The optical absorption spectrum of a perylene diimide (PDI) dye in acetonitrile solution is simulated using the recently developed (J. Chem. Theory Comput. 2020, 16, 1215–1231) Ad-MD|gVH method. This mixed quantum-classical (MQC) approach is based on an adiabatic (Ad) separation of soft­(classical)/stiff­(quantum) nuclear degrees of freedom and expresses the spectrum as a conformational average (over the soft coordinates) of vibronic spectra (for the stiff coordinates) obtained through the generalized vertical Hessian (gVH) vibronic approach. The average is performed over snapshots extracted from classical molecular dynamics (MD) runs, performed with a specifically parameterized quantum-mechanically derived force field (QMD-FF). A comprehensive assessment of the reliability of different approaches, designed to reproduce spectral shapes of flexible molecules, is here presented. First, the differences in the sampled configurational space and their consequences on the prediction of the absorption spectra are evaluated by comparing the results obtained by means of the specific QMD-FF and of a general-purpose transferable FF with those of a reference ab initio MD (AIMD) in the gas phase, in both a purely classical scheme (ensemble average) and in the Ad-MD|gVH framework. Next, classical ensemble average and MQC predictions are also obtained for the PDI dynamics in solution and compared with the results of a ″static″ approach, based on vibronic calculations carried out on a single optimized perylene diimide structure. In the classical ensemble average approach, the remarkably different samplings obtained with the two FFs lead to sizeable changes in both position and intensity of the predicted spectra, with the one computed along the QMD-FF trajectory closely matching its AIMD counterpart. Conversely, at the Ad-MD|gVH level of theory, the different samplings deliver very similar vibronic spectra, indicating that the error found in the absorption spectra obtained with the general-purpose FF mainly concerns the stiff modes. In fact, it can be effectively corrected by the quadratic extrapolation performed by gVH to locate the minima of the ground- and excited-state potential energy surfaces along such coordinates. Furthermore, in the perspective of studying the self-assembling process of PDI dyes and the vibronic spectra of large-size aggregates, the use of a molecule-specific QMD-FF also appears mandatory, considering the significant errors found in the GAFF trajectory in the flexible lateral chain populations, which dictate the supramolecular aggregation properties.

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In this contribution we present a mixed quantum-classical dynamical approach for the computation of vibronic absorption spectra of molecular aggregates and their nonadiabatic dynamics, taking into account the coupling between local excitations (LE) and charge-transfer (CT) states. The approach is based on an adiabatic (Ad) separation between the soft degrees of freedom (DoFs) of the system and the stiff vibrations, which are described by the quantum dynamics (QD) of wave packets (WPs) moving on the coupled potential energy surfaces (PESs) of the LE and CT states. These PESs are described with a linear vibronic coupling (LVC) Hamiltonian, parameterized by an overlap-based diabatization on the grounds of time-dependent density functional theory computations. The WPs time evolution is computed with the multiconfiguration time-dependent Hartree method, using effective modes defined through a hierarchical representation of the LVC Hamiltonian. The soft DoFs are sampled with classical molecular dynamics (MD), and the coupling between the slow and fast DoFs is included by recomputing the key parameters of the LVC Hamiltonians, specifically for each MD configuration. This method, named Ad-MD|gLVC, is applied to a perylene diimide (PDI) dimer in acetonitrile and water solutions, and it is shown to accurately reproduce the change in the vibronic features of the absorption spectrum upon aggregation. Moreover, the microscopic insight offered by the MD trajectories allows for a detailed understanding of the role played by the fluctuation of the aggregate structure on the shape of the vibronic spectrum and on the population of LE and CT states. The nonadiabatic QD predicts an extremely fast (∼50 fs) energy transfer between the two LEs. CT states have only a moderate effect on the absorption spectrum, despite the fact that after photoexcitation they are shown to acquire a fast and non-negligible population, highlighting their relevance in dictating the charge separation and transport in PDI-based optical devices.

Effects of aggregation on excited states properties in solution of perylene diimide self-assembled helixlike structures of different size are investigated by means of first principle Density Functional Theory (DFT), Time-Dependent DFT (TD-DFT) and classical Molecular Dynamic (MD) simulations. Excited state analysis based on the 1-particle transition density matrices is then used to study the exciton nature and its delocalization as a function of the thermal motion and aggregate size. Overall the results point to a rather small delocalization of the Frenkel excitonic state even in large aggregates also related to a concerted motion of blocks of 4 monomers along the MD trajectories. Although dynamic effects do not remarkably affect the calculated position and shape of the absorption spectrum, they cause the appearance of several low-energy states of charge transfer character, and hence of weak intensity (dark states), that might be populated along the ultrafast exciton relaxation process potentially influencing the charge separation processes in PDI-sensitized photoactive heterointerfaces.