A time-dependent formulation for electron-hole excitations in extended finite systems, based on the Bethe-Salpeter equation (BSE), is developed using a stochastic wave function approach. The time-dependent formulation builds on the connection between time-dependent Hartree-Fock (TDHF) theory and the configuration-interaction with single substitution (CIS) method. This results in a time-dependent Schrödinger-like equation for the quasiparticle orbital dynamics based on an effective Hamiltonian containing direct Hartree and screened exchange terms, where screening is described within the random-phase approximation (RPA). To solve for the optical-absorption spectrum, we develop a stochastic formulation in which the quasiparticle orbitals are replaced by stochastic orbitals to evaluate the direct and exchange terms in the Hamiltonian as well as the RPA screening. This leads to an overall quadratic scaling, a significant improvement over the equivalent symplectic eigenvalue representation of the BSE. Application of the time-dependent stochastic BSE (TDsBSE) approach to silicon and CdSe nanocrystals up to size of  3000 electrons is presented and discussed.

A stochastic approach to time-dependent density functional theory is developed for computing the absorption cross section and the random phase approximation (RPA) correlation energy. The core idea of the approach involves time-propagation of a small set of stochastic orbitals which are first projected on the occupied space and then propagated in time according to the time-dependent Kohn-Sham equations. The evolving electron density is exactly represented when the number of random orbitals is infinite, but even a small number ( 16) of such orbitals is enough to obtain meaningful results for absorption spectrum and the RPA correlation energy per electron. We implement the approach for silicon nanocrystals using real-space grids and find that the overall scaling of the algorithm is sublinear with computational time and memory.

We develop a formalism to calculate the quasiparticle energy within the GW many-body perturbation correction to the density functional theory. The occupied and virtual orbitals of the Kohn-Sham Hamiltonian are replaced by stochastic orbitals used to evaluate the Green function G, the polarization potential W, and, thereby, the GW self-energy. The stochastic GW (sGW) formalism relies on novel theoretical concepts such as stochastic time-dependent Hartree propagation, stochastic matrix compression, and spatial or 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.

Using a combination of density functional theory and quantum master equations approach, we study the effect of electromagnetic (EM) coupling on the nonequilibrium steady-state behavior of a recently introduced gated molecular junction. This junction was demonstrated in a previous publication to exhibit sharp current switching near a certain critical DC field Ez*, which induces intramolecular charge transfer, and here, we analyze the steady-state population and current when an AC EM field (EMF) is present. The AC EMF at frequency $ømega_0$ produces pronounced population and current features at gate fields Ez = Ez* ± $\hbar ømega_0/ez$ (where $e_z$ is the dipole of the charge-transfer state) and thus allows additional sharp switching capability at lower gate fields. We found that even when EMF is absent, the EM coupling itself changes the overall steady-state population and current distributions because it allows for relaxation via spontaneous emission

Density functional theory with optimally tuned range-separated hybrid (OT-RSH) functionals has been recently suggested [Refaely-Abramson et al. Phys. Rev. Lett. 2012, 109, 226405] as a nonempirical approach to predict the outer-valence electronic structure of molecules with the same accuracy as many-body perturbation theory. Here, we provide a quantitative evaluation of the OT-RSH approach by examining its performance in predicting the outer-valence electron spectra of several prototypical gas-phase molecules, from aromatic rings (benzene, pyridine, and pyrimidine) to more complex organic systems (terpyrimidinethiol and copper phthalocyanine). For a range up to several electronvolts away from the frontier orbital energies, we find that the outer-valence electronic structure obtained from the OT-RSH method agrees very well (typically within  0.1–0.2 eV) with both experimental photoemission and theoretical many-body perturbation theory data in the GW approximation. In particular, we find that with new strategies for an optimal choice of the short-range fraction of Fock exchange, the OT-RSH approach offers a balanced description of localized and delocalized states. We discuss in detail the sole exception found—a high-symmetry orbital, particular to small aromatic rings, which is relatively deep inside the valence state manifold. Overall, the OT-RSH method is an accurate DFT-based method for outer-valence electronic structure prediction for such systems and is of essentially the same level of accuracy as contemporary GW approaches, at a reduced computational cost.

We study the role of the effective mass, band mixing, and phonon emission on multiexciton generation in IV–VI nanocrystals. A four-band k · p effective mass model, which allows for an independent variation of these parameters, is adopted to describe the electronic structure of the nanocrystals. Multiexciton generation efficiencies are calculated using a Green’s function formalism, providing results that are numerically similar to impact excitation. We find that multiexciton generation efficiencies are maximized when the effective mass of the electron and hole are small and similar. Contact with recent experimental results for multiexciton generation in PbS and PbSe is made.

A fast stochastic method for calculating the second order Møller-Plesset (MP2) correction to the correlation energy of large systems of electrons is presented. The approach is based on reducing the exact summation over occupied and unoccupied states to a time-dependent trace formula amenable to stochastic sampling. We demonstrate the abilities of the method to treat systems with thousands of electrons using hydrogen passivated silicon spherical nanocrystals represented on a real space grid, much beyond the capabilities of present day MP2 implementations.

A fast method is developed for calculating the random phase approximation (RPA) correlation energy for density functional theory. The correlation energy is given by a trace over a projected RPA response matrix, and the trace is taken by a stochastic approach using random perturbation vectors. For a fixed statistical error in the total energy per electron, the method scales, at most, quadratically with the system size; however, in practice, due to self-averaging, it requires less statistical sampling as the system grows, and the performance is close to linear scaling. We demonstrate the method by calculating the RPA correlation energy for cadmium selenide and silicon nanocrystals with over 1500 electrons. We find that the RPA correlation energies per electron are largely independent of the nanocrystal size. In addition, we show that a correlated sampling technique enables calculation of the energy difference between two slightly distorted configurations with scaling and a statistical error similar to that of the total energy per electron.

We develop an alternative formulation in the energy-domain to calculate the second order Møller–Plesset (MP2) perturbation energies. The approach is based on repeatedly choosing four random energies using a nonseparable guiding function, filtering four random orbitals at these energies, and averaging the resulting Coulomb matrix elements to obtain a statistical estimate of the MP2 correlation energy. In contrast to our time-domain formulation, the present approach is useful for both quantum chemistry and real-space/plane wave basis sets. The scaling of the MP2 calculation is roughly linear with system size, providing a useful tool to study dispersion energies in large systems. This is demonstrated on a structure of 64 fullerenes within the SZ basis as well as on silicon nanocrystals using real-space grids.

A stochastic method is developed to calculate the multiexciton generation (MEG) rates in semiconductor nanocrystals (NCs). The numerical effort scales near-linearly with system size allowing the study of MEG rates up to diameters and exciton energies previously unattainable using atomistic calculations. Illustrations are given for CdSe NCs of sizes and energies relevant to current experimental setups, where direct methods require treatment of over 1011 states. The approach is not limited to the study of MEG and can be applied to calculate other correlated electronic processes.

Systematically varying the optical gap that is associated with charge-transfer excitations is an important step in the design of light-harvesting molecules. So far the guidance that time-dependent density functional theory could give in this process was limited by the traditional functionals' inability to describe charge-transfer excitations. We show that a nonempirical range-separated hybrid approach allows to reliably predict charge-transfer excitations for molecules of practically relevant complexity. Calculated absorption energies agree with measured ones. We predict from theory that by varying the number of thiophenes in donor-acceptor-donor molecules, the energy of the lowest optical absorption can be tuned to the lower end of the visible spectrum. Saturation sets in at about five thiophene rings. (C) 2011 American Institute of Physics. [doi:10.1063/1.3581788]

We present a broadly applicable, physically motivated, first-principles approach to determining the fundamental gap of finite systems from single-electron orbital energies. The approach is based on using a range-separated hybrid functional within the generalized Kohn-Sham approach to density functional theory. Its key element is the choice of a range-separation parameter such that Koopmans’ theorem for both neutral and anion is obeyed as closely as possible. We demonstrate the validity, accuracy, and advantages of this approach on first, second and third row atoms, the oligoacene family of molecules, and a set of hydrogen-passivated silicon nanocrystals. This extends the quantitative usage of density functional theory to an area long believed to be outside its reach.

We develop a generalized framework based on a Green’s function formalism to calculate the efficiency of multiexciton generation in nanocrystal quantum dots. The direct/indirect absorption and coherent/incoherent impact ionization mechanisms, often used to describe multiexciton generation in nanocrystals, are reviewed and rederived from the unified theory as certain approximations. In addition, two new limits are described systematically – the weak Coulomb coupling limit and the semi-wide band limit. We show that the description of multiexciton generation in nanocrystals can be described as incoherent process and we discuss the scaling of multiexciton generation with respect to the photon energy and nanocrystal size. Illustrations are given for three prototype systems: CdSe, InAs and silicon quantum dots.

We address recent experiments (Science 2009, 325, 1367) reporting on highly efficient multiplication of electron?hole pairs in carbon nanotube photodiodes at photon energies near the carrier multiplication threshold (twice the quasi-particle band gap). This result is surprising in light of recent experimental and theoretical work on multiexciton generation in other confined materials, such as semiconducting nanocrystals. We propose a detailed mechanism based on carrier dynamics and impact excitation resulting in highly efficient multiplication of electron?hole pairs. We discuss the important time and energy scales of the problem and provide analysis of the role of temperature and the length of the diode.

Density functional theory (DFT) with semilocal functionals such as the local-density and generalized gradients approximations predicts that the dissociative adsorption of oxygen on Al (111) goes through without a barrier in stark contradiction to experimental findings. This problem motivated our study of the reaction of oxygen colliding with a small aluminum cluster Al-5. We found semilocal functionals predict a minute barrier to sticking, associated with smeared long-range charge transfer from the metal to the oxygen. Hybrid B3LYP predicts a larger barrier while the range-separated the Baer-Neuhauser-Livshits (BNL, Phys. Chem. Chem. Phys. 2007, 9, 2932.) functional finds a more prominent barrier. BNL predicts short-ranged and more abrupt charge transfer from the surface to the oxygen. We conclude that spurious self-repulsion inherent in semilocal functionals causes early electron-transfer, long-range attraction toward the surface and low reaction barriers for these systems. The results indicate that the missing DFT barrier for O-2 sticking on Al (111) may be due to Spurious self-repulsion.

We developed a method for calculating the ground-state properties and fundamental band-gaps of solids, using a generalized Kohn-Sham approach combining a local density approximation (LDA) functional with a long-range explicit exchange orbital functional. We found that when the range parameter is selected according to the formula gamma = A/(epsilon(infinity) (epsilon) over tilde) where epsilon(infinity) is the optical dielectric constant of the solid and (epsilon) over tilde = 0.84 and A = 0.216 a(0)(-1), predictions of the fundamental band-gap close to the experimental values are obtained for a variety of solids of different types. For most solids the range parameter g is small (i.e. explicit exchange is needed only at long distances) so the predicted values for lattice constants and bulk moduli are similar to those based on conventional LDA calculations. Preliminary calculations on silicon give a general band structure in good agreement with experiment.

It has been known for quite some time that approximate density functional (ADF) theories fail disastrously when describing the dissociative symmetric radical cations R2+. By considering this dissociation limit, previous work has shown that Hartree-Fock (HF) theory favors the R+1-R-0 charge distribution, whereas DF approximations favor the R+(0.5)-R+0.5. Yet, general quantum mechanical principles indicate that both these (as well as all intermediate) average charge distributions are asymptotically energy degenerate. Thus, HF and ADF theories mistakenly break the symmetry but in a contradicting way. In this letter, we show how to construct system-dependent long-range corrected (LC) density functionals that can successfully treat this class of molecules, avoiding the spurious symmetry breaking. Examples and comparisons to experimental data is given for R = H, He, and Ne, and it is shown that the new LC theory improves considerably the theoretical description of the R-2(+) bond properties, the long-range form of the asymptotic potential curve, and the atomic polarizability. The broader impact of this finding is discussed as well, and it is argued that the widespread semiempirical approach which advocates treating the LC parameter as a system-independent parameter is in fact inappropriate under general circumstances.

Electron dynamics in metallic clusters are examined using a time-dependent density functional theory that includes a “memory term,” i.e., attempts to describe temporal nonlocal correlations. Using the Iwamoto, Gross, and Kohn exchange-correlation XC kernel, we construct a translationally invariant memory action from which an XC potential is derived that is translationally covariant and exerts zero net force on the electrons. An efficient and stable numerical method to solve the resulting Kohn-Sham equations is presented. Using this framework, we study memory effects on electron dynamics in spherical jellium gold clusters. We find memory significantly broadens the surface plasmon absorption line, yet considerably less than measured in real gold clusters, attributed to the inadequacy of the jellium model. Memory effects on nonlinear spectroscopy are studied as well: a real-time pump-probe setup is used to study the temporal decay profile of the plasmon, finding a fast decay followed by slower tail; and in high harmonic generation, we show that memory narrows and redshifts emission lines.

An iterative approach for calculating the frequency domain linear response of molecular systems within time-dependent density-functional theory is presented. The method completely avoids computing the exchange-correlation kernel which is typically the most expensive step for large systems. In particular, virtual orbitals are not needed. This approach may be useful for treating the response of large systems. We give an outline of the theory and a demonstration on a jellium model of an elliptic gold cluster. A detailed theory is appended discussing the computation of conductance and ac impedance of molecular junctions under bias.

Today, most application of time-dependent density functional theory (TDDFT) use adiabatic exchange- correlation (XC) potentials that do not take into account non-local temporal effects. Incorporating such "memory" terms into XC potentials is complicated by the constraint that the derived force and torque densities must integrate to zero at every instance. This requirement can be met by deriving the potentials from an XC action that is Galilean in-variant (GI). We develop a class of simple but flexible forms for an action that respect these constraints. The basic idea is to formulate the action in terms of the Eularian-Lagrangian transformation (ELT) metric tensor, which is itself GI. The general form of the XC potentials in this class is then derived and the linear response limit is derived as well.