Vu Nam, DePrince A Eugene
Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA.
J Chem Phys. 2020 Jun 28;152(24):244103. doi: 10.1063/5.0011637.
The doubly occupied configuration interaction (DOCI) approach can provide an accurate black-box description of nondynamic electron correlation at a computational cost that increases combinatorially with the system size. Remarkably, a pair coupled-cluster doubles (pCCD) approach (also known as the antisymmetrized product of one-reference orbital geminals) can reproduce DOCI energies with only a quadratic number of wave function parameters, and, when neglecting the cost associated with any two-electron integral transformations, these parameters can be determined at a cubic computational cost. Other simpler seniority-zero approaches derived from size-extensive modified configuration interaction doubles functionals can also provide approximations to DOCI energies at similar computational costs. We develop seniority-zero formulations of the coupled-electron pair approximation, the averaged coupled-pair functional, averaged quadratic coupled-cluster, and the parametric two-electron reduced density matrix (p2RDM) approach. These methods are Hermitian and thus offer several potential advantages over pCCD theory, including a reduction in the number of variable parameters and simplified definitions of reduced density matrices. Of the methods investigated, only the pair p2RDM (pp2RDM) approach yields energies that are comparable in quality to pCCD and DOCI. For the molecular systems investigated, pp2RDM-derived RDMs are found to be better approximations to DOCI ones than those obtained from pCCD.
双占据组态相互作用（DOCI）方法能够以与系统大小呈组合增长的计算成本，提供非动态电子关联的精确黑箱描述。值得注意的是，一种双对耦合簇双激发（pCCD）方法（也称为单参考轨道双电子对的反对称化乘积）仅用二次数量的波函数参数就能重现DOCI能量，并且，在忽略与任何双电子积分变换相关的成本时，这些参数可以以三次计算成本确定。从具有广延性的修正组态相互作用双激发泛函导出的其他更简单的零 seniority 方法，也能以类似的计算成本提供对 DOCI 能量的近似。我们开发了耦合电子对近似、平均耦合对泛函、平均二次耦合簇以及参数化双电子约化密度矩阵（p2RDM）方法的零 seniority 形式。这些方法是厄米的，因此与 pCCD 理论相比具有几个潜在优势，包括减少可变参数的数量以及简化约化密度矩阵的定义。在所研究的方法中，只有双对 p2RDM（pp2RDM）方法产生的能量在质量上与 pCCD 和 DOCI 相当。对于所研究的分子系统，发现从 pp2RDM 导出的约化密度矩阵比从 pCCD 获得的约化密度矩阵更接近 DOCI 的约化密度矩阵。
