A new efficient method for calculation of Frenkel exciton parameters in molecular aggregates

Abstract

The Frenkel exciton Hamiltonian is at the heart of many simulations of excitation energy transfer in molecular aggregates. It separates the aggregate into Coulomb-coupled monomers. Here it is shown that the respective parameters, i.e., monomeric excitation energies and Coulomb couplings between transition densities can be efficiently calculated using time-dependent tight-binding-based density functional theory (TD-DFTB). Specifically, Coulomb couplings are expressed in terms of self-consistently determined Mulliken transition charges. The approach is applied to two dimer systems. First, formaldehyde oxime for which a detailed comparison with standard DFT using the B3LYP and the PBE functionals as well as with SCS-CC2 is provided. Second, the Coulomb coupling is explored in dependence on the intermolecular coordinates for a perylene bisimide dimer. This provides structural evidence for the previously observed biphasic aggregation behavior of this dye.

Exciton–vibrational coupling in the dynamics and spectroscopy of Frenkel excitons in molecular aggregates

“…classical force fields and semiempirical or density functional theory based excitation energies. Recently, it has been proposed to employ selfconsistent charge time-dependent tight-binding density functional theory for this purpose [120]. It provides a single framework for nuclear dynamics and electronic excitation energies, which can be consistently and systematically improved.…”

“…Yet another approach makes use of the Mulliken transition charges that are central in the self-consistent charge tight-binding based density functional theory. Due to efficiency of this method, this formulation of the CC facilitates the treatment of the classical nuclear dynamics and the excitonic coupling on the same footing, even for large systems [120]. While these approaches are based on the separation of the total system into interacting monomers, at least for molecular dimers the supermolecule approach is frequently used.…”

Dissipative Exciton Dynamics in Light-Harvesting Complexes

“…(2.21), can be evaluated, e.g., by employing a transition dipole approximation, assuming that the separation of the monomers is large compared to the spatial extension of the transition density [31]. However, more elaborate methods, such as the transition density cube [5], the transition charge from electrostatic potential method [42], or time-dependent tight-binding-based density functional theory [43], facilitate the calculation of more accurate Coulomb coupling matrix elements.…”

Density-functional tight-binding: basic concepts and applications to molecules and clusters

“…where Ψ m A is the intramolecular excited state on A correlated with the exciton band. Within the DFTB formalism this integral becomes [147,148]…”

“…Electronic excited states of molecular clusters have also been investigated via DFTB-based schemes. The excitation energy transfer in molecular aggregates has been described through a Frenkel Hamiltonian whose parameters are computed from TD-DFTB [147,148,366,367]. The combination of non-adiabatic dynamics with long-range corrected DFTB [200] has been used to simulate the dynamical evolution of excitons in clusters of tetracene [362] and perylene diimides [363].…”