perturbative term of standard RPA and SOSEX calculations scales as O(Nk-1), where Nk is the number of grid points in a Monkhorst-Pack mesh.