Spin-restricted open-shell Kohn-Sham method

Filatov, M., Shaik, S., 1999, Application of Spin-Restricted Open-Shell Kohn-Sham Method to Atomic and Molecular Multiplet States , J. Chem. Phys., 110, 116. 

The exact energy functional (and the exchange correlation functional) are indeed functionals of the total density, even for open-shell systems [47]. However, for the construction of approximate functionals of closed as well as open-shell systems, it has been advantageous to consider functionals with more flexibility, where the a- and j8-densities can be varied separately, i.e. E[p, p ]. The variational search for a minimum of tire E[p, p ] functional can be carried out by unrestricted and spin-restricted approaches. The two methods differ only by the conditions of constraint imposed in minimization and lead to different sets of Kohn-Sham equations for the spin orbitals. The unrestricted Kohn-Sham approach is the one most commonly used and is implemented in various standard quantum chemistry software packages. However, this method has a major disadvantage, namely a spin contamination problem, and in recent years the alternative spin-restricted Kohn-Sham approach has become a popular contester [48-50]. 

Hyperfine couplings, in particular the isotropic part which measures the spin density at the nuclei, puts special demands on spin-restricted wave-functions. For example, complete active space (CAS) approaches are designed for a correlated treatment of the valence orbitals, while the core orbitals are doubly occupied. This leaves little flexibility in the wave function for calculating properties of this kind that depend on the spin polarization near the nucleus. This is equally true for self-consistent field methods, like restricted open-shell Hartree-Fock (ROHF) or Kohn-Sham (ROKS) methods. On the other hand, unrestricted methods introduce spin contamination in the reference (ground) state resulting in overestimation of the spin-polarization. 

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