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Density functional calculations of Rydberg excited states up to high energyare carried out for several molecules using an approach where the orbitals arevariationally optimized by converging on saddle points on the electronic energysurface within a real space grid representation. Remarkably good agreement withexperimental estimates of the excitation energy is obtained using thegeneralized gradient approximation (GGA) functional of Perdew, Burke andErnzerhof (PBE) when Perdew-Zunger self-interaction correction is applied incombination with complex-valued orbitals. Even without the correction, the PBEfunctional gives quite good results despite the fact that corresponding Rydbergvirtual orbitals have positive energy in the ground state calculation. Resultsobtained using the TPSS and r2SCAN meta-GGA functionals are also presented, butthey do not provide a systematic improvement over the results from theuncorrected PBE functional. The grid representation combined with the projectoraugmented-wave approach gives a simpler and better representation of thediffuse Rydberg orbitals than a linear combination of atomic orbitals withcommonly used basis sets, the latter leading to an overestimation of theexcitation energy due to confinement of the excited states.

Orbital-optimized Density Functional Calculations of Molecular Rydberg  Excited States with Real Space Grid Representation and Self-Interaction  Correction