Crystal field splitting rules

Electron configuration of Bp" is (6s) (6p) yielding a Pip ground state and a crystal field split Pap excited state (Hamstra et al. 1994). Because the emission is a 6p inter-configurational transition Pap- Pip. which is confirmed by the yellow excitation band presence, it is formally parity forbidden. Since the uneven crystal-field terms mix with the (65) (75) Si/2 and the Pap and Pip states, the parity selection rule becomes partly lifted. The excitation transition -Pl/2- S 1/2 is the allowed one and it demands photons with higher energy. 

We first note that an isolated atom with an odd number of electrons will necessarily have a magnetic moment. In this book we discuss mainly moments on impurity centres (donors) in semiconductors, which carry one electron, and also the d-shells of transitional-metal ions in compounds, which often carry several In the latter case coupling by Hund s rule will line up all the spins parallel to one another, unless prevented from doing so by crystal-field splitting. Hund s-rule coupling arises because, if a pair of electrons in different orbital states have an antisymmetrical orbital wave function, this wave function vanishes where r12=0 and so the positive contribution to the energy from the term e2/r12 is less than for the symmetrical state. The antisymmetrical orbital state implies a symmetrical spin state, and thus parallel spins and a spin triplet. The two-electron orbital functions of electrons in states with one-electron wave functions a(x) and b(x) are, to first order,... 

The Nd has the electron configuration [Xe]4f. Because it is a rare-earth element, spin-orbit coupling would be expected and hence, Eqs. 8.24-8.25 to apply. Furthermore, crystal-field splitting is usually unimportant for rare-earth ions because their partially filled 4f shells lie deep inside the ions, beneath filled 5s and 5p shells. Thus, the seven f orbitals would be degenerate and their occupancy would be a high-spin configuration, with the maximum value of S and L, in accordance with Hund s first and second rules ... 

Symmetry considerations have a profound effect on the interpretation of lanthanide spectra. We have already mentioned the effect of symmetry on selection rules for electric and magnetic dipole transitions and on the classification of crystal-field split energy levels. In this section, we consider the effect of symmetry on the crystal-field Hamiltonian itself. 

Thus, if we are concerned only with the line strength for transitions between J-levels (as opposed to crystal-field split sublevels), the intensities are characterized by three parameters fij, fl4, and Hs. Selection rules imposed by the reduced matrix elements of in eq. (58) are... 

T FIGURE 23.30 shows what happens to crystal-field splitting when the ligand is varied in a series of chromium(III) complexes. Because the Cr atom has an [Ar]3d 4s electron configuration, Cr has the configuration [Ar]3d and therefore is a d ion. Consistent with Hund s rule, the three 3d electrons occupy the t2 set of orbitals, with one electron in each orbital and all the spins the same. (Section 6.8) As the crystal field exerted by the six ligands increases, A increases. Because the absorption spectrum is related to this energy separation, these complexes vary in color. 

Figure 15.22 Molecular-orbital energy-level diagram for the octahedral complex FeFs . The (T molecular orbitals are essentially pure and orbitals of the central metal ion. In this complex, the crystal field splitting (A) between the three nonbonding orbitals d, dy, and and the two cr orbitals is small F is a weak-field ligand) so Hund s rule applies, and these five orbitals each contain one electron with all the spins parallel.

Since the splitting parameter in the tetrahedral field is smaller than in the octahedral field, the tetrahedral field is always a weak field, Aptetrahedral field, the highest values of CFSE correspond to d and d configurations. Figure 3.9 presents the comparative crystal field splitting of d orbitals of the central ion in complexes of geometry tetrahedral, octahedral, tetragonal, and square-planar. 

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