Assessment of higher-order spin–orbit effects on electronic g-tensors of d 1 transition-metal complexes by relativistic two- and four-component methods
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The electronic g-tensors of a series of V, Cr, Mo, W, Tc, and Re d1 transition-metal complexes have been studied systematically by density functional theory (DFT) methods. The comparison between one-component second-order perturbation theory calculations with two- and four-component first-order perturbation calculations has allowed an assessment of the importance of higher-order spin-orbit contributions. Using an efficient matrix Dirac–Kohn–Sham implementation with relativistic kinetic balance basis sets, it has been possible for the first time to apply four-component DFT also to g-tensors of larger models for biological vanadium, molybdenum, and tungsten metal sites. Higher-order spin–orbit effects are generally crucial for an accurate determination of the g-tensors in such complexes, in many cases more important than the choice of non-hybrid or hybrid density functional. A systematic scaling analysis of the spin–orbit integrals shows that second-order spin–orbit effects may be of the same size as the leading first-order effects and thus alter the computed g-tensors fundamentally, in particular for the 5d species. In the latter case, even third-order effects may be non-negligible.
KeywordsBiological transition-metal sites Density functional theory (DFT) Dirac–Kohn–Sham method Douglas–Kroll–Hess Hamiltonian Electron paramagnetic resonance (EPR) g-Tensor Relativistic effects Spin–orbit coupling Transition-metal complexes
This work has been supported by Deutsche Forschungsgemeinschaft (project KA1187/12-1), the Berlin cluster of excellence on “Unified Concepts in Catalysis” (UniCat), and Slovak grant agencies VEGA (Grant No. 2/0079/09) and APVV (Grant No. VVCE-0004-07). P. H. is indebted to the Alexander von Humboldt Foundation for a post-doctoral fellowship. The authors are also grateful to Vladimir Malkin and Olga Malkina for particularly fruitful discussions and comments.
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