Density-functional theory for systems with noncollinear spin: Orbital-dependent exchange-correlation functionals and their application to the Hubbard dimer

A class of orbital-dependent exchange-correlation potentials for applications in noncollinear spin-density-functional theory is developed. Starting from the optimized effective potential formalism for the exact exchange potential-generalized to the noncollinear case-correlation effects are added via a self-consistent procedure inspired by the Singwi-Tosi-Land-Sjolander method. The orbital-dependent exchange-correlation potentials are applied to the Hubbard dimer in uniform and noncollinear magnetic fields and compared to exact diagonalization and to the Bethe-ansatz local spin-density approximation. The Singwi-Tosi-Land-Sjolander method gives the overall best performance for total energies, densities, andmagnetizations, particularly in the weakly to moderately correlated regime.