This study investigates the extent of \(\pi \) -orbital delocalization in Kohn-Sham (KS) density functional calculations in relation to the KS delocalization error (DE) for different classes of \(\pi \) -conjugated organic molecules. The set of molecules includes conjugated polyenes, Hückel aromatic cyclic polyenes, cyanines, and merocyanines. The DE, as probed by the curvature of the energy E(N) as a function of the electron number N in fractional-electron calculations, causes corresponding trends in the extent of the delocalization of the \(\pi \) orbitals when the latter are chosen to be localized. The DE is assessed in comparison with calculations based on ‘optimally tuned’ functionals with range-separated exchange (OT-RSH) and varying fractions of exact exchange in the short-range limit of the interelectronic separation. The OT-RSH calculations produce negligible E(N) curvature for all tested systems. An interpolation for E(N) proposed in the literature, which only requires integer-N calculations, gives excellent agreement with the fractional-N KS data, with the exception of the longer-chain merocyanines in conjunction with Hartree-Fock calculations. The breakdown of the fractional-electron calculations for the latter cases goes along with a triplet instability of the closed-shell singlet electronic structures.
