Force Fields for Metal Coordination Compounds

The latter functional form contains a constant n that determines the periodicity of the potential (r is a phase factor), and allows bending energies with multiple minima, analogously to the torsional energy. It does, however, have problems of unwanted oscillations if an energy minimum with a natural angle close to 180° is desired (this requires 

The barrier towards linearity is given implicitly by the force constant in both the potentials in eqs (2.39) and (2.40). A more general expression, which allows even quite complicated energy functionals to be fitted, is a Fourier expansion. 

4- coordinated metal, for example, may either be tetrahedral or square planar, and a 

The multiple minima nature of the bending energy and the low barriers for interconversion resemble the torsional energy for organic molecules. An expansion of bend in tenns of cosine or sine functions of the angle is therefore more natural than a 

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MOMEC is a force field for describing transition metal coordination compounds. It was originally parameterized to use four valence terms, but not an electrostatic term. The metal-ligand interactions consist of a bond-stretch term only. The coordination sphere is maintained by nonbond interactions between ligands. MOMEC generally works reasonably well for octahedrally coordinated compounds. 

Molecular mechanics calculations have been used to describe low- 471-473] and high-order metal-metal bonds[473,474]. These will be discussed here although many relevant examples are classical rather than organometallic coordination compounds. The force constant for Rh-Rh single bonds has been determined from the vibrational frequency of the metal-metal bond and the strain-free value was fitted using a conventional force field for the ligand systems and a series of experimentally determined structures (Fig. 14.6). The Rh-Rh bond distances cover a range of ca. 0.25 A, and the experimentally observed trends are reasonably well reproduced by the calculations (Table 14.2). 

Note that a combination of various types of potentials can be activated. For example, the coordination geometry for octahedral transition metal compounds can be modeled by 1,3-nonbonded interactions in combination with a multiple harmonic function. This is the approach used in the MOMEC97 force field for a number of metal complexes. Also, for four-coordinate compounds one or both of these potentials can be combined with a plane twist potential that enforces square-planar geometry. 

The Extendible Systematic Force Field (ESFF) [96] is a general force field for organic, organometallic, and transition metal compounds. The parameters used are based solely on data derived from first principles, from which all parameters needed for the force field are determined by a set of mles. The ESFF uses a systematic approach to atom types, based on hybridization, oxidation state, and coordination number, as well as flexible types attached to the atom which can vary depending on the chemical environment. 

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