Optimisation of the dipole-Coulomb approximation for high-l Rydberg states of polar molecules

The present work deals with the question of the origin choice to get the maximal accuracy of the dipole-Coulomb approximation in the theory of molecular Rydberg states with high orbital momentum l. Concerning birefringence in polar molecules, the question of adequate origin choice has first been raised in the classical work by Buckingham & Longuet-Higgins in 1968, where it has been taken into account that the dipole moment of a polar molecular core (cation) depends on the origin choice. This dependence also leads to inseparability of dipole and quadrupole corrections to the Rydberg electron spectra in polar molecules. In the present work a new option for the problem is proposed as applied to the dipole-Coulomb approximation. Considering a simplified model of a molecular core as a system of N effective fixed point charges, we show both analytically and numerically that the optimal choice of origin, at least for a linear core, is the geometric centre of the core. On the other hand, results of the present work as well as previous publications show that the problem raised by Buckingham and Longuet-Higgins does not have a universal solution.