Correlation crystal-field

Correlation crystal fields 547 6. Electron-phonon interaction 580... 

K GiQ correlation crystal-field parameters S total spin angular momentum... 

SCCF spin-correlated crystal field K isothermal compressibility... 

Improvement of the crystal-field splitting calculation has been achieved by two different approaches. On one hand the basis set of wavefunctions was extended to include also excited configurations. This approach will be dealt with in sect. 4.4.6. On the other hand, the one-electron approximation has been relaxed to take into account electron correlation effects. The original formulation of the correlation crystal-field parameterization has been proposed by Bishton and Newman (1968). Judd (1977) and Reid (1987) redefined the operators to ensure their mutual orthogonality ... 

Another possibility to address the problem of the correlation crystal fields is an approach based on different wavefunctions for the spin-up and spin-down electrons. This spin-correlated crystal-field model merely doubles the number of crystal-field parameters and thus can be applied in most cases. Shen and Holzapfel (1995c) presented a high pressure study on spin-correlated crystal fields in MFCl Sm2+ (M = Ba, Sr, Ca). In particular, they considered the splitting ratio R of the 5Di and 7Fi multiplets, which should be equal to 0.298 within the conventional one-electron crystal-field theory and independent of the host crystal. In a first step, Shen and Holzapfel (1995c) considered ambient pressure as well as high pressure data of the isoelectronic Eu3+ ion. In this case they found a ratio of R = 0.238, which could be explained by taking into account a spin-correlated crystal-field parameter C2 = —0.007(3). 

Recently, the 5-function model has also been employed to analyze high-pressure results on LaCl3 Pr3+ and LaCl3 Nd3+ (Burdick and Troster, 2003). This model assumes the dominant contributions to the correlation crystal field interactions arising from paired electrons within the same orbital. It has been shown that this model is capable to greatly improve the description of anomalous multiplets like the lT>2 multiplet of Pr3+ at ambient pressure (Burdick and Richardson, 1997). 

The one-electron crystal field Hamiltonian does not take into account electron correlation effects. For some systems, it has been useful to augment the crystal field Hamiltonian with additional terms representing the two-electron, correlated crystal field. The additional terms most commonly used (see, for example, Peijzel et al., 2005b Wegh et al., 2003) are from the simplified delta-function correlation crystal field model first proposed by Judd (1978) that assumes electron interaction takes place only when two electrons are located at the same position (hence the name delta-function ). This simplified model, developed by Lo and Reid (1993), adds additional terms, given as,... 

The correlation crystal-field extension to the Hamiltonian becomes more important when many high-energy states are observed. For the 4P 4f transitions, many new energy lev-... 

Spin-correlated crystal field 276 4.5. The configuration interaction model ... 

But we must still investigate the non-trivial ( 2 0) two-electron operators, i.e. the correlated crystal field. 

The term correlated crystal field designates the two-electron part of the crystal field Hamiltonian. Although a concept of the 1970s, correlation is a keyword of the late 1980s and 1990s. 

An important point must be stressed here, i.e., the prediction that correlated parameters for k = 2 and 4 should be the most important. The demonstration is made that the correlated crystal field can be formally accounted for by a term dependent one-electron crystal field and also that the superposition principle holds for separate ligand contributions as for the one-electron crystal field. This allows a drastic reduction of the number of correlated parameters however, there are still 23 for each metal-ligand distance. 

The ordinary correlated crystal-field operators as defined above are not mutually orthogonal as are the one-electron operators. Besides the conceptual disturbance, a practical inconvenience is the instability of numerical fit procedures. Judd (1977a) has described the two-electron crystal field operators on a group-adapted basis insuring their... 

Searching along the lines of selective modification of the radial wavefunctions, Newman (1970) and Judd (1977b) found another source of correlated crystal field in the exchange forces between 4f electrons with similarly directed spins. They introduce a correction of the type s, S (where s,- is the zth electron spin and S the total spin) as a multiplicative factor to apply to the operators. The effective crystal field Hamiltonian therefore becomes ... 

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