Lundbeck Foundation Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark.
J Chem Phys. 2012 Jan 7;136(1):014105. doi: 10.1063/1.3667266.
Previously, we have introduced the linear scaling coupled cluster (CC) divide-expand-consolidate (DEC) method, using an occupied space partitioning of the standard correlation energy. In this article, we show that the correlation energy may alternatively be expressed using a virtual space partitioning, and that the Lagrangian correlation energy may be partitioned using elements from both the occupied and virtual partitioning schemes. The partitionings of the correlation energy leads to atomic site and pair interaction energies which are term-wise invariant with respect to an orthogonal transformation among the occupied or the virtual orbitals. Evaluating the atomic site and pair interaction energies using local orbitals leads to a linear scaling algorithm and a distinction between Coulomb hole and dispersion energy contributions to the correlation energy. Further, a detailed error analysis is performed illustrating the error control imposed on all components of the energy by the chosen energy threshold. This error control is ultimately used to show how to reduce the computational cost for evaluating dispersion energy contributions in DEC.
此前，我们介绍了使用标准相关能量的占据空间分区的线性标度耦合簇 (CC) 划分-扩展-合并 (DEC) 方法。在本文中，我们表明可以使用虚拟空间分区来表示相关能量，并且可以使用占据和虚拟分区方案的元素来划分拉格朗日相关能量。相关能量的分区导致原子位点和对相互作用能在占据或虚拟轨道之间的正交变换方面是逐项不变的。使用局部轨道评估原子位点和对相互作用能导致线性标度算法以及库仑空洞和色散能对相关能量的贡献之间的区分。此外，进行了详细的误差分析，说明了所选能量阈值对能量所有分量施加的误差控制。这种误差控制最终用于展示如何降低 DEC 中评估色散能贡献的计算成本。
