ACCURATE EMPIRICAL SPIN-ORBIT-COUPLING PARAMETERS ZETA(ND) FOR GASEOUS ND(Q) TRANSITION-METAL IONS - THE PARAMETRICAL MULTIPLET TERM MODEL

A comprehensive and up-to-date tabulation of one-electron spin-orbit coupling parameters zeta(nd) for atomic nd(q) systems of chemical relevance is provided. The results are obtained from an effective-operator analysis that projects out of the empirical nd(q) data a complete parametrization as far as eigenvalues and eigenstates of the configuration's multiplet terms are concerned. The only additional parameter is zeta(nd). In the language of the literature we have made the Coulomb analysis mathematically complete for the experimentally sufficiently known d3, d4, d5, d6, and d7 systems. This was done 40 years ago for d2 and dg, while an extension to other dq systems has been approached many times ever since. Although the method is not in a simple way related to first principles, it is not merely a data-reduction machinery using a well-defined procedure. Thus, the model parameters for a given ndq System are interpretable as the multiplet-term energies and zeta(nd). Therefore, not only do the procedure's parametric results serve as a guide to academic overviews over the periodic table but its parameter values may also serve as reference values in ligand-field and magnetism contexts. The present method has an advantage in its straightforward relationship with current methods for obtaining zeta(nd) values, viz. the use of the Lande interval rule or of the Slater-Condon-Shortley model. The paper includes a discussion of the present model in relation to the Slater-Condon-Shortley framework, which no longer can be considered a conventional physical model but still can be used pragmatically with considerable success. Sets of mutually orthogonal operators have served our analyses both as a conceptual and a practical tool. It is, however, demonstrated that the use of orthogonal sets of operators does not imply that their associated parameters will be uncorrelated, but it makes the correlation analysis more transparent. The general conclusion is that all nd(q) systems of chemical relevance are parametrizable, quite accurately and in a chemically useful way.