Addressing the Frenkel and charge transfer character of exciton states with a model Hamiltonian based on dimer calculations: Application to large aggregates of perylene bisimide

Abstract

To understand the influence of interchromophoric arrangements on photoinduced processes and optical properties of aggregates it is fundamental to assess the contribution of local excitations (charge transfer (CT) and Frenkel (FE)), to exciton states. Here we apply a general procedure to analyze the adiabatic exciton states derived from timedependent density functional theory calculations, in terms of diabatic states chosen to coincide with local excitations within a restricted orbital space. In parallel, motivated by the need of cost-effective approaches to afford the study of larger aggregates, we propose to build a model Hamiltonian based on calculations carried out on dimers composing the aggregate. Both approaches are applied to study excitation energy profiles and CT character modulation induced by interchromophore rearrangements in perylene bisimide aggregates up to a tetramer.The dimer-based approach closely reproduces the results of full-aggregate calculations and an analysis in terms of symmetry-adapted diabatic states discloses the effects of CT/FE interactions on the interchange of the H-/J-character for small longitudinal shifts of the chromophores. 1.Introduction.Improvements in material design and fabrication has determined tremendous advances and applications in the field of organic optoelectronic materials. [1-3] Intermolecular interactions, which strongly depend on the packing arrangement, play a key role in determining the photoinduced processes in aggregates of organic chromophores and the control of chromophore's assembly has become a challenging target in supramolecular chemistry. [4-14] A parallel effort in conceptual comprehension of the underlying fundamental physics of photoinduced processes has led to deep advancements in understanding the influence of interchromophoric arrangements on the optical properties of aggregates, [15][16][17] and in modeling the photoinduced relaxation processes leading to excimer formation. [18][19][20]

Impact of Charge-Resonance Excitations on CT-Mediated J-Type Aggregation in Singlet and Triplet Exciton States of Perylene Di-Imide Aggregates: A TDDFT Investigation

“…The protocol employed to analyze the character of exciton states transforms TDDFT amplitudes from the basis of single excitations between the aggregate's orbitals (the delocalized excitation (DE) basis) to the basis of single excitations between molecular site orbitals, the latter defining the diabatic states. It has been previously described [60] and is briefly summarized here. To analyze the exciton character, we express each relevant exciton state in terms of LEs and CTs.…”

“…Perylene-bis(dicarboximide) (PDI) and its derivatives have attracted great interest as chromophores for energy and charge-transport studies, thanks to their propensity to self-organize into ordered assemblies, both in solution and in the solid state via π−πstacking interactions [11,12,58]. Numerous computational investigations on PDI aggregates have been focused on the prediction of exciton states with different quantum-chemical (QC) approaches, including configuration interaction truncated to single excitations (CIS), time-dependent density functional theory (TDDFT) [22,27,46,47,59,60], and highly accurate levels of theory [61][62][63].…”

“…To this end, we analyze exciton states in terms of LE and CT contributions, along the lines described in ref. [60], with three major objectives. First, we validate the protocol of ref.…”

“…[60] by comparing the computed exciton states character (for both singlet and triplet exciton states) with the results obtained from the character-analysis tool, TheoDORE [66]. Second, we show that for triplet exciton states the modulation of CR/FE interactions along the longitudinal translation coordinate determines a switch in the symmetry (A g /B u ) of the lowest triplet exciton state, which corresponds to the unconventional H-/J-character alternation previously documented for singlet excitons [8,9,60]. Finally, we demonstrate that the selection of the functional is less critical for triplet excitons compared to singlet excitons and show that the CAM-B3LYP and ωB97X-D results are very close to each other.…”

Low-Scaling Excited State Calculation Using the Block Interaction Product State

“…Secondly, the accurate derivation of parameter values from quantum chemical calculations is challenging, owing to the co-existence of short-range exchange interactions and long-range Coulomb interactions. [50][51][52] To construct the basis for the excitonic model, a widely used and straightforward strategy hinted by the numerical renormalization group (NRG), 53 is to take the direct product of energetically low-lying local states for each subsystem as the effective bases. This approach is adopted in contractor renormalization group (CORE), 54 active space decomposition method (ASD) 55,56 and renormalization group method (REM), [57][58][59][60][61] where the low-lying states of a system can be expressed as the linear superposition of the effective base configurations, which are the direct products of several energetically low-lying local subsystem wavefunctions.…”