We develop a formalism to calculate the quasi-particle energy within the GW many-body perturbation correction to the density functional theory (DFT). The occupied and virtual orbitals of the Kohn-Sham (KS) Hamiltonian are replaced by stochastic orbitals used to evaluate the Green function, the polarization potential, and thereby the GW self-energy. The stochastic GW (sGW) relies on novel theoretical concepts such as stochastic time-dependent Hartree propagation, stochastic matrix compression and spatial/temporal stochastic decoupling techniques. Beyond the theoretical interest, the formalism enables linear scaling GW calculations breaking the theoretical scaling limit for GW as well as circumventing the need for energy cutoff approximations. We illustrate the method for silicon nanocrystals of varying sizes with Ne > 3000 electrons.The GW approximation [1, 2] to many-body perturbation theory (MBPT) [3] offers a reliable and accessible theory for quasi-particles (QPs) and their energies [2,[4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], enabling estimation of electronic excitations [19][20][21][22][23][24][25] quantum conductance [26][27][28][29][30] and level alignment in hybrid systems [31,32]. Practical use of GW for large systems is severely limited because of the steep CPU and memory requirements as system size increases. The most computationally intensive element in the GW method, the calculation of the polarization potential (screen Coulomb interaction), involves an algorithmic complexity that scales as the fourth power of the system size [33,34]. Various approaches have been developed to reduce the computational bottlenecks of the GW approach [8,18,23,[33][34][35][36][37]. Despite these advances, GW calculations are still quite expensive for many of the intended applications in the fields of materials science, surface science and nanoscience.In this letter we develop a stochastic, orbital-less, formalism for the GW theory, unique in that it does not reference occupied or virtual orbitals and orbital energies of the KS Hamiltonian. While the approach is inspired by recent developments in electronic structure theory using stochastic orbitals [38][39][40][41][42] it introduces three powerful and basic notions: Stochastic decoupling, stochastic matrix compression and stochastic time-dependent Hartree (sTDH) propagation. The result is a stochastic formulation of GW, where the QP energies become random variables sampled from a distribution with a mean equal to the exact GW energies and a statistical error proportional to the inverse number of stochastic orbitals (iterations, I sGW ).We illustrate the sGW formalism for silicon nanocrystals (NCs) with varying sizes and band gaps [43,44] and demonstrate that the CPU time and memory required by sGW scales nearly linearly with system size, thereby providing means to study QPs excitations in large systems of experimental and technological interest.In the reformulation of the GW approach, we treat the QP energy (ε QP = ω QP ) as a perturbative correction to th...

We develop near-field (NF), a very efficient finite-difference time-dependent (FDTD) approach for simulating electromagnetic systems in the near-field regime. NF is essentially a time-dependent version of the quasistatic frequency-dependent Poisson algorithm. We assume that the electric field is longitudinal, and hence propagates only a set of time-dependent polarizations and currents. For near-field scales, the time step (dt) is much larger than in the usual Maxwell FDTD approach, as it is not related to the velocity of light; rather, it is determined by the rate of damping and plasma oscillations in the material, so dt = 2.5 a.u. was well converged in our simulations. The propagation in time is done via a leapfrog algorithm much like Yee's method, and only a single spatial convolution is needed per time step. In conjunction, we also develop a new and very accurate 8 and 9 Drude-oscillators fit to the permittivity of gold and silver, desired here because we use a large time step. We show that NF agrees with Mie-theory in the limit of small spheres and that it also accurately describes the evolution of the spectral shape as a function of the separation between two gold or silver spheres. The NF algorithm is especially efficient for systems with small scale dynamics and makes it very simple to introduce additional effects such as embedding.

The efficiency of bulk heterojunction (BHJ) organic photovoltaics is sensitive to the morphology of the fullerene network that transports electrons through the device. This sensitivity makes it difficult to distinguish the contrasting roles of local electron mobility (how easily electrons can transfer between neighboring fullerene molecules) and macroscopic electron mobility (how well‐connected is the fullerene network on device length scales) in solar cell performance. In this work, a combination of density functional theory (DFT) calculations, flash‐photolysis time‐resolved microwave conductivity (TRMC) experiments, and space‐charge‐limit current (SCLC) mobility estimates are used to examine the roles of local and macroscopic electron mobility in conjugated polymer/fullerene BHJ photovoltaics. The local mobility of different pentaaryl fullerene derivatives (so‐called ‘shuttlecock’ molecules) is similar, so that differences in solar cell efficiency and SCLC mobilities result directly from the different propensities of these molecules to self‐assemble on macroscopic length scales. These experiments and calculations also demonstrate that the local mobility of phenyl‐C60 butyl methyl ester (PCBM) is an order of magnitude higher than that of other fullerene derivatives, explaining why PCBM has been the acceptor of choice for conjugated polymer BHJ devices even though it does not form an optimal macroscopic network. The DFT calculations indicate that PCBM's superior local mobility comes from the near‐spherical nature of its molecular orbitals, which allow strong electronic coupling between adjacent molecules. In combination, DFT and TRMC techniques provide a tool for screening new fullerene derivatives for good local mobility when designing new molecules that can improve on the macroscopic electron mobility offered by PCBM.

Proton exchange membrane fuel cells (PEMFCs) are promising to become the next generation of energy conversion devices that are efficient, lightweight, and have clean emissions. In these cells, a hydrated polymer membrane acts as an electrolyte layer through which protons travel. Due to the complex nature of the membranes used, the optimization of fuel cell performance is a difficult task, and relies on a number of factors, such as hydration level, polymer side chain length and composition, equivalent weight, morphology, and chemical and mechanical stabilities. Molecular dynamics is a particularly powerful tool for studying PEMs, as it provides the computational efficiency to study length and time scales relevant to these systems. In this review, we present results from several computational papers that use reactive molecular dynamics, which explicitly describe bond breaking and formation, to study proton transport in several polymers commonly used in PEMs. The results presented demonstrate the importance of the interaction between hydronium and the charged side chains and the morphology on the performance of PEM fuel cells.

Modulation of plasmon transport between silver nanoparticles by a yellow fluorophore, tartrazine, is studied theoretically. The system is studied by combining a finite-difference time-domain Maxwell treatment of the electric field and the plasmons with a time-dependent parameterized method number 3 simulation of the tartrazine, resulting in an effective Maxwell∕Schrödinger (i.e., classical∕quantum) method. The modeled system has three linearly arranged small silver nanoparticles with a radius of 2 nm and a center-to-center separation of 4 nm; the molecule is centered between the second and third nanoparticles. We initiate an x-polarized current on the first nanoparticle and monitor the transmission through the system. The molecule rotates much of the x-polarized current into the y-direction and greatly reduces the overall transmission of x-polarized current.