On the calculation of second-order magnetic properties using subsystem approaches in the relativistic framework

International audience; We report an implementation of the nuclear magnetic resonance (NMR) shielding (σ), isotope-independent indirect spin-spin coupling (K) and the magnetizability (χ) tensors in the frozen density embedding (FDE) scheme using the four-component (4c) relativistic Dirac--Coulomb (DC) Hamiltonian and the non-collinear spin density functional theory (SDFT). The formalism takes into account the magnetic balance between the large and the small components of molecular spinors and assures the gauge-origin independence of NMR shielding and magnetizability results. This implementation has been applied to hydrogen-bonded HXH⋯OH2 complexes (X = Se, Te, Po) and compared with the supermolecular calculations and with the approach based on the integration of the magnetically induced current density vector. A comparison with the approximate Zeroth-Order Regular Approximation (ZORA) Hamiltonian indicates non-negligible differences in σ and K in the HPoH⋯OH2 complex, and calls for a thourough comparison of ZORA and DC in the description of environment effects on NMR parameters for molecular systems with heavy elements.