In the framework of DFT, the lowest triplet excited state, T1​, can be
evaluated using multiple formulations, the most straightforward of which are
UDFT and TDDFT. Assuming the exact 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 S1​. Inspired by the optimal tuning
strategy for frontier orbital energies [Stein, Kronik, and Baer, {\it J. Am.
Chem. Soc.} {\bf 2009}, 131, 2818], we proposed a novel and non-empirical
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 hybrid of
PBE and HF functionals [Rohrdanz, Martins, and Herbert, {\it J. Chem. Phys.}
{\bf 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​, ES​, ΔEST​, and
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