Power-series expansions as fitting functions of potential-energy curves

Abstract

A comparative study of the most important power-series expansions, Dunham, Simons–Parr–Finland, Ogilvie–Tipping, Thakkar, Engelke, Mattera, Surkus and Huffaker, as fitting functions of potential-energy curves is reported. A study of the leading terms and intervals of convergence is also shown. As an example, the calculation of the interval of convergence for an Engelke's series is given. The method is applied to the molecules: CO (X ¹Σ⁺), H₂(X ¹Σ⁺_g) and ⁷LiH (X ¹Σ⁺ and A ¹Σ⁺). An analysis of the variation for the leading term of the power-series expansions with two non-linear parameters is presented for CO(X ¹Σ⁺). The optimum non-linear parameters are obtained when the left-hand side of the interval of convergence is very near and below the first point of the input potential. Moreover, we observed that a good fit through the leading term of a power-series expansion is obtained for Engelke, Mattera or Surkus functions with two non-linear parameters. For fitting power-series expansions with an intermediate number of basis functions it is better to use a Thakkar or Huffaker type function with only one non-linear parameter.