Spin Hamiltonian simulation

Answer The authors did indeed evaluate the Mossbauer data by spin Hamiltonian simulations assnming an 5 = 2 as well as an 5 = 1 gronnd state. In this way they conld dednce two sets of hyperfine and fine stmctme parameters simnlations assnming an A = 1 gronnd state yield an axial hyperfine tensor A = -33.3 T. 

Figure 15 (a) The 4.2 K Mossbauer spectra of [(Fe(IV)=0)(TMC)(NCCH3)](0Tf)2 in acetonitrile recorded in (A) zero field and (B)a parallel field of 6.5 T. The solid line represents a spin Hamilton simulation with the parameters described in the text, (b) Mossbauer spectra of [Fe(lV)=(0)(TMCS)] recorded at temperatures and applied fields that are indicated. The solid lines represent spin Hamiltonian simulations with parameters described in the text. The spectra were simulated in the slow (at 4.2 K) and fast (at 30 K) spin fluctuation limit. The applied field was directed parallel to the observed y radiation. The doublet drawn above the topmost experimental spectrum (0 T, 4 K) represents a 7% Fe(ll) contribution from the starting complex. (From J. U. Rohde et al. (2003) Science 299 1037-1039. Reprinted with permission from AAAS)... 

Figure 8 Mossbauer spectrum of a frozen aqueous solution of [ Fe +]-ferrioxamine B (12mM) employing BSA (lOOmM) as a dilutant to minimize spin-spin relaxation. The solid line represents a simulation based on a spin Hamiltonian line width = 0.35 mm s zero-field splitting, D = 1.2 cm E rhombicity parameter, E/D = 0.33 8 = 0.52mms A q = —0.84mms asymmetry parameter, rj = and isotropic hyperfine coupling tensor Axx/gN/XN = Ayy/gNMN = Azz/gx/XN = —22.1 T. The simulation does not completely fit the experimental data. This discrepancy is caused by relaxation effects that are not dealt with in the spin Hamiltonian simulation...

Figure 12 Field-dependent Mossbauer spectra of the ferric low-spin heme complex [TPPFe(NH2PzH)2]Cl. The solid lines are spin Hamiltonian simulations for 5=1 /2 with parameters discussed in the text and given in Ref. 42 (From Schiinemann et With kind permission from Springer Science Business Media)...

The EPR spectra of cell walls saturated with copper has been fitted to the numerical solutions of the spin hamiltonian describing the EPR lineshape of cupric ions. Two simulations have been performed. The first one (Fig. 4.a) considers that all uronic acids of the cell walls are similar the best fit is rather poor. The second one assumes existence of two populations of exchange sites with different parameters. In this case, the optimization is much better and confirms the existence of two different types of uronic acids in the cell wall (Fig. 4.b). 

The spin-Hamiltonian concept, as proposed by Van Vleck [79], was introduced to EPR spectroscopy by Pryce [50, 74] and others [75, 80, 81]. H. H. Wickmann was the first to simulate paramagnetic Mossbauer spectra [82, 83], and E. Miinck and P. Debmnner published the first computer routine for magnetically split Mossbauer spectra [84] which then became the basis of other simulation packages [85]. Concise introductions to the related modem EPR techniques can be found in the book by Schweiger and Jeschke [86]. Magnetic susceptibility is covered in textbooks on molecular magnetism [87-89]. An introduction to MCD spectroscopy is provided by [90-92]. Various aspects of the analysis of applied-field Mossbauer spectra of paramagnetic systems have been covered by a number of articles and reviews in the past [93-100]. 

However, when it comes to the simulation of NFS spectra fi om a polycrystalline paramagnetic system exposed to a magnetic field, it turns out that this is not a straightforward task, especially if no information is available from conventional Mossbauer studies. Our eyes are much better adjusted to energy-domain spectra and much less to their Fourier transform therefore, a first guess of spin-Hamiltonian and hyperfine-interaction parameters is facilitated by recording conventional Mossbauer spectra. 

Figure 3. MOssbauer spectra of the reduced Rieske protein Thermus Thermophilus. (A) Spectrum taken at 230 K. The brackets indicate the doublets of the trapped-valence Fe2+ and Fe3+ sites. (B) 4.2 K spectrum of the same sample. The solid line is a spectral simulation based on an S = 1/2 spin Hamiltonian. S = 1/2 is the system spin resulting from coupling S = Sa + Sb according to H = JSa-Sb for J > 0 Sa = 5/2 and Sb = 2.

One of the problems to extract structural information from EPR lies in the correct simulation of the experimental spectra. Misra536 reviewed spin Hamiltonians applicable to exchange-coupled Mn complexes, and described techniques for simulation of EPR spectra. Various structural models for the Mm-cluster in PS II were presented. 

A combination of the two techniques was shown to be a useful method for the determination of solution structures of weakly coupled dicopper(II) complexes (Fig. 9.4)[119]. The MM-EPR approach involves a conformational analysis of the dimeric structure, the simulation of the EPR spectrum with the geometric parameters resulting from the calculated structures and spin hamiltonian parameters derived from similar complexes, and the refinement of the structure by successive molecular mechanics calculation and EPR simulation cycles. This method was successfully tested with two dinuclear complexes with known X-ray structures and applied to the determination of a copper(II) dimer with unknown structure (Fig. 9.5 and Table 9.9)[119]. 

The above experimental developments represent powerful tools for the exploration of molecular structure and dynamics complementary to other techniques. However, as is often the case for spectroscopic techniques, only interactions with effective and reliable computational models allow interpretation in structural and dynamical terms. The tools needed by EPR spectroscopists are from the world of quantum mechanics (QM), as far as the parameters of the spin Hamiltonian are concerned, and from the world of molecular dynamics (MD) and statistical thermodynamics for the simulation of spectral line shapes. The introduction of methods rooted into the Density Functional Theory (DFT) represents a turning point for the calculations of spin-dependent properties [7],... 

In order to quantitatively reproduce the observed periodicity we included fourth-order terms in the spin Hamiltonian, Eq. (1), as employed in the simulation of inelastic neutron scattering measurements [45, 46] and performed a diagonalization of the [21x21] matrix describing the S = 10 system. For the calculation of the tunnel splitting we used D = 0.289 K, = 0.055 K [Eq. 1] and the fourth-order terms as defined in [45] with... 

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