Lawler Keith V, Beran Gregory J O, Head-Gordon Martin
Department of Chemistry and Chemical Sciences Division, Lawrence Berkeley National Laboratory, University of California, Berkeley, California 94720, USA.
J Chem Phys. 2008 Jan 14;128(2):024107. doi: 10.1063/1.2817600.
The origin of symmetry breaking (SB) in benzene in generalized valence bond methods is investigated within a coupled cluster formalism that correlates all valence electrons. Retention of a limited number of pair correlation amplitudes (as in the perfect- and imperfect-pairing models) that incompletely describes interpair correlations leads to symmetry breaking as the orbitals and amplitudes are optimized. Local correlation models that are exact for one, two, and three interacting pairs at the doubles excitation level are compared against the exact pair correlation treatment, which correlates four interacting pairs at once in the connected double substitution operator. For simplicity, this comparison is performed with a second-order model of electron correlation, which is reasonably faithful to the infinite-order result. The significant SB known for the one-pair model (perfect pairing) is not eliminated at the two-pair level, but is virtually eliminated at the three-pair level. Therefore, a tractable hybrid model is proposed, which combines three-pair correlations at the second-order level and infinite-order treatment for the strong imperfect-pairing correlations involving one and two-pair correlations. This model greatly reduces SB in benzene and larger delocalized pi systems such as naphthalene and the phenalenyl cation and anion. The resulting optimized orbitals are localized in the sigma space but exhibit significant delocalization in the pi space. This means that correlation effects associated with different resonance structures are treated in a more balanced way than if the pi orbitals localize, leading to reduced SB.
在一种关联所有价电子的耦合簇形式体系内，研究了广义价键方法中苯的对称性破缺（SB）的起源。保留有限数量的对相关振幅（如在完美配对和不完美配对模型中），由于其不能完全描述对间相关性，当轨道和振幅被优化时会导致对称性破缺。将在双激发水平下对一、二和三个相互作用对精确的局域相关模型与精确对相关处理进行比较，精确对相关处理在连接双取代算符中同时关联四个相互作用对。为简单起见，这种比较是在二阶电子相关模型下进行的，该模型相当忠实地反映了无穷阶结果。单对模型（完美配对）中已知的显著SB在两对水平上并未消除，但在三对水平上几乎消除。因此，提出了一种易于处理的混合模型，该模型结合了二阶水平的三对相关性和对涉及一对和两对相关性的强不完美配对相关性的无穷阶处理。该模型极大地降低了苯以及更大的离域π体系（如萘和苯并菲阳离子及阴离子）中的SB。由此得到的优化轨道在σ空间中是局域化的，但在π空间中表现出显著的离域性。这意味着与不同共振结构相关的相关效应比π轨道局域化时得到了更平衡的处理，从而导致SB降低。
