A long-range-corrected density functional that performs well for both ground-state properties and time-dependent density functional theory excitation energies, including charge-transfer excited states

Abstract

We introduce a hybrid density functional that asymptotically incorporates full Hartree–Fock exchange, based on the long-range-corrected exchange-hole model of Henderson et al. [J. Chem. Phys. 128, 194105 (2008)]. The performance of this functional, for ground-state properties and for vertical excitation energies within time-dependent density functional theory, is systematically evaluated, and optimal values are determined for the range-separation parameter, ω, and for the fraction of short-range Hartree–Fock exchange. We denote the new functional as LRC-ωPBEh, since it reduces to the standard PBEh hybrid functional (also known as PBE0 or PBE1PBE) for a certain choice of its two parameters. Upon optimization of these parameters against a set of ground- and excited-state benchmarks, the LRC-ωPBEh functional fulfills three important requirements: (i) It outperforms the PBEh hybrid functional for ground-state atomization energies and reaction barrier heights; (ii) it yields statistical errors comparable to PBEh for valence excitation energies in both small and medium-sized molecules; and (iii) its performance for charge-transfer excitations is comparable to its performance for valence excitations. LRC-ωPBEh, with the parameters determined herein, is the first density functional that satisfies all three criteria. Notably, short-range Hartree–Fock exchange appears to be necessary in order to obtain accurate ground-state properties and vertical excitation energies using the same value of ω.