POWER-SERIES EXPANSIONS AS FITTING FUNCTIONS OF POTENTIAL-ENERGY CURVES

A comparative study of the most important power-series expansions, Dun ham, Simons-Parr-Finland, Ogilvie-Tipping, Thakkar, Engelke, Mattera, Surkus and Huffaker, as fitting functions of potential-energy curves i s reported. A study of the leading terms and intervals of convergence is also shown. As an example, the calculation of the interval of conve rgence for an Engelke's series is given. The method is applied to the molecules: CO (X(1) Sigma(+)), H-2 (X(1) Sigma(g)(+)) and (LiH)-Li-7 ( X(1) Sigma(+) and A1 Sigma+). An analysis of the variation for the lea ding term of the power-series expansions with two non-linear parameter s is presented for CO (X(1) Sigma(+)). The optimum non-linear paramete rs are obtained when the left-hand side of the interval of convergence is very near and below the first point of the input potential. Moreov er, we observed that a good fit through the leading term of a power-se ries expansion is obtained for Engelke, Mattera or Surkus functions wi th two non-linear parameters. For fitting power-series expansions with an intermediate number of basis functions it is better to use a Thakk ar or Huffaker type function with only one non-linear parameter.