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

TL;DR

This paper presents a relativistic subsystem approach for calculating NMR shielding, spin-spin coupling, and magnetizability tensors, ensuring gauge-origin independence and applying it to heavy-element hydrogen-bonded complexes.

Contribution

The implementation of relativistic FDE for NMR properties using the Dirac--Coulomb Hamiltonian and non-collinear SDFT is novel and improves accuracy for heavy-element systems.

Findings

Relativistic FDE yields results comparable to supermolecular calculations.

Significant differences observed between DC and ZORA Hamiltonians for heavy elements.

Environment effects on NMR parameters are sensitive to the choice of relativistic Hamiltonian.

Abstract

We report an implementation of the nuclear magnetic resonance (NMR) shielding ($\sigma$), isotope-independent indirect spin-spin coupling ($K$) and the magnetizability ($\xi$) 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$\cdots$OH$_2$ 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 $\sigma$ and $K$ in the HPoH$\cdots$OH$_2$ 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.