基于迭代线性化戴森方程的GW约化密度矩阵
$GW$ reduced density matrix from iterated linearized Dyson equation
AI总结：
研究通过迭代戴森方程处理GW近似来求单体约化密度矩阵，对比其与变分Z向量方法在不同起点下的差异，通过与耦合簇参考值比较，发现迭代戴森方程能改进分子系统密度矩阵，且参考耦合簇激发等级影响结论。
AI中文摘要：
通过将戴森方程与自能的静态部分进行迭代，可从任何自能近似中得到简洁且可能改进的单体约化密度矩阵表达式。本文将此方法应用于赫丁的GW近似。已知基于非迭代GW的密度矩阵能为分子系统生成精确的密度矩阵。我们表明，基于戴森方程的方法等同于应用于随机相位近似能量泛函的所谓变分Z向量方法，但仅在哈特里 - 福克平均场起点的情况下。当采用广义科恩 - 沈方案时，这两种方法不同。通过将34个小分子的基准集密度矩阵与耦合簇参考值进行比较，我们得出结论，迭代戴森方程确实为分子系统产生了改进的密度矩阵。有趣的是，我们观察到参考耦合簇的激发等级很重要，并且与单双激发耦合簇（CCSD）相比，包含三激发（CCSDT）在定量上改变了基准的结论。
英文摘要：
Iterating the Dyson equation with the static part of the self-energy leads to a concise and possibly improved expression of the one-body reduced density matrix from any self-energy approximation. Here we apply the procedure to Hedin's $GW$ approximation. The non-iterated $GW$ based density matrix was already known to yield accurate density matrices for molecular systems. We show that the Dyson-equation-based procedure is equivalent to the so-called variational Z-vector approach applied to the Random-Phase approximation energy functional, but only in the case of a Hartree-Fock mean-field starting point. When a generalized Kohn-Sham scheme is employed instead, the two approaches differ. By comparing the density matrix for a benchmark set of 34 small molecules to coupled-cluster reference values, we conclude that the iterated Dyson equation indeed produces improved density matrices for molecular systems. Interestingly, we observe that the excitation rank of the reference coupled-cluster matters much and that the inclusion of triple excitations (CCSDT) quantitatively changes the conclusions of the benchmark as compared to single and double excitations coupled-cluster (CCSD).
