Accurate Crystal Field Hamiltonians of Single-Ion Magnets at Mean-Field Cost

The effective crystal field Hamiltonian provides the key description of the electronic properties of single-ion magnets, but obtaining its parameters from an ab initio computation is challenging. We introduce a simple approach to derive the effective crystal field Hamiltonian through density functional calculations of randomly rotated mean-field states within the low-energy manifold. In benchmarks on five lanthanide-based complexes, we find that we compute with mean-field cost an effective crystal field Hamiltonian that matches the state-of-the-art from much more expensive multiconfigurational quantum chemistry methods. In addition, we are able to reproduce the experimental low-energy spectrum and magnetic properties with an accuracy exceeding those of prior attempts. Due to its low cost, our approach provides a crucial ingredient in the computational design of single-ion magnets with tailored physical properties and low-energy spectra.