Hartree-Fock symmetry breaking around conical intersections.

Area of Science:

• Quantum chemistry
• Computational chemistry
• Molecular physics

Background:

• Conical intersections are critical regions in molecular potential energy surfaces where electronic states become degenerate.
• Symmetry breaking in Hartree-Fock (HF) solutions can occur due to accidental degeneracies, leading to instabilities.
• Generalized Hartree-Fock (GHF) solutions, involving spin-orbital mixing, are known to arise under geometric frustration.

Purpose of the Study:

• To investigate the behavior of Hartree-Fock (HF) solutions near conical intersections.
• To characterize novel symmetry-breaking solutions, including coplanar GHF solutions, that appear in these regions.
• To analyze the implications of these solutions for understanding molecular electronic structure.

Main Methods:

• Analysis of HF and GHF solution behavior in the vicinity of conical intersections.
• Examination of symmetry properties, including complex conjugation and time-reversal.
• Application of a magnetization diagnostic to characterize the emergent solutions.
• Study of prototypical examples from conical intersection literature and a Jahn-Teller active H8+2 system.

Main Results:

• Near conical intersections, HF solutions can evolve into coplanar GHF solutions that break all symmetries.
• These symmetry-broken solutions do not possess good quantum numbers.
• The study provides examples and utilizes a magnetization diagnostic to characterize these complex solutions.
• A Jahn-Teller active H8+2 geometry is analyzed as a case study.

Conclusions:

• Conical intersections can lead to profound symmetry breaking in electronic structure calculations.
• The emergence of novel GHF solutions highlights the complexity of electronic behavior in degenerate regions.
• These findings are crucial for accurate theoretical modeling of molecular systems exhibiting conical intersections.