Improvement on Van Vleckʹs formula for diatomic nonadiabatic energy shifts

A formula ΔEivJ ≈ 〈vJ|[2m(EivJ − UJi)B2ij + (dBij/dR)2]/ΔUij|vJ〉/m2, where m is the reduced molecular mass, Bij = 〈i|∂/∂R|j〉 is the radial nonadiabatic coupling matrix element for two interactive electronic states i and j, and ΔUij = UJi(R) − UJj(R) is the difference in the corresponding effective adiabatic internuclear potentials, is offered to approximate a nonadiabatic shift of the rovibronic term EivJ arising from regular homogeneous perturbations in diatomic molecules. The formula has been numerically tested for B 1Σ+u, B′ 1Σ+u, C1Πu and D 1Πu states of molecular hydrogen. It is demonstrated that the present approximation is more accurate than the original Van Vleck formula for high v-values and has a high efficiency for nondiagonal systems with significant continuum contribution.