High accuracy wave functions and eigenenergies for vibration–rotation states of diatomic molecules

A solution of the wave equation for the rotational–vibrational motion in diatomic molecules with a new exponential potential function is carried out in detail. The solution gives simple expressions for the wave functions, eigenenergies, and other related spectroscopic constants. With these expressions Franck–Condon factors for the R branches of the A 1 ∑   u − ‐ X 1 ∑   g +band system of Ca 2 , have been calculated which are in excellent agreement with experiment. Various strengths and weaknesses of the present method are also discussed.