F electron systems

Rosenberg M, Farris F. Electronic systems and decision making. Curr Drug Discov 2003 3 1-4. 

In general, the FEUDAL model appears to answer many of the fundamental questions regarding the bonding within f-electron systems however, certain discrepancies exist within the physical data of the actinide systems and the theoretical understanding of the radial distribution functions of the actinides. Evidence that the f orbitals are accessible for covalent bonding continues to be found. 

An overview is presented of the state-of-the-art for quantum chemical calculations for d- and f- electron systems. The present role and the potential of ab-initio, density functional and semi-empirical methods are discussed with reference to contemporary developments in related e35>erimental disciplines. Progress towards a true computational chemistry including the transition metals, lanthanides, and actinides is outlined with emphasis both on achievements and on the remaining barriers. 

Table IV. Some Semi-Empirical Methods Used for d and f Electron Systems...

At the Toronto meeting we saw the first signs of progress towards both theoretical and computational chemistry for the d- and f- electron systems. Dynamics are definitely on the agenda for the next few years as are the development of convenient computer interfaces and the extraction of force fields and the like that will allow more and more experimentalists in inorganic chemistry to spend some of their time fruitfully at the computer keyboard. 

A discussion is given of electron correlations in d- and f-electron systems. In the former case we concentrate on transition metals for which the correlated ground-state wave function can be calculated when a model Hamiltonian is used, i.e. a five-band Hubbard Hamiltonian. Various correlation effects are discussed. In f-electron systems a singlet ground-state forms due to the strong correlations. It is pointed out how quasiparticle excitations can be computed for Ce systems. 

Similar experience has been made for other f-electron systems. Nevertheless, we should point out that by applying the LDA+U scheme we leave the framework of DFT. This does not apply to the SIC (self-interaction correction) formalism (Dreizler and Gross 1990), for which a proper relativistic formulation has been worked out recently (Forstreuter et al. 1997 Temmerman et al. 1997) and applied to magnetic solids (Temmerman et al. 1997). 

A. Energy Level Parameterization Scheme. The parameterization scheme to derive the free-ion properties of the f-electron system is based upon direct physical assumptions. 

Figure 2 illustrates the role played by the highest occupied and lowest unoccupied KS eigenvalues, and their relation to observables. For molecules, HOMO(N) is the highest-occupied molecular orbital of the A-electron system, HOMO(N+I) that of the N + f-electron system, and LUMO(N) the lowest unoccupied orbital of the A-electron system. In solids with a gap,... 

Zaplinski, P., D. Meschede, D. Pliimacher, W. Schlabitz and H. Schneider, 1980, in Crystalline Electric Fields and Structural Effects in f-electron Systems, eds J.E. Crow, R.P. Guertin and T.M. Mihalishin (Plenum, New York) p. 295. 

Here Xt is the static susceptibility of the f-electron system, E is the magnetic relaxation rate of the f-state and Kff denotes the coupling constant of the spin of the ESR probe to the f moment via the indirect RKKY exchange. A schematic representation of the interactions which are described in eq. (34) and are responsible for the linewidth broadening in HFS is shown in fig. 41. 

The second half of this review deals with newly developed branches of solid state physics. Here it is evident that ESR made major contributions to the physics of electronically highly correlated systems, like heavy-fermion systems and intermediate-valence compounds. In the latter compounds it still has to be proven that the low density of states, which have been detected experimentally, results from the so-called Kondo whole and is a characteristic feature of IVCs. Certainly a further interesting area of ESR will be the study of Kondo insulators. In KI a hybridization gap, as a consequence of the interaction of the band states with the f-electron system, develops at low temperatures. In KI a non-magnetic impurity will reveal an effective spin i and, hence, one expects that non-magnetic impurities become ESR active below a characteristic temperature. So far we are not aware of any ESR experiments of that type in Kondo insulators. 

As discussed by Gunnarsson and Schonhammer in chapter 64 of this book, the parameters relevant to the extended Anderson single impurity model, originally proposed in 1977 for the description of the core level lineshapes of adsorbates (see scheme in fig. 2), and now to be used to describe core level XPS data of f-electron systems, are ... 

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