Sparkle/PM6 Parameters for all Lanthanide Trications from La(III) to Lu(III)

PM6 is the first semiempirical method to be released already parametrized for the elements of the periodic table, from hydrogen to bismuth (Z = 83), with the exception of the lanthanides from cerium (Z = 58) to ytterbium (Z = 70). In order to fill this gap, we present in this article a generalization of our Sparkle Model for the quantum chemical semiempirical calculation of lanthanide complexes to PM6. Accordingly, we present Sparkle/PM6 parameters for all lanthanide trications from La(III) to Lu(III). The validation procedure again considered only high-quality crystallographic structures and included 633 complexes. Sparkle/PM6 unsigned mean errors UME((Ln-L))s, corresponding to all the interatomic distances between the lanthanide ion and the atoms directly coordinated to it, range from 0.066 to 0.086 angstrom for Gd(III) and Ce(III), respectively. These minimum and maximum UME((Ln-L))s across the lanthanide series are comparable to the Sparkle/AM1 values of 0.054 and 0.085 angstrom for Ho(III) and Pr(III), respectively, as well as to the values for Sparkle/PM3 of 0.064 and 0.093 angstrom for Gd(III) and Pr(III), respectively. Moreover, for all 15 lanthanide ions, these interatomic distance deviations follow a gamma distribution within a 95% level of confidence, indicating that these errors appear to be random around a mean, freeing the model of systematic errors, at least within the validation set. Sparkle/PM6 presented here, therefore, broadens the range of applicability of PM6 to the coordination compounds of the rare earth metals.