Accurate and unequivocal determination of the crystal-field parameters of lanthanide ions via a multitechnique approach

Understanding the crystal field of lanthanide complexes is pivotal for the testing of Stevens operator equivalents and the development of lanthanide-based molecular magnets. Intense theoretical investigation is aimed at the determination of the Hamiltonian parameters, but accurate experimental tests often suffer from overparametrization. Because of this, clear-cut experimental determinations are missing even high-symmetry environments. Here we present a detailed study of the crystal-field parameters of Pr(III) ions in a high-symmetry environment, using the cyano-based molecular magnetic material $\mathrm{Pr}[\mathrm{Co}{(\mathrm{CN})}_{6}]\ifmmode\cdot\else\textperiodcentered\fi{}5{\mathrm{H}}_{2}\mathrm{O}$. The problem of multiple solutions is considered with particular detail, and we show how unequivocal determination of the parameters becomes possible only by combining different spectroscopic and magnetometric techniques. Eventually we compare the solution with fitting methodologies that are commonly employed and we highlight the level of information that can be gained by such procedures.