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 c oupling parameters zeta(nd) for atomic nd(q) systems of chemical relev ance is provided. The results are obtained from an effective-operator analysis that projects out of the empirical nd(q) data a complete para metrization as far as eigenvalues and eigenstates of the configuration 's multiplet terms are concerned. The only additional parameter is zet a(nd). In the language of the literature we have made the Coulomb anal ysis 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 t imes 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 Sy stem are interpretable as the multiplet-term energies and zeta(nd). Th erefore, not only do the procedure's parametric results serve as a gui de to academic overviews over the periodic table but its parameter val ues may also serve as reference values in ligand-field and magnetism c ontexts. The present method has an advantage in its straightforward re lationship with current methods for obtaining zeta(nd) values, viz. th e use of the Lande interval rule or of the Slater-Condon-Shortley mode l. The paper includes a discussion of the present model in relation to the Slater-Condon-Shortley framework, which no longer can be consider ed a conventional physical model but still can be used pragmatically w ith considerable success. Sets of mutually orthogonal operators have s erved our analyses both as a conceptual and a practical tool. It is, h owever, 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 conclu sion is that all nd(q) systems of chemical relevance are parametrizabl e, quite accurately and in a chemically useful way.