Generalized spin σ-SCF method.

Area of Science:

• Quantum chemistry
• Computational physics
• Materials science

Background:

• The σ-SCF method approximates electronic states by minimizing Hamiltonian variance.
• Accurately describing noncollinear spin states, especially excited states, remains a challenge in quantum chemistry.

Purpose of the Study:

• To generalize the σ-SCF method for approximating noncollinear spin ground and excited states.
• To develop a computational approach that treats ground and excited noncollinear spin states equally.
• To investigate systems exhibiting geometric spin frustration.

Main Methods:

• Introduced a generalized σ-SCF method minimizing Hamiltonian variance.
• Implemented a two-stage approach: simulated annealing for broad exploration and mean-field iteration for convergence.
• Utilized random complex rotations of the density matrix during simulated annealing.
• Employed an effective Fockian derived from variance for the self-consistent field stage.

Main Results:

• Successfully approximated noncollinear spin ground and excited states.
• Demonstrated the method's ability to find complex spin structures without complex initial guess manipulation.
• Applied the method to Hn (n=3-7) rings and clusters with geometric spin frustration.
• Identified noncollinear spin excited states in these systems, linked to geometric spin frustration.

Conclusions:

• The generalized σ-SCF methodology effectively finds approximate noncollinear spin structures as mean-field excited states.
• The method provides a powerful tool for studying systems with geometric spin frustration.
• This approach overcomes limitations of energy minimization methods in targeting excited states.