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Excitonic chromophore aggregates have wide-ranging applicability in fields such as imaging and energy harvesting; however their rational design requires adapting principles of self-assembly to the requirements of excited state coupling.

We review a suite of stochastic vector computational approaches for studying the electronic structure of extended condensed matter systems. These techniques help reduce algorithmic complexity, facilitate efficient parallelization, simplify computational tasks, accelerate calculations, and diminish memory requirements. While their scope is vast, we limit our study to ground-state and finite temperature density functional theory (DFT) and second-order many-body perturbation theory. More advanced topics, such as quasiparticle (charge) and optical (neutral) excitations and higher-order processes, are covered elsewhere. We start by explaining how to use stochastic vectors in computations, characterizing the associated statistical errors. Next, we show how to estimate the electron density in DFT and discuss effective techniques to reduce statistical errors. Finally, we review the use of stochastic vectors for calculating correlation energies within the second-order Møller-Plesset perturbation theory and its finite temperature variational form. Example calculation results are presented and used to demonstrate the efficacy of the methods.

We develop an improved stochastic formalism for the Bethe-Salpeter equation, based on an exact separation of the effective-interaction $W$ to two parts, $W=(W-v_W)+v_W$ where the latter is formally any translationally-invariant interaction $v_W(r-r')$. When optimizing the fit of $v_W$ exchange kernel to $W$, by using a stochastic sampling of $W$, the difference $W-v_W$ becomes quite small. Then, in the main BSE routine, this small difference is stochastically sampled. The number of stochastic samples needed for an accurate spectrum is then largely independent of system size. While the method is formally cubic in scaling, the scaling prefactor is small due to the constant number of stochastic orbitals needed for sampling $W$., 9 pages, 5 figures, 2 tables

Plasmonic nano-objects have shown great potential in enhancing applications like biological/chemical sensing, light harvesting and energy transfer, and optical/quantum computing. Therefore, an extensive effort has been vested in optimizing plasmonic systems and exploiting their field enhancement properties. Super-resolution imaging with quantum dots (QDs) is a promising method to probe plasmonic near-fields but is hindered by the distortion of the QD radiation pattern. Here, we investigate the interaction between QDs and "L-shaped" gold nanoantennas and demonstrate both theoretically and experimentally that this strong interaction can induce polarization-dependent modifications to the apparent QD emission intensity, polarization, and localization. Based on FDTD simulations and polarization-modulated single-molecule microscopy, we show that the displacement of the emitter's localization is due to the position-dependent interference between the emitter and the induced dipole, and can be up to 100 nm. Our results help pave a pathway for higher precision plasmonic near-field mapping and its underlying applications.

We develop the gapped-filtering method, whereby a short Chebyshev expansion accurately represents the density-matrix operator. The method optimizes the Chebyshev coefficients to give the correct density matrix at all energies except within the gapped region where there are no eigenstates. Gapped filtering reduces the number of required terms in the Chebyshev expansion compared to traditional expansion methods, as long as one knows or can determine efficiently the HOMO and LUMO positions. The reduction is especially noticeable (factors of 2-3) when high accuracy is sought. To exemplify the method, we use gapped-filtering to increase the efficiency of stochastic-GW calculations., Comment: 8 pages, 6 figures

We present a highly efficient method for the extraction of optical properties of very large molecules via the Bethe-Salpeter equation. The crutch of this approach is the calculation of the action of the effective Coulombic interaction, $W$, through a stochastic TD Hartree propagation, which uses only 10 stochastic orbitals rather than propagating the full sea of occupied states. This leads to a scaling that is at most cubic in system size, with trivial MPI parallelization. We apply this new method to calculate the spectra and electronic density of the dominant excitons of a carbon-nanohoop bound fullerene system with 520 electrons, using less than 4000 core hours., 6 pages, 3 figures, communication

Molecular aggregates with long-range excitonic couplings have drastically different photophysical properties compared to their monomer counterparts. From Kasha's model for one-dimensional systems, positive or negative excitonic couplings lead to blue or red-shifted optical spectra with respect to the monomers, labeled H-and J-aggregates, respectively. The overall excitonic couplings in higher dimensional systems are much more complicated and cannot be simply classified from their spectral shifts alone. Here, we provide a unified classification for extended 2D aggregates using temperature dependent peak shifts, thermal broadening, and quantum yields. We discuss the examples of six 2D aggregates with J-like absorption spectra but quite drastic changes in quantum yields and superradiance. We find the origin of the differences is, in fact, a different excitonic band structure where the bright state is lower energy than the monomer but still away from the band edge. We call this an “I-aggregate.” Our results provide a description of the complex excitonic behaviors that cannot be explained solely on Kasha's model. Furthermore, such properties can be tuned with the packing geometries within the aggregates providing supramolecular pathways for controlling them. This will allow for precise optimizations of aggregate properties in their applications across the areas of optoelectronics, photonics, excitonic energy transfer, and shortwave infrared technologies.