Ab initio calculations of g values of free radicals by finite perturbation theory

Basis set error estimation for DFT calculations of electronic g-tensors for transition metal complexes

We present a detailed study of the basis set dependence of electronic g-tensors for transition metal complexes calculated using Kohn-Sham density functional theory. Focus is on the use of locally dense basis set schemes where the metal is treated using either the same or a more flexible basis set than used for the ligand sphere. The performance of all basis set schemes is compared to the extrapolated complete basis set limit results. Furthermore, we test the performance of the aug-cc-pVTZ-J basis set developed for calculations of NMR spin-spin and electron paramagnetic resonance hyperfine coupling constants. Our results show that reasonable results can be obtain when using small basis sets for the ligand sphere, and very accurate results are obtained when an aug-cc-pVTZ basis set or similar is used for all atoms in the complex.

Gauge invariance of the spin-other-orbit contribution to the g-tensors of electron paramagnetic resonance

The spin-other-orbit (SOO) contribution to the g-tensor (DeltagSOO) of electron paramagnetic resonance arises due to the interaction of electron-spin magnetic moment with the magnetic field produced by the orbital motion of other electrons. A similar mechanism is responsible for the leading term in nuclear magnetic-shielding tensors sigma. We demonstrate that analogous to sigma, paramagnetic DeltagSOO contribution exhibits a pronounced dependence on the choice of the magnetic-field gauge. The gauge corrections to DeltagSOO are similar in magnitude, and opposite in sign, to the paramagnetic SOO term. We calculate gauge-invariant DeltagSOO values using gauge-including atomic orbitals and density-functional theory. For organic radicals, complete gauge-invariant DeltagSOO values typically amount to less than 500 parts per million (ppm), and are small compared to other g-tensor contributions. For the first-row transition-metal compounds, DeltagSOO may contribute several thousand ppm to the g-tensor, but are negligible compared to the remaining deviations from experiment. With popular choices for the magnetic-field gauge, the individual gauge-variant contributions may be an order of magnitude higher, and do not provide a reliable estimation of DeltagSOO.