Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering, Peking University, Beijing 100871, People's Republic of China.
J Chem Phys. 2012 Jan 14;136(2):024105. doi: 10.1063/1.3672083.
We present in this paper a comprehensive formulation of a spin-adapted size-extensive state-specific multi-reference second-order perturbation theory (SA-SSMRPT2) as a tool for applications to molecular states of arbitrary complexity and generality. The perturbative theory emerges in the development as a result of a physically appealing quasi-linearization of a rigorously size-extensive state-specific multi-reference coupled cluster (SSMRCC) formalism [U. S. Mahapatra, B. Datta, and D. Mukherjee, J. Chem. Phys. 110, 6171 (1999)]. The formulation is intruder-free as long as the state-energy is energetically well-separated from the virtual functions. SA-SSMRPT2 works with a complete active space (CAS), and treats each of the model space functions on the same footing. This thus has the twin advantages of being capable of handling varying degrees of quasi-degeneracy and of ensuring size-extensivity. This strategy is attractive in terms of the applicability to bigger systems. A very desirable property of the parent SSMRCC theory is the explicit maintenance of size-extensivity under a variety of approximations of the working equations. We show how to generate both the Rayleigh-Schrödinger (RS) and the Brillouin-Wigner (BW) versions of SA-SSMRPT2. Unlike the traditional naive formulations, both the RS and the BW variants are manifestly size-extensive and both share the avoidance of intruders in the same manner as the parent SSMRCC. We discuss the various features of the RS as well as the BW version using several partitioning strategies of the hamiltonian. Unlike the other CAS based MRPTs, the SA-SSMRPT2 is intrinsically flexible in the sense that it is constructed in a manner that it can relax the coefficients of the reference function, or keep the coefficients frozen if we so desire. We delineate the issues pertaining to the spin-adaptation of the working equations of the SA-SSMRPT2, starting from SSMRCC, which would allow us to incorporate essentially any type open-shell configuration-state functions (CSF) within the CAS. The formalisms presented here will be applied extensively in a companion paper to assess their efficacy.
我们在本文中提出了一种全面的自旋自适应尺寸扩展态特定多参考二级微扰理论（SA-SSMRPT2）公式，作为应用于任意复杂度和一般性的分子态的工具。该微扰理论是在发展过程中出现的，是对严格尺寸扩展态特定多参考耦合簇（SSMRCC）形式主义的物理上吸引人的准线性化的结果[U.S. Mahapatra、B. Datta 和 D. Mukherjee，J. Chem. Phys. 110，6171（1999）]。只要态能量与虚拟函数在能量上很好地分离，该公式就是无侵入式的。SA-SSMRPT2 适用于完全激活空间（CAS），并平等对待模型空间中的每个函数。这因此具有处理不同程度准简并性和确保尺寸扩展性的双重优势。这种策略在适用于更大系统方面具有吸引力。母体 SSMRCC 理论的一个非常理想的性质是在工作方程的各种近似下明确保持尺寸扩展性。我们展示了如何生成 Rayleigh-Schrödinger（RS）和 Brillouin-Wigner（BW）版本的 SA-SSMRPT2。与传统的天真公式不同，RS 和 BW 变体都是明显的尺寸扩展性，并且都以与母体 SSMRCC 相同的方式避免侵入者。我们使用哈密顿量的几种分区策略讨论了 RS 和 BW 版本的各种特征。与其他基于 CAS 的 MRPT 不同，SA-SSMRPT2 在本质上是灵活的，因为它以一种可以放松参考函数系数的方式构建，或者如果我们愿意，保持系数冻结。我们阐述了与 SA-SSMRPT2 的工作方程的自旋适应相关的问题，从 SSMRCC 开始，这将允许我们在 CAS 中包含本质上任何类型的开壳组态态函数（CSF）。本文介绍的形式主义将在一篇配套论文中广泛应用，以评估它们的有效性。
