Radial Coupling and Adiabatic Correction for the LiRb Molecule

Abstract

The radial couplings between the adiabatic states dissociating into Rb(5s, 5p, 4d, 6s, 6p, 5d, 7s, 6d) + Li(2s, 2p), ${\mathrm{Li}}^{+} +{ \mathrm{Rb}}^{-}$ and ${\mathrm{Li}}^{-} +{ \mathrm{Rb}}^{+}$ determined from accurate diabatic and adiabatic previous data for the LiRb molecule. The accuracy of adiabatic and diabatic results is shown by a comparison with previous ab initio calculations and experimental results. To evaluate the radial couplings we have used two methods which are numerical differentiation of the rotation matrix connecting the diabatic and adiabatic representations and the Hellmann-Feynman expression. The first and second derivatives present many peaks, associated to neutral-neutral and ionic-neutral crossings in the diabatic representation. These peaks can be interpreted from the diabatic potential energy curves. The radial coupling is then used to determine the adiabatic correction for several electronic states of LiRb molecule. This correction is about 100 cm^{− 1} for some electronic states around particular distances related to avoided crossings and peaks of the second derivative. It is added to the Born-Oppenheimer potential energy curves to estimate the change in spectroscopic constants, which is significant mainly for the higher excited states. The vibrational levels are evaluated using corrected and uncorrected potential energies to determine the vibronic shift for the ¹Σ⁺ and ³Σ⁺ states. This shift, which is the difference between the adiabatic levels and the corrected ones, has been determined for 20 singlet and triplet Σ⁺ states. A shift of order 10 cm^{− 1} for some vibrational levels is observed, which shows the breakdown of the Born-Oppenheimer approximation.