Fe quadrupole splitting

Fig. 5.7 Comparison of calculated and measured Fe quadrupole splittings. Nuclear quadrupole moments of 0.158 bam (nonrelativistic DFT) and 0.156 bam (ZORA) were used in the calculations (taken from [25])...

In the preceding discussion we have been considering polarised sources which are not monochromatic. The assignment of hyperfine components in a complex spectrum would obviously be easier if the source were effectively polarised and monochromatic so that resonant absorption would only be observed in those transitions with the same polarisation. This method was first demonstrated in 1968 [43]. The spectrum of a Fe quadrupole splitting observed in a direction perpendicular to the principal value of an axially symmetric electric field gradient consists of two lines in the intensity ratio 5 3. The weaker line is linearly polarised in the plane parallel to while the other is 40%unpolarised and 60% linearly polarised perpendicular to Fz2. If the latter can be filtered out a linearly polarised source will result. 

Parameters for the 1,10-phenanthroline complexes, Fe(phen)2X2, with X == Cl", Br", I , NCS , NCSe", Ns" are listed in Table 6.5. The local symmetry is lower than in the Fe(py)4X2 complexes because of the bidentate phenanthroline group, and this results in a larger Fe + quadrupole splitting and smaller magnetic moment. Of particular interest are Fe(phen)2(NCS)2... 

Fig. 10.22 The dependence of six-coordinate Fe quadrupole splitting on the degree of distortion from octahedral symmetry. [Ref. 212, Fig. 6]...

Time Isomer shift (6/mms" versus a-Fe) Quadrupole splitting (A/mm s ) A(%) Assignment Figure... 

Table 1. The 72-atom model examined by different theoretical methods. The energy differences (AE in kcal/mol) are calculated with respect to the lowest SCF energy. q(Fe) stands for Mulliken population charges on the Fe atoms q(S) and SS(b.i.) are the Mulliken population charges and the bond index for the bridging S atoms, respectively AEq is the calculated Mossbauer quadrupole splitting constant [mm/sec]. The PUHF spin states are those projected from the UHF wavefunction with 5 = 5,. 

The results of the XRD measurement showed that the Fe jAl, jPO catalyst was almost in amorphous state. Only a very broad peak at 29 of ca. 23 degree was observed. The Mossbauer spectroscopic study on this catalyst showed one doublet of iron with the isomeric shift of 0.31 mm s (a-Fe was used as the reference) and the quadrupole splitting of 0.62 mm s. These parameters are very close to those observed for FePO [13, 14], suggesting that the iron cation in the catalyst is tetrahedrally coordinated with oxygen and isolated by four PO tetrahedral units. Such coordination circumstance was suggested to be a key factor for the iron site effective for the oxidation of CH to CHjOH by H -Oj gas mixture [15]. 

Sample Fe state Isomer shift (mm/s) Quadrupol splitting AE(mm/s) Reference... 

A unique situation is encountered if Fe-M6ssbauer spectroscopy is applied for the study of spin-state transitions in iron complexes. The half-life of the excited state of the Fe nucleus involved in the Mossbauer experiment is tj/2 = 0.977 X 10 s which is related to the decay constant k by tj/2 = ln2/fe. The lifetime t = l//c is therefore = 1.410 x 10 s which value is just at the centre of the range estimated for the spin-state lifetime Tl = I/Zclh- Thus both the situations discussed above are expected to appear under suitable conditions in the Mossbauer spectra. The quantity of importance is here the nuclear Larmor precession frequency co . If the spin-state lifetime Tl = 1/feLH is long relative to the nuclear precession time l/co , i.e. Tl > l/o) , individual and sharp resonance lines for the two spin states are observed. On the other hand, if the spin-state lifetime is short and thus < l/o) , averaged spectra with intermediate values of quadrupole splitting A q and isomer shift 5 are found. For the intermediate case where Tl 1/cl , broadened and asymmetric resonance lines are obtained. These may be the subject of a lineshape analysis that will eventually produce values of rate constants for the dynamic spin-state inter-conversion process. The rate constants extracted from the spectra will be necessarily of the order of 10 -10 s"F... 

The spin state of the compounds XFe(R2dtc)2 is 3/2 (64). Mossbauer spectra of ClFe(Et2 tc)2 in solution are almost identical with the spectrum of the six-coordinated Fe(Et2magnetic susceptibility and in the isomer shift and quadrupole splitting parameters suggests a geometrical correspondency in solution, which can be attained by the binding of a solvent molecule to the sixth coordination site of the ClFe(Et2[Pg.98]

Fig. 4.6 Quadrupole splitting of the excited state of Fe with I = 3/2 and the resulting Mossbauer spectrum. Quadrupole interaction splits the spin quartet into two degenerate sublevels 7, OT/) with energy separation A q = 2 q. The ground state with I = 1/2 remains unsplit. The nuclear states are additionally shifted by electric monopole interaction giving rise to the isomer shift 8...

In a conventional Fe Mossbauer experiment with a powder sample, one would observe a so-called quadrupole doublet with two resonance lines of equal intensities. The separation of the lines, as given by (4.36), represents the quadrupole splitting The parameter Afg is of immense importance for chemical applications of the Mossbauer effect. It provides information about bond properties and local symmetry of the iron site. Since the quadrupole interaction does not alter the mean energy of the nuclear ground and excited states, the isomer shift S can also be derived from the spectrum it is given by the shift of the center of the quadrupole spectrum from zero velocity. 

The experimentally observed quadrupole splitting AEq for Fe in inorganic compounds, metals, and solids reaches from 0 to more than 6 mm s [30, 32]. The range of AEq for other Mossbauer isotopes may be completely different because of the different nuclear quadrupole moment Q of the respective Mossbauer nucleus, and also because the EFG values may be intrinsically different due to markedly different radial distributions of the atomic orbitals (vide infra). As Q is constant for a given isotope, variations in the quadrupole coupling constants eQV can only arise from... 

The general influence of covalency can be qualitatively explained in a very basic MO scheme. For example, we may consider the p-oxo Fe(III) dimers that are encountered in inorganic complexes and nonheme iron proteins, such as ribonucleotide reductase. In spite of a half-filled crystal-field model), the ferric high-spin ions show quadrupole splittings as large as 2.45 mm s < 0, 5 = 0.53 mm s 4.2-77 K) [61, 62]. This is explained... 

Fig. 4.13 Combined magnetic hyperfine interaction for Fe with strong electric quadrupole interaction. Top left, electric quadrupole splitting of the ground (g) and excited state (e). Top right first-order perturbation by magnetic dipole interaction arising from a weak field along the main component > 0 of the EFG fq = 0). Bottom the resultant Mossbauer spectrum is shown for a single-crystal type measurement with B fixed perpendicular to the y-rays and B oriented along...

If the electric quadrupole splitting of the 7 = 3/2 nuclear state of Fe is larger than the magnetic perturbation, as shown in Fig. 4.13, the nij = l/2) and 3/2) states can be treated as independent doublets and their Zeeman splitting can be described independently by effective nuclear g factors and two effective spins 7 = 1/2, one for each doublet [67]. The approach corresponds exactly to the spin-Hamiltonian concept for electronic spins (see Sect. 4.7.1). The nuclear spin Hamiltonian for each of the two Kramers doublets of the Fe nucleus is ... 

Quadrupole splittings are often interpreted from ligand field models with simple rules for the contributions from each occupied f-orbital (see discussion above). However, these models fail even qualitatively in the case of more covalent metal-ligand bonds. An example concerns the quadrupole spUttings of Fe(IV)-oxo sites in their 5 = 1 or 5 = 2 spin states. Here, ligand field considerations do not even provide the correct sign of the quadrupole splitting [60]. 

Mossbauer spectroscopy is particularly suitable to study ST since (1) the spectral parameters associated with the HS and LS states of iron(II) clearly differ and (2) the time-scale of the technique ( 10 s) allows the detection of the separate spin states in the course of the transition. Typically, Mossbauer spectra of HS iron(II) show relatively high quadrupole splitting (AEq 2-3 mm s ) and isomer shift (3 1 mm s ), while for LS iron(II), these parameters are generally smaller (AEq < 1 mm s 3 < 0.5 mm s ). Among the early applications of Mossbauer spectroscopy to study ST phenomena in iron(II) complexes is the work of Dezsi et al. [7] on [Fe (phen)2(NCS)2] (phen = 1,10-phenanthroline) as a function of temperature (Fig. 8.2). The transition from the HS ( 12) state (quadrupole doublet of outer two lines with AEq 3 mm s ) to the LS CAi) state (quadrupole... 

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