The role of relativistic effects in anisotropy for NMR shielding tensors: A study using the LRESC model

We present a generalization of the Linear Response Elimination of the Small Component (LRESC) formalism for the calculation of the nuclear magnetic shielding tensor, extending the method to account for the shielding anisotropic parameters, asymmetry, and anisotropy in molecules of any symmetry. The most significant contributions to the off-diagonal tensor elements come from terms related to the angular momentum and spin in the paramagnetic term. Among these, the σSOS correction, related to the spin Zeeman and the spin-orbit mechanisms, plays a crucial role. This term was previously computed only for molecules with linear symmetry, and we successfully extend its inclusion to systems of arbitrary symmetry. This is performed through two different approaches, although further development is required to evaluate it directly in the Schrödinger manifold of states. We apply the LRESC model to HX, SnH3X, and chiral CHFClX molecular systems (X = Br, I). The resulting anisotropic parameters are in very good agreement with those obtained from four component Dirac-Hartree-Fock calculations. We show that only the ligand-like group of LRESC corrections, to which σSOS belongs, is enough to describe the anisotropic parameters, instead of using the whole set of LRESC corrections. LRESC is proved to be a powerful tool for elucidating the electronic mechanisms that give rise to relativistic effects also in the anisotropic parameters in systems containing heavy atoms up to the fifth row of the Periodic Table.