Abstract
The evaluation of the first and second derivative of the non adiabatic coupling between the several
1Σ
+ adiabatic states of LiH, RbH and CsH molecules, is considered from accurate diabatic and adiabatic data. Such derivatives of the electronic wave function are determined through a numerical differentiation of the rotational matrix connecting the diabatic and adiabatic representations. The first as well as the second derivative presents many peaks, related to ionic–neutral and neutral–neutral coupling between the
1Σ
+ states. Such radial coupling has been exploited to calculate the first adiabatic correction, which corresponds to the diagonal term of the second derivative divided by the reduced mass, for the ground and some excited states of the three molecules. The second adiabatic correction has been determined using the Virial theorem.
The first adiabatic correction was added to the adiabatic potential energy curves to re-determine the corrected spectroscopic constants and vibrational energy levels. The vibrational shift, which is the difference between the corrected and the adiabatic levels, has been calculated for X, A, C and D
1Σ
+ states of the three molecules. A shift of some 10
cm
−1 is observed for some vibrational levels showing the breakdown of the Born–Oppenheimer approximation.