D matrix analysis of the Renner-Teller effect: An accurate three-state diabatization for NH₂

Some time ago we published our first article on the Renner-Teller (RT) model to treat the electronic interaction for a triatomic molecule [J. Chem. Phys. 124, 081106 (2006)]. The main purpose of that Communication was to suggest considering the RT phenomenon as a topological effect, just like the Jahn-Teller phenomenon. However, whereas in the first publication we just summarized a few basic features to support that idea, here in the present article, we extend the topological approach and show that all the expected features that characterize a three (multi) state RT-type'3 system of a triatomic molecule can be studied and analyzed within the framework of that approach. This, among other things, enables us to employ the topological D matrix [Phys. Rev. A 62, 032506 (2000)] to determine, a priori, under what conditions a three-state system can be diabatized. The theoretical presentation is accompanied by a detailed numerical study as carried out for the HNH system. The D-matrix analysis shows that the two original electronic states ²A₁ and ²B₁ (evolving from the collinear degenerate II doublet), frequently used to study this Renner-Teller-type system, are insufficient for diabatization. This is true, in particular, for the stable ground-state configurations of the HNH molecule. However, by including just one additional electronic state - a B state (originating from a collinear ∑ state) - it is found that a rigorous, meaningful three-state diabatization can be carried out for large regions of configuration space, particularly for those, near the stable configuration of NH₂. This opens the way for an accurate study of this important molecule even where the electronic angular momentum deviates significantly from an integer value.