Raman Center for Atomic, Molecular and Optical Sciences, Indian Association for the Cultivation of Science, Kolkata 700 032, India.
J Chem Phys. 2012 Jul 14;137(2):024105. doi: 10.1063/1.4731341.
We present the formulation and the implementation of a spin-free state-specific multi-reference coupled cluster (SSMRCC) theory, realized via the unitary group adapted (UGA) approach, using a multi-exponential type of cluster expansion of the wave-operator Ω. The cluster operators are defined in terms of spin-free unitary generators, and normal ordered exponential parametrization is utilized for cluster expansion instead of pure exponentials. Our Ansatz for Ω is a natural spin-free extension of the spinorbital based Jeziorski-Monkhorst (JM) Ansatz. The normal ordered cluster Ansatz for Ω results in a terminating series of the direct term of the MRCC equations, and it uses ordinary Wick algebra to generate the working equations in a straightforward manner. We call our formulation as UGA-SSMRCC theory. Just as in the case of the spinorbital based SSMRCC theory, there are redundancies in the cluster operators, which are exploited to ensure size-extensivity and avoidance of intruders via suitable sufficiency conditions. Although there already exists in the literature a spin-free JM-like Ansatz, introduced by Datta and Mukherjee, its structure is considerably more complex than ours. The UGA-SSMRCC offers an easier access to spin-free MRCC formulation as compared to the Datta-Mukherjee Ansatz, which at the same time provides with quite accurate description of electron correlation. We will demonstrate the efficacy of the UGA-SSMRCC formulation with a set of numerical results. For non-singlet cases, there is pronounced M(s) dependence of the energy for the spinorbital based SSMRCC results. Although M(s) = 1 results are closer to full configuration interaction (FCI), the extent of spin-contamination is more. In most of the cases, our UGA-SSMRCC results are closer to FCI than the spinorbital M(s) = 0 results.
我们提出了一种无自旋定域多参考耦合簇（SSMRCC）理论的公式和实现方法，该理论通过使用波算子Ω的多指数型簇展开，实现了幺正群适配（UGA）方法。簇算符是根据无自旋幺正生成器定义的，并且使用无规化指数参数化来代替纯指数进行簇展开。我们的Ω假设是基于自旋轨道的 Jeziorski-Monkhorst（JM）假设的自然无自旋扩展。Ω的无规化簇假设导致了 MRCC 方程的直接项的终止级数，并且它使用普通 Wick 代数以直接的方式生成工作方程。我们将我们的方法称为 UGA-SSMRCC 理论。就像基于自旋轨道的 SSMRCC 理论一样，在簇算符中存在冗余，这些冗余被利用来确保大小扩展性并通过合适的充分性条件避免闯入者。尽管文献中已经存在由 Datta 和 Mukherjee 引入的无自旋 JM 型假设，但它的结构比我们的假设复杂得多。与 Datta-Mukherjee 假设相比，UGA-SSMRCC 为无自旋 MRCC 公式提供了更容易的途径，同时为电子相关提供了相当准确的描述。我们将用一系列数值结果来证明 UGA-SSMRCC 公式的有效性。对于非单重态情况，基于自旋轨道的 SSMRCC 结果的能量具有明显的 M(s)依赖性。虽然 M(s) = 1 结果更接近全组态相互作用（FCI），但自旋污染的程度更大。在大多数情况下，我们的 UGA-SSMRCC 结果比基于自旋轨道的 M(s) = 0 结果更接近 FCI。
