Crystal field state

The magnetic properties of Pu compounds in different oxidation states are reviewed. New measurements on Pu(C8H8)2, PuFi, [(C2Hs)itN]2PuCl6, and [ (C2H5)itN]itPu(NCS)s are presented. The interpretation of the data is based on intermediate, j-j mixed crystal field states and orbital reduction due to covalency. Especially in the case of the organometallic compounds a large orbital reduction is found. 

High-valent iron can occur in a wide variety of electronic configurations. Figure 8.25 (a-c, e-i) presents a summary of the corresponding one-electron crystal-field states for the 3(/, 3J, and 3J electron configurations, allocated to HS and LS states in distorted octahedral and tetrahedral symmetry. Part d, in addition, depicts the case of low-low-spin iron(IV) found in some trigonal... 

Fig. 8.25 Schematic presentation of the one-electron crystal-field states for the Set, Set, and Set electron configurations of iron(IV), (V), and (VI). Case (g) has not been observed yet...

Figure 3 Crystal field states (left-hand panel) and potential energy surfaces (right-hand panel) for an octahedral complex of nickel(II) in the 3Tig/1Eg energy range. Calculated spectra for the transition to each electronic state are shown in the central panel. Lines with markers connect electronic states and their corresponding calculated spectra. The total calculated spectrum (calc.) is obtained as the sum of the four individual spectra and is compared to the experimental spectrum of Ni(H20)62+ measured at 5K336 (reprinted with permission from ref. 336 1998, American Chemical Society).

The situation is different for d2 in a tetrahedral field. In this case the 3F state gives an orbital singlet as the ground state, with the crystal field states at much higher energies. In this case we would expect longer relaxation times and smaller values of Z), because the excited states that contribute are further removed from the ground state. Thus detection of the ESR in tetrahedral fields should be easier. 

Table 9. Contributions (in %) of the (t2 I)3 crystal field states to the eigenvectors of the lowest r8 levels...

ZT Y r A A A A A AC dimensionless thermoelectric figure of merit electronic coefficient of heat capacity (1+ZT)F2 crystal field singlet non-Kramers doublet (crystal field state) crystal field triplet crystal field triplet hybridization gap jump in heat capacity at Tc K KL -min P 6>d X JCO total thermal conductivity of solid thermal conductivity of electrons or holes thermal conductivity of lattice minimum lattice thermal conductivity electrical resistivity Debye temperature magnetic susceptibility magnetic susceptibility at T = 0... 

Fig. 5. Splitting of the five 4f75d crystal-field states of Tb3+ in UYF4 (taken from van Pieterson et al., 2002b). The parameter A represents the f-d interactions as explained in the text. On the left (A = 0) the parameters for these interactions are set to zero and on the right (A = 1) they have the values from Hartree-Fock calculations for the free...

When we use this formula to derive crystal field states of a complex, we have made the assumption that spin-orbit interaction is weak and hence is ignored. 

The energy level diagram for Ti3+ in fig. 3.4 shows the manner by which the 2D spectroscopic term is resolved into two different levels, or crystal field states, when the cation is situated in an octahedral crystal field produced by surrounding ligands. In a similar manner the spectroscopic terms for each 3d" configuration become separated into one or more crystal field states when the transition metal ion is located in a coordination site in a crystal structure. The extent to which each spectroscopic term is split into crystal field states can be obtained by semi-empirical calculations based on the interelectronic repulsion Racah B and C parameters derived from atomic spectra (Lever, 1984, p. 126). 

Table 3.4. Crystal field states arising from free ion spectroscopic terms of transition metals in octahedral coordination...

Figure 3.6. Electronic configurations of the ground state and some of the excited crystal field states of the Fe2+ (3d6) ion in octahedral coordination.

Figure 3.7 Simplified energy level diagram for 3d6 ions (e.g., Fe2+ and Co3+) in an octahedral crystal field. The diagram shows that in a high intensity field the 1Alg crystal field state, corresponding to the low-spin configuration (t2gf, becomes the ground state.

Figure 3.8 Tanabe-Sugano energy level diagram for a 3d6 ion in an octahedral crystal field. Note that some of the highest energy triplet and singlet crystal field states listed in table 3.3 are not shown in the diagram.

This transition results in no change in the number of unpaired electrons in Fe2+ and is referred to as a spin-allowed transition. The sharp peaks at 20,000 cm-1 and 22,200 cm-1 in fig. 3.2 correspond to transitions to the triplet states 3Tlg and respectively (cf. fig. 3.6), having lower spin-multiplicities than the quintet ground state. Such transitions leading to fewer unpaired electrons in excited crystal field states are termed spin-forbidden transitions. 

Figure 3.10 Partial energy level diagram for the Fe3+ or Mn2+ ions with 3tfi configurations in high-spin states in an octahedral crystal field. Only sextet and quartet spectroscopic terms and crystal field states are shown. Note that the same energy level diagram applies to the cations in tetrahedral crystal fields (with g subscripts omitted from the state symbols for the acentric coordination site).

The Orgel diagrams illustrated in figs 3.11 and 3.12 indicate that, for electronic transitions between crystal field states of highest spin-multiplicities, one absorption band only is expected in the spectra of 3d1,3d4,3d6 and 3d9 cations in octahedral coordination, whereas three bands should occur in the spectra of octahedrally coordinated 3d2, 3d3, 3d7 and 3d8 ions. Thus, if a crystal structure is known to contain cations in regular octahedral sites, the number and positions of absorption bands in a spectrum might be used to identify the presence and valence of a transition metal ion in these sites. However, this method of cation identification must be used with caution. Multiple and displaced absorption bands may occur in the spectra of transition metal ions situated in low-symmetry distorted coordination sites. 

Figure 3.13 Crystal field states and electronic configurations of Fe2+ ions in regular octahedral and tetragonally distorted octahedral sites. The tetragonally distorted octahedron is elongated along the tetrad axis.

Table 3.5. Crystal field states ofFe2+ in coordination sites of different...

Symmetry of crystal field Symmetry notation Crystal field states Mineral examples... 

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