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

In the framework of density functional theory (DFT), the lowest triplet excited state (T 1 ) 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 T 1 ( E T ), 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 T 1 and the lowest singlet excited state (S 1 ). 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 E T 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 E T, the optical band gap ( E S ), the singlet–triplet gap (Δ E ST ), 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.