Calculation of molecular g-tensors using the zeroth-order regular approximation and density functional theory: Expectation value versus linear response approaches

Density functional theory (DFT) calculations of molecular g-tensors were implemented as a second derivative property within the two-component relativistic zeroth-order regular approximation (ZORA). g-tensors were computed for systems ranging from light atomic radicals to molecules with heavy d and f block elements. For comparison, computations were also performed with a ZORA first-order derivative approach and with a second derivative method based on the Pauli Hamiltonian. In each set of computations, Slater-type basis sets have been used. The new ZORA implementation allows for non-hybrid and hybrid DFT calculations. A comparison of the PBE non-hybrid and the PBE0 hybrid functional yielded mixed results for our test set. For the lanthanide complex [Ce(DPA)₃]^3- (DPA = pyridine-2,6-dicarboxylate), calculations of the g-tensor were used to estimate paramagnetic NMR pseudocontact shifts for protons and carbon atoms in the ligands. The results are in reasonable agreement with experimental data.