Triplet Tuning: A Novel Family of Non-Empirical Exchange–Correlation Functionals

Abstract

In the framework of density functional theory (DFT), the lowest triplet excited state (T1) can be evaluated using multiple formulations, the most straightforward of which are unrestricted density functional theory (UDFT) and time-dependent density functional theory (TDDFT). Assuming the exact exchange–correlation (XC) functional is applied, UDFT and TDDFT provide identical energies for T1 (ET), which is also a constraint that we require our XC functionals to obey. However, this condition is not satisfied by most of the popular XC functionals, leading to inaccurate predictions of low-lying, spectroscopically and photochemically important excited states, such as T1 and the lowest singlet excited state (S1). Inspired by the optimal tuning strategy for frontier orbital energies [T. Stein, L. Kronik, and R. Baer, J. Am. Chem. Soc. 2009, 131, 2818], we proposed a novel and nonempirical prescription of constructing an XC functional in which the agreement between UDFT and TDDFT in ET is strictly enforced. Referred to as “triplet tuning”, our procedure allows us to formulate the XC functional on a case-by-case basis, using the molecular structure as the exclusive input, without fitting to any experimental data. The first triplet tuned XC functional, TT-ωPBEh, is formulated as a long-range-corrected (LRC) hybrid of Perdew–Burke–Ernzerhof (PBE) and Hartree–Fock (HF) functionals [M. A. Rohrdanz, K. M. Martins, and J. M. Herbert, J. Chem. Phys. 2009, 130, 054112] and tested on four sets of large organic molecules. Compared to existing functionals, TT-ωPBEh manages to provide more accurate predictions for key spectroscopic and photochemical observables, including but not limited to ET, the optical band gap (ES), the singlet–triplet gap (ΔEST), and the vertical ionization potential (I⊥), as it adjusts the effective electron–hole interactions to arrive at the correct excitation energies. This promising triplet tuning scheme can be applied to a broad range of systems that were notorious in DFT for being extremely challenging