Geometric Direct Minimization for Low-Spin Restricted Open-Shell Hartree-Fock Theory

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Electronic Structure Theory

Background:

• Configuration state functions (CSFs) with local orbitals offer compact references for low-spin open-shell systems.
• Optimizing low-spin configurations via self-consistent field (SCF) theory is challenging due to differing Fock operators for each orbital.

Purpose of the Study:

• Introduce a novel low-spin restricted open-shell Hartree-Fock (ROHF) algorithm.
• Enable optimization of any CSF at mean-field cost for improved electronic structure calculations.

Main Methods:

• Developed a quasi-Newton Riemannian optimization on the orbital constraint manifold.
• Extended geometric direct minimization to open-shell systems with arbitrary spin coupling.

Main Results:

• Achieved robust convergence for low-spin open-shell electronic structures.
• Demonstrated improved convergence for transition metal aquo complexes compared to existing methods.
• Identified local CSF energy minima in iron-sulfur complexes.
• Revealed polyradical character onset in polyacenes with increasing chain length.

Conclusions:

• The new ROHF algorithm provides an efficient and robust method for optimizing CSFs in low-spin open-shell systems.
• The approach enhances the study of complex electronic structures, including transition metal complexes and organic materials.