Spin symmetry requirements in density functional theory: The proper way to predict magnetic coupling constants in molecules and solids

In this paper it is argued that the use of density functional theory (DFT) to solve the exact, non-relativistic, many-electron problem, for magnetic systems requires imposing space and spin symmetry constraints exactly in the same way as it is currently done in ab initio wave function theory. This strong statement is supported on pertinent calculations for selected systems representative of organic diradicals, molecular magnets and antiferromagnetic solids. These calculations include several wave function methods of increasing accuracy and different forms of the exchange-correlation functional. The comparisons of numerical results carried out always within the same standard Gaussian Type Orbital atomic basis set show that imposing or not the spin and space constraints (restricted or unrestricted formalisms) leads to contradictory results. Therefore, it appears that, in the case of the Heisenberg magnetic constant, the present exchange-correlation functionals may provide reasonable numerical results although for the wrong physical reasons thus evidencing the failure of the current DFT methods to properly describe magnetic systems.