Optimized attenuated interaction: Enabling stochastic Bethe-Salpeter spectra for large systems.

We develop an improved stochastic formalism for the Bethe-Salpeter equation (BSE), based on an exact separation of the effective-interaction W into two parts, W = (W - vW) + vW, where the latter is formally any translationally invariant interaction, vW(r - r'). When optimizing the fit of the exchange kernel vW to W, using a stochastic sampling W, the difference W - vW 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.

Bethe-Salpeter equation spectra for very large systems.

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 time-dependent Hartree propagation, which uses only ten 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 parallelization of the calculation. 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.

Stochastically Realized Observables for Excitonic Molecular Aggregates.

We show that a stochastic approach enables calculations of the optical properties of large 2-dimensional and nanotubular excitonic molecular aggregates. Previous studies of such systems relied on numerically diagonalizing the dense and disordered Frenkel Hamiltonian, which scales approximately as O(N3) for N dye molecules. Our approach scales much more efficiently as O(Nlog(N)), enabling quick study of systems with a million of coupled molecules on the micrometer size scale. We calculate several important experimental observables, including the optical absorption spectrum and density of states, and develop a stochastic formalism for the participation ratio. Quantitative agreement with traditional matrix diagonalization methods is demonstrated for both small- and intermediate-size systems. The stochastic methodology enables the study of the effects of spatial-correlation in site energies on the optical signatures of large 2D aggregates. Our results demonstrate that stochastic methods present a path forward for screening structural parameters and validating experiments and theoretical predictions in large excitonic aggregates.

A fluorogenic aryl fluorosulfate for intraorganellar transthyretin imaging in living cells and in Caenorhabditis elegans.

Fluorogenic probes, due to their often greater spatial and temporal sensitivity in comparison to permanently fluorescent small molecules, represent powerful tools to study protein localization and function in the context of living systems. Herein, we report fluorogenic probe 4, a 1,3,4-oxadiazole designed to bind selectively to transthyretin (TTR). Probe 4 comprises a fluorosulfate group not previously used in an environment-sensitive fluorophore. The fluorosulfate functional group does not react covalently with TTR on the time scale required for cellular imaging, but does red shift the emission maximum of probe 4 in comparison to its nonfluorosulfated analogue. We demonstrate that probe 4 is dark in aqueous buffers, whereas the TTR·4 complex exhibits a fluorescence emission maximum at 481 nm. The addition of probe 4 to living HEK293T cells allows efficient binding to and imaging of exogenous TTR within intracellular organelles, including the mitochondria and the endoplasmic reticulum. Furthermore, live Caenorhabditis elegans expressing human TTR transgenically and treated with probe 4 display TTR·4 fluorescence in macrophage-like coelomocytes. An analogue of fluorosulfate probe 4 does react selectively with TTR without labeling the remainder of the cellular proteome. Studies on this analogue suggest that certain aryl fluorosulfates, due to their cell and organelle permeability and activatable reactivity, could be considered for the development of protein-selective covalent probes.

Sparse-Stochastic Fragmented Exchange for Large-Scale Hybrid Time-Dependent Density Functional Theory Calculations.

We extend our recently developed sparse-stochastic fragmented exchange formalism for ground-state near-gap hybrid DFT to calculate absorption spectra within linear-response time-dependent generalized Kohn-Sham DFT (LR-GKS-TDDFT) for systems consisting of thousands of valence electrons within a grid-based/plane-wave representation. A mixed deterministic/fragmented-stochastic compression of the exchange kernel, here using long-range explicit exchange functionals, provides an efficient method for accurate optical spectra. Both real-time propagation as well as frequency-resolved Casida-equation-type approaches for spectra are presented, and the method is applied to large molecular dyes.

Deterministic/Fragmented-Stochastic Exchange for Large-Scale Hybrid DFT Calculations.

We develop an efficient approach to evaluate range-separated exact exchange for grid- or plane-wave-based representations within the generalized Kohn-Sham-density functional theory (GKS-DFT) framework. The Coulomb kernel is fragmented in reciprocal space, and we employ a mixed deterministic-stochastic representation, retaining long-wavelength (low-k) contributions deterministically and using a sparse ("fragmented") stochastic basis for the high-k part. Coupled with a projection of the Hamiltonian onto a subspace of valence and conduction states from a prior local-DFT calculation, this method allows for the calculation of the long-range exchange of large molecular systems with hundreds and potentially thousands of coupled valence states delocalized over millions of grid points. We find that even a small number of valence and conduction states is sufficient for converging the HOMO and LUMO energies of the GKS-DFT. Excellent tuning of long-range separated hybrids (RSH) is easily obtained in the method for very large systems, as exemplified here for the chlorophyll hexamer of Photosystem II with 1320 electrons.

Exploring the design of superradiant J-aggregates from amphiphilic monomer units.

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. Using the well-studied amphiphilic cyanine dye C8S3 as a template-known to assemble into tubular excitonic aggregates-we synthesize several redshifted variants and study their self-assembly and photophysics. The new pentamethine dyes retain their tubular self-assembly and demonstrate nearly identical bathochromic shifts and lineshapes well into near-infrared wavelengths. However, detailed photophysical analysis finds that the new aggregates show a significant decline in superradiance. Additionally, cryo-TEM reveals that these aggregates readily form short bundles of nanotubes that have nearly half the radii of their trimethine comparators. We employ computational screening to gain intuition on how the structural components of these new aggregates affect their excitonic states, finding that the narrower tubes are able to assemble into a larger number of arrangements, resulting in more disordered aggregates (i.e. less superradiant) with highly similar degrees of redshift.