We develop a stochastic formulation of the optimally tuned range-separated hybrid density functional theory that enables significant reduction of the computational effort and scaling of the nonlocal exchange operator at the price of introducing a controllable statistical error. Our method is based on stochastic representations of the Coulomb convolution integral and of the generalized Kohn–Sham density matrix. The computational cost of the approach is similar to that of usual Kohn–Sham density functional theory, yet it provides a much more accurate description of the quasiparticle energies for the frontier orbitals. This is illustrated for a series of silicon nanocrystals up to sizes exceeding 3000 electrons. Comparison with the stochastic GW many-body perturbation technique indicates excellent agreement for the fundamental band gap energies, good agreement for the band edge quasiparticle excitations, and very low statistical errors in the total energy for large systems. The present approach has a major advantage over one-shot GW by providing a self-consistent Hamiltonian that is central for additional postprocessing, for example, in the stochastic Bethe–Salpeter approach.

We examine the possibility of using a Metropolis algorithm for computing the exchange energy in a large molecular system. Following ideas set forth in a recent publication (Baer, Neuhauser, and Rabani, Phys. Rev. Lett. 111, 106402 (2013)) we focus on obtaining the exchange energy per particle (ExPE, as opposed to the total exchange energy) to a predefined statistical error and on determining the numerical scaling of the calculation achieving this. For this we assume that the occupied molecular orbitals (MOs) are known and given in terms of a standard Gaussian atomic basis set. The Metropolis random walk produces a sequence of pairs of three-dimensional points (x,x′), which are distributed in proportion to ρ(x,x′)2, where ρ(x,x′) is the density matrix. The exchange energy per particle is then simply the average of the Coulomb repulsion energy υC(|x–x′|) over these pairs. To reduce the statistical error we separate the exchange energy into a short-range term that can be calculated deterministically in a linear scaling fashion and a long-range term that is treated by the Metropolis method. We demonstrate the method on water clusters and silicon nanocrystals showing the magnitude of the ExPE standard deviation is independent of system size. In the water clusters a longer random walk was necessary to obtain full ergodicity as Metropolis walkers tended to get stuck for a while in localized regions. We developed a diagnostic tool that can alert a user when such a situation occurs. The calculation effort scales linearly with system size if one uses an atom screening procedure that can be made numerically exact. In systems where the MOs can be localized efficiently the ExPE can even be computed with “sublinear scaling” as the MOs themselves can be screened.

We propose a general theme, labeled mechanical electrodynamics, where the relative three-dimensional (3-D) orientation of particles with nontrivial geometries is tracked based on the details of the absorption spectrum beyond a one-dimensional (1-D) distance dependence. Specifically, we simulate absorption spectra of a subwavelength denture-like nanostructure with freely moving parts. The nanodentures are made of two gold nanoarches that either open and close or rotate about a single arch base (hinge rotation). We show how the absorption spectrum for the nanodentures changes depending on orientation and position. There is a ∼0.1–0.2 eV shift in absorbance peak frequencies as the denture closes, corresponding to an increased coupling between the two gold arches, while a hinge rotation results in a depletion of one absorbance peak (1.48 eV) with the simultaneous emergence of a new absorbance peak at lower frequencies (0.88 eV). The unique spectral signature of each position and orientation of the nanodentures points to a variety of applications. One will be experimentally tracking and measuring orientation and position of plasmonic-coupled nanoparticles using simple methods such as UV–vis or IR spectral analysis. Additionally, the denture structure will tune in and out of different plasmon resonance frequencies, or turn “on and off,” depending on its orientation. The simulations were performed efficiently by the recent near-field (NF) approach, which is a time-dependent Poisson algorithm that shares a lot of the machinery of full-fledged Maxwell equations but allows for much larger time steps and therefore can treat large systems.

The low-lying excited states (La and Lb) of polyacenes from naphthalene to heptacene (N = 2–7) are studied using various time-dependent computational approaches. We perform high-level excited-state calculations using equation of motion coupled cluster with singles and doubles (EOMCCSD) and completely renormalized equation of motion coupled cluster with singles, doubles, and perturbative triples (CR-EOMCCSD(T)) and use these results to evaluate the performance of various range-separated exchange-correlation functionals within linear-response (LR) and real-time (RT) time-dependent density functional theories (TDDFT). As has been reported recently, we find that the range-separated family of functionals addresses the well-documented TDDFT failures in describing these low-lying singlet excited states to a large extent and are as about as accurate as results from EOMCCSD on average. Real-time TDDFT visualization shows that the excited state charged densities are consistent with the predictions of the perimeter free electron orbital (PFEO) model. This corresponds to particle-on-a-ring confinement, which leads to the well-known red-shift of the excitations with acene length. We also use time-dependent semiempirical methods like TD-PM3 and TD-ZINDO, which are capable of handling very large systems. Once reparametrized to match the CR-EOMCCSD(T) results, TD-ZINDO becomes roughly as accurate as range-separated TDDFT, which opens the door to modeling systems such as large molecular assemblies.

We present density functional theory (DFT) and time-dependent DFT (TD-DFT) study of the structures and electronic spectra of small CdSe nanocluster-adenine complexes CdnSen−adenine (n = 3, 6, 10, 13). We examine the changes in the geometries and excitation spectra of the nanoclusters induced by DNA base-binding. By comparing the results calculated for the bare (CdnSen), hydrogen-passivated (CdnSenH2n), as well as the corresponding adenine (Ade)-bound clusters (CdnSen−Ade, CdnSenH2n−Ade, CdnSenH2n−2−Ade), we find that binding with Ade slightly blue-shifts (up to 0.18 eV) the electronic excitations of bare nanoclusters but strongly red-shifts (<1.2 eV) those of hydrogen-passivated nanoclusters. Natural bond orbital analysis shows that the LUMO of CdnSenH2n−Ade is a π* orbital located on the purine ring.

We use Hückel theory to examine interference effects on conductance of a wire when a `lollypop' side-chain is bonded to it, acting as a resonance cavity. A clear signature of interference is found at these ballistic conducting systems, stronger in small systems. Gating effects are enhanced by the presence of the loop, where the electronic wavefunctions can experience large changes in phase. Using an `interference index', I=mod(S,2)+mod(L,4), where S,L are stick and loop lengths, respectively, we conclude that interference is constructive (destructive) and conductance high (low) when I=0,4(I=2).