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

We report an implementation of nuclear magnetic resonance (NMR) shielding (sigma), isotope-independent indirect spin-spin coupling (K) and the magnetizability (xi) tensors in a frozen density embedding scheme using the four-component (4c) relativistic Dirac-Coulomb (DC) Hamiltonian and non-collinear spin density functional theory. 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 the NMR shielding and magnetizability results. This implementation has been applied to hydrogen-bonded HXH...OH2 complexes (X = Se, Te, Po) and compared with supermolecular calculations and with an 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 s and K in the HPoH...OH2 complex, and calls for a thorough comparison of ZORA and DC Hamiltonians in the description of environment effects on NMR parameters for molecular systems with heavy elements.