  The cluster-based Mean Field method (cMF) and it's second order perturbative
correction[1], was introduced by Jim\'enez-Hoyos and Scuseria to reduce the
cost of modeling strongly correlated systems by dividing an active space up
into small clusters, which are individually solved in the mean-field presence
of each other. In that work, clusters with unpaired electrons are treated
naturally, by allowing the $\alpha$ and $\beta$ orbitals to spin polarize.
While that provided significant energetic stabilization, the resulting cMF
wavefunction was spin-contaminated, making it difficult to use as a reference
state for spin-pure post-cMF methods. In this work, we propose the Restricted
Open-shell cMF (RO-cMF) method, extending the cMF approach to systems with
open-shell clusters, while not permitting spin-polarization. While the
resulting RO-cMF energies are necessarily higher in energy than the
unrestricted orbital cMF, the new RO-cMF provides a simple reference state for
post-cMF methods that recover the missing inter-cluster correlations. We
provide a detailed explanation of the method, and report demonstrative
calculations of exchange coupling constants for three systems: a di-iron
complex, a di-chromium complex, and a dimerized organic radical. We also report
the first perturbatively corrected RO-cMF-PT2 results as well.
