Excited-state Properties Beyond the Excitation Energy from Orbital-Optimized Density Functional Calculations I: Dipole Moments of Rydberg States

Rydberg excited states are challenging to describe due to their highly diffuse character. Orbital-optimized density functional calculations provide a better description of Rydberg states than time-dependent density functional theory. However, benchmarks have so far focused on the excitation energy, while assessments of dipole moments remain limited to the lowest excited state. Here, orbital-optimized density functional calculations with a plane waves basis set are used to compute the dipole moments of several Rydberg states of a set of molecules. Plane waves provide a flexible representation of the diffuse Rydberg orbitals, revealing limitations of atomic orbitals basis sets. A commonly used single-augmented atomic basis set yields inaccurate dipole moments even when the excitation energy is insensitive to the basis representation, and discrepancies with plane waves calculations persist for the most diffuse states even when extra augmented diffuse functions are added. The generalized gradient approximation functional PBE gives good agreement with higher-level calculations where available. The hybrid functional PBE0 further improves the results, while PBE with globally scaled explicit Perdew-Zunger self-interaction correction leads to larger errors and an overestimation of the dipole moment, despite restoring the correct asymptotic $-1/r$ behavior of the effective Kohn--Sham potential.