Symmetry-breaking in the independent particle model: nature of the singular behavior of Hartree-Fock potentials
Symmetry-breaking in the independent particle model: nature of the singular behavior of Hartree-Fock potentials
复制标题
独立粒子模型中的对称性破缺：Hartree-Fock 势奇异行为的本质
DOI：
10.1007/s10910-012-0093-8
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发表时间：
2013
影响因子：
1.7
通讯作者：
G.H.F. Diercksen
中科院分区：
文献类型：
--
作者：
J. Paldus;T. Sako;X. Li;G.H.F. Diercksen
利用Pariser-Parr-Pople半经验哈密顿量描述的烯丙基自由基的简单π电子模型，讨论了在相关限制HF解的自旋保持不稳定性存在时，HF势能面奇异行为的本质.这个三电子模型系统的简单性源于一个低维的适当的变分空间，使一个独立的直接分析方法，说明适当的限制开壳HF（ROHF）解决方案的双重稳定条件。在同一时间，它允许推导出明确的表达式的能量提供了一个完整的描述燕尾或Whitney折叠突变奇点上相应的PES出现的发病的双重不稳定。特别是，这个简单的模型，使计算的PES与不稳定的ROHF解决方案的一部分，这将是困难的，如果不是不可能在更复杂的情况下，通过标准的自洽场迭代过程中产生的全部一般性。
The nature of the singular behavior of Hartree–Fock (HF) potential energy surfaces (PESs) that arises in the presence of a spin-preserving instability of the relevant restricted HF solutions is illustrated by a simpleπ-electron model of the allyl radical as described by the Pariser–Parr–Pople semi-empirical Hamiltonian. The simplicity of this three-electron model system stems from a low dimension of the appropriate variational space which enables an independent direct analytical approach illustrating the appropriateness of doublet stability conditions for restricted open-shell HF (ROHF) solutions. At the same time it permits the derivation of explicit expressions for the energy providing a complete description of swallowtail or Whitney-fold catastrophe singularities on the corresponding PES that arise with the onset of a doublet instability. In particular, this simple model enables the computation of the part of the PES that is associated with unstable ROHF solutions and which would be difficult if not impossible to generate in full generality via standard self-consistent field iterative procedures in more complex situations.