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

It has recently been shown that configuration state functions (CSFs) with local orbitals can provide a compact reference state for low-spin open-shell electronic structures, such as antiferromagnetic states. However, optimizing a low-spin configuration using self-consistent field (SCF) theory has been a long-standing challenge since each orbital must be an eigenfunction of a different Fock operator. We introduce a low-spin restricted open-shell Hartree–Fock (ROHF) algorithm to optimize any CSF at mean-field cost. This algorithm employs quasi-Newton Riemannian optimization on the orbital constraint manifold to provide robust convergence, extending the geometric direct minimization approach to open-shell electronic structures with arbitrary genealogical spin coupling. Numerical calculations on transition metal aquo complexes show improved convergence over existing methodology, while the possibility of local CSF energy minima is demonstrated for iron–sulfur complexes. Finally, open-shell CSFs with different spin coupling patterns are used to qualitatively study the singlet ground state in polyacenes, revealing the onset of polyradical character as the chain length increases.