Holomorphic Hartree-Fock Theory: The Nature of Two-Electron Problems
Holomorphic Hartree-Fock Theory: The Nature of Two-Electron Problems
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DOI：
10.1021/acs.jctc.7b00980
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发表时间：
2018-02-01
影响因子：
5.5
通讯作者：
Thom, Alex J. W.
中科院分区：
文献类型：
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作者：
Burton, Hugh G. A.;Gross, Mark;Thom, Alex J. W.
研究了双电子问题的全纯限制Hartree-Fock（h-RHF）解的存在性和行为.通过代数几何，具有n个基函数的解的确切数目被严格地确定为1/2（3“”- 1），证明了对于所有分子几何结构，状态必须存在。对HZ（STO-3G）的h-RHF态的详细研究表明，当几何形状或原子电荷变化时，全纯解的守恒性以及在合并点出现复杂的h-RHF解。使用突变理论，这些聚结点的性质进行了描述，突出分子对称性的影响。比较了HHeH ~（2+）和HHeH（STO-3G）的h-RHF态，说明了双电子双空穴体系的同构性.最后，我们探讨了乙烯的h-RHF态（STO-3G），通过考虑π电子作为一个两电子的问题，并采用NOCI来确定交叉的最低能量的单重态和三重态在垂直的几何形状。
We explore the existence and behavior of holomorphic restricted Hartree-Fock (h-RHF) solutions for two-electron problems. Through algebraic geometry, the exact number of solutions with n basis functions is rigorously identified as 1/2(3 '' - 1), proving that states must exist for all molecular geometries. A detailed study on the h-RHF states of HZ (STO-3G) then demonstrates both the conservation of holomorphic solutions as geometry or atomic charges are varied and the emergence of complex h-RHF solutions at coalescence points. Using catastrophe theory, the nature of these coalescence points is described, highlighting the influence of molecular symmetry. The h-RHF states of HHeH2+ and HHeH (STO-3G) are then compared, illustrating the isomorphism between systems with two electrons and two electron holes. Finally, we explore the h-RHF states of ethene (STO-3G) by considering the pi electrons as a two-electron problem and employ NOCI to identify a crossing of the lowest energy singlet and triplet states at the perpendicular geometry.