Chromium-based rings within the DFT and Falicov–Kimball model approach

We present a comprehensive study of electronic and magnetic properties of octometallic homo- and heteronuclear chromium-based molecular rings Cr7MF8(O2CH)16 (in short Cr7M, M = Cr, Cd and Ni) by the first-principle density functional theory (DFT) and pseudopotential ideas. Their radii are around 1 nm. For each Cr7M, the antiferromagnetic configuration corresponds to the ground state and the ferromagnetic (high spin HS) configuration to the highest energy state. Using the broken symmetry (BS) approach, the differences between the total energies of the HS configuration and all the nonequivalent low spin configurations with s = ±3/2 are calculated and exploited to extract the coupling parameters J between the magnetic ions. Magnetic moments are found to be well localised on the Cr and Ni centres, although the localisation of spin density on Ni is weaker. Having calculated the excess energies for an unprecedented number of configurations, a family of the Ising-like models with the nearest- and the next-nearest-neighbour interactions has been considered. For each Cr7M, the values of the interaction parameters found within the unprojected method are coherent, despite the overdetermination problem and demonstrate that the next-nearest-neighbour couplings are negligible. The DFT estimates of the nearest-neighbour coupling calculated are overestimated and the relation J Cr–Cr/J Cr–Ni < 1 is not fulfilled. However, the improvement in these estimates has been achieved with respect to earlier calculations. Relying on the DFT results, the molecule is considered as a system of localised spins (or ions) S = ±3/2 and the idea to describe their interactions with itinerant electrons by the Falicov–Kimball (FK) model is suggested. In our approach, the effective magnetic interactions between ions are generated by local (on-site) Hund couplings between the ions and itinerant electrons. We demonstrate that the BS state energies obtained within DFT for Cr7M can be successfully represented by the FK model with a unique set of parameters.