RM1 Model for the Prediction of Geometries of Complexes of the Trications of Eu, Gd, and Tb

All versions of our previous Sparkle Model were very accurate in predicting lanthanide–lanthanide distances in complexes where the two lanthanide ions directly face each other, and mainly lanthanide–oxygen, and lanthanide–nitrogen distances, which are by far the most common ones in lanthanide complexes. In this article, we are advancing for the first time the RM1 model for lanthanides. Designed to be a much more general NDDO model, the RM1 model for lanthanides is capable of predicting geometries of lanthanide complexes for the cases when the central lanthanide trication is directly coordinated to any other atoms, not only oxygen or nitrogen. The RM1 model for lanthanides is defined by three important attributes: (a) the orbitals, the lanthanide ion has now three electrons and a NDDO basis set made of 5d, 6s, and 6p functions; (b) the parametrization, via cluster analysis and an adequate sampling; and (c), the statistical validation of the parameters to make sure the errors behave as random around a mean. All three aspects are described in detail in the article. Results indicate that the RM1 model does extend the accuracy of the previous Sparkle Models to types of coordinating bonds other than Ln–O and Ln–N; the most common ones for Eu, Gd, and Tb, being Ln–C, Ln–S, Ln–Cl, and Ln–Br. Overall, these other coordinating bonds are now predicted within 0.06 Å of their correct values. Therefore, the RM1 model here presented is capable of predicting geometries of lanthanide complexes, materials, metal–organic frameworks, etc., with useful accuracy.