Metals force constant models

The Universal Force Field, UFF, is one of the so-called whole periodic table force fields. It was developed by A. Rappe, W Goddard III, and others. It is a set of simple functional forms and parameters used to model the structure, movement, and interaction of molecules containing any combination of elements in the periodic table. The parameters are defined empirically or by combining atomic parameters based on certain rules. Force constants and geometry parameters depend on hybridization considerations rather than individual values for every combination of atoms in a bond, angle, or dihedral. The equilibrium bond lengths were derived from a combination of atomic radii. The parameters [22, 23], including metal ions [24], were published in several papers. 

Whereas the quasi-chemical theory has been eminently successful in describing the broad outlines, and even some of the details, of the order-disorder phenomenon in metallic solid solutions, several of its assumptions have been shown to be invalid. The manner of its failure, as well as the failure of the average-potential model to describe metallic solutions, indicates that metal atom interactions change radically in going from the pure state to the solution state. It is clear that little further progress may be expected in the formulation of statistical models for metallic solutions until the electronic interactions between solute and solvent species are better understood. In the area of solvent-solute interactions, the elastic model is unfruitful. Better understanding also is needed of the vibrational characteristics of metallic solutions, with respect to the changes in harmonic force constants and those in the anharmonicity of the vibrations. 

Fractionation factors are calculated for a large variety of trigonal-planar (XY3) and tetrahedral XY4) molecules and molecule-like complexes, with a particular focus on metal halides. Empirical force-held models (MUBFF) are used to estimate vibrational frequencies for the rarer isotopic forms of the substances studied, and aqueous and crystalline moleculelike species are modeled as gas-phase molecules. In the tabulation below the original equilibrium constants have been converted to fractionation factors (a R-x)-... 

How may force constants for these functions be obtained that correctly model the balance between the metal ion requirement (e.g., square planar) and the steric requirement of the ligand (e.g., tetrahedral) ... 

Molecular mechanics and dynamics studies of metal-nucleotide and metal-DNA interactions to date have been limited almost exclusively to modeling the interactions involving platinum-based anticancer drugs. As with metal-amino-acid complexes, there have been surprisingly few molecular mechanics studies of simple metal-nucleotide complexes that provide a means of deriving reliable force field parameters. A study of bis(purine)diamine-platinum(II) complexes successfully reproduced the structures of such complexes and demonstrated how steric factors influenced the barriers to rotation about the Pt(II)-N(purine) coordinate bonds and interconversion of the head-to-head (HTH) to head-to-tail (HTT) isomers (Fig. 12.4)[2011. In the process, force field parameters for the Pt(II)/nucleotide interactions were developed. A promising new approach involving the use of ab-initio calculations to calculate force constants has been applied to the interaction between Pt(II) and adenine[202]. 

Whether the use of 1,3-interactions in place of L-M-L force constants is a valid approach depends on the metal ion being considered. If it is a metal for which the M-L bonding is primarily electrostatic, such as an alkali, alkaline earth or rare earth metal, then 1,3-interactions are definitely preferable. In such cases it may be important to include an electrostatic component in the 1,3-interactions in addition to the usual van der Waals term. If, however, the metal ion is one that has a clear preference for a particular coordination geometry, then inclusion of at least a component of the L-M-L force constants may be indicated (see Chapter 11, Section 11.1). Recently, a model which includes both 1,3-interactions and force constants for the L-M-L angles has been described1 lsl Other approaches are discussed in Chapter 2, Section 2.2.2. 

An alternative approach to modeling the L-M-L angles is to set the force constants to zero and include nonbonded 1,3-interactions between the ligand atoms. In most force fields, 1,3-interactions are not explicitly included for any atoms, instead they are taken up in the force constants for the valence angle terms. This is an approximation because the 1,3-interactions are most often repulsive and thus the function used to calculate the strain energy arising from valence angle deformation should be asymmetric. It was shown that the nonbonded 1,3-interactions around the metal atom are in many cases a major determinant of the coordination... 

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