Alternative hyperspherical adiabatic decoupling scheme for tetratomic molecules: quantum two-dimensional study of the ammonia umbrella motion

Abstract

The prototypical example of the inversion of ammonia is studied as an approach to hyperspheric decoupling schemes for tetratomic molecule. We perform two-dimensional calculations including totally symmetric stretching and inversion modes, associated to the hyperradius and an hyperangle. Two adiabatic procedures are employed: the hyperradial one where the hyperangular part is solved to give hyperradial adiabatic curves, and the hyperangular one where the hyperradial part is solved to give hyperangular adiabatic curves. Two methodologies are employed: the hyperquantization algorithm and the finite element method. For completeness a diabatic procedure is also formulated.