A comparison of density functional theory (DFT) methods for estimating the singlet–triplet (S 0–T 1) excitation energies of benzene and polyacenes

Abstract

Singlet–triplet (S 0–T 1) well-to-well (WWE S–T) and adiabatic (AE S–T) excitation energies of benzene and the linear polyacenes naphthalene through decacene were estimated using a range of density functional theory (DFT) methods and basis sets along with the assumption of a closed-shell singlet state. Via single exponential decay regression based extrapolations to the polymeric limit, significant variability in theoretically obtained WWE S–T/AE S–T predicted for longer polyacenes is evident that is primarily dependent on the model chemistry employed, with minor variations due to basis set incompleteness and zero-point energy (ZPE) corrections. With the exception of the B2PLYPD density functional (which, along with the mPW2PLYPD functional, combines exact HF exchange with an MP2-like correlation to the DFT calculation), all DFT methods investigated predict a negative WWE S–T/AE S–T (ground state triplet) at the polymer limit, with most functionals predicting a transition from a singlet to triplet ground state between octacene and decacene. Extrapolation of the B2PLYPD results predicts a vanishingly small singlet–triplet gap at the polymeric limit for an infinitely long homolog. Hartree–Fock calculations significantly underestimate the polyacene WWE S–T/AE S–T, whereas MPn methods overestimate the singlet–triplet gap but display a convergence toward experimental values with increasing truncation order and substitutions. The B2PLYPD and mPW2PLYPD functionals appear to balance the WWE S–T/AE S–T underestimating tendency of HF/DFT methods for longer polyacenes against the propensity for MPn methods to overestimate the WWE S–T/AE S–T for these compounds, and predict all acenes from benzene through decacene will be ground state singlets with positive singlet–triplet gaps.