Department of Chemistry and Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA.
J Chem Phys. 2013 Sep 14;139(10):104113. doi: 10.1063/1.4820557.
We establish a formal connection between the particle-particle (pp) random phase approximation (RPA) and the ladder channel of the coupled cluster doubles (CCD) equations. The relationship between RPA and CCD is best understood within a Bogoliubov quasiparticle (qp) RPA formalism. This work is a follow-up to our previous formal proof on the connection between particle-hole (ph) RPA and ring-CCD. Whereas RPA is a quasibosonic approximation, CC theory is a "correct bosonization" in the sense that the wavefunction and Hilbert space are exactly fermionic, yet the amplitude equations can be interpreted as adding different quasibosonic RPA channels together. Coupled cluster theory achieves this goal by interacting the ph (ring) and pp (ladder) diagrams via a third channel that we here call "crossed-ring" whose presence allows for full fermionic antisymmetry. Additionally, coupled cluster incorporates what we call "mosaic" terms which can be absorbed into defining a new effective one-body Hamiltonian. The inclusion of these mosaic terms seems to be quite important. The pp-RPA and qp-RPA equations are textbook material in nuclear structure physics but are largely unknown in quantum chemistry, where particle number fluctuations and Bogoliubov determinants are rarely used. We believe that the ideas and connections discussed in this paper may help design improved ways of incorporating RPA correlation into density functionals based on a CC perspective.
我们在粒子-粒子（pp）随机相位近似（RPA）和耦合簇双激发（CCD）方程的 ladder 通道之间建立了一个正式的联系。在 Bogoliubov 准粒子（qp）RPA 形式体系中，RPA 和 CCD 之间的关系最容易理解。这项工作是我们之前关于粒子-空穴（ph）RPA 和环 CCD 之间联系的正式证明的后续。虽然 RPA 是一种准玻色子近似，但 CC 理论是一种“正确的玻色化”，因为波函数和 Hilbert 空间是完全费米子的，但是振幅方程可以被解释为将不同的准玻色子 RPA 通道加在一起。通过通过我们称之为“交叉环”的第三个通道相互作用 ph（环）和 pp（ladder）图，耦合簇理论实现了这一目标，其存在允许完全的费米子反对称性。此外，耦合簇还包含了我们称之为“马赛克”项，可以将其吸收到定义新的有效单粒子哈密顿量中。这些马赛克项的包含似乎非常重要。pp-RPA 和 qp-RPA 方程是核结构物理中的教科书内容，但在量子化学中却鲜为人知，在量子化学中很少使用粒子数涨落和 Bogoliubov 行列式。我们相信，本文讨论的思想和联系可能有助于从 CC 角度设计改进的方法，将 RPA 相关内容纳入基于密度泛函理论的方法中。
