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 Cr 7 MF 8 (O 2 CH) 16 (in short Cr 7 M, M = Cr, Cd and Ni) by the first-principle density functional theory (DFT) and pseudopotential ideas. Their radii are around 1 nm. For each Cr 7 M, 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 Cr 7 M, 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