Department of Chemistry, University of California, Berkeley, California 94720, USA.
Phys Chem Chem Phys. 2019 Feb 27;21(9):4763-4778. doi: 10.1039/c8cp07613h.
We present a thorough analysis of symmetry breaking observed in Hartree-Fock (HF) solutions of the C60, C36, and C20 fullerenes in order to characterize the nature of electron correlation in them. Our analysis is based on (1) the critical regularization strength to restore symmetry breaking in the recently developed regularized orbital optimized second-order Møller-Plesset perturbation theory (κ-OOMP2), (2) singlet-triplet gaps from various MP2 methods, and (3) natural orbital occupation numbers from restricted coupled-cluster with singles and doubles (RCCSD) and coupled-cluster valence bond with singles and doubles (CCVB-SD). Based on these three independent probes, we conclude that C36 (D6h) exhibits genuine strong correlation and symmetry breaking whereas C60 exhibits artificial HF symmetry breaking and is not strongly correlated. Investigating the critical regularization strength, we discuss strong correlation in C20 at the Jahn-Teller distorted geometries (C2h, D2h, Ci, and D3h) and the Ih geometry. Only C20 (Ih) was found to be strongly correlated while others exhibit artificial HF symmetry breaking. This analysis highlights a useful feature of the recommended κ-OOMP2 method. It is an electronic structure method that describes dynamic correlation, and attenuates strong correlation in MP2 towards zero by regularization. Therefore, κ-OOMP2 will exhibit symmetry breaking in its reference determinant only when correlation is strong (i.e., essential symmetry breaking). Artificial symmetry breaking (arising in HF due to neglect of dynamic correlation) thus appears to be removed in κ-OOMP2.
我们对 C60、C36 和 C20 富勒烯的哈特ree-fock（HF）解中的对称破缺进行了彻底分析，以便表征它们中的电子相关的性质。我们的分析基于以下三个独立的探针：（1）最近开发的正则化轨道优化二阶 Møller-Plesset 微扰理论（κ-OOMP2）中恢复对称破缺的临界正则化强度，（2）来自各种 MP2 方法的单重态-三重态能隙，以及（3）来自受限耦合簇与单重和双重（RCCSD）和耦合簇价键与单重和双重（CCVB-SD）的自然轨道占据数。基于这三个独立的探针，我们得出结论，C36（D6h）表现出真正的强相关和对称破缺，而 C60 表现出人为的 HF 对称破缺，并且不是强相关的。研究临界正则化强度时，我们讨论了 Jahn-Teller 畸变几何（C2h、D2h、Ci 和 D3h）和 Ih 几何中 C20 的强相关性。只有 C20（Ih）被发现是强相关的，而其他的则表现出人为的 HF 对称破缺。这种分析突出了推荐的 κ-OOMP2 方法的一个有用特性。它是一种电子结构方法，描述了动态相关，并通过正则化将 MP2 中的强相关衰减到零。因此，只有当相关很强时（即本质上的对称破缺），κ-OOMP2 才会在其参考行列式中表现出对称破缺。人工对称破缺（由于忽略动态相关而在 HF 中出现）因此似乎在 κ-OOMP2 中被消除了。
