Gauge invariance of the spin-other-orbit contribution to the g-tensors of electron paramagnetic resonance -: art. no. 214101

The spin-other-orbit (SOO) contribution to the g-tensor (Delta g(SOO)) 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 Delta g(SOO) contribution exhibits a pronounced dependence on the choice of the magnetic-field gauge. The gauge corrections to Delta g(SOO) are similar in magnitude, and opposite in sign, to the paramagnetic SOO term. We calculate gauge-invariant Delta g(SOO) values using gauge-including atomic orbitals and density-functional theory. For organic radicals, complete gauge-invariant Delta g(SOO) 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, Delta g(SOO) 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 Delta g(SOO).