### Inhalt des Dokuments

## 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 [1]). 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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### References

[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] C*alculation 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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## Chair

**Prof. Dr. M. Kaupp**

Theoretical Chemistry

Quantum Chemistry

Website [2]

## Contact

- Dr. Alexey Arbuznikov [3]

ch/quantum_chemical_method_development/relativistic_all

_electron_approaches/

ns/team/prof_dr_martin_kaupp/parameter/en/

us/team/dr_alexey_arbuznikov/