Operatorization and Unitary Transformation Approaches to Product Jahn--Teller Problems

The product Jahn--Teller (JT) system with two doubly-degenerate electronic open shells coupling to a single e-mode is studied using an operatorization approach followed by unitary transformation. It is found that the structure of the adiabatic potential energy surface can give anyone of the two different troughs based on the coupling constants, and the symmetry of the product JT system EoplusE can be decomposed into EoplusA₁oplus A₂. The present approach is conceptually simple and can be extended to other product JT systems.