  For accurate ab initio description of Rydberg excited states the study
suggests generating the appropriate diffuse basis functions by a cheap
variational optimization of virtual orbitals of the corresponding ion core. By
following this approach, dozens of converged correlated lithium Rydberg states,
namely all the states up to 24S, 25P, 14D, 16F and 16G, not yet achieved by
other ab initio approaches, could be obtained at the EOM-CCSD level of theory
with compact and mostly state-selective contracted Gaussian basis sets. Despite
its small size and Gaussian character, the optimized basis leads to highly
accurate excitation energies that differ merely in the order of meV from the
reference state-of-the-art explicitly correlated Gaussian method and even
surpass Full-CI results on Slater basis by an order of magnitude.
