Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Abstract

Rational design of disordered molecular aggregates and solids for optoelectronic applications relies on our ability to predict the properties of such materials using theoretical and computational methods. However, large molecular systems where disorder is too significant to be considered in the perturbative limit cannot be described using either first principles quantum chemistry or band theory. Multiscale modeling is a promising approach to understanding and optimizing the optoelectronic properties of such systems. It uses first-principles quantum chemical methods to calculate the properties of individual molecules, then constructs model Hamiltonians of molecular aggregates or bulk materials based on these calculations. In this paper, we present a protocol for constructing a tight-binding Hamiltonian that represents the excited states of a molecular material in the basis of Frenckel excitons: electron-hole pairs that are localized on individual molecules that make up the material. The Hamiltonian parametrization proposed here accounts for excitonic couplings between molecules, as well as for electrostatic polarization of the electron density on a molecule by the charge distribution on surrounding molecules. Such model Hamiltonians can be used to calculate optical absorption spectra and other optoelectronic properties of molecular aggregates and solids. Video Link The video component of this article can be found at https://www.jove.com/video/60598/ 13,14 and time-dependent density functional theory (TD-DFT) 15,16. Organic molecules with applications in optoelectronics typically have relatively large π-conjugated systems; many also have donor and acceptor groups. Capturing the correct charge-transfer behavior in such molecules is essential to calculating their optoelectronic properties, but it can only be accomplished using long-range corrected hybrid functionals in TD-DFT 17,18,19,20. Calculations that use such functionals scale super linearly with the size of the system and, at present, they are only practical for modeling the optoelectronic properties of individual organic molecules or small molecular aggregates that can be described using no more thañ 10 4 atomic basis functions. A simulation method that could describe disordered materials that consist of large numbers of chromophores would be very useful for modeling these systems.

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

“…As an alternative to full-aggregate QC calculations, exciton models with different flavors of parametrization protocols have been proposed. [32,[62][63][64][65][66][67][68] Motivated by the need of costeffective approaches providing results of quality comparable to full-aggregate calculations, and inspired by previous pioneering work in which the dimer approach was introduced [57] or used to parametrize exciton Hamiltonians [65] here we propose and test a model Hamiltonian (mH) built on the basis of QC calculations carried out only on the dimers composing the aggregate.…”