Stability of the complex generalized Hartree-Fock equations

Area of Science:

• Quantum chemistry
• Computational materials science
• Molecular magnetism

Background:

• Finding the lowest energy state of molecules with complex magnetic interactions often requires breaking symmetry in electronic structure calculations.
• The complex generalized Hartree-Fock (GHF) method allows for broken symmetry but can converge to higher energy solutions due to relaxed variational constraints.

Purpose of the Study:

• To implement and validate a stability test for complex GHF equations.
• To develop an orbital update scheme to address instabilities encountered during GHF calculations.
• To demonstrate the utility of the broken symmetry GHF method for exploring complex magnetic systems.

Main Methods:

• Implementation of a stability test for complex GHF solutions.
• Development of an orbital update algorithm for unstable GHF solutions.
• Application of the methodology to spin-frustrated hydrogen rings and the molecular magnet Cr3.

Main Results:

• The study successfully implemented a stability test and an orbital update scheme for complex GHF.
• The methodology was applied to identify local minima in spin-frustrated hydrogen rings.
• The approach was also used to analyze the non-collinear molecular magnet Cr3, revealing nuances of the broken symmetry GHF method.

Conclusions:

• The developed stability test and update scheme enhance the reliability of the complex GHF method for finding true energy minima.
• This approach is valuable for studying molecules with competing magnetic interactions, including spin frustration and non-collinear magnetism.
• The work highlights the practical utility and lesser-known aspects of broken symmetry GHF calculations in computational chemistry.