Representing potential energy functions by expansions in orthogonal polynomials. Generalized SPF potentials

A study of the analytical representations of the energy, W(R) = W(S), and the generation of the analytical series, W(S) =sigma(S)summation(sub n) b(sub n) P(sub n)[S(sub n)], where P(sub n)(S) are the orthogonal polynomials with weight function sigma(S) over the range (-1, +1), for S for a diatomic molecule is presented. The results show that for neutral diatomic, the Jacobi polynomials, P(sup 1.6)(sub n) (S) with weight function (1+s)(1-S)(sup 6), is appropriate when the potential for large R is of special interest.