Computing decay widths of autoionizing Rydberg states with complex-variable coupled cluster theory

We compute autoionization widths of various Rydberg states of neon and dinitrogen by equation-of-motion coupled-cluster theory combined with complex scaling and complex basis functions. This represents the first time that complex-variable methods are applied to Rydberg states represented in Gaussian basis sets. A new computational protocol based on Kaufmann basis functions is designed to make these methods applicable to atomic and molecular Rydberg states. As a first step, we apply our protocol to the neon atom and computed widths of the $3s$, $3p$, $4p$ and $3d$ Rydberg states. We then proceed to compute the widths of the $3s{\sigma }_g$, $3d{\sigma }_g$, and $3d{\pi }_g$ Rydberg states of dinitrogen, which belong to the Hopfield series. Our results demonstrate a decrease in the decay width for increasing angular momentum and principal quantum number within both Rydberg series.