An Alternative Perturbation Method for the Molecular Vibration-Rotation Problem II- Calculation ab initio of observables, application to the dipole moment of methane

The rst article of this series has introduced an alternative perturbation scheme to nd approximate solutions of the spectral problem for the rotation-vibration molecular Hamiltonian. The convergence of our method for the methane vibrational ground state rotational energy levels was quicker than that of the traditional method, as expected, and our predictions were quantitative. In this second article, we study the convergence of the calculation ab initio of eective dipole moments for methane within the same theoretical frame. The rst order of perturbation when applied to the electric dipole moment operator of a spherical top gives the expression used in previous spectroscopic studies. Higher orders of perturbation give corrections corresponding to higher centrifugal distorsion contributions and are calculated accurately for the rst time. Two potential energy surfaces of the