Geometry optimization of metal complexes using natural internal coordinates: Representation of skeletal degrees of freedom

The geometry optimization using natural internal coordinates was applied for transition metal complexes. The original definitions were extended here for the skeletal degrees of freedom which are related to the translational and rotational displacements of the ηⁿ-bonded ligands. We suggest definitions for skeletal coordinates of ηⁿ-bonded small unsaturated rings and chains. The performance of geometry optimizations using the suggested coordinates were tested on various conformers of 14 complexes. Consideration was given to alternative representations of the skeletal internal coordinates, and the performance of optimization is compared. Using the skeletal internal coordinates presented here, most transition metal complexes were optimized between 10 and 20 geometry optimization cycles in spite of the usually poor starting geometry and crude approximation for the Hessian. We also optimized the geometry of some complexes in Cartesian coordinates using the Hessian from a parametrized redundant force field. We found that it took between two and three times as many iterations to reach convergence in Cartesian coordinates than using natural internal coordinates. © 1997 by John Wiley & Sons, Inc.