论文标题
生成自旋适应和自旋完整替代操作员（高旋转）开放式耦合群集的任意顺序
Generation of Spin-Adapted and Spin-Complete Substitution Operators for (High-Spin) Open-Shell Coupled Cluster of Arbitrary Order
论文作者
论文摘要
提出了严格的自旋适应（无自旋）替代操作员，用于高旋转（$ s = s_z $）任意替代顺序和自旋量子数$ s $的参考。当应用于参考并跨越完整的自旋空间时，生成的操作员会导致线性独立但非正交的CSF。为了结合旋转完整性，引入了观察替换（例如$ \ hat {e} _ {iv}^{va} $）。提出的程序利用Löwdin的旋转本特征功能生成的投影操作方法来确保旋转完整性。明确检查了生成的运算符的（i）其线性独立性，以及（ii）其旋转完整性最多可替换10倍，并多达$ 2S+1 = 11 $。在耦合群集（CC）计算中使用生成的运算符的概念证明成功地应用于硼原子的高旋转状态。结果表明，与脊柱状CC相比，纯自旋状态以及对相关能量的影响很小。与自旋适应但自旋分配的CC的比较显示出明显的自旋不完整误差。
A rigorous generation of spin-adapted (spin-free) substitution operators for high spin ($S=S_z$) references of arbitrary substitution order and spin quantum number $S$ is presented. The generated operators lead to linearly independent but non-orthogonal CSFs when applied to the reference and span the complete spin space. To incorporate spin completeness, spectating substitutions (as e.g. $\hat{E}_{iv}^{va}$) are introduced. The presented procedure utilizes Löwdin's projection operator method of spin eigenfunction generation to ensure spin completeness. The generated operators are explicitly checked for (i) their linear independence and (ii) their spin completeness for up to 10-fold substitutions and up to a multiplicity of $2S+1 = 11$. A proof of concept implementation utilizing the generated operators in a coupled cluster (CC) calculation was successfully applied to the high spin states of the Boron atom. The results show pure spin states as well as small effects on the correlation energy compared to spinorbital CC. A comparison to spin-adapted but spin-incomplete CC shows a significant spin incompleteness error.
