Analytical treatment of the quadratic and nonrelativistic Renner-Teller effect for a triatomic molecule in a Π electronic state

Abstract

This work presents the first analytical approach to the Renner-Teller effect from a quantal viewpoint, and deals with a linear triatomic molecule in a Π electronic state within the harmonic oscillator approach, ignoring the spin-orbit coupling. A proper integral transformation permits us to obtain from this 2-dimensional and two-channel vibronic problem a second order ordinary differential equation in the complex plane that is very useful for analytical work. For large energies this equation is of the singular perturbation type and has been solved by means of the matched asymptotic expansions method. The energy splittings at the Fermi resonance points were then determined and, taking into account earlier semiclassical results, it has also been possible to formulate a reasonably good quantization condition for the vibronic energy levels.