F Transitions

Figure Bl.15.12. ESEEM spectroscopy. (A) Top energy level diagram and the corresponding stick spectrum for the two allowed (a) and two forbidden (f) transitions. Bottom time behaviour of the magnetization of an allowed (a) spin packet and a forbidden (f) spin packet during a two-pulse ESE sequence (see figure Bl.15.11 (A)). (B) The HYSCORE pulse sequence.

Electronic absorption spectra are produced when electromagnetic radiation promotes the ions from their ground state to excited states. For the lanthanides the most common of such transitions involve excited states which are either components of the ground term or else belong to excited terms which arise from the same 4f" configuration as the ground term. In either case the transitions therefore involve only a redistribution of electrons within the 4f orbitals (i.e. f—>f transitions) and so are orbitally forbidden just like d—>d transitions. In the case of the latter the rule is partially relaxed by a mechanism which depends on the effect of the crystal field in distorting the symmetry of the metal ion. However, it has already been pointed out that crystal field effects are very much smaller in the case of ions and they... 

Table ll.f Transition function table for Langton s self-reproducing loops (taken from table... 

Metal-centered emission is found in several rare-earth complexes, for example europium diketone chelates [29]. These compounds emit relatively narrow spectra associated with the d-f transitions of the metal ion. Relatively few comprehensive studies of this class have been carried out to date, but the available evidence [30] seems to indicate that the photoluminescent efficiencies are somewhat lower than the ligand-centered emitters. 

Prediction of the energy level structure for Pu2+ (5f ) is of particular interest since no spectra for this valence state of Pu have been reported. On the basis of what is known of the spectra of Am2+ (26), Cf2" (27), and Es2+ (28), there appears to be evidence for a very small crystal-field splitting of the free-ion levels. Such evidence encourages use of a free-ion calculation in this particular case. The parameter values selected are indicated in Table V. Based on the systematics given by Brewer (19), the first f- d transition should occur near 11000 cm-, so the f- -f transitions at higher energies would be expected to be at least partially obscured. A... 

Sinha SP (1976) A Systematic Correlation of the Properties of the f-Transition Metal Ions. 30 1-64... 

Oelkrug, D. Absorption Spectra and Ligand Field Parameters of Tetragonal 3Transition Metal Fluorides. Vol. 9, pp. 1—26. 

Schulz, J., VOgtle, F. Transition Metal Complexes of (Strained) Cyclophanes. 172, 41-86 (1994). 

This paper is concerned with some of our experiments in this field. Our purpose was to obtain polymers with extremely high stereoregularity. In the first part we will report on the homopolymerization of butadiene with f-transition metal catalysts. 

Homopolymerization of Butadiene. It appeared to us that catalysts based on f-transition metals were the ones most likely to enable us to prepare polybutadiene with an extremely high cis content. We began by investigating catalysts based on uranium compounds. Two such systems were known at the beginning of our work. 

Other f-transition metal catalysts have been described by von Dohlen (4) and Throckmorton (5) as well as by Chinese (6, 7) and Italian (8-10) scientists. They generally consist of a rare earth compound, an aluminum alkyl, and a halide, the halogens being bound to the rare earth element or aluminum. 

The other notable feature of the optical spectroscopy of the lanthanide ions is that their absorption bands generally have very low extinction coefficients, because f-f transitions are... 

The colors are characteristic of the ions themselves and are due to transitions between the partly filled d orbitals of transition metals (d-d transitions) or the partly filled / orbitals of lanthanides (f-f transitions). In the 3d transition-metal ions, the 3d orbitals contain one or more electrons. When these ions are introduced into a solid, the orbital energies are split by interactions with the surrounding anions. The color observed is due to transitions between these split energy levels. The color observed varies considerably as the interactions are dependent upon the... 

Tapia, O., Cardenas, R., Andres. J. and Colonna-Cesari, F. Transition structure for hydride transfer to pyridinium cation from methanolate. Modeling of LADH catalyzed reaction, J. Am. Chem. Soc., 110 (1988), 4046-4047... 

Tapia, O., Jacob, O. and Colonna, F. Transition structures for carbon dioxide and formaldehyde hydroxylation reactions in the coordinate sphere of zinc, Theor. Chim. Acta, 8.5 (1993), 217-230... 

Finally, we should remember that f f transitions are parity-forbidden. However, most of them become partially allowed at the electric dipole order as a result of mixing with other orbitals that have different parity because of a noninversion symmetry crystal field (see Section 5.3). Thus, a proper choice of the crystal host (or the site symmetry) can cause a variety of (RE) + transitions to become forced electric dipole transitions. 

However, although f f transitions are, in principle, forbidden by the Laporte parity rule, most of the transitions in (RE) + ions occur at the electric dipole (ED) order. As we have already mentioned, this is an ED allowance due to the admixture of the 4f" states with opposite parity excited states 4f" 5d, as a result of the lack of inversion symmetry (ED forced transitions). The oscillator strength, /, for a / f absorption band can be estimated using expression (5.19). We now rewrite this expression as follows ... 

Judd (1962) and Ofelt (1962) demonstrated that, for electric dipole f f transitions and under certain approximations, the square of the matrix element in Equation (6.6) can be written as follows ... 

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