Department of Chemistry, University of California, Berkeley, California 94720, USA.
J Chem Phys. 2011 Nov 21;135(19):194306. doi: 10.1063/1.3661158.
The ground state restricted Hartree Fock (RHF) wave function of C(60) is found to be unstable with respect to spin symmetry breaking, and further minimization leads to a significantly spin contaminated unrestricted Hartree Fock (UHF) solution (<S(2)> = 7.5, 9.6 for singlet and triplet, respectively). The nature of the symmetry breaking in C(60) relative to the radicaloid fullerene, C(36), is assessed by energy lowering of the UHF solution, <S(2)>, and the unpaired electron number. We conclude that the high value of each of these measures in C(60) is not attributable to strong correlation behavior as is the case for C(36). Instead, their origin is from the collective effect of relatively weak, global correlations present in the π space of both fullerenes. Second order perturbation (MP2) calculations of the singlet triplet gap are significantly more accurate with RHF orbitals than UHF orbitals, while orbital optimized opposite spin second order correlation (O2) performs even better.
C(60) 的基态限制哈特利-福克（RHF）波函数对于自旋对称性破缺是不稳定的，进一步的最小化导致了一个明显的自旋污染的非限制哈特利-福克（UHF）解（分别为<S(2)> = 7.5 和 9.6，用于单重态和三重态）。通过 UHF 解的能量降低、<S(2)>和未配对电子数来评估 C(60) 相对于自由基富勒烯 C(36) 的对称破缺的性质。我们得出的结论是，这些措施中的每一个在 C(60)中的高值都不是归因于强相关行为，就像 C(36)中的情况一样。相反，它们的起源是来自于两个富勒烯的π空间中存在的相对较弱的、全局相关性的集体效应。用 RHF 轨道进行的单重态三重态能隙的二阶微扰（MP2）计算比 UHF 轨道更准确，而轨道优化的相反自旋二阶相关（O2）则表现得更好。
