  We explore Riemannian optimization methods for Restricted-Open-shell
Hartree-Fock (ROHF) and Complete Active Space Self-Consistent Field (CASSCF)
methods. After showing that ROHF and CASSCF can be reformulated as optimization
problems on so-called flag manifolds, we review Riemannian optimization basics
and their application to these specific problems. We compare these methods to
traditional ones and find robust convergence properties without fine-tuning of
numerical parameters. Our study suggests Riemannian optimization as a valuable
addition to orbital optimization for ROHF and CASSCF, warranting further
investigation.
