4.3.1 Simulation and Fit of EPR Spectra
EPR Spectra of Frozen Solutions The EPR powder spectra were simulated using the in-house pro-grams ELSI [121] and SPLEEN [78].
Single Crystal EPR and Determination of the g-Tensor The g-tensor is characterized by three prin-cipal values: g1, g2, and g3. The orientation of the principal axes with respect to the laboratory frame is obtained from analyses of the angular dependence of EPR transitions of single crystals. Experimentally, the respective spectral positions gθφ are obtained from the resonance condition
hν gθφβB0 (4.1)
where h is Planck’s constant, ν is the spectrometer frequency, β is the Bohr magneton, and gθφ the effective g-value. The angles θ and φdescribe the orientation of the g-tensor principal axes with respect to the magnetic field B0. Depending on the number j of magnetically inequivalent molecules per unit cell (sites) a corresponding number of resonance positions is observed [122]. In the case of the space group P212121 four magnetically distinct molecules are found in the unit cell; thus one expects a maximum of four resonance lines in the EPR spectrum. If the magnetic field is located in a crystallographic plane, two signals pairwise coincide and a maximum of two signals is observed. If B0 is parallel to one of the crystallographic axes only one 4-fold degenerate resonance line is detected.
In this work, the g-tensor principal axes have been determined by investigation of arbitrarily ori-ented single crystals. Three right-handed, orthogonal reference frames were defined: the laboratory frame (L), the crystal frame (C), and the intrinsic frame (I). In the latter, the g- and g2-tensors are diagonal and i 12 3 represents the tensor principal axes. These three frames are related by rotations, which can be described by three Euler angles each. In the analysis, the direction cosines of the g-tensor principal axes (1,2,3) in the crystal frame (abc) were determined. The fit routine always attributes the largest principal g-value to g1and the smallest to g3. Detailed information about the fit algorithm used can be found in ref. [85].
The effective g-values gjθφ of the four sites j, were collected from EPR spectra of single crystals in an arbitrary orientation rotated about an axis perpendicular to the magnetic field by an angle α. By a simultaneous fit of all four sites using a numerical fit routine based on a simplex algorithm described in detail in ref. [78], the three principal g-values and the six Euler angles defining the relations between the frames L and C, and between C and I have been determined.
34 4.3 Spectra Analysis 4.3.2 Simulation of ENDOR Spectra
Simulation of orientation selected ENDOR spectra yields besides the magnitudes of the hyperfine cou-pling constants geometrical information about the locus of the coucou-pling nuclei.
In the case of anisotropic g- and hfc-tensors the ENDOR transition energies depend on the orienta-tion of the magnetic field relative to the molecular axes. At a given field, only a subset of molecules with appropriate orientations contributes to the EPR intensity and thus to the ENDOR spectrum recorded at this field value. Orientation selected ENDOR spectroscopy allows full determination of electron-nuclear interaction tensors in favorable cases. These values can only be derived by simulation of the spectra, which was done with the in-house simulation program SPLEEN [78]. A detailed description of the algorithm is available in [78].
For the determination of the exact g-values at a given field value the EPR spectrum was first sim-ulated. The ENDOR frequencies were then calculated for the chosen respective field values. The orientation of the hyperfine tensor axes was given by three Euler angles, relating the orientation of the hyperfine tensor to the orientation of the principal axes of the g-tensor. By means of comparing the set of the simulated ENDOR spectra to the experimental set and by stepwise adjusting the simulation parameters, the principal values of the nuclear hyperfine tensors and the orientation of the hfc tensors relative to the g-tensor principal axes were ascertained. Transformation to the crystal frame yielded the directions of the dipolar axes and thus, the desired structural information about the locus of the coupling nuclei.
4.3.3 ESEEM and HYSCORE Spectra
Data Manipulation All the pulse EPR spectra were processed using the program Xepr of Bruker. In order to minimize interfering contributions, like the mostly unavoidable unmodulated relaxation decay and a baseline shift, a correction was done by subtraction of a polynomial function of 2nd-3rd order or a function of exponential decay from the data. The choice of the respective function depended on the value of T1. The time traces were then multiplied with a Hamming function. Prior to Fourier transformation, the spectra were expanded to the next power of two by zero-filling (512 by 512 or 1024 by 1024 points) if needed. For the interpretation the absolute of the spectra was taken.
Simulation Procedure An in-house simulation program was used that based on an ESEEM simula-tion procedure [123] which was modified according to [120]. The principal g-values were determined by simulation of the respective EPR spectra. Initial values for the hfc of the H/D nuclei, aiso and adip, were determined from the spectra according to the method described by P¨oppl et al. [110]. The orienta-tion of the principal axes of the hyperfine tensor relative to the g-tensor principal axes was described by three Euler angles. The latter five values were carefully adjusted during the simulation process of the spectra recorded at different field values. A transformation back to the crystal frame yielded the relative
Experimental Details and Methods for Evaluation of Results 35 positions of the paramagnetic nuclei with an error of about 10 . The distance of the coupled nucleus was determined applying Equation (3.9).
36 4.3 Spectra Analysis
37
Chapter 5
Determination of the g-Tensor Principal Axes of the Ni-C and Ni-L States
EPR spectroscopic studies in frozen solutions yield only the g-tensor principal values [59]. A direct determination of the orientation of the principal axes of the g-tensor with respect to the crystal structure, which can be related to the molecular structure, is available from EPR studies on single crystals. This has been demonstrated earlier by Geßner et al. [85] and Trofanchuk et al. [79] for the oxidized states of the enzyme using single crystals of the hydrogenase from D. vulgaris Miyazaki F.
This chapter presents the results of single crystal EPR studies of the hydrogenase in the Ni-C and the Ni-L state. The availability of an X-ray structure at high resolution of the reduced hydrogenase from D. vulgaris Miyazaki F [24] allowed to relate the g-tensor orientation of the Ni-C and Ni-L states to the molecular structure. Furthermore, the derived experimental g-tensor magnitudes and orientations are compared with those proposed by density functional theory (DFT) calculations, performed on various geometrically optimized models of the active sites in the Ni-C and Ni-L form [124,125]. The results are compared with the work of M¨uller et al. [126] who determined the g-tensor orientation for Ni-C based on EPR and ENDOR data on two different hydrogenases in frozen solution and obtained a different orientation. On the basis of the experimental work presented in this Chapter in combination with earlier results of DFT calculations [81,124,125], several of the open questions in hydrogenase research will be addressed, namely the formal oxidation states of the nickel in all its paramagnetic intermediate states, the structure of the [NiFe]-cluster, including the most probable type of the third bridging ligand between the metals, and the functional role of the active center of the enzyme in the hydrogen conversion process.