Research Article: RM1 Semiempirical Quantum Chemistry: Parameters for Trivalent Lanthanum, Cerium and Praseodymium

Date Published: July 1, 2015

Publisher: Public Library of Science

Author(s): José Diogo L. Dutra, Manoel A. M. Filho, Gerd B. Rocha, Alfredo M. Simas, Ricardo O. Freire, Dennis Salahub.


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.

Partial Text

Lanthanum complexes find their usage as catalysts, for example, in the transesterification of triglycerides to monoesters [1], important in the making of biodiesel fuel, in the synthesis of novel antioxidants with high superoxide scavenging activity [2], in asymmetric epoxidation reactions [3], in P4 activation by lanthanum naphthalene complex [4], etc. Furthermore, lanthanum complexes may serve as extreme pressure lubrication additives in paraffin oil [5], they may display pH sensitivity [6], and are of interest to studies on chelator design [7] and polymer build up [8].

As indicated before, the RM1 model for the lanthanides assumes that the electronic configuration [Xe]4fn with n = 0,1,2, for La(III), Ce(III) and Pr(III), respectively, can be correctly described by the semiempirical core of charge +3. In addition, the model attaches a set of semiempirical 5d, 6s, and 6p orbitals to describe the valence shell, which always contains 3 electrons for all lanthanide trications. As a result, 22 parameters need to be optimized for each of the lanthanides.

Table 4 presents unsigned mean errors for each of the specific types of distances between the lanthanide ion and its directly coordinated atoms found in the universe of complexes for La(III), both for the present RM1 model for the lanthanides and for each of the previous sparkle models. In order to facilitate interpretation of the table, the smallest error in each line is being bolded. Clearly, for dinuclear complexes, the La-La bond is more accurately predicted by Sparkle/PM3. However, its error is relatively close to the RM1 error. The same happens for La-O bonds, where Sparkle/PM3 is again the best model. However, its unsigned mean error of 0.0610Å is too close to the RM1 error of 0.0698Å. However, for all other distances, RM1 presents the smallest errors while the previous Sparkle models sometimes display huge errors as is the case of La-S bonds when the average errors of the Sparkle models is 0.4345Å, a value more than 6 times larger than the RM1 error of 0.0680Å. In Table 4, La-L refers to the unsigned mean error of all distances of all types between the central lanthanum ion and its directly coordinated other atoms, whereas L-L includes all interatomic distances between all directly coordinated atoms, and is, indirectly, a measure of the angles within the coordinated polyhedron. Clearly, RM1, with its unsigned mean error of 0.1704Å is 52% smaller than the average of the previous sparkle models, a situation similar to what happens to the next unsigned mean error, which includes all 5315 types of distances for all lanthanum complexes considered: La-L, La-La, and L,L’, when RM1 displays an error which is 56% smaller than the average error of all previous sparkle models.

The new RM1 model was applied to predict the structure of tetramer of praseodymium, [Pr4Cl10(OH)2(thiazole)8(H2O)2][20]. The RM1 structure was calculated using MOPAC 2009 software and keywords used were the following: RM1 (the Hamiltonian used), PRECISE, GNORM = 0.25, SCFCRT = 1.D-10 (in order to increase the SCF convergence criterion) and XYZ (the geometry optimizations were performed in cartesian coordinates).

The overall advantage of the RM1 model for the lanthanides presented in this article is that it can perform a full geometry optimization on a complex such as the tetramer of praseodymium, [Pr4Cl10(OH)2(thiazole)8(H2O)2], with relative ease; something that would be exceedingly difficult for an ab initio type calculation. The same can be said of calculations on the three-dimensional 5-aminoisophtalate Pr(III) polymeric complex, which presents good gas storage capabilities [21]. Even if ab initio calculations would be later needed for specific properties that could not be obtained at useful accuracy levels by any other means, they could be carried out on RM1 optimized geometries—something that could save an enormous amount of computing time and resources.