The use of continued fractions to describe the highly excited rotational states of a H2O molecule

Abstract

Continued fractions D(a, x) were used in the analysis of the highly excited (J ≤ 42, Ka ≤ 32) rotational levels of the first eight vibrational states of a H216O molecule. The fractions depend on the rotational operator Jz, defined by the variable x, and the shape parameter a, which determines the asymptotic behavior of the calculated energy levels. Continued fractions D(a, x) are new forms of the generating functions for the effective rotational Hamiltonian of some nonrigid molecule of the H2X type.