Simultaneous determination of ligand-field parameters of isostructural lanthanide complexes by multidimensional optimization

A new approach is proposed for the determination of the ligand-field (LF) parameters of a set of isostructural lanthanide complexes, and this approach is examined in terms of uniqueness and accuracy of the solutions. The method employs a multidimensional optimization algorithm to find a set of parameters that gives a least-squares fit to either or both of two types of experimental data, namely H-1 NMR paramagnetic shifts and the temperature dependence of the magnetic susceptibility. To produce an overdetermined situation, each LF parameter is approximated as a linear function of the atomic number of the lanthanide ion. Simultaneous use of the experimental data sets of multiple lanthanide complexes under this restriction efficiently reduces the range of possible solutions from that determined when using a data set of a single lanthanide complex. The use of either NMR or magnetic susceptibility experimental data does not give a complete conversion, although it can provide an approximate estimate of the LF parameters. It is demonstrated that a search for parameters that satisfy both types of experimental data sets is essential to obtain the unique solution.