  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.
