Raman Center for Atomic, Molecular and Optical Sciences, Indian Association for the Cultivation of Science, Kolkata 700 032, India.
J Chem Phys. 2012 Sep 7;137(9):094104. doi: 10.1063/1.4747702.
Any multi-reference coupled cluster (MRCC) development based on the Jeziorski-Monkhorst (JM) multi-exponential ansatz for the wave-operator Ω suffers from spin-contamination problem for non-singlet states. We have very recently proposed a spin-free unitary group adapted (UGA) analogue of the JM ansatz, where the cluster operators are defined in terms of spin-free unitary generators and a normal ordered, rather than ordinary, exponential parametrization of Ω is used. A consequence of the latter choice is the emergence of the "direct term" of the MRCC equations that terminates at exactly the quartic power of the cluster amplitudes. Our UGA-MRCC ansatz has been utilized to generate both the spin-free state specific (SS) and the state universal MRCC formalisms. It is well-known that the SSMRCC theory requires suitable sufficiency conditions to resolve the redundancy of the cluster amplitudes. In this paper, we propose an alternative variant of the UGA-SSMRCC theory, where the sufficiency conditions are used for all cluster operators containing active orbitals and the single excitations with inactive orbitals, while the inactive double excitations are assumed to be independent of the model functions they act upon. The working equations for the inactive double excitations are thus derived in an internally contracted (IC) manner in the sense that the matrix elements entering the MRCC equations involve excitations from an entire combination of the model functions. We call this theory as UGA-ICID-MRCC, where ICID is the acronym for "Internally Contracted treatment of Inactive Double excitations." Since the number of such excitations are the most numerous, choosing them to be independent of the model functions will lead to very significant reduction in the number of cluster amplitudes for large active spaces, and is worth exploring. Moreover, unlike for the excitations involving active orbitals, where there is inadequate coupling between the model and the virtual functions in the SSMRCC equations generated from sufficiency conditions, our internally contracted treatment of inactive double excitations involves much more complete couplings. Numerical implementation of our formalism amply demonstrates the efficacy of the formalism.
任何基于 Jeziorski-Monkhorst（JM）多指数波算子 Ω 展开式的多参考耦合簇（MRCC）发展都存在非单重态的自旋污染问题。我们最近提出了一种无自旋幺正群自适应（UGA）JM 展开式的类似物，其中簇算符是根据无自旋幺正生成元定义的，并且使用的是无规有序而非普通的 Ω 的指数参数化。后一种选择的结果是 MRCC 方程的“直接项”的出现，它恰好终止于簇振幅的四次方。我们的 UGA-MRCC 展开式已被用于生成无自旋特定态（SS）和态普遍的 MRCC 形式。众所周知，SSMRCC 理论需要合适的充分性条件来解决簇振幅的冗余问题。在本文中，我们提出了 UGA-SSMRCC 理论的另一种变体，其中充分性条件适用于包含活性轨道的所有簇算符以及具有非活性轨道的单激发，而假设非活性双激发与它们作用的模型函数无关。因此，非活性双激发的工作方程是以内部收缩（IC）的方式推导的，即在进入 MRCC 方程的矩阵元中涉及到模型函数的整个组合的激发。我们称这个理论为 UGA-ICID-MRCC，其中 ICID 是“Internally Contracted treatment of Inactive Double excitations”的缩写。由于这样的激发数量最多，选择它们与模型函数无关将导致在大的活性空间中大大减少簇振幅的数量，这是值得探索的。此外，与涉及活性轨道的激发不同，在由充分性条件生成的 SSMRCC 方程中，模型和虚拟函数之间的耦合不足，我们对非活性双激发的内部收缩处理涉及到更完整的耦合。我们形式主义的数值实现充分证明了该形式主义的有效性。
