Lanthanide crystal field theory

Brief history of lanthanide crystal field theory. 575... 

The crystal-field interaction in lanthanide-ion spectra in solids is weak in the sense that perturbations that shift the positions of the free-ion levels are small (compared to corresponding shifts in transition-metal spectra) and the effects of coupling different free-ion levels by the crystal field are small. The weakness of the lanthanide crystal-field interaction is a consequence of the shielding of the 4r configuration by the outer 5s and 5p atomic shells and is reflected in the historical sequence of theoretical advances in lanthanide crystal-field theory. 

Mononuclear Lanthanide Complexes Use of the Crystal Field Theory to Design Single-Ion Magnets and Spin Qubits... 

Ab Initio Versus Phenomenological Crystal Field Theory for Lanthanides... 

Newman, D.J., 1971. Theory of lanthanide crystal fields. Adv. Phys. 20, 197. 

Pursuing a systematic interpretation of the electronic energy level structure of lanthanides and actinides within the framework of crystal-field theory led to the most important accomplishments in Bill s scientific career. In the 1980s, powerful computer programs were devel-... 

Crystal field theory is one of several chemical bonding models and one that is applicable solely to the transition metal and lanthanide elements. The theory, which utilizes thermodynamic data obtained from absorption bands in the visible and near-infrared regions of the electromagnetic spectrum, has met with widespread applications and successful interpretations of diverse physical and chemical properties of elements of the first transition series. These elements comprise scandium, titanium, vanadium, chromium, manganese, iron, cobalt, nickel and copper. The position of the first transition series in the periodic table is shown in fig. 1.1. Transition elements constitute almost forty weight per cent, or eighteen atom per cent, of the Earth (Appendix 1) and occur in most minerals in the Crust, Mantle and Core. As a result, there are many aspects of transition metal geochemistry that are amenable to interpretation by crystal field theory. 

Having discussed the theoretical principles of crystal field theory, theories of intensity of the hypersensitive transitions, it is logical to examine the absorption spectral features of lanthanide ions in aqueous solutions. It is probably worthwhile looking into the historical development of the spectra of lanthanides. The most prominent era in the development is the 1930 s. Prandtl and Scheiner [118] presented a complete collection of absorption spectra of trivalent lanthanides in solution. The covered region is 7000-2000 A. An apparent symmetry in the region of absorption with band structure shifting toward the ultraviolet in approaching the centre of the series from both ends was observed. 

Crystal field theory, intensities of 4f-4f transitions, Judd-Ofelt theory of electric-dipole transitions, covalency model of hypersensitivity, dynamic coupling mechanism, solution spectra, spectral data for complexes, solvent effects, fluorescence and photochemistry of lanthanide complexes are dealt with in spectroscopy of lanthanide complexes. 

In the crystal field theory of the intensities of f-f transitions in lanthanide complexes the development of Eq. (2) gives, for the oscillator strength of the transition connecting a ground state f fSLJJ) to an excited state lf"[S L ]J ) at the wavenumber Pjj" the expression 9)j... 

We do not attempt to give a full review of crystal-field theory, although we do include a substantial discussion that is perhaps somewhat lengthy. We believe that this is warranted from the point of view of the unique role that crystal-field theory has in the interpretation of lanthanide spectra. Numerous questions in this field still remain unanswered, and many of the major contributors over the years are stUl quite active, indicating that this area of research is mature but by no means exhausted. It is hoped that, by providing an extensive compendium of experimental data on lanthanide-ion spectroscopy, we will provide a further incentive for theoretical advances. 

Historically, the first extensive developments in crystal-field theory made use of the fact that the crystal-field coupling in lanthanide ions is small. In the operator-equivalent method (Stevens, 1952 Elliot and Stevens, 1953), the coupling of different free-ion levels by the crystal-field interaction is ignored and the crystal-field splitting of each Lj level is treated separately. Traditionally, in this method, the crystal-field Hamiltonian is written as... 

This relation is also known as the closure relation. It is frequently applied in the context of the crystal field theory of the lanthanides. 

Interpretation and systemization of the magnetic properties of lanthanide compounds are based on crystal field theory which has been rqjeatedly discussed in literature, in particular by Morrison and Leavitt (1982) in volume 5 of this Handbook. So we begin our chapter with a short account of crystal field theory in a comparatively simple form with a minimal number of initial parameters with a clear physical meaning. This immediately provides the interaction hamiltonians of 4f electrons with deformations and vibrations of the crystal lattice. Within the framework of this theory one can easily calculate the distortions of the crystal field near impurity ions. A clear idea of the nature of magnetic phenomena in simple dielectric lanthanide compounds is certainly useful for consideration of systems with a more complicated electron structirre. 

Estimates of exchange int rals according to different measurement data depend critically on the g-values used for calculation of magnetic dipole-dipole interactions. The g-values calculated within the framework of the crystal field theories usually differ from the experimental results (EPR, magnetization) by up to 10%. This difference may be due to the covalency of lanthanide ion-ligand bonds (Abragam and Bleaney 1970) and to the vibronic reduction effects (Ham 1965). 

Spectra from lanthanides were in fact first observed originating from a solid compound by Becquerel (1906), of course, the quantum theoretical framework was not in place at that time to allow analysis of the relatively unusual spectra observed in these materials. Since then due to the contributions of Bethe (1929), Kramers (1930) and Van Vleck (1937) the theory of the sharp line spectra of crystals containing lanthanides is now well established in terms of crystal field theory and its various extensions, see Hufner (1978) and references therein. 

---