Orbital-optimized density functional calculations of molecular Rydberg excited states with real space grid representation and self-interaction correction.

This article focuses on time-independent, variational density functional theory (DFT) calculations of Rydberg excited states in molecules, specifically examining the accuracy of excitation energies predicted by various Kohn–Sham (KS) functionals. Using a direct orbital optimization method on a real space grid combined with the projector augmented-wave (PAW) approach, the study evaluates 31 singlet and triplet Rydberg excitations in ethylene (C₂H₄), formaldehyde (CH₂O), ammonia (NH₃), and water (H₂O). The Perdew–Zunger self-interaction correction (PZ-SIC) applied to the generalized gradient approximation (GGA) PBE functional, especially when combined with complex-valued orbitals, yields excitation energies in remarkable agreement with experimental estimates, outperforming uncorrected PBE and meta-GGA functionals (TPSS and r2SCAN). The work also highlights that commonly used linear combination of atomic orbitals (LCAO) basis sets tend to overestimate excitation energies due to confinement of diffuse Rydberg orbitals, an issue mitigated by the real space grid representation. Overall, the study demonstrates that PZ-SIC with complex orbitals improves the long-range potential description critical for Rydberg states and suggests further testing on larger and more diverse molecular systems.