Expansion of the generating-function approach for non-rigid X₂Y-type molecules by means of the Borel-type summation

The application of the generating-function approach in the Borel-type summation method leads to a new kind of generating function for an effective rotational Hamiltonian of non-rigid X₂Y-type molecules. These functions are based on the incomplete gamma function Γ(a,x). The integrand exponent parameter a determines the asymptotic behaviour of the calculated energy levels. A new type of generating function was tested in the calculations of rotational energies of the (040) vibrational state of H₂O and the ground state of CH₂ molecules.