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arXiv · 1801.04141

Holomorphic Hartree-Fock Theory: The Nature of Two-Electron Problems

Hugh G. A. Burton·Mark Gross·Alex J. W. Thom
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Abstract

We explore the existence and behaviour 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 $\frac{1}{2}(3^n - 1)$, 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 HHeH$^{2+}$ 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.

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Hugh G. A. Burton, Mark Gross, Alex J. W. Thom. 2018-01-12. Holomorphic Hartree-Fock Theory: The Nature of Two-Electron Problems. https://doi.org/10.1021/acs.jctc.7b00980

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