Time-dependent density functional theory (TDDFT) modelling of Pechmann dyes: from accurate absorption maximum prediction to virtual dye screening.

The red Pechmann dye (λ(max) = 550 nm) is the exo-dimer of 4-phenyl-3-butenolide connected at the α-carbon by a double bond in a trans-fashion. The ring system is easily rearranged to the trans-endo-fused bicyclic 6-membered lactone dimer (yellow). Both lactones can be singly or doubly amidated with primary amines leading to further colour changes. The nature of the core heterocycle (exo- vs. endo-; 5- or 6-membered ring), core heteroatom (O vs. N) and additional substituents on the phenyl ring allows for exquisite control over colour achievable within a single dye family. Herein we present a detailed investigation of the modelling of the electronic spectra of the Pechmann dye family by time-dependent density functional theory (TDDFT). Whereas pure Hartree-Fock (TDHF) ab-initio calculation underestimates the UV/Vis absorption maximum, pure TDDFT leads to a large overestimation. The accuracy of the prediction is highly dependent on the mix of HF and DFT, with BMK (42% HF) and M06-2X (54% HF) giving the closest match with the experimental value. Among all basis sets evaluated, the computationally-efficient, DFT-optimized DGDZVP showed the best chemical accuracy/size profile. Finally, the dispersion interaction-corrected (SMD) implicit solvation model was found to be advantageous compared to the original IEFPCM. The absorption maxima of substituted Pechmann dyes and their rearranged lactone counterparts can be predicted with excellent accuracy (±6 nm) at the optimal SMD(toluene)/TD-BMK/DGDZVP//SMD(toluene)B3LYP/DGDZVP level of theory. Using this procedure, a small virtual library of novel, heterocycle-substituted Pechmann dyes were screened. Such substitution was shown to be a viable strategy for colour tuning, giving λ(max) from 522 (4-pyridyl) to 627 (2-indolyl) nm.