Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry , University of Munich (LMU) , D-81377 Munich , Germany.
Max Planck Institute for Solid State Research , Heisenbergstraße 1 , 70569 Stuttgart , Germany.
J Chem Theory Comput. 2018 May 8;14(5):2505-2515. doi: 10.1021/acs.jctc.8b00177. Epub 2018 Apr 16.
An efficient algorithm for calculating the random phase approximation (RPA) correlation energy is presented that is as accurate as the canonical molecular orbital resolution-of-the-identity RPA (RI-RPA) with the important advantage of an effective linear-scaling behavior (instead of quartic) for large systems due to a formulation in the local atomic orbital space. The high accuracy is achieved by utilizing optimized minimax integration schemes and the local Coulomb metric attenuated by the complementary error function for the RI approximation. The memory bottleneck of former atomic orbital (AO)-RI-RPA implementations ( Schurkus, H. F.; Ochsenfeld, C. J. Chem. Phys. 2016 , 144 , 031101 and Luenser, A.; Schurkus, H. F.; Ochsenfeld, C. J. Chem. Theory Comput. 2017 , 13 , 1647 - 1655 ) is addressed by precontraction of the large 3-center integral matrix with the Cholesky factors of the ground state density reducing the memory requirements of that matrix by a factor of [Formula: see text]. Furthermore, we present a parallel implementation of our method, which not only leads to faster RPA correlation energy calculations but also to a scalable decrease in memory requirements, opening the door for investigations of large molecules even on small- to medium-sized computing clusters. Although it is known that AO methods are highly efficient for extended systems, where sparsity allows for reaching the linear-scaling regime, we show that our work also extends the applicability when considering highly delocalized systems for which no linear scaling can be achieved. As an example, the interlayer distance of two covalent organic framework pore fragments (comprising 384 atoms in total) is analyzed.
提出了一种计算随机相位近似（RPA）相关能量的高效算法，该算法与正则分子轨道离域的 RPA（RI-RPA）一样准确，具有重要的优势，即在大系统中具有有效的线性标度行为（而不是四次），因为它是在局部原子轨道空间中进行的。通过利用优化的最小最大化积分方案和 RI 逼近的互补误差函数衰减的局部库仑度量，实现了高精度。前原子轨道（AO）-RI-RPA 实现的内存瓶颈（Schurkus，H. F.；Ochsenfeld，C. J. Chem. Phys. 2016 ，144 ，031101 和 Luenser，A.；Schurkus，H. F.；Ochsenfeld，C. J. Chem. Theory Comput. 2017 ，13 ，1647 - 1655）通过用基态密度的 Cholesky 因子对大 3 中心积分矩阵进行预收缩来解决，这将矩阵的内存需求降低了[公式：请参见文本]。此外，我们还提出了我们方法的并行实现，这不仅导致更快的 RPA 相关能量计算，而且还导致可扩展的内存需求减少，为在小型到中型计算集群上研究大型分子开辟了道路。尽管众所周知，AO 方法对于扩展系统非常高效，其中稀疏性允许达到线性标度范围，但我们表明，当考虑到无法实现线性标度的高度离域系统时，我们的工作也扩展了适用性。例如，分析了两个共价有机骨架孔片段（总共包含 384 个原子）的层间距离。
