The Simulation of Solvent Polarizabilities and Dipolarities with Polarizable Continuum Model

The ability of polarizable continuum models (PCM) to simulate nonspecific solvent effects (dipolarity and polarizability) was evaluated by calculating the transition energies of 1,1,10,10-tetrabutyldecanonaene (ttbp9) and 2-N,N-dimethylamino-7-nitrofluorene (DMANF), basis of Catalán's polarizability (SP) and dipolarity (SdP) solvent scales, respectively. Time-dependent density-functional theory (TD-DFT) calculations were performed at different levels of theory, employing four basis sets in 10 different solvents, covering the full range of the normalized SP and SdP scales. Transition energies were calculated using linear response (LR) and corrected linear response (cLR²) schemes. Although these methods yielded variable mean absolute errors, the LR-PCM calculations reproduced medium polarizability and dipolarity trends. While calculated ttbp9 transition energies correlated with SP and Laurence's dispersion-induced (DI) scales, the DMANF transition energies correlated poorly with SdP or Laurence's ES dipolarity scales. This result agrees with the fact that DMANF solvatochromism is "contaminated" by solvent polarizability and HB acidity. The incorporation of SP or DI contributions led to much better (r² > 0.95) correlations with the DMANF-calculated transitions. The results offer a clearer picture of the limitations of continuum models in simulating the behavior of solvatochromic dyes in solution by pointing out their poor performance when specific solvent effects, such as hydrogen-bond interactions, play a significant role in their solvatochromism.