RESUMEN

The RM1 quantum chemical model for the calculation of complexes of Tm(III), Yb(III) and Lu(III) is advanced. Subsequently, we tested the models by fully optimizing the geometries of 126 complexes. We then compared the optimized structures with known crystallographic ones from the Cambridge Structural Database. Results indicate that, for thulium complexes, the accuracy in terms of the distances between the lanthanide ion and its directly coordinated atoms is about 2%. Corresponding results for ytterbium and lutetium are both 3%, levels of accuracy useful for the design of lanthanide complexes, targeting their countless applications.

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RESUMEN

The RM1 model for the lanthanides is parameterized for complexes of the trications of lanthanum, cerium, and praseodymium. The semiempirical quantum chemical model core stands for the [Xe]4fn electronic configuration, with n =0,1,2 for La(III), Ce(III), and Pr(III), respectively. In addition, the valence shell is described by three electrons in a set of 5d, 6s, and 6p orbitals. Results indicate that the present model is more accurate than the previous sparkle models, although these are still very good methods provided the ligands only possess oxygen or nitrogen atoms directly coordinated to the lanthanide ion. For all other different types of coordination, the present RM1 model for the lanthanides is much superior and must definitely be used. Overall, the accuracy of the model is of the order of 0.07Å for La(III) and Pr(III), and 0.08Å for Ce(III) for lanthanide-ligand atom distances which lie mostly around the 2.3Å to 2.6Å interval, implying an error around 3% only.

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Complexes of dysprosium, holmium, and erbium find many applications as single-molecule magnets, as contrast agents for magnetic resonance imaging, as anti-cancer agents, in optical telecommunications, etc. Therefore, the development of tools that can be proven helpful to complex design is presently an active area of research. In this article, we advance a major improvement to the semiempirical description of lanthanide complexes: the Recife Model 1, RM1, model for the lanthanides, parameterized for the trications of Dy, Ho, and Er. By representing such lanthanide in the RM1 calculation as a three-electron atom with a set of 5 d, 6 s, and 6 p semiempirical orbitals, the accuracy of the previous sparkle models, mainly concentrated on lanthanide-oxygen and lanthanide-nitrogen distances, is extended to other types of bonds in the trication complexes' coordination polyhedra, such as lanthanide-carbon, lanthanide-chlorine, etc. This is even more important as, for example, lanthanide-carbon atom distances in the coordination polyhedra of the complexes comprise about 30% of all distances for all complexes of Dy, Ho, and Er considered. Our results indicate that the average unsigned mean error for the lanthanide-carbon distances dropped from an average of 0.30 Å, for the sparkle models, to 0.04 Å for the RM1 model for the lanthanides; for a total of 509 such distances for the set of all Dy, Ho, and Er complexes considered. A similar behavior took place for the other distances as well, such as lanthanide-chlorine, lanthanide-bromine, lanthanide, phosphorus and lanthanide-sulfur. Thus, the RM1 model for the lanthanides, being advanced in this article, broadens the range of application of semiempirical models to lanthanide complexes by including comprehensively many other types of bonds not adequately described by the previous models.

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RESUMEN

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.

RESUMEN

The recently published Parametric Method number 7, PM7, is the first semiempirical method to be successfully tested by modeling crystal structures and heats of formation of solids. PM7 is thus also capable of producing results of useful accuracy for materials science, and constitutes a great improvement over its predecessor, PM6. In this article, we present Sparkle Model parameters to be used with PM7 that allow the prediction of geometries of metal complexes and materials which contain lanthanide trications. Accordingly, we considered the geometries of 224 high-quality crystallographic structures of complexes for the parameterization set and 395 more for the validation of the parameterization for the whole lanthanide series, from La(III) to Lu(III). The average unsigned error for Sparkle/PM7 for the distances between the metal ion and its coordinating atoms is 0.063Å for all lanthanides, ranging from a minimum of 0.052Å for Tb(III) to 0.088Å for Ce(III), comparable to the equivalent errors in the distances predicted by PM7 for other metals. These distance deviations follow a gamma distribution within a 95% level of confidence, signifying that they appear to be random around a mean, confirming that Sparkle/PM7 is a well-tempered method. We conclude by carrying out a Sparkle/PM7 full geometry optimization of two spatial groups of the same thulium-containing metal organic framework, with unit cells accommodating 376 atoms, of which 16 are Tm(III) cations; the optimized geometries were in good agreement with the crystallographic ones. These results emphasize the capability of the use of the Sparkle Model for the prediction of geometries of compounds containing lanthanide trications within the PM7 semiempirical model, as well as the usefulness of such semiempirical calculations for materials modeling. Sparkle/PM7 is available in the software package MOPAC2012, at no cost for academics and can be obtained from http://openmopac.net.