Theoretical analysis of the solvatochromism of organic dyes differing by the conjugation sequence

Absorption peak maxima of two organic dyes differing by the position of the methine unit differ by 61 nm in dioxane and by up to 139 nm in polar solvents. It was previously reported that the difference is not reproduced by time-dependent density functional theory (TDDFT) using ab initio or hybrid functionals. TDDFT errors are different between the molecules, leading to a qualitative failure of TDDFT to predict relative energetics of the dyes. We focus on the effect of polar solvents (acetonitrile, DMSO, methanol, and 2-propanol) on the absorption spectrum, specifically, on the different between the two molecules sign of the solvatochromic shift versus dioxane. Using the correction due to Peach et al., the absolute TDDFT errors can be brought within acceptable ranges of 0.2 to 0.3 eV, and the blue shift versus dioxane is reproduced, although both dyes are predicted to exhibit positive solvatochromism. The inclusion of explicit solvent molecules did not appreciably change either TDDFT energies or the correction term. These results show that in dye design by changing the conjugation order, computational errors are expected to be more important than in the case of an extension of the size of conjugation, especially when polar solvents are used.