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

TL;DR

This paper introduces a non-empirical 'triplet tuning' method for constructing exchange-correlation functionals in density functional theory, ensuring UDFT and TDDFT agree on triplet excitation energies, leading to improved predictions for challenging systems.

Contribution

It proposes a novel triplet tuning approach for creating exchange-correlation functionals that enforce consistency between UDFT and TDDFT for triplet states without relying on experimental data.

Findings

TT-ωPBEh outperforms existing functionals in predicting excitation energies

Triplet tuning improves accuracy for spectroscopic and photochemical properties

Method applicable to challenging molecular systems

Abstract

In the framework of DFT, the lowest triplet excited state, T$_1$, 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 T$_1$ ($E_{\rm T}$), 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 S$_1$. 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 $E_{\rm T}$ 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-$\omega$PBEh, 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-$\omega$PBEh manages to provide more accurate predictions for key spectroscopic and photochemical observables, including but not limited to $E_{\rm T}$, $E_{\rm S}$, $\Delta E_{\rm ST}$, 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.