Accurate First-Principles Calculation of the Vibronic Spectrum of Stacked Perylene Tetracarboxylic Acid Diimides.

π-stacked organic electronic materials are tunable light absorbers with many potential applications in optoelectronics. The optical properties of such molecules are highly dependent on the nature and energy of electron-hole pairs or excitons formed upon light absorption, which in turn are determined by intra- and intermolecular electronic and vibrational excitations. Here, we present a first-principles approach for describing the optical spectrum of stacked organic molecules with strong vibronic coupling. For stacked perylene tetracarboxylic acid diimides, we describe optical excitations by using the time-dependent density functional theory with a Franck-Condon Herzberg-Teller approximation of vibronic effects and validate our approach with comparison to experimental ultraviolet-visible (UV-vis) absorption measurements of solvated model systems. We determine that for larger macromolecules, unlike for single molecules, the sampling of the ground-state potential energy surface significantly influences the optical absorption spectrum. We account for this effect by applying our analysis to ∼100 structures extracted from equilibrated molecular dynamics simulations and averaging the optical spectrum over the entire ensemble. Additionally, we demonstrate that intermolecular electronic coupling within the stacks results in multiple low-energy electronically excited states that all contribute to the optical spectrum. This study provides a computationally feasible recipe for describing the spectroscopic properties of stacked organic chromophores via first-principles density functional theory.