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## Quantum chemical studies in bioinorganic chemistry

A particularly interesting application field in transition-metal chemistry are metalloenzyme sites, and the use of quantum-chemical calculations to contribute to the elucidation of their structure and function. We use in particular the computation of EPR (or NMR [1]) parameters and comparisons with experimental EPR, ENDOR or ESEEM data in this context.

Initial work focused on the early transition metals V, Mo and W in biological surroundings, building on prior validation work on transition-metal EPR in general. For example, **vanadyl(IV)** complexes are of both biological and catalytic relevance. Their EPR parameters have been studied systematically [2], and both hyperfine and g-tensor data are best reproduced with hybrid functionals when substantial amounts of exact exchange are included (and including spin-orbit terms). This holds also for another biologically relevant V(IV) complex, **amavadine** [3]. Dependence on exchange-correlation functional is similar for **Mo complexes** [4], yet the importance of spin-orbit corrections to the Mo hyperfine couplings, and of higher-order spin-orbit contributions to g-tensors is even larger for the 4d element Mo, and even more so for the 5d-element tungsten [5,6]. The higher-order SO effects have been evaluated by two- and four-component calculations.

Subsequent applications were to to **larger, nonsymmetrical Mo(V) complexes** that model molybdopterin active sites in various enzymes [7]. Here we could demonstrate, that quantum chemical methods may allow the otherwise very difficult **assignment of X-band powder spectra of isotopically non-enriched biological samples or models**. This is due to the fact that assignment of the hyperfine tensor and of the Euler angles between g- and A-tensors is often not unambiguous in such samples for low-symmetry complexes [7]. Further connection points to molybdenum and tungsten redox enzymes (oxotransferases) result from our interest in **„non-VSEPR“ structures of early transition metal complexes** [8].

In a recent application of our DFT methodology, we have studied the interrelations between spin-density distribution and EPR parameters (g-tensors, Cu and ligand hyperfine tensors) for **blue-copper protein sites**, with some emphasis on the spectroscopically well-studied enzyme ** azurin** [9]. Using hybrid functionals with substantial exact-exchange admixture, reasonable agreement with experimental EPR parameters may be obtained. A main result has been the

**unusually large spin-orbit contributions to the Cu hyperfine tensors**in these highly distorted Cu(II) systems (Figure 1), leading to the characteristically low hyperfine couplings and thus misleadingly indicating a lower Cu spin density than is actually present [9].

Manganese is another important transition metal in bioinorganic chemistry, and in the focus of our ongoing work. With more complex enzyme sites and the oxygen-evolving cluster of photosystem II in mind, we started systematic studies of EPR parameters of Mn complexes in different oxidation states. After the experimentally well-studied Mn site of the saccharide-binding protein ** concanavalin A** [10] as a first example, we turned to dinuclear mixed-valent Mn

^{III}Mn

^{IV }sites, including models for

**, to gather experience on the necessary**

*manganese catalase***spin-projection procedures**[11]. This all served as a basis on which we initiated studies of the EPR parameters of the

**oxygen-evolving cluster**: Broken-symmetry DFT calculations on a wide variety of model complexes followed by spin projection allowed us the study of

^{55}Mn and

^{14,15}N hyperfine tensors [12]. The comparison with experimental EPR and ESEEM data for the S

_{2}-state of the OEC provided substantial insights. Already the computed manganese hyperfine couplings excluded many of the suggested model structures. Even more conclusive evidence was obtained from the

^{14}N hyperfine anisotropy of a manganese-bound histidine ligand [13], where computational

**results agreed only for one model structure, which had been suggested by Siegbahn**[13].

**Figure 2.**Local environment of the unique, pentacoordinated Mn^{III}site in Siegbahn’s OEC model [13] (see [12]).- © M. Kaupp

Significantly, these calculations showed that only a situation in which the **histidine is bound to the unique Mn ^{III} site** (Figure 2) matches the observed nitrogen hyperfine tensor [12]. Very recently, Siegbahn’s model has been corroborated by a

**new crystal structure**at higher resolution [14], thus supporting our conclusions based on the comparison between computed and experimental EPR parameters. To be able to obtain even more accaurate treatments of the full hyperfine tensors in such exchange-coupled systems, we have recently extended the spin-projection procedure by including fully the hyperfine-anisotropy transfer induced by local zero-field interactions and tested this for dinuclear Mn

^{III}Mn

^{IV}systems [15].

Further current activities within the unicat excellence cluster include work on the Ni-Fe carbon-monoxide dehydrogenase (CODH) and on membrane-bound hydrogenase (MBH).

### References

[1] *Density Functional Study of ^{17}O NMR Chemical Shift and Nuclear Quadrupole Coupling Tensors in Oxyheme Model Complexes* M. Kaupp, C. Rovira, M. Parrinello

*J. Phys. Chem. B*

**2000**,

*104*, 5200-5208.

[2]

*A Density Functional Study of EPR-Parameters for Vanadyl Complexes Containing Schiff Base Ligands*M. L. Munzarová, M. Kaupp

*J. Phys. Chem. B*

**2001**,

*105*, 12644-12652.

[3]

*A Comparative Density Functional Study of the EPR-Parameters of Amavadin*C. Remenyi, M. L. Munzarová, M. Kaupp

*J. Phys. Chem.*

**2005**,

*109*, 4227-4233.

[4]

*Computational Studies of EPR Parameters for Paramagnetic Molybdenum Complexes. I. Method Validation on Small and Medium-Sized Systems*J. Fritscher, P. Hrobárik, M. Kaupp

*J. Phys. Chem. B*

**2007**,

*111*, 4616-4629.

[5]

*Relativistic Two-Component Calculations of Electronic g-Tensor for Oxo-Molybdenum(V) and Oxo-Tungsten(V) Complexes: The Important Role of Higher-Order Spin-Orbit Contributions*P. Hrobárik, O. L. Malkina, V. G. Malkin, M. Kaupp

*Chem. Phys.*

**2009**,

*356*, 229-235.

[6]

*Assessment of Higher-Order Spin-Orbit Effects on Electronic g-Tensors of d1 Transition-Metal Complexes by Relativistic Two- and Four-Component Methods*P. Hrobárik, M. Repiský, S. Komorovský, V. Hrobáriková, M. Kaupp

*Theor. Chem. Acc.*

**2011**,

*129*, 715-725.

[7]

*Computational Studies of EPR Parameters for Paramagnetic Molybdenum Complexes. II. Larger MoV Systems Relevant to Molybdenum Enzymes*J. Fritscher, P. Hrobárik, M. Kaupp

*Inorg. Chem.*

**2007**,

*46*, 8146-8161.

[8]

*Trigonal Prismatic or not Trigonal Prismatic? On the Mechanisms of Oxygen-Atom Transfer in Molybdopterin-Based Enzymes*M. Kaupp

*Angew. Chemie*

**2004**,

*116*, 554-558; M. Kaupp

*Angew. Chemie, Int. Ed. Engl.*

**2004**,

*43,*546-549.

[9]

*Density Functional Study of EPR Parameters and Spin-Density Distribution of Azurin and Other Blue-Copper Proteins*C. Remenyi, R. Reviakine, M. Kaupp

*J. Phys. Chem. B*

**2007**,

*111*, 8290-8304.

[10]

*Structure and Electron Paramagnetic Resonance Parameters of the Manganese Site of Concanavalin A Studied by Density Functional Methods*S. Schinzel, R. Müller, M. Kaupp

*Theor. Chem. Acc.*

**2008**,

*120*, 437-445.

[11]

*Validation of Broken-Symmetry Density Functional Methods for the Calculation of Electron Paramagnetic Resonance Parameters of Dinuclear Mixed-Valence Mn*S. Schinzel, M. Kaupp

^{IV}Mn^{III}Complexes*Can. J. Chem.*

**2009**,

*87*, 1521-1539.

[12]

*Density Functional Calculations of*S. Schinzel, J. Schraut, A. V. Arbuznikov, P. E. M. Siegbahn, M. Kaupp

^{55}Mn,^{14}N and^{13}C Electron Paramagnetic Resonance Parameters Support an Energetically Feasible Model System for the S_{2}State of the Oxygen-Evolving Complex of Photosystem II*Chem. Eur. J.*

**2010**,

*16*, 10424-10438.

[13] P. E. M. Siegbahn

*Acc. Chem. Res.*

**2009**,

*42*, 1871.

[14] Y. Umena, K. Kawakami, J.-R. Shen, N. Kamiya

*Nature*

**2011**,

*473*, 55.

[15]

*Computation of Hyperfine Tensors for Dinuclear Mn*J. Schraut, A. V. Arbuznikov, S. Schinzel, M. Kaupp

^{III}Mn^{IV}Complexes by Broken-Symmetry Approaches: Anisotropy Transfer Induced by Local Zero-Field Splitting*ChemPhysChem*

**2011**,

*12*, 3170-3179.

### Zusatzinformationen / Extras

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## Auxiliary Functions

## Chair

**Prof. Dr. M. Kaupp**

Theoretical Chemistry

Quantum Chemistry

http://www.quantenchemie.tu-berlin.de/menue/ueber_uns/team/prof_dr_martin_kaupp/parameter/en/