Constrained Active Space Unrestricted Mean-Field Approaches for Controlling Spin-Contamination

We have recently shown that unrestricted Hartree-Fock (UHF) variationally reduces to high-spin restricted open-shell Hartree-Fock when constraints are imposed on the eigenvalues of the spin density matrix [T. Tsuchimochi and G. E. Scuseria, J. Chem. Phys. {\bf 133}, 141102 (2010)]. We here generalize these ideas and propose to control spin-contamination in UHF by releasing the constraints in an active space while imposing them elsewhere. If the active space is properly chosen, our constrained UHF (CUHF) method greatly benefits from a controlled broken-symmetry effect while avoiding the massive spin contamination arising in the traditional UHF. We apply L$\rm{\ddot{o}}$wdin's projection operator to CUHF and obtain multireference wave functions with moderate computational cost. We report results on singlet-triplet energy gaps to show that our constrained scheme outperforms fully unrestricted methods. This constrained approach can be readily used in Kohn-Sham (KS) density functional theory with similar favorable effects, provided that spin-contamination is given by the KS orbitals as in UHF.