On the multiple solutions of the complex absorbing potential method for resonances

The complex absorbing potential (CAP) method is an effective approach to model anionic resonances. However, the existing optimization criteria for the CAP strength give rise to multiple solutions, and the common practice has been to pick a single one as describing the resonant state and to discard the rest as unphysical. Here, we challenge this view by demonstrating that several solutions can be acceptable approximations for the resonance. This ambiguity introduces an important source of uncertainty in CAP calculations that we show to be generally larger than the errors stemming from the basis set incompleteness and the approximate electronic structure method, affecting energies and properties alike. Moreover, various strategies that have been proposed to mitigate the appearance of multiple solutions are shown to be ineffective, like enlarging the basis set, subtracting the energy contribution from the CAP, and introducing a real perturbative potential. Although the CAP method has proven merits in the description of anionic resonances, the existence of multiple solutions emerges as a critical and unsolved problem.