Use of bound state methods to calculate partial and total widths of shape resonances.

In this work we study the 2Π resonances of a two-site model system designed to mimic a smooth transition from the 2Πg temporary anion of N2 to the 2Π temporary anion of CO. The model system possesses the advantage that scattering and bound state (L2) methods can be directly compared without obfuscating electron-correlation effects. Specifically, we compare resonance parameters obtained with the complex Kohn variational (CKV) method with those from stabilization, complex absorbing potential, and regularized analytical continuation calculations. The CKV calculations provide p-wave and d-wave widths, the sum of which provides a good approximation of the total width. Then we demonstrate that the width obtained with modified bound state methods depends on the basis set employed: It can be the total width, a partial width, or an ill-defined sum of partial widths. Provided the basis set is chosen appropriately, widths from bound state methods agree well with the CKV results.

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.

A Fresh Look at the Role of the Coupling of a Discrete State with a Pseudocontinuum State in the Stabilization Method for Characterizing Metastable States.

The stabilization method is widely used to theoretically characterize temporary anions and other systems displaying resonances. In this approach, information about a metastable state is encoded in the interaction of a diabatic discrete state and discretized continuum solutions, the energy of which are varied by scaling the extent of the basis set. In this work, we identify the aspects of the coupling between the discrete state and the discretized continuum states that encode information about the existence of complex stationary points and, hence, complex resonance energies in stabilization graphs. This allows us to design a simple two-level model for extracting complex resonance energies from stabilization graphs. The resulting model is applied to the 2Πg anion state of N2.