Estimation of maximum absorption wavelength of polymethine dyes in visible and near-infrared region based on time-dependent density functional theory

Highlights: • The maximum absorption wavelength (${\lambda }_{\max }$) is an important property in the design of dyes. • We calculated (${\lambda }_{\max }$) of 70 polymethine dyes using TD-DFT with various XC functionals. • We confirmed a strong correlation between the calculated (${\lambda }_{\max }$) with experimental ones. • The largest $R^2$ was obtained using M06-2X functional ($R^2=0.985$). • Topological descriptors are useful in categorization of dyes. -- Abstract: Polymethine dyes have been utilized in various applications, including optical functional materials. The maximum absorption wavelength (${\lambda }_{\max }$) of polymethine dyes is the key for designing optical functional materials. However, there have been few theoretical studies on ${\lambda }_{\max }$, especially in the near-infrared region. Therefore, using time-dependent density functional theory (TD-DFT), we calculated the excited states of 70 polymethine dyes with ${\lambda }_{\max }$ ranging in the visible-to-near infrared region. We also compared these calculated ${\lambda }_{\max }$ values with experimental ones, using linear regression analysis, and confirmed a strong correlation between the experimental and theoretical ${\lambda }_{\max }$ values when the portion of the Hartree-Fock exchange in exchange–correlation functionals is relatively high. Linear regression analysis revealed that the experimental ${\lambda }_{\max }$ values of the polymethine dyes can be quantitatively estimated by combining the TD-DFT calculations with the regression curves. Although several polymethine dyes may exhibit different behaviors at ${\lambda }_{\max }$, we could categorize these dyes into a few groups and estimate their excitation energies using regression curves suitable for the respective groups.