How to Choose a Better Box: Complex Absorbing Potential Optimization for Anionic Resonances

Electronic-structure calculations using complex absorbing potentials (CAPs) to stabilize temporary anion states are very sensitive to the CAP configuration, including the coupling strength (η) and boundary geometry. We present high-resolution surveys of several two-dimensional parameter spaces (CAP spaces for short) for the CO^- (²Π) and N₂^- (²Π_g) resonances and propose an efficient optimization strategy for box-CAPs that relies on Gyamfi and Jagau's ξ error function [J. Chem. Theory Comput. 2024, 20, 1096-1107]. In all CAP spaces probed, only narrow parameter ranges yield the highest-quality results (ξ ∼ 10^-4-10^-5) that minimize wave function reflections and perturbations. Such optimal conditions are unlikely to be found by ad hoc methods, necessitating a systematic optimization protocol. Ours begins with (η, r^o)_L optimization trajectories, where r^o is a geometric variable controlling the CAP boundary and L is a distinct parameter such as the box elongation. Unlike extensively studied η- and r^o-trajectories, the (η, r^o)_L trajectories are optimum-seeking paths in two-dimensional CAP spaces searching for ξ minima. After optimizing CAPs across multiple (η, r^o)_L spaces with varying L, CAP strength minimization along the L-trajectory defines the overall optimal configuration in the higher-dimensional (η, r^o, L) space. This hierarchical optimization, min ξ ≻ min η (where "≻" denotes lexicographic precedence), produces a low-error description of the resonance (min ξ) stabilized by the weakest (but sufficient) CAP possible, i.e., min η subject to the min ξ constraint.