Sinha Mahapatra U, Datta B, Mukherjee D
Department of Physical Chemistry, Indian Association for the Cultivation of Science, Calcutta 700-032, India.
J Phys Chem A. 1999 Mar 25;103(12):1822-30. doi: 10.1021/jp9832995.
We explore in this paper the efficacy of the Rayleigh-Schrödinger (RS) and the Brillouin-Wigner (BW) perturbative counterparts of our recently developed multireference state-specific coupled-cluster formalism (SS-MRCC) with a complete active space (CAS). It is size-extensive and is designed to avoid intruders. The parent SS-MRCC method uses a sum-of-exponentials type of Ansatz for the wave operator. The redundancy inherent in such a choice is resolved by postulating suitable sufficiency conditions which at the same time ensure size-extensivity and size-consistency. The combining coefficients c μ for φμ's are completely relaxed and are obtained by diagonalizing an effective operator in the model space, one root of which is the target eigenvalue of our interest. By invokation of a suitable partitioning of the Hamiltonian, very convenient perturbative versions of the formalism in both the RS and the BW forms are developed for the second-order energy. The unperturbed Hamiltonian is akin to the Epstein-Nesbet type when at least one of the orbitals is inactive and is the entire active portion of the Hamiltonian when all the orbitals involved are active. Illustrative numerical applications are presented for potential energy surfaces (PES) of a number of model and realistic systems where intruders exist and for molecules in their ground states with pronounced multireference character. Single reference MBPT and effective Hamiltonian-based multireference MBPT second-order results are also presented for comparisons. The results indicate the smooth performance of our state-specific perturbative formalisms in and around the region of intruders in the PES, indicating their suitability in bypassing intruders. In contrast, the effective Hamiltonian-based MBPT methods behave poorly in the regions of intruders.
在本文中，我们探讨了瑞利 - 薛定谔（RS）微扰理论以及我们最近开发的具有完全活性空间（CAS）的多参考态特定耦合簇形式（SS - MRCC）的布里渊 - 维格纳（BW）微扰理论的有效性。它具有规模扩展性，旨在避免出现侵入态。母本SS - MRCC方法对波算子采用指数和类型的假设。通过假定合适的充分条件来解决这种选择中固有的冗余问题，这些条件同时确保了规模扩展性和规模一致性。对于φμ的组合系数cμ完全松弛，并通过在模型空间中对一个有效算子进行对角化来获得，其中一个根是我们感兴趣的目标本征值。通过对哈密顿量进行合适的划分，针对二阶能量开发了RS和BW形式的非常方便的微扰版本。当至少有一个轨道非活性时，未微扰的哈密顿量类似于爱泼斯坦 - 内斯比特类型，而当所有涉及的轨道都是活性时，它是哈密顿量的整个活性部分。文中给出了一些存在侵入态的模型和实际系统的势能面（PES）以及具有明显多参考特征的基态分子的数值示例。还给出了单参考多体微扰理论（MBPT）和基于有效哈密顿量的多参考MBPT二阶结果用于比较。结果表明，我们的态特定微扰理论在PES中侵入态区域及其周围表现平滑，表明它们适用于绕过侵入态。相比之下，基于有效哈密顿量的MBPT方法在侵入态区域表现不佳。
