Zhang Ning, Liu Wenjian, Hoffmann Mark R
Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Beijing 100871, China.
Qingdao Institute for Theoretical and Computational Sciences, Shandong University, Qingdao, Shandong 266237, China.
J Chem Theory Comput. 2020 Apr 14;16(4):2296-2316. doi: 10.1021/acs.jctc.9b01200. Epub 2020 Mar 16.
Even when starting with very poor initial guess, the iterative configuration interaction (iCI) approach [ 1169 (2016)] for strongly correlated electrons can converge from above to full CI (FCI) very quickly by constructing and diagonalizing a very small Hamiltonian matrix at each macro/micro-iteration. However, as a direct solver of the FCI problem, iCI is computationally very expensive. The problem can be mitigated by observing that a vast number of configurations have little weights in the wave function and hence do not contribute discernibly to the correlation energy. The real questions are as follows: (a) how to identify those important configurations as early as possible in the calculation and (b) how to account for the residual contributions of those unimportant configurations. It is generally true that if a high-quality yet compact variational space can be determined for describing static correlation, a low-order treatment of the residual dynamic correlation would then be sufficient. While this is common to all selected CI schemes, the "iCI with selection" scheme presented here has the following distinctive features: (1) the full spin symmetry is always maintained by taking configuration state functions (CSF) as the many-electron basis. (2) Although the selection is performed on individual CSFs, it is orbital configurations (oCFGs) that are used as the organizing units. (3) Given a coefficient pruning-threshold (which determines the size of the variational space for static correlation), the selection of important oCFGs/CSFs is performed iteratively until convergence. (4) At each iteration, for the growth of the wave function, the first-order interacting space is decomposed into disjoint subspaces so as to reduce memory requirement on the one hand and facilitate parallelization on the other hand. (5) Upper bounds (which involve only two-electron integrals) for the interactions between doubly connected oCFG pairs are used to screen each first-order interacting subspace before the first-order coefficients of individual CSFs are evaluated. (6) Upon convergence of the static correlation for a given Cmin, dynamic correlation is estimated using the state-specific Epstein-Nesbet second-order perturbation theory (PT2). The efficacy of the iCIPT2 scheme is demonstrated numerically using benchmark examples, including C, O, Cr, and CH.
即使从非常差的初始猜测开始，用于强关联电子的迭代组态相互作用（iCI）方法[1169(2016)]通过在每个宏/微迭代中构造并对角化一个非常小的哈密顿矩阵，也能从上方非常快速地收敛到完全组态相互作用（FCI）。然而，作为FCI问题的直接求解器，iCI的计算成本非常高。通过观察到大量组态在波函数中的权重很小，因此对关联能的贡献不明显，这个问题可以得到缓解。真正的问题如下：（a）如何在计算中尽早识别那些重要组态，以及（b）如何考虑那些不重要组态的残余贡献。一般来说，如果能确定一个高质量且紧凑的变分空间来描述静态关联，那么对残余动态关联进行低阶处理就足够了。虽然这是所有选定组态相互作用方案的共同特点，但这里提出的“带选择的iCI”方案有以下独特特征：（1）通过将组态态函数（CSF）作为多电子基，始终保持完全自旋对称性。（2）虽然选择是对单个CSF进行的，但用作组织单元的是轨道组态（oCFG）。（3）给定一个系数修剪阈值（它决定了静态关联的变分空间大小），对重要oCFG/CSF的选择迭代进行直到收敛。（4）在每次迭代中，为了波函数的增长，将一阶相互作用空间分解为不相交的子空间，一方面减少内存需求，另一方面便于并行化。（5）在评估单个CSF的一阶系数之前，使用双连通oCFG对之间相互作用的上限（仅涉及双电子积分）来筛选每个一阶相互作用子空间。（6）对于给定的Cmin，当静态关联收敛时，使用态特定的爱泼斯坦 - 内斯比特二阶微扰理论（PT2）估计动态关联。使用包括C、O、Cr和CH在内的基准示例，通过数值方法证明了iCIPT2方案的有效性。
