Precise estimation method for electronic absorption of metalloporphyrin dye molecules based on phenomenological formulation

Molecular electronic absorption is the most important property that determines the optical behavior and functions of molecules. However, accurate estimation of molecular electronic absorption using theoretical calculations is difficult for relatively large molecules, such as organic dyes and pigments, even at a substantial computational cost. Consequently, it is determined through experimental trial-and-error and empirical guesswork. Development of a unified rule and a practical formula for electronic absorption would enable easier, faster, and more accurate prediction of molecular electronic absorption through direct linkage between such an experimental science and emerging data-driven science. Using porphyrin complexes as a typical dye molecule, this study is the first to demonstrate the concept of a phenomenological formulation for the precise estimation of their electronic absorption. Systematic spectrophotometric analysis of porphyrins in the same environmental condition showed that the spectral parameters associated with wavenumbers and extinction coefficients exhibit a linear or near-linear relationship with various structural factors. By formulating photophysical parameters based on these rules, we identify a new spectral factor as a single function and successfully represent the electronic absorption of porphyrins as a simple formula, which we believe will help in predicting unknown dye molecules and bridging established empirical rules with modern data-driven science.