First and second derivative of the wave function of the1Σ+states of the KH molecule

Abstract

First and second derivative of the nonadiabatic coupling between the several ${}^{1}\ensuremath{\Sigma}{}^{+}$ adiabatic states of the KH molecule considered from accurate diabatic and adiabatic data have been evaluated. 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 present many peaks related to ionic-neutral and neutral-neutral coupling between the ${}^{1}\ensuremath{\Sigma}{}^{+}$ 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 KH molecule. The second adiabatic correction has been determined using the virial theorem. The first adiabatic correction was added to the adiabatic potential energy curves to redetermine 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 $D$ ${}^{1}\ensuremath{\Sigma}{}^{+}$ states of the KH molecule. A shift of some 10 cm${}^{\ensuremath{-}1}$ is observed for some vibrational levels showing the breakdown of the Born-Oppenheimer approximation.