Chemically accurate and computationally-efficient time-dependent density functional theory (TDDFT) modeling of the UV/Vis spectra of Pechmann dyes and related compounds

The red Pechmann dye 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 trans-endo-fused bicyclic 6-membered lactone dimer (yellow). Both lactones can be singly or doubly amidated with primary amines leading to further color changes. The nature of the core heterocycle (exo- vs endo-), core heteroatom (O vs N) and additional substituents on the phenyl ring allows for exquisite control over color achievable within a single dye family. Herein we present a detailed investigation of modeling of the electronic spectra of the Pechmann dye family by time-dependent density functional theory (TDDFT). Whereas pure Hartree-Fock (HF) ab-initio calculation underestimates the UV/Vis absorption maximum, pure DFT leads to large overestimation. The accuracy of the prediction is highly dependent of 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 use of dispersion interaction-corrected (SMD) implicit solvation model was advantageous compared to the original IEFPCM. The absorption maxima of substituted Pechmann dyes and their rearranged lactone counterparts can be predicted with excellent accuracy (±6nm) at the optimal SCRF=SMD, toluene/TDBMK/DGDZVP//B3LYP/DGDZVP level of theory. Larger deviations were observed for amidated analogs or in more polar solvents (i.e., chloroform)