Assessment of the time correlation function-based approach for absorption spectrum calculations using time-dependent density functional theory and molecular dynamics simulations

Electronic spectra, including absorption spectra, provide crucial insight into the electronic properties of molecular systems. Single-point excited-state calculations using quantum chemical (QC) methods, such as time-dependent density functional theory, can predict peak positions and their intensities of the spectra; however, these methods are inherently incapable of capturing spectral broadening effects. Herein, we present a comprehensive assessment of an approach based on time correlation functions (TCFs) that enables the computational prediction of spectra, including broadening effects, by integrating QC calculations with classical molecular dynamics simulations. We systematically compared the absorption spectral shapes calculated using five levels of TCF-based spectral formulas, including the second-order cumulant approach, which are hierarchically related through successive approximations. To evaluate the applicability of the TCF-based approach, we selected two small organic pigment molecules, 3,4,5,6-tetrachlorofluorescein (FLU) and crystal violet (CST), as test cases. By assessing the impact of different approximations on the predicted spectral shapes, we found that for FLU, all approximation levels yielded comparable results, whereas for CST, certain approximations led to significant deviations. These discrepancies may be caused by rapid fluctuations of transition dipole moments in CST, which has a flexible molecular skeleton, in contrast to FLU, which has a relatively rigid structure. In addition, using Kubo's stochastic theory allowed us to investigate the relationship between the timescale of molecular fluctuations and spectral broadening. Our analysis confirms that molecular rigidity plays a critical role in determining the accuracy of spectral shape predictions.