# Ab Initio - Basis Set Rare Earth Lanthanide

**Coordination Polyhedron Geometry**

In a metal complex, the coordination polyhedron is a solid figure defined by the positions of the ligand atoms directly attached to the central atom. In the case of rare earth complexes, the central atom is usually a trivalent lanthanide ion.

The geometry of the coordination polyhedron of a **lanthanide complex** is the *single most important feature for complex design*. Indeed, knowledge of the coordination polyhedron geometry is essential for the modeling of the influence of the chemical ambiance on the 4fn **lanthanide ion** configuration and its effect on the spectrocopic and magnetic properties of the complexes.

In 2005, a few MWB effective core potential calculations were carried out on some lanthanide complexes in order to confirm the speed and accuracy of the Lanthanide Complexes Sparkle Model. Curiously, it was noticed that by enlarging the basis set from STO-3G, to 3-21G, and finally to 6-31G*, a * decrease in the average accuracy* of the predicted coordination polyhedra was observed.

A few months later, a confirmation was obtained that RHF/STO-3G, with the MWB effective core potential (ECP), appears to be the most efficient ab initio model chemistry for the prediction of coordination polyhedra of **lanthanide complexes**.

Recently, the so far most thorough and complete investigation of this matter has been achieved. As a result, a very extensive study was published reporting an investigation of the ability of various ab initio model chemistries in reproducing the coordination polyhedron geometries of various **lanthanide complexes**. A total of 80 calculations were carried out on 52 complexes of the trivalent ions of samarium, europium, gadolinium, terbium, dysprosium, holmium, erbium and thulium - the largest one containing 164 atoms:

Lanthanide complex coordination polyhedron geometry accuracies of ab initio effective core potential calculations

Ricardo Oliveira Freire, Gerd Bruno Rocha and Alfredo Mayall Simas.

Journal of Molecular Modeling **12**, 373-389 (2006).

All the obtained results consistently confirmed that RHF/STO-3G/ECP appears to be the most efficient model chemistry in terms of coordination polyhedron crystallographic geometry predictions from isolated lanthanide complex ion calculations.

However, although RHF/STO-3G/ECP calculations produce excellent **lanthanide complexes** coordination polyhedra, geometries of the organic ligands may be less accurately predicted.

On the other hand, by enlarging the basis set and by including electron correlation, a better description of the geometry of the ligands is obtained - at the expense of a lower quality coordination polyhedron.

That is why the Lanthanide Complexes Sparkle Model is a useful computational chemistry technique for the calculation of **lanthanide complexes**: not only the geometries of the coordination polyhedra are as accurate as RHF/STO-3G with the MWB effective core potential, but the ligands are well described too. Besides, Sparkle calculations are hundreds of times faster.