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 ²Π_g 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.