A perturbative approach for the construction of the non-adiabatic nuclear kinetic energy operator for diatomic and triatomic systems

In this work, we derive an effective non-adiabatic kinetic energy operator for nuclear motion in triatomic molecules on the basis of perturbation theory. For this purpose, we extended the approach of Herman and Asgharian (J Mol Spectr 19:305, 1966) originally developed for diatomic systems. General perturbative-type expressions for effective distance-dependent reduced nuclear masses have been obtained for a triatomic system. It is shown that in the diatomic limit our method reproduces correctly the previous known result of Herman and Asgharian.