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

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Gross, Mark 
Thom, Alex JW 

Abstract

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(3n - 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 π 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.

Description

Keywords

physics.chem-ph, physics.chem-ph

Journal Title

J Chem Theory Comput

Conference Name

Journal ISSN

1549-9618
1549-9626

Volume Title

14

Publisher

American Chemical Society (ACS)
Sponsorship
Royal Society (uf110161)
Royal Society (UF160398)
Engineering and Physical Sciences Research Council (EP/N03189X/1)