Orthogonal correlation crystal field

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 ... 

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... 

A further analysis due to Li and Reid (1990) showed that this effect could be well interpreted via the correlated crystal field, by selecting mainly one among Judd s fourth-rank orthogonal crystal field operators g, namely g4 This operator arises reportedly from 4f— rtf excitations considered by Ng and Newman (1987a,b). Besides rare earths, successful fits were also performed on actinide compounds (Reid and Li 1991). Recently, Faucher et al. (1993) utilized a complete set of fourth-rank (non-orthogonal) correlated operators. The transformation of the final fitted parameters into Judd s orthogonal set did not seem to show the exclusive occurrence of one particular operator. Correlation crystal field parameters built as combinations f7 fi) (S> C/ (r2) with ki,lc2 odd and even are efficient to eliminate discrepancies. Combinations of Wyboume s (which arise in the development of 1/r) are not, since combinations with ki, ki odd lead to vanishing matrix elements. 

---