Morse potentials force field methods

Many other useful forms have been proposed (Steele and Lippincott, 1962) and their parameters were related to spectroscopic constants as will be given for the Morse potential by Eq. (1.14). Quite often, the potential V(r) is expanded as a power series in the displacement from equilibrium (force field method)... 

Demiralp E, Cagin T, Goddard WA(1999) Morse stretch potential charge equilibrium force field for ceramics Application to the quartz-stishovite phase transition and to silica glass. Phys Rev l tt 82 1708-1711 Dewar MJS (1977) Ground states of molecules. The MNDO method. Approximations and parameters. J Am Chem Soc 99 4899-4907... 

COSMIC [181] method uses only harmonic potential with respect to displacements in the diagonal force fields. Neither improper torsion nor cross terms are included. The nonbonding interactions are the sum of van der Waals interactions represented by the Morse potential and the charge-based Coulomb energy. 

Figure 28-7 In force field calculations, different levels of approximations are used to reproduce the stretching and compression of chemical bonds The plot shows a Morse potential energy function siipenmposed with various power series approximations (quadratic, cubic, and quartic functions) Note that the bottoms of the curves, representing the bond length for most chemical bonds of interest to medicinal chemists, almost overlap exactly. This nearly perfect fit in the bonding region is the reason simple harmonic functions can be used to calculate tx>nd lengths for unstrained molecular structures in the force lield method.

Results using this technique are better for force fields made to describe geometries away from equilibrium. For example, it is better to use Morse potentials than harmonic potentials to describe bond stretching. Some researchers have created force fields for a specific reaction. These are made by fitting to the potential energy surface obtained from ab initio calculations. This is useful for examining dynamics on the surface, but it is much more work than simply using ab initio methods to find a transition structrue. 

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