Role of Overlap between the Discrete State and Pseudocontinuum States in Stabilization Calculations of Metastable States

In a diabatic picture metastable states subject to decay by electron detachment can be viewed as arising from the coupling between a discrete state and a continuum. In treating such states with bound-state quantum chemical methods, the continuum is discretized. In this study, we elucidate the role of overlap in this interaction in the application of the stabilization method to temporary anion states. This is accomplished by use of a minimalist stabilization calculation on the lowest energy l = 2 (D) resonance of the finite spherical well potential using two basis functions, one describing the diabatic discrete state and the other a diabatic discretized continuum state. We show that even such a simple treatment predicts a complex resonance energy in good agreement with the exact result. If the energy of the discrete state is assumed to be constant, which is tantamount to orthogonalizing the discretized continuum state to the discrete state, it is demonstrated that the square of the off-diagonal coupling has a maximum close to the crossing point of the orthogonalized diabatic curves and that the curvature in the coupling is responsible for the complex stationary point associated with the resonance. Moreover, this curvature is a consequence of the overlap between the two diabatic states.

Automated summary

This study elucidates the role of overlap in the interaction between discrete and discretized continuum states in the application of the stabilization method to temporary anion states. The results show that even a simple treatment can predict a complex resonance energy in good agreement with the exact result, and the curvature in the coupling between states is responsible for the complex stationary point associated with the resonance.