Obtaining Simons-Parr-Finlan coefficients using Murrell-Sorbie parameters

It is known that the Simons-Parr-Finlan (SPF) molecular potential energy function is impeccable near equilibrium covalent bond length while the Murrell-Sorbie molecular potential energy function gives a highly realistic description for large bond stretching. Hence the conversion of Murrell-Sorbie parameters into SPF parameters is useful for plotting SPF potential energy in long range application while the conversion of SPF parameters into Murrell-Sorbie parameters is beneficial for plotting Murrell-Sorbie potential energy in short range application. In this paper, parameters of both potential functions are related in terms of factorials and binomial coefficients through implementation of Taylor series expansion and followed by appropriate comparison of corresponding terms. Verification of the parameter relations was achieved by plotting the SPF and Murrell-Sorbie functions based solely on the latter's parameters for the diatomic chloride molecules AlCl, BeCl, BCl, CCl, ClCl, ClF, HCl, LiCl, NaCl, ClO and SiCl. The good agreement exhibited near ground state in the plotted results established the developed relations. Away from the equilibrium bond length, the SPF function underestimates and overestimates the Murrell-Sorbie energy curve for bond compression and stretching, respectively, for most diatoms. This suggests the comparative advantage of the Murrell-Sorbie and SPF functions in modeling bond compression and bond stretching, respectively, in conservative materials design.