Theoretical Chemistry Accounts

, Volume 129, Issue 3–5, pp 715–725 | Cite as

Assessment of higher-order spin–orbit effects on electronic g-tensors of d 1 transition-metal complexes by relativistic two- and four-component methods

  • Peter HrobárikEmail author
  • Michal Repiský
  • Stanislav Komorovský
  • Veronika Hrobáriková
  • Martin KauppEmail author
Regular Article


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.


Biological 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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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Peter Hrobárik
    • 1
    • 2
    Email author
  • Michal Repiský
    • 2
    • 3
  • Stanislav Komorovský
    • 2
  • Veronika Hrobáriková
    • 1
  • Martin Kaupp
    • 1
    Email author
  1. 1.Technische Universität Berlin, Institut für ChemieTheoretische ChemieBerlinGermany
  2. 2.Institute of Inorganic ChemistrySlovak Academy of SciencesBratislavaSlovakia
  3. 3.Department of Chemistry, Centre for Theoretical and Computational Chemistry (CTCC)University of TromsøTromsøNorway

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