Dependence of UV–Visible Absorption Characteristics on the Migration Distance and the Hyperconjugation Effect of a Methine Chain

The coumarin-based dyes containing a methine chain have π–π* conjugation and p−π* hyperconjugation effects in electron excitation due to their special conjugated structure. Some of the dye molecules containing a methylene group also have the characteristics of long chain length and large charge transfer distance. The excitation energy of the electron-conjugated system is related to the degree of electron conjugation, but the quantitative relationship is not clear. In some applications where the molecular absorption spectrum needs to be controlled, it is necessary to know the definite relationship between these parameters. In this work, we analyze the excitation characteristics of coumarin-based dye molecules using the natural transition orbital theory. Then, we apply the method of quantum chemistry and wave function analysis to analyze the dependence of the excitation energy on the electron conjugation/hyperconjugation intensity, the charge transfer length, and the charge transfer direction. In our analyses, the natural bond orbital second-order perturbation energy represents the electron conjugation/hyperconjugation intensity; the migration distance represents the degree of the charge transfer length; and the molecular surface electrostatic potential is calculated to analyze the charge transfer direction. Finally, the exponential decay curve of the excitation energy and the second-order perturbation energy dependent on the migration distance are fitted.