Quadratic Spin-Orbit Mechanism of the Electronic g-Tensor.

Understanding how the electronic g-tensor is linked to the electronic structure is desirable for the correct interpretation of electron paramagnetic resonance spectra. For heavy-element compounds with large spin-orbit (SO) effects, this is still not completely clear. We report our investigation of quadratic SO contributions to the g-shift in heavy transition metal complexes. We implemented third-order perturbation theory in order to analyze the contributions arising from frontier molecular spin orbitals (MSOs). We show that the dominant quadratic SO term─spin-Zeeman (SO2/SZ)─generally makes a negative contribution to the g-shift, irrespective of the particular electronic configuration or molecular symmetry. We further analyze how the SO2/SZ contribution adds to or subtracts from the linear orbital-Zeeman (SO/OZ) contribution to the individual principal components of the g-tensor. Our study suggests that the SO2/SZ mechanism decreases the anisotropy of the g-tensor in early transition metal complexes and increases it in late transition metal complexes. Finally, we apply MSO analysis to the investigation of g-tensor trends in a set of closely related Ir and Rh pincer complexes and evaluate the influence of different chemical factors (the nuclear charge of the central atom and the terminal ligand) on the magnitudes of the g-shifts. We expect our conclusions to aid the understanding of spectra in magnetic resonance investigations of heavy transition metal compounds.

The four-component DFT method for the calculation of the EPR g-tensor using a restricted magnetically balanced basis and London atomic orbitals.

Four-component relativistic treatments of the electron paramagnetic resonance g-tensor have so far been based on a common gauge origin and a restricted kinetically balanced basis. The results of such calculations are prone to exhibit a dependence on the choice of the gauge origin for the vector potential associated with uniform magnetic field and a related dependence on the basis set quality. In this work, this gauge problem is addressed by a distributed-origin scheme based on the London atomic orbitals, also called gauge-including atomic orbitals (GIAOs), which have proven to be a practical approach for calculations of other magnetic properties. Furthermore, in the four-component relativistic domain, it has previously been shown that a restricted magnetically balanced (RMB) basis for the small component of the four-component wavefunctions is necessary for achieving robust convergence with regard to the basis set size. We present the implementation of a four-component density functional theory (DFT) method for calculating the g-tensor, incorporating both the GIAOs and RMB basis and based on the Dirac-Coulomb Hamiltonian. The approach utilizes the state-of-the-art noncollinear Kramers-unrestricted DFT methodology to achieve rotationally invariant results and inclusion of spin-polarization effects in the calculation. We also show that the gauge dependence of the results obtained is connected to the nonvanishing integral of the current density in a finite basis, explain why the results of cluster calculations exhibit surprisingly low gauge dependence, and demonstrate that the gauge problem disappears for systems with certain point-group symmetries.