Density-functional calculation of the quadrupole splitting in the 23Na NMR spectrum of the ferric wheel Na@Fe6(tea)6+ for various broken-symmetry states of the Heisenberg spin model

The quadrupole splitting in the ²³Na nuclear magnetic resonance (NMR) spectrum of the hexanuclear ferric wheel Na@Fe₆(tea)₆ ⁺ has been computed via an evaluation of the electric-field gradient (EFG) at the Na nucleus in the framework of density-functional theory (DFT). The simulated spectrum is compared with experimental data. A total of 2⁶ = 64 Kohn-Sham determinants (a number that reduces to eight symmetry-unique determinants due to the high S₆ symmetry of the ferric wheel) with six localised high-spin Fe(III) centres (S = 5/2) could be optimised in a self-consistent manner, and the corresponding DFT energies of all of these (broken-symmetry) determinants coincide almost perfectly according to the Ising Hamiltonian solutions, especially when the energy is computed from the B3LYP functional. The EFG at the Na atom does not depend much on the specific Kohn-Sham determinant but depends on the geometry of the ferric wheel and on the basis set used in the DFT calculations (particularly with regard to the atomic functions on the Na atom).