A Simplified Spin-Flip Time-Dependent Density Functional Theory Approach for the Electronic Excitation Spectra of Very Large Diradicals

Experimentalists working with diradicals are often facing the question of what kind of species among singlet or triplet diradicals or closed-shell molecules are observed. To treat large diradicals with a high density of electronic states, we propose a simplified version of the spin-flip time-dependent density functional theory (SF-TD-DFT) method for a fast computation of their state energies and absorption spectra with an accuracy similar to the non-simplified scheme. An ultrafast tight-binding variant called SF-sTD-DFT-xTB is also developed to treat even larger systems. For a benchmark set of nine diradicals, good agreement between simplified and conventional SF excitation energies for standard functionals is found. This shows that the proposed parameterization is robust for a wide range of Fock exchange mixing values. With the asymptotically correct response integrals used in SF-sTD-DFT and a correction factor of root 2 for the transition moments, the SF-sTD-DFT/B5050LYP/cc-pVDZ method even outperforms the nonsimplified scheme at drastically reduced computational effort when comparing to the experimental absorption spectra for this set of diradicals. To showcase the actual performance of the method, absorption spectra of two mu-hydroxo-bridged dimers of corrole tape Ga(III) complex derivatives were computed and compared to the experiment, providing good qualitative agreement. Finally, a comparison with the high-spin triplet spectrum of a perylene bisimide biradical and the one determined at the SF-sTD-DFT level showed that at room temperature, mostly triplet diradicals are present in solution.