Hamiltonians, Mossbauer spectroscopy

Cytochromes from bacterial, yeast, and mammalian sources have been investigated by Mossbauer spectroscopy (114—117). Horseheart cytochrome c and the c-type cytochrome from T. utilis show spectra characteristic of low-spin Fe(III) in the oxidized form of the protein and low-spin Fe(II) for the reduced form of the protein. Lang et al. (115) have analyzed the Mossbauer data in terms of a low-spin Hamiltonian in some detail. Cooke and Debrunner (116) present quadrupole data on dehydrated forms of oxidized and reduced cytochrome c the quadrupole splittings for hydrated and dehydrated forms of the reduced protein are quite similar in contrast to a difference of the oxidized form. No spin-state change is reported for either form of cytochrome c. 

The Spin Hamiltonian Formalism Determination of Zero-Field Splitting D and Rhombicity E/D of Paramagnetic Iron Centers by Mossbauer Spectroscopy... 

A. X. Trautwein, E. BiU, E. L. Bominaar and H. Winkler, Struct. Bonding, 1991, 78, 1. A thorough overview on spin-Hamiltonian parameters and Mossbauer spectroscopy with a lot of examples of spin-coupled systems. 

However, this freely recoiling state is not a stationary state of the Hamiltonian in relevant experimental situations, where the Fe nucleus is bound to other atoms in a condensed phase. In general, a series of discrete lines appear in the spectrum (Figure 1, bottom), corresponding to a range of possible final states. Conventional Mossbauer spectroscopy relies on the presence of a narrow line ( f = i) at Eo, with an area proportional to the recoilless fraction... 

Since one is dealing with the same set of energy levels in each experiment one should look for a model consistant with each experiment. In the case of the iron transport compounds the experimental results are parameterized by the coupling coefficients D, X, p. A, P in the spin Hamiltonian to be discussed in the next section. The parameter P in 57 Fe can be measured only with Mossbauer spectroscopy since it comes about through the excited nuclear state which is not available in an ESR experiment. 

A. THE STOCHASTIC RELAXATION MODEL. The most general theories of magnetic relaxation in Mossbauer spectroscopy involve stochastic models see, for example. Ref. 283 for a review. A formalism using superoperators (Liouville operators) was introduced by Blume, who presented a general solution for the lineshape of radiation emitted (absorbed) by a system whose Hamiltonian jumps at random as a function of time between a finite number of possible forms that do not necessarily commute with one another. The solution can be written down in a compact form using the superoperator formalism. 

In Mossbauer spectroscopy it is necessary to evaluate the eigenvalues of the 77q Hamiltonian, that is the energies q for the ground state and for the excited state, the transition from which is followed by the emission of a Mossbauer y-quantum (see Figure 4A). The line positions in Mossbauer spectra... 

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]. 

The spin Hamiltonian formalism, which is also needed to interpret, for example, electron paramagnetic resonance or magnetic circular dichroism spectra see Magnetic Circular Dichroism (MCD) Spectroscopy), was first applied to the interpretation of magnetic Mossbauer spectra by Wickmann, Klein and Shirley and was implemented into a computer program by Miinck et al. in the early 1970s. For most studies of mononuclear iron centers with electron spin quantum number S, the following electronic Hamiltonian is used ... 

As an example of how to determine the electronic ground state of a low-spin iron(lll) compound, we present work on the ferric low-spin heme complex [TPPFe(NH2PzH)2]Cl, which has been shown to have a (dxy) (dxz, dj, ) electronic ground state. The field-dependent Mossbauer spectra of [TPP Fe(NH2PzH)2]Cl displayed in Fignre 12 are well reproduced by simulations, which yield 5 =0.25mms , AEq = ( )2.50imns, an asymmetry parameter rj = —3, and an anisotropic A tensor of" / nMn = (-47.6, 6.7, 18.3)T. The g values necessary for the 5" = 1 /2 spin Hamiltonian (g z = 2.39, gyy = 2.28, and gxx = L87) have been taken from a combined EPR and electron spin echo envelope modulation spectroscopy ESEEM analysis. 

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