Poster presented at the Symposium
"Applications of Molecular Mechanics to Metal Complexes"
Amer. Chem. Soc. Spring 2000 National Meeting,
March 26-30, 2000 San-Francisco.

Molecular mechanics study of the mixed-ligand lanthanide complexes using Gillespie-Kepert model

Michael G. Razumov, Vladimir L. Melnikov, and Igor V. Pletnev

Department of Chemistry, Moscow State University, Moscow, 119899 Russia


Lanthanide ion complexes are useful reagents in practically important applications, like chemical vapour deposition and magnetic resonance imaging. However, the application, as well as the design of novel reagents, are significantly hindered by insufficient theoretical study of structure - property relationships.

In our opinion, molecular mechanics (MM) is the most useful tool, considering cost-efficiency ratio, in this concern.

A conventional MM method has been developed for organic compounds and still meets difficulties when applied to the metal ion complexes, especially when the latter feature deformed coordination polyhedra and large coordination numbers, like in lanthanide complexes.

The strongest challenge is the modeling of the coordination sphere. There are two popular approaches: valence force field (VFF) and points-on-sphere (POS) model. Both of them have disadvantages: VFF - idealization of coordination polyhedron, POS - presence of attractive term in the conventional van der Waals (VDW) potentials.

Previously, we have developed the version of MM complemented by the well-known Gillespie-Kepert model for coordination polyhedron (MM-GK), which is free of these disadvantages. Within MM-GK, the same parameters are applicable to complexes of different coordination numbers/polyhedra.

Herein, we report on the force field (FF) and MM-GK calculations for beta-diketonate-, aqua-, and mixed aqua-beta-diketonate lanthanide ion complexes.


All MM calculations were performed with the use of the custom-made program MMPC. The ligand subsystem is described using the CHARMM force field, which was complemented with parameters for beta-diketonate fragment. The metal ion coordination sphere was described using Gillespie-Kepert model.

Gillespie-Kepert model

According to MM-GK model, the arrangement of donor atoms around the metal is dictated by mutual repulsion between all metal-ligand (M-L) bonds. It is assumed that the repulsion occurs between the effective centers of repulsion lying on the bonds M-L on distance reff from metal ion as on the scheme.


where Rij^2 = (Ri,eff)^2 + (Rj,eff)^2 - 2*Ri,eff * Rj,eff * cos(XiMXj);
Ri,eff = R(MXi)*Deff,i
(Ai; Aj; Deff,i; Deff,j - computational parameters).

Parameterization: analysis of forces on atoms

Calibration of parameters was carried out with the use of analysis of forces on atoms. The basic idea of this method is that the stable conformation of molecule corresponds to a minimum of its potential energy and zero energy gradient. Thus, the task consists in finding the FF that gives (near to) zero energy gradient for experimental structures and, consequently, low deviation of calculated structures from experimental.

Initial X-ray experimental structures were taken from The Cambrige Crystal Structural DataBase and from literature sources. FF parameters were adjusted to fit the structures of calibration set of molecules. Gillespie-Kepert parameters were the same for all lanthanides, while r0 were tabulated as a linear function of ionic radius:

r0(Ln-Oaq) (Ln) = 2.5[Rion(Ln)-1.0] + 1.776 A;
r0(Ln-Odik)(Ln) = 2.5[Rion(Ln)-1.0] + 1.738 A.


Structure of complexes

Using derived computational parameters, we calculated the geometry of 39 lanthanide ion nonaaqua complexes, 6 octaaqua complexes and 18 beta- diketonate and aqua-beta-diketonate complexes. The folowing Chart1, Chart2, Chart3 and Chart 4 illustrate the results.

As is seen, in the most cases there is a good agreement between calculated and experimental (C-E) structures. Since the coordination polyhedron in lanthanide beta-diketonates due to steric factors is more flexible, in contrast to aqua complexes, we also compared C-E structures of these complexes by Porai-Koshits and Muetterties polyhedron dihedral angles criteria. There is good agreement, too.

Energy of isomers

To check a possibility of application of the presented parameters to the calculation of not only geometry, but also the relative energy of complexes, we determined the most favourable coordination isomers for diaqua-trisacetilacetonate complexes of a range of lanthanides.

Possible coordination isomers of Ln(acac)3(H2O)2

Water oxygen atoms are shown as Ow. Chelate cycles are shown in bold.

Basically, it would be possible to check up energy of isomers for all lanthanides, but the three representative cations would be enough: La, Eu, and Yb (beginning, middle and end of rare-earth row).

The calculated energies (kcal/mol) relative to global minimum are as shown on the chart.

The first isomer is calculated to be the most stable. Notably, it is the form, actually observed in X-ray experiment for all of these complexes.