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NMR/EPR properties under perturbation theoretical inclusion of spin-orbit coupling

Many parameters of magnetic resonance depend critically on spin-orbit effects. This has often hampered the theoretical and computational access up to now [1]. Our group, in collaboration with the groups of V. G. Malkin and O. L. Malkina (Bratislava), J. Vaara (Helsinki), and B. Schimmelpfennig (now in Karlsruhe), has developed over the years a machinery for the efficient and accurate perturbation theoretical treatment of such spin-orbit effects [2-7,9,11]. While this was done initially within the framework of the deMon-NMR/EPR code, during the past ten years the work has concentrated on the new, more flexible ReSpect program package (and more recently a fully relativistic version thereof). A distinct advantage of these implementations is the use of efficient and accurate ab initio approximations to the full microscopic one- and two-electron spin-orbit operators. These are (i) the all-electron „atomic meanfield approximation“ (AMFI), and  (ii) spin-orbit pseudopotentials. This allows us to treat, with moderate computational effort, large systems, without employing the commonly used empirical parameters [2-7,9,11]. However, semi-empirical SO-operators and even the full one- and two-electron Breit-Pauli SO Hamiltonian are also available in the MAG-ReSpect program.

The first implementations have focused on (i) spin-orbit corrections to NMR chemical shifts in triple perturbation theory [2,3], and on (ii) calculations of electronic g-tensors in double perturbation theory [4,5]. The methodology was then extended to the computation of the important spin-orbit corrections to hyperfine coupling constants in second-order perturbation theory [6,7]. These correction terms improve agreement with experiment considerably already for 3d-metal complexes, and they afford the experimentally accessible antisymmetric contributions to the hyperfine matrix.

A further important magnetic resonance parameter that is dominated by spin-orbit effects is zero-field splitting (ZFS). This parameter is of central importance in the field of molecular magnetism, as it determines the tunneling splitting of single-molecule magnets. In this field, the ZFS has often been computed by a simple perturbation theoretical approach due to Pederson and Khanna [8]. We have implemented that approach (using AMFI SO operators and SO-ECPs), as well as a two-component non-collinear DFT approach and compared the two in detail for various species [9]. Meanwhile a full coupled-perturbed Kohn-Sham implementation is available, including the spin-spin contributions.

Last but not least, all of these spin-orbit-dependent MR parameters have to be combined to compute NMR chemical shifts of open-shell systems, as g-tensors, hyperfine tensors (with SO corrections), orbital shifts, and ZFS enter the perturbation expressions for this parameter. The first implementation for systems with arbitrary spin multiplicity has recently been reported [10] (see also ref. [11]). First applications have been made, for example, to the elucidation of enantioselective catalysis mechanisms [12], and to magnetic materials [13].

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[1] Calculation of NMR and EPR Parameters. Theory and Applications (Eds. M. Kaupp, M. Bühl, V. G. Malkin) Wiley-VCH, Weinheim 2004.

[2] Spin-Orbit Corrections to NMR Shielding Constants from Density Functional Theory. How Important are the Two-Electron Terms? O. L. Malkina, B. Schimmelpfennig, M. Kaupp, B. A. Hess, P. Chandra, U. Wahlgren, V. G. Malkin Chem. Phys. Lett. 1998, 296, 93-104.

[3] Study of Relativistic Effects on Nuclear Shieldings Using Density-Functional Theory and Spin-Orbit Pseudopotentials J. Vaara, O. L. Malkina, H. Stoll, V. G. Malkin, M. Kaupp J. Chem. Phys. 2001, 114, 61-71.

[4] Density-Functional Calculations of Electronic g-Tensors Using Spin-Orbit Pseudopotentials and/or Mean-Field All-Electron Spin-Orbit Operators O. L. Malkina, J. Vaara, B. Schimmelpfennig, M. L. Munzarová, V. G. Malkin, M. Kaupp J. Am. Chem. Soc. 2000, 122, 9206-9218.

[5] Calculation of Electronic g-Tensors for Transition Metal Complexes Using Hybrid Density Functionals and Atomic Meanfield Spin-Orbit Operators M. Kaupp, R. Reviakine, O. L. Malkina, A. Arbuznikov, B. Schimmelpfennig, V. G. Malkin J. Comput. Chem. 2002, 23, 794-803.

[6] Relativistic Spin-Orbit Effects on Hyperfine Coupling Tensors by Density Functional Theory A. V. Arbuznikov, J. Vaara, M. Kaupp J. Chem. Phys. 2004, 120, 2127-2139.

[7] Spin-Orbit Effects on Hyperfine Coupling Tensors in Transition Metal Complexes Using Hybrid Density Functionals and Accurate Spin-Orbit Operators C. Remenyi, A. V. Arbuznikov, R. Reviakine, J. Vaara, M. Kaupp J. Phys. Chem. A 2004, 108, 5026-5033.

[8] M. R. Pederson, S.N. Khanna Phys. Rev. B 1999, 60, 9566.

[9] Calculation of Zero-Field Splitting Parameters. Comparison of a Two-Component Non-Collinear Density Functional Method and a One-Component Perturbational Approach R. Reviakine, A. V. Arbuznikov, J.-C. Tremblay, C. Remenyi, O. L. Malkina, V. G. Malkin, M. Kaupp J. Chem. Phys. 2006, 125, 054110/1-12.

[10] Density Functional Calculations of NMR Chemical Shift Tensors for Paramagnetic Systems with Arbitrary Spin Multiplicity. Validation on 3d-Metallocenes P. Hrobárik, R. Reviakine, A. V. Arbuznikov, O. L. Malkina, V. G. Malkin, F. H. Köhler, M. Kaupp J. Chem. Phys. 2007, 126, 024107/1-19.

[11] T. Pennanen, J. Vaara Phys. Rev. Lett. 2008, 100, 133002.

[12] Jacobsen’s Catalyst for Hydrolytic Kinetic Resolution: Structure Elucidation of Paramagnetic Co(III) Salen Complexes in Solution via Combined NMR and Quantum Chemical Studies S. Kemper, P. Hrobarik, M. Kaupp. N. E. Schloerer J. Am. Chem. Soc. 2009, 131, 4172-4173. Erratum: J. Am. Chem. Soc. 2009, 131, 6641-6641.

[13] Combining NMR spectroscopy and quantum chemistry as tools to quantify spin density distributions in molecular magnetic compounds M. Kaupp, F. H. Köhler Coord. Chem. Rev. 2009, 253, 2376-2386.

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Prof. Dr. M. Kaupp
Theoretical Chemistry
Quantum Chemistry