Obtaining the Morse parameter for large bond-stretching using Murrell-Sorbie parameters

Although the second derivative approach has been shown to provide good parameter relationships between any two interatomic potential functions, these relations are valid only at and near the equilibrium point. Arising from the significant discrepancy between connected potential functions for large stretching of covalent bonds by the second derivative approach, an integral approach is developed herein. By equating interatomic energy integral from equilibrium to bond dissociation, the overall discrepancy is minimized for that range between the Morse and Murrell-Sorbie potential functions. Plotted results reveal two observations. First of all, the second derivative approach is appropriate for bond compression and infinitesimal bond stretching, while the integral approach is more suitable when the extent of bond stretching is significant. Secondly, the Morse function exactly fits the Murrell-Sorbie curve when the Morse shape parameters based on the second derivative and integral approaches are equal. Hence a criterion for determining the accuracy level of Murrell-Sorbie parameters for conversion to Morse parameter is established. Finally, a demonstration was made for cases where a clear discrepancy was observed in the potential energy curves. It was found that the integral approach gives a more conservative and more realistic interatomic force curve than those of derivative approach. Figure Morse potential force using Murrell-Sorbie parameters