Morse basis expansion applied to diatomic molecules

This work explores the use of the eigenfunctions of the Morse potential with a infinite barrier at long range to solve the radial Schrödinger equation for diatomic molecules. Analytical formulas are obtained for the kinetic energy operator matrix elements in the Morse basis. The Morse basis expansion is applied to find the vibrational–rotational levels of the sodium molecule in the electronic ground state.

► The Morse potential basis is invoked to find the rovibrational levels of diatomic molecules.
► Analytical formulas for the kinetic energy operator in the Morse basis are obtained.
► The results of the Morse basis expansion show good agreement with the Fourier Grid technique.