Spin-Adapted Restricted Open-Shell Hartree-Fock and Its Dynamic Correlation Extension

We report a spin-adapted configuration-state-function restricted open-shell Hartree-Fock implementation in OpenMolcas, hereafter denoted CSF-ROHF. The implementation is based on the Graphical Unitary Group Approach for reduced density matrix evaluation, and on the Generalized Active Space and super-configuration interaction algorithms for the orbital optimization. The method enables orbital optimization of a single spin-pure electronic configuration at mean-field cost. Analysis of CSF-ROHF convergence reveals that the initial orbital ordering is decisive for avoiding and escaping local minima during optimization. The computational efficiency of the method, in terms of both iteration count and wall time, is demonstrated on {[Ni^II(H₂O)₄]_nO_n-1(H₂O)₂}²⁺ (n = 1, ..., 10) model systems. For spin gaps of iron-sulfur clusters, CSF-ROHF exhibits intrinsic limitations yielding qualitatively incorrect gaps and offering minimal-to-no advantages over conventional high-spin ROHF. To address these limitations, we introduce a near-mean-field-cost orbital optimization protocol that incorporates dynamic correlation via a second-order, spin-adapted perturbation strategy relying on the recently developed Stochastic-SplitGAS algorithm. The resulting perturbatively corrected state representations are substantially improved relative to the bare CSF-ROHF results, yielding energies and spin gaps in excellent agreement with far more expensive Complete Active Space Self-Consistent Field calculations.