Impact of the Kohn-Sham delocalization error on organic $$\pi $$-conjugated systems

Abstract This study investigates the extent of $$\pi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>π</mml:mi> </mml:math> -orbital delocalization in Kohn-Sham (KS) density functional calculations in relation to the KS delocalization error (DE) for different classes of $$\pi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>π</mml:mi> </mml:math> -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 $$\pi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>π</mml:mi> </mml:math> 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.