Stability of Hartree–Fock solutions and symmetry breaking in the independent particle model: A b i n i t i o case study of the LCAO–MO–SCF solutions for finite chains of hydrogen atoms

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Abstract
The stability of restricted Hartree–Fock solutions and the implied spin and/or space broken symmetry Hartree–Fock solutions are studied using ab initio models of finite chains of hydrogen atoms with Born–Kármán boundary conditions and nondegenerate ground state. We also examined the basis set effects, the role of the nuclear framework distortion as related to the bond‐length alternation problem in cyclic polyenes and the higher order instabilities for a large range of internuclear separations. The possible physical implications of the symmetry breaking in the independent particle model are discussed and studied in a considerable detail for the smallest cycle considered, containing six hydrogen atoms. An excellent agreement with the existing infinite chain results is also pointed out. Finally, the relationship with the stability problem and broken symmetry solutions for cyclic polyene models and the sources of these instabilities are examined and discussed as well as their implications for the character and reliability of the self‐consistent field potential energy surfaces.