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.
- 1.Abragam A, Bleaney B (1970) Electron paramagnetic resonance of transition ions. Oxford Clarendon Press, OxfordGoogle Scholar
- 2.Harriman JE (1978) Theoretical foundations of electron spin resonance. Academic Press, New YorkGoogle Scholar
- 10.Schreckenbach G, Ziegler T (1998) Theor Chem Acc 99(2):71Google Scholar
- 20.Hrobarik P, Hrobarikova V, Meier F, Repisky M, Komorovsky S, Kaupp M (2011) J Phys Chem A (in press)Google Scholar
- 21.TURBOMOLE (2009) version 6.0, a development of University of Karlsruhe and Forschungszentrum Karlsruhe GmbHGoogle Scholar
- 22.Eichkorn K, Weigend F, Treutler O, Ahlrichs R (1997) Theor Chem Acc 97(1–4):119Google Scholar
- 26.Sproules SA, Morgan HT, Doonan CJ, White JM, Young CG (2005) Dalton Trans (21):3552Google Scholar
- 27.Malkin VG, Malkina OL, Reviakine R, Arbuznikov AV, Kaupp M, Schimmelpfennig B, Malkin I, Repisky M, Komorovsky S, Hrobarik P, Malkin E, Helgaker T, Ruud K (2010) MAG-ReSpect, version 2.3Google Scholar
- 28.Repisky M (2009) Development and implementation of efficient relativistic methods for calculations of NMR and EPR parameters. Ph.D. Thesis, BratislavaGoogle Scholar
- 38.Kutzelnigg W, Fleischer U, Schindler M (1991) In: Diehl P, Fluck E, Günther H, Kosfeld R, Seelig J (eds) NMR basic principles and progress. Springer, BerlinGoogle Scholar
- 39.Schimmelpfennig B, AMFI (1996) Atomic spin-orbit mean-field integral program. Stockholms Universitet, StockholmGoogle Scholar