Octahedral Fe$^{2+}$ molecules are particularly interesting as they often exhibit a spin-crossover transition. In spite of the many efforts aimed at assessing the performances of density functional theory for such systems, an exchange-correlation fun
ctional able to account accurately for the energetic of the various possible spin-states has not been identified yet. Here we critically discuss the issues related to the theoretical description of this class of molecules from first principles. In particular we present a comparison between different density functionals for four ions, namely [Fe(H$_2$O)$_6$]$^{2+}$, [Fe(NH$_3$)$_6$]$^{2+}$, [Fe(NCH)$_6$]$^{2+}$ and [Fe(CO)$_6$]$^{2+}$. These are characterized by different ligand-field splittings and ground state spin multiplicities. Since no experimental data are available for the gas phase, the density functional theory results are benchmarked against those obtained with diffusion Monte Carlo, one of the most accurate methods available to compute ground state total energies of quantum systems. On the one hand, we show that most of the functionals considered provide a good description of the geometry and of the shape of the potential energy surfaces. On the other hand, the same functionals fail badly in predicting the energy differences between the various spin states. In the case of [Fe(H$_2$O)$_6$]$^{2+}$, [Fe(NH$_3$)$_6$]$^{2+}$, [Fe(NCH)$_6$]$^{2+}$, this failure is related to the drastic underestimation of the exchange energy. Therefore quite accurate results can be achieved with hybrid functionals including about 50% of Hartree-Fock exchange. In contrast, in the case of [Fe(CO)$_6$]$^{2+}$, the failure is likely to be caused by the multiconfigurational character of the ground state wave-function and no suitable exchange and correlation functional has been identified.
The electronic structure of the neutral and singly charged Mg vacancy in MgO is investigated using density functional theory. For both defects, semilocal exchange correlation functionals such as the local spin density approximation incorrectly predic
t a delocalized degenerate ground state. In contrast functionals that take strong correlation effects into account predict a localized solution, in agreement with spin resonance experiments. Our results, obtained with the HSE hybrid, atomic self-interaction corrected and LDA+U functionals, provide a number of constraints to the possibility of ferromagnetism in hole doped MgO.
Density functional theory calculations demonstrate that rocksalt MgN is a magnetic material at the verge of half-metallicity, with an electronic structure robust against strong correlations and spin-orbit interaction. Furthermore the calculated heat
of formation describes the compound as metastable and suggests that it can be fabricated by tuning the relative Mg and N abundance during growth. Intriguingly the equilibrium lattice constant is close to that of MgO, so that MgN is likely to form as an inclusion during the fabrication of N-doped MgO. We then speculate that the MgO/MgN system may represent a unique materials platform for magnetic tunnel junctions not incorporating any transition metals.
Predicting magnetism originating from 2$p$ orbitals is a delicate problem, which depends on the subtle interplay between covalency and Hunds coupling. Calculations based on density functional theory and the local spin density approximation fail in tw
o remarkably different ways. On the one hand the excessive delocalization of spin-polarized holes leads to half-metallic ground states and the expectation of room temperature ferromagnetism. On the other hand, in some cases a magnetic ground state may not be predicted at all. We demonstrate that a simple self-interaction correction scheme modifies both these situations via an enhanced localization of the holes responsible for the magnetism and possibly Jahn-Teller distortion. In both cases the ground state becomes insulating and the magnetic coupling between the impurities weak.
