Computational Quantification of the Zwitterionic/Quinoid Ratio of Phenolate Dyes for Their Solvatochromic Prediction

Solvatochromic dyes are utilized in various chemical and biological media as chemical sensors. Unfortunately, there is no simple way to predict the type of solvatochromism based on the structure of the dye alone, which restricts their design and synthesis. The most important family of solvatochromic sensors, pyridinium phenolate dyes, has the strongest solvatochromism. Using a natural population analysis (NPA) of the natural bond orbitals (NBO) of the phenolate group in the frontier molecular orbitals, it is possible to calculate the relative polarity of the ground state and excited state and, thus to develop a model that can predict the three types of solvatochromism observed for this family: negative, positive, and inverted. This methodology has been applied to thirteen representative examples from the literature. Our results demonstrate that the difference in the electron density of the phenolate moiety in the frontier molecular orbitals is a simple and inexpensive theoretical indicator for calculating the relative polarity of the ground and excited states of a representative library of pyridinium phenolate sensors, and thus predicting their solvatochromism. Comparing the results with the bond length alternation (BLA) and bond order alternation (BOA) indices showed that the NPA/NBO method is a better way to predict solvatochromic behavior.