Singlet–triplet (S0 → T1) excitation energies of the [4 × n] rectangular graphene nanoribbon series (n = 2–6): A comparative theoretical study

Singlet–triplet (S0 → T1) well-to-well (WWES–T) and vertical (VES–T) excitation energies of the [4 × n] rectangular graphene nanoribbon series (n = 2–6) were estimated using various semiempirical, Hartree–Fock (HF), density functional (DFT), and second order Moller–Plesset perturbation theory methods with the assumption of a closed-shell singlet state. Significant model chemistry dependent variability in theoretically obtained WWES–T/VES–T is evident for the rectangular graphene nanoribbons. With the exception of the B2PLYP density functional (which, along with the mPW2PLYP functional, combines exact HF exchange with an MP2-like correlation to the DFT calculation), all DFT, semiempirical, and HF methods investigated predict the onset of a negative WWES–T/VES–T (ground state triplet) starting somewhere between the [4 × 3] through [4 × 6] derivatives, with most functionals predicting a transition from a singlet to triplet ground state between the [4 × 4] and [4 × 5] rectangular graphene nanoribbons. Consistent with previous work on the n-acene series, MP2 WWES–T/VES–T estimates have a significant positive systematic bias and HF estimates have substantial negative systematic biases. Extrapolation of the B2PLYP results, which are in excellent agreement with prior FPA-QZ VES–T estimates, for any [m × n] rectangular graphene nanoribbon derivatives predicts a vanishingly small singlet–triplet gap at the polymeric limit (m → ∞ and/or n → ∞).