Accurate excitation energies of molecules and oligomers from a semilocal density functional.

Excitation energy plays an important role in energy conversion, biological processes, and optical devices. In this work, we apply the Tao-Mo (TM) nonempirical meta-generalized gradient approximation and the combination TMTPSS (TMx + TPSSc), with TPSSc being the correlation part of the original TPSS (Tao-Perdew-Staroverov-Scuseria) to study excitation energies of small molecules and oligomers. Our test set consists of 17 molecules with 134 total excited states, including singlet, triplet, valence, and Rydberg excited states. Our calculation shows that both the TMTPSS and TM functionals yield good overall performance, with mean absolute errors (MAEs) of 0.37 eV and 0.42 eV, respectively, outperforming commonly used semilocal functionals LSDA (MAE = 0.55 eV), PBE (MAE = 0.58 eV), and TPSS (MAE = 0.47 eV). In particular, TMTPSS can yield nearly the same accuracy of B3LYP (MAE = 0.36 eV), with lower computational cost. The accuracy for semilocal density functional theory continues to hold for conjugated oligomers, but they become less accurate than hybrid functionals, due to the insufficient nonlocality.