Unraveling Excitonic Effects for the First Hyperpolarizabilities of Chromophore Aggregates

Excitonic interactions often significantly affect the optoelectronic properties of molecular materials. However, their role in determining the nonlinear optical response of organic electro-optic materials remains poorly understood. In this paper, we explore the effects of excitonic interactions on the first hyperpolarizability for aggregates of donor–acceptor chromophores. We show that calculations of the first hyperpolarizabilty of chromophore aggregates based on a two-state model agree well with the more rigorous coupled perturbed Hartree–Fock method. We then use both time-dependent density functional theory calculations and the molecular exciton approximation to parametrize the two-state model. Use of the molecular exciton approximation to the two-state model (i) is appropriate for disordered aggregates (unlike band theory), (ii) is computationally efficient enough for calculating the first hyperpolarizability of materials that consist of thousands of interacting chromophores, and (iii) allows the unraveling of the effects of both excitonic interactions and electrostatic polarization of the chromophore electron density by its environment on the first hyperpolarizability of molecular materials. We find that use of the molecular exciton approximation to the two-state model does not introduce significant additional errors compared to those introduced by applying the two-state model alone. We determine that the absolute change to the first hyperpolarizability of chromophore aggregates due to excitonic interactions increases with the size of the aggregate. For all sizes of disordered aggregates of chromophores considered in this paper, the inclusion of excitonic interactions on average decreases the magnitude of the first hyperpolarizability by 12–14% compared to the case of non-interacting chromophores. Finally, we present a method for analytically calculating the first hyperpolarizability of a one-dimensional periodic array of chromophores within the molecular exciton approximation to the two-state model. This technique can be used to include an approximate correction for excitonic effects when simulating the electro-optic response of disordered and ordered organic materials.