Raman Center for Atomic, Molecular, and Optical Sciences, Indian Association for the Cultivation of Science, Kolkata 700 032, India.
J Chem Phys. 2012 Aug 21;137(7):074104. doi: 10.1063/1.4742058.
The traditional state universal multi-reference coupled cluster (SUMRCC) theory uses the Jeziorski-Monkhorst (JM) based Ansatz of the wave operator: Ω = Σ(μ)Ω(μ)|φ(μ)><φ(μ)|, where Ω(μ) = exp(T(μ)) is the cluster representation of the component of Ω inducing virtual excitations from the model function φ(μ). In the first formulations, φ(μ)s were chosen to be single determinants and T(μ)s were defined in terms of spinorbitals. This leads to spin-contamination for the non-singlet cases. In this paper, we propose and implement an explicitly spin-free realization of the SUMRCC theory. This method uses spin-free unitary generators in defining the cluster operators, {T(μ)}, which even at singles-doubles truncation, generates non-commuting cluster operators. We propose the use of normal-ordered exponential parameterization for Ω:Σ(μ){exp(T(μ))}|φ(μ)><φ(μ)|, where {} denotes the normal ordering with respect to a common closed shell vacuum which makes the "direct term" of the SUMRCC equations terminate at the quartic power. We choose our model functions {φ(μ)} as unitary group adapted (UGA) Gel'fand states which is why we call our theory UGA-SUMRCC. In the spirit of the original SUMRCC, we choose exactly the right number of linearly independent cluster operators in {T(μ)} such that no redundancies in the virtual functions {χ(μ)(l)} are involved. Using example applications for electron detached/attached and h-p excited states relative to a closed shell ground state we discuss how to choose the most compact and non-redundant cluster operators. Although there exists a more elaborate spin-adapted JM-like ansatz of Datta and Mukherjee (known as combinatoric open-shell CC (COS-CC), its working equations are more complex. Results are compared with those from COS-CC, equation of motion coupled cluster methods, restricted open-shell Hartree-Fock coupled cluster, and full configuration interaction. We observe that our results are more accurate with respect to most other theories as a result of the use of the cluster expansion structure for our wave operator. Our results are comparable to those from the more involved COS-CC, indicating that our theory captures the most important aspects of physics with a considerably simpler scheme.
传统的状态普遍多参考耦合簇（SUMRCC）理论使用基于 Jeziorski-Monkhorst（JM）的波算子假设：Ω=Σ（μ）Ω（μ）|φ（μ）><φ（μ）|，其中Ω（μ）=exp（T（μ））是从模型函数φ（μ）中诱导虚拟激发的组分的簇表示。在最初的公式中，φ（μ）被选择为单行列式，T（μ）被定义为自旋轨道。这导致非单重情况的自旋污染。在本文中，我们提出并实现了 SUMRCC 理论的显式无自旋实现。该方法在定义簇算子{ T（μ）}时使用无自旋幺正生成器，即使在单双截断时，也会产生非交换簇算子。我们提出对Ω使用规范有序指数参数化：Σ（μ）{ exp（T（μ））} |φ（μ）><φ（μ）|，其中{}表示相对于公共闭壳真空的规范排序，这使得 SUMRCC 方程的“直接项”在四次方终止。我们选择模型函数{φ（μ）}作为幺正群适应（UGA）Gel'fand 态，这就是为什么我们称我们的理论为 UGA-SUMRCC。本着原始 SUMRCC 的精神，我们在{ T（μ）}中选择了完全独立的簇算子的正确数量，从而不涉及虚拟函数{χ（μ）（l）}中的冗余。通过应用于相对于闭壳基态的电子脱离/附加和 h-p 激发态的示例，我们讨论了如何选择最紧凑和非冗余的簇算子。尽管存在 Datta 和 Mukherjee 的更精细的自旋适应的 JM 类假设（称为组合开壳 CC（COS-CC）），但其工作方程更为复杂。结果与 COS-CC、运动方程耦合簇方法、限制开壳 Hartree-Fock 耦合簇和完全组态相互作用的结果进行了比较。我们观察到，由于我们的波算子使用簇展开结构，因此与大多数其他理论相比，我们的结果更准确。我们的结果与更复杂的 COS-CC 的结果相当，这表明我们的理论以相当简单的方案捕捉到了物理的最重要方面。
