Spin Hamiltonian Parameters from Spectra

Once a hyperfine pattern has been recognized, the line position information can be summarized by the spin Hamiltonian parameters, g and at. These parameters can be extracted from spectra by a linear least-squares fit of experimental line positions to eqn (2.3). However, for high-spin nuclei and/or large couplings, one soon finds that the lines are not evenly spaced as predicted by eqn (2.3) and second-order corrections must be made. Solving the spin Hamiltonian, eqn (2.1), to second order in perturbation theory, eqn (2.3) becomes 4 

Second-order effects on hyperfine structure in organometallic compounds are discussed in Chapter 3. 

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The simulation procedure presented here, among others, is eminently exploitable to estimation of spin-Hamiltonian parameters from a powder spectrum by the least-squares fitting (LSF) procedure in conjunction with numerical diagonalization of the spin-Hamiltonian matrix similar to that proposed by Misra (1976) in context... 

The spectrum of the low-spin manganese(n) complex, [Mn(dppe)2(CO)(CN-Bu)]2+, (dppe = Ph2PCH2CH2PPh2), in a CH2C12/THF glass is shown in Figure 4.4(a).24 The spin Hamiltonian parameters, obtained from least-squares... 

When the anisotropic spin Hamiltonian parameters g, and are obtained from the powder spectrum in the rigid limit, one can dehne the quantities... 

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]. 

Fig. 8.15 shows changes in the low-field part of the V4+ EPR spectrum for the samples prepared using Hombicat-100 powders at various V4+ content. One can see from this figure that there exist up to three types of surface V4+ centers (a, b, c) with slightly different spin-Hamiltonian parameters Ay = 180 2 G, gy = 1.948 (a) Ay = 179 3 G, gy = 1.973 (b) Ay = 195 2 G, gy = 1.954 (c). It should be noted that gy values were calculated without the second-order correction (A and gx values could not be evaluated because of the over-lapping of the EPR spectra of (a), (b) and (c) species), hence, gy parameters are relative. For V02+ ions in the same experimental conditions, Ay = 200 2 G, gy = 1.951. Comparing these data with those known from literature [19, 21, 207], etc., the probable surface structures of V4+ centers have been proposed [217] (see thje next page). 

As a result, the reduction of cobalt from the divalent to the zero-valent state changes the chemistry of the system, since Co° readily forms complexes with hydrocarbons. This was confirmed by subsequent adsorption of propene, which produced the EPR spectrum shown in Figure 1.23D, with spin Hamiltonian parameters ofg, = 2.096, gy = 1.924, = 2.297, A = 12, Ay = 52, = 99G. This... 

Fig. 11. Calculated Mossbauer spectra with the same spin Hamiltonian parameters D = 0.50 cm-1, A = 0.0, fi = 0.75, A = 1.51 mm/sec, P = —0.15 mm/sec in rhombic (left) and trigonal (right) symmetry. The bottom spectrum is a Boltzmann average of the contributions from each of the three Kramers doublets shown above. We assume for this calculation that the sample is at 4.2 K in an applied field of 1.3 kOe perpendicular to the gamma beam. One can observe the marked difference in the spectra for the trigonal and rhombic model calculations...

The ESR experiment by Aasa (27) yields two sets of spin Hamiltonian parameters — one for each iron site. A Mossbauer spectrum calculated from each set of Aasa s parameters has been found to be no different from the calculation assuming identical sites. This indicates that the ESR experiment is much more sensitive to small effects than the Mossbauer technique. 

It should be noted here that a correct determination of fine and hyperfine structure parameters should be done in such a way that spectra taken under different experimental conditions (variable external fields and/or variable temperatures) are reproduced with the same parameter set. This reproduction of the experimental data is often a bit less accurate than when one fits only a single experimental spectrum. However, owing to the many parameters involved in the simulation it makes absolutely no sense to deduce a complete spin Hamiltonian parameter set of a paramagnetic iron center from just one Mossbauer spectrum. 

Figure 3. (a) Spectrum of N4 in irradiated KN3 for H 1 [100]. The arrows indicate satellite lines, due possibly to exchange-coupled pairs of N4 ions or to N3 ions, (b) Computer simulation of spectrum expected from an molecular ion with spin-Hamiltonian parameters of reference [34]. The simulation predicts lines (indicated by arrows) which agree in position but not intensity with satellite lines in (a). The simulated spectrum also predicts lines at the low- and high-field ends not observed experimentally. 

Neilson and Symons observed a complex spectrum in KN3 powders which were UV irradiated at 77°K [34]. The spectrum was interpreted on the basis of an Nl model and the assumption that the spin-Hamiltonian parameters were essentially the same as those observed for N3" in BaN6 [52]. However, no attempt was made to generate a theoretical powder spectrum by computeraveraging the single-crystal spectrum calculated from these parameters over all possible orientations. Therefore, the assignment must be considered tentative. 

In Fig. 3.32, one can see the room temperature EPR spectra of Fe + paramagnetic centers substituted for Ti + ions in BaTiOs nanopowders. The mean size of the particles decreased from several hundreds nm to several tens nm at annealing temperature decrease from 1,350 to 900 °C [101]. It has been established, that in some samples the size distribution function has one peak while in the other ones it has two peaks In particular, fc the sample annealed at 900 °C, these two peaks positions were R 40 nm and R 140 nm. In Fig. 3.32, the calculated powder spectrum is reported. The spectrum has been calculated with the help of spin-hamiltonian parameters measured earlier for Fe + in BaTiOs single crystals [106]. It follows from Fig. 3.32, that the spectrum for the largest particles (about pm) contains all the transitions inherent in bulk samples so that the powders consisting of micron size particles can be considered as bulk ones. The cubic symmetry line... 

The temperature dependence of the Gd + spin Hamiltonian parameters in PrV04 and of the resonance line width was investigated by Mehran et al. (1980) and Andronenko et al. (1981). A measurement of the Tm + ion spectrum in the VV paramagnet HoND (holmium nicotinate dihydrate) should also be noted (Baker et al. 1986b). The EPR in TbND has shown a spectrum from a relatively rare species of a paramagnetic ion (defect sites) in an undiluted compound of the same paramagnetic ion (Baker et al. 1987). 

Allouche et alP calculated chemical shifts (5 values) and SSCCs (/values) for the putrescine molecule, a polyamine present in prostate tissue, using a B3LYP-DFT/6-311-I-- -G(/,/))/PCM/GIAO (gauge-including atomic orbital) approach. From the computed and J values, the H NMR spectrum of putrescine was simulated. Comparisons between the calculated and the experimental NMR spectra at 400 MHz showed a good agreement and allowed to propose reliable values for the NMR spin Hamiltonian parameters of putrescine to be used for further development of quantitative analytical methods of metabolites in prostate tissue. 

The peak positions of the spectra illustrated in Figure 13 vary with the Zeeman field, and numerical assignments to spin Hamiltonian parameters based on inspection and a Townes-Dailey ZF-NQI interpretation will yield incorrect values of s Qqzz and Tj. The exact cancellation-like spectral profile is retained over a wide span of microwave frequencies and one does not a priori know from a single ESEEM spectrum whether one is near true exact cancellation. In other words, one cannot simply tune up the spectrometer, locate a frequency/field combination that... 

While it is not neeessary for the user to have an understanding of the spin Hamiltonian and the relationship of the spin Hamiltonian parameters to the spectrum, the program provides useful information and feedback. The sensitivity of the field position of a peak to eaeh of the spin Hamiltonian parameters ean be determined from the derivatives. 

Figure 6. -7/2 and -5/2 low-field parallel resonances lines of the Irozen solution (T= 130 K) EPR spectrum (a) 1 1 VOSO4 and apo-Tf, (b) 2 1 VOSO4 and apo-Tf (c) VO(ma)j and apo-Tf (d) 2 1 VO(ma)2 and apo-Tf, with Gaussian peak fit for determination of the relative amounts of A and B binding conformatirais (solid lines). Every 4th experimental point is shown. The lower spectra (a -d ) correspond to the sum of the individual Gaussian peaks shown in (a-d). In (d) an additional peak is required to fit the spectrum. Its spin Hamiltonian parameters correlate very well with free VO(ma)2 in aqueous solution. Reprinted with permission from [80]. Copyright 2005, American Chemical Society. 

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