Thousands Of Electrons Research Articles

Stochastic Resolution of Identity to CC2 for Large Systems: Ground State and Triplet Excitation Energy Calculations.

An implementation of stochastic resolution of identity to the CC2 (sRI-CC2) ground state energy followed by triplet excitation energy calculations is presented. A set of stochastic orbitals is introduced to further decouple the expensive 4-index electron repulsion integrals on the basis of RI approximation. A Laplace transformation of the orbital energy difference denominators into numerical summations is adopted to obtain a third-order overall scaling. We select a series of hydrogen dimer chains with nearly thousands of electrons, as well as some other molecules, for sRI-CC2 energies and test the accuracy and time consumption in comparison with those of RI-CC2. Our sRI-CC2 results reproduce a modest agreement with the RI-CC2 in Q-Chem program package and it allows a steep scaling reduction from O(N5) to O(N3). Besides, the unrestricted sRI-CC2 calculations also fit well with the restricted results. Thus, our sRI-CC2 implementation of ground state energy and triplet excitation energy provides a cost-efficient alternative approach, especially for some large-sized systems.

Stochastic Resolution of Identity to CC2 for Large Systems: Excited State Properties.

We apply a stochastic resolution of identity approximation (sRI) to the CC2 method for the excitation energy calculations. A set of stochastic orbitals are employed to decouple the crucial 4-index electron repulsion integrals and optimize the contraction steps in CC2 response theory. The CC2 response for excitations builds upon sRI-CC2 ground-state calculations, which scales as O(N3), where N is a measure for the system size. Overall, the current algorithm for excited states also allows a sharp scaling reduction from original O(N5) to O(N3). We test the sRI-CC2 for different molecular systems and basis sets, and we show that our sRI-CC2 method can accurately reproduce the results of the deterministic CC2 approach. Our sRI-CC2 exhibits an experimental scaling of O(N2.59) for a series of olefin chains, allowing us to calculate systems with nearly thousands of electrons.

Beyond Single-Reference Fixed-Node Approximation in Ab Initio Diffusion Monte Carlo Using Antisymmetrized Geminal Power Applied to Systems with Hundreds of Electrons.

Diffusion Monte Carlo (DMC) is an exact technique to project out the ground state (GS) of a Hamiltonian. Since the GS is always bosonic, in Fermionic systems, the projection needs to be carried out while imposing antisymmetric constraints, which is a nondeterministic polynomial hard problem. In practice, therefore, the application of DMC on electronic structure problems is made by employing the fixed-node (FN) approximation, consisting of performing DMC with the constraint of having a fixed, predefined nodal surface. How do we get the nodal surface? The typical approach, applied in systems having up to hundreds or even thousands of electrons, is to obtain the nodal surface from a preliminary mean-field approach (typically, a density functional theory calculation) used to obtain a single Slater determinant. This is known as single reference. In this paper, we propose a new approach, applicable to systems as large as the C60 fullerene, which improves the nodes by going beyond the single reference. In practice, we employ an implicitly multireference ansatz (antisymmetrized geminal power wave function constraint with molecular orbitals), initialized on the preliminary mean-field approach, which is relaxed by optimizing a few parameters of the wave function determining the nodal surface by minimizing the FN-DMC energy. We highlight the improvements of the proposed approach over the standard single-reference method on several examples and, where feasible, the computational gain over the standard multireference ansatz, which makes the methods applicable to large systems. We also show that physical properties relying on relative energies, such as binding energies, are affordable and reliable within the proposed scheme.

A multi-GPU implementation of Real-Time Time-Dependent Auxiliary Density Functional Theory for the investigation of nanosystems irradiations

We report a new Multi-GPU (Graphical Processor Unit) implementation of real-time time-dependent Auxiliary Density Functional Theory (DFT) for simulations of attosecond electronic dynamics in molecular systems subjected to strong perturbations. Our code relies on the Kohn-Sham formalism of DFT and has been implemented in the deMon2k Fortran code. We expand single-particle wave functions (i.e molecular orbitals) as linear combinations of Gaussian-type-orbitals centered on atoms. The density matrix propagation is carried out on GPU while the Kohn-Sham potential is operated on CPUs (Central Processor Unit) with the help of variationally fitted densities. We propose a parallelization strategy using the MAGMA/CUDA libraries to calculate the exponential of dense Hermitian matrices entering the mathematical definition of the propagator, here using Taylor expansions. We report performance benchmarks on water droplets and on fullerenes (C50 to C540). They show a clear advantage of GPU over CPU (using the Scalapack library). The benchmarks also show the benefit of using more than one GPU for systems comprised of up to more than 10,000 basis functions. There, a speed-up of almost 40 between pure 40 CPU and four 4 GPU is obtained. Attosecond electron dynamics simulation in molecular systems comprised of several thousands of electrons becomes amenable to routine simulations in our code. We assess the accuracy of the GPU implementation considering various applications, namely, the calculation of extreme UV absorption spectra with non-Hermitian dynamics, the response of C180 to an electric perturbation, and finally the irradiation of a DNA/protein complex by a 0.4 MeV proton. The results demonstrate the robustness of the implementation. This work also paves the way for future even more efficient implementations. Program SummaryProgram title: deMon2k-RT-TDDFTCPC Library link to program files: https://doi.org/10.17632/whwc5zkst5.1Developer's repository link: DOI: 10.5281/zenodo.8301468Licensing provisions: CeCILL Free Software License Agreement v2.1Programming language: FortranExternal routines/libraries: MPI, BLAS/LAPACK, CUDA, MAGMASupplementary material: User manual, installation instructions, test cases. Nature of problem: Electron dynamics within molecular systems is amenable to simulation with Real-Time Time-Dependent Density Functional Theory (RT-TD-DFT). The methodology consists in propagating on the attosecond time scale the single particle electronic wave functions on the underlying Kohn-Sham potential [1,2]. In deMon2k-RT-TDDFT, the propagation is coupled to the Auxiliary DFT framework for fast evaluation of the potential [3]. A remaining computational bottleneck is the matrix exponential calculation of the Hermitian Hamiltonian matrix. This task is achieved in deMon2k via diagolanization or expansions formulas (Taylor, Chebychev or Baker-Campbell-Hausdorff). The operation is cumbersome on central-processor-unit machines for large matrices (e.g. > 5000 × 5000), which corresponds to molecular systems comprising around 2,000 electrons. Alternatives are needed to overcome this bottleneck.Solution method: We propose to carry out the matrix exponentiation on graphical-processor-units thanks to the MAGMA[4]/CUDA libraries. The code permits a drastic reduction of the computational cost, opening the attosecond dynamic simulations of large molecular systems comprised thousands of electrons with controlled accuracy. The method is tested here for Taylor expansions. Additional comments including restrictions and unusual features: The code described in this article opens the realization of RT-TD-ADFT simulations. The code is linked to the Master version 6.1.6 of deMon2k (http://www.demon-software.com), which must be pre-installed by the user.

Quantum-classical hybrid algorithm for the simulation of all-electron correlation.

While chemical systems containing hundreds to thousands of electrons remain beyond the reach of quantum devices, hybrid quantum-classical algorithms present a promising pathway toward a quantum advantage. Hybrid algorithms treat the exponentially scaling part of the calculation-the static correlation-on the quantum computer and the non-exponentially scaling part-the dynamic correlation-on the classical computer. While a variety of algorithms have been proposed, the dependence of many methods on the total wave function limits the development of easy-to-use classical post-processing implementations. Here, we present a novel combination of quantum and classical algorithms, which computes the all-electron energy of a strongly correlated molecular system on the classical computer from the 2-electron reduced density matrix (2-RDM) evaluated on the quantum device. Significantly, we circumvent the wave function in the all-electron calculations by using density matrix methods that only require input of the statically correlated 2-RDM. Although the algorithm is completely general, we test it with two classical density matrix methods, the anti-Hermitian contracted Schrödinger equation (ACSE) and multiconfiguration pair-density functional theories, using the recently developed quantum ACSE method for simulating the statically correlated 2-RDM. We obtain experimental accuracy for the relative energies of all three benzyne isomers and thereby demonstrate the ability of the developed algorithm to achieve chemically relevant and accurate results on noisy intermediate-scale quantum devices.

Nano-photoluminescence of natural anyon molecules and topological quantum computation

The proposal of fault-tolerant quantum computations, which promise to dramatically improve the operation of quantum computers and to accelerate the development of the compact hardware for them, is based on topological quantum field theories, which rely on the existence in Nature of physical systems described by a Lagrangian containing a non-Abelian (NA) topological term. These are solid-state systems having two-dimensional electrons, which are coupled to magnetic-flux-quanta vortexes, forming complex particles, known as anyons. Topological quantum computing (TQC) operations thus represent a physical realization of the mathematical operations involving NA representations of a braid group Bn, generated by a set of n localized anyons, which can be braided and fused using a “tweezer” and controlled by a detector. For most of the potential TQC material systems known so far, which are 2D-electron–gas semiconductor structure at high magnetic field and a variety of hybrid superconductor/topological-material heterostructures, the realization of anyon localization versus tweezing and detecting meets serious obstacles, chief among which are the necessity of using current control, i.e., mobile particles, of the TQC operations and high density electron puddles (containing thousands of electrons) to generate a single vortex. Here we demonstrate a novel system, in which these obstacles can be overcome, and in which vortexes are generated by a single electron. This is a ~ 150 nm size many electron InP/GaInP2 self-organized quantum dot, in which molecules, consisting of a few localized anyons, are naturally formed and exist at zero external magnetic field. We used high-spatial-resolution scanning magneto-photoluminescence spectroscopy measurements of a set of the dots having five and six electrons, together with many-body quantum mechanical calculations to demonstrate spontaneous formation of the anyon magneto-electron particles (eν) having fractional charge ν = n/k, where n = 1–4 and k = 3–15 are the number of electrons and vortexes, respectively, arranged in molecular structures having a built-in (internal) magnetic field of 6–12 T. Using direct imaging of the molecular configurations we observed fusion and braiding of eν-anyons under photo-excitation and revealed the possibility of using charge sensing for their control. Our investigations show that InP/GaInP2 anyon-molecule QDs, which have intrinsic transformations of localized eν-anyons compatible with TQC operations and capable of being probed by charge sensing, are very promising for the realization of TQC.

Correlated Double-Electron Additions at the Edge of a Two-Dimensional Electronic System.

We create laterally large and low-disorder GaAs quantum-well-based quantum dots that act as small two-dimensional electron systems. We monitor tunneling of single electrons to the dots by means of capacitance measurements and identify single-electron capacitance peaks in the addition spectrum from occupancies of one up to thousands of electrons. The data show two remarkable phenomena in the Landau level filling factor range ν=2 to ν=5 in selective probing of the edge states of the dot: (i)Coulomb blockade peaks arise from the entrance of two electrons rather than one; (ii)at and near ν=5/2 and at fixed gate voltage, these double-height peaks appear uniformly in a magnetic field with a flux periodicity of h/2e, but they group into pairs at other filling factors.

Electron-Hole Correlations Govern Auger Recombination in Nanostructures.

The fast nonradiative decay of multiexcitonic states via Auger recombination is a fundamental process affecting a variety of applications based on semiconductor nanostructures. From a theoretical perspective, the description of Auger recombination in confined semiconductor nanostructures is a challenging task due to the large number of valence electrons and exponentially growing number of excited excitonic and biexcitonic states that are coupled by the Coulomb interaction. These challenges have restricted the treatment of Auger recombination to simple, noninteracting electron-hole models. Herein we present a novel approach for calculating Auger recombination lifetimes in confined nanostructures having thousands to tens of thousands of electrons, explicitly including electron-hole interactions. We demonstrate that the inclusion of electron-hole correlations are imperative to capture the correct scaling of the Auger recombination lifetime with the size and shape of the nanostructure. In addition, correlation effects are required to obtain quantitatively accurate lifetimes even for systems smaller than the exciton Bohr radius. Neglecting such correlations can result in lifetimes that are two orders of magnitude too long. We establish the utility of the new approach for CdSe quantum dots of varying sizes and for CdSe nanorods of varying diameters and lengths. Our new approach is the first theoretical method to postdict the experimentally known "universal volume scaling law" for quantum dots and makes novel predictions for the scaling of the Auger recombination lifetimes in nanorods.

Simple eigenvalue-self-consistent .

We show that a rigid scissors-like GW self-consistency approach, labeled here , can be trivially implemented at zero additional cost for large scale one-shot G 0 W 0 calculations. The method significantly improves one-shot G 0 W 0 and for large systems is very accurate. is similar in spirit to evGW 0 where the self-consistency is only applied on the eigenvalues entering Green's function, while both W and the eigenvectors of Green's function are held fixed. further assumes that the shift of the eigenvalues is rigid scissors-like so that all occupied states are shifted by the same amount and analogously for all the unoccupied states. We show that this results in a trivial modification of the time-dependent G 0 W 0 self-energy, enabling an a posteriori self-consistency cycle. The method is applicable for our recent stochastic-GW approach, thereby enabling self-consistent calculations for giant systems with thousands of electrons. The accuracy of increases with the system size. For molecules, it is up to 0.4-0.5 eV away from coupled-cluster single double triple (CCSD(T)), but for tetracene and hexacene, it matches the ionization energies from both CCSD(T) and evGW 0 to better than 0.05 eV. For solids, as exemplified here by periodic supercells of semiconductors and insulators with 6192 valence electrons, the method matches evGW 0 quite well and both methods are in good agreement with the experiment.

Characterizing subpixel spatial resolution of a hybrid CMOS detector

Soft x-rays (0.1 to 10 keV) will liberate between tens and thousands of electrons from the absorber array of a depleted silicon detector. These electrons tend to diffuse outward into what is referred to as the charge cloud, which is then picked up by several pixels and forms a specific pattern based on the exact incident location of the x-ray. By performing the first ever application of a “mesh experiment” on a hybrid CMOS detector (HCD), we have experimentally determined the charge cloud shape and used it to perform subpixel localization of incident x-rays on a photon-by-photon basis for a custom 36-μm pixel pitch H2RG HCD. We find that significant spatial resolution improvement is possible for all events, with 68% confidence regions equal to 7.1 × 7.1, 0.4 × 7.1, and 0.4 × 0.4 μm for 1-pixel, 2-pixel, and 3- to 4-pixel events, respectively. This represents a much finer resolution than that provided by containment within a single pixel.

Modeling Plasmon-Induced Hot-Carrier Transfer

In this issue of Chem , Zhang et al. use first-principle simulations (i.e., no empirically adjustable parameters) to elucidate the detailed mechanisms of plasmon-induced hot-carrier transfer at a heterojunction interface between a plasmonic gold nanomaterial and a semiconductor. Together with earlier work by Long and Prezhdo, this study shows how the donor-acceptor interaction at the interface determines the mechanism by which plasmonic excitations lead to hot-electron transfer at interfaces.

Two-Level Chebyshev Filter Based Complementary Subspace Method: Pushing the Envelope of Large-Scale Electronic Structure Calculations.

We describe a novel iterative strategy for Kohn-Sham density functional theory calculations aimed at large systems (>1,000 electrons), applicable to metals and insulators alike. In lieu of explicit diagonalization of the Kohn-Sham Hamiltonian on every self-consistent field (SCF) iteration, we employ a two-level Chebyshev polynomial filter based complementary subspace strategy to (1) compute a set of vectors that span the occupied subspace of the Hamiltonian; (2) reduce subspace diagonalization to just partially occupied states; and (3) obtain those states in an efficient, scalable manner via an inner Chebyshev filter iteration. By reducing the necessary computation to just partially occupied states and obtaining these through an inner Chebyshev iteration, our approach reduces the cost of large metallic calculations significantly, while eliminating subspace diagonalization for insulating systems altogether. We describe the implementation of the method within the framework of the discontinuous Galerkin (DG) electronic structure method and show that this results in a computational scheme that can effectively tackle bulk and nano systems containing tens of thousands of electrons, with chemical accuracy, within a few minutes or less of wall clock time per SCF iteration on large-scale computing platforms. We anticipate that our method will be instrumental in pushing the envelope of large-scale ab initio molecular dynamics. As a demonstration of this, we simulate a bulk silicon system containing 8,000 atoms at finite temperature, and obtain an average SCF step wall time of 51 s on 34,560 processors; thus allowing us to carry out 1.0 ps of ab initio molecular dynamics in approximately 28 h (of wall time).

SPARC: Accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory: Extended systems

As the second component of SPARC (Simulation Package for Ab-initio Real-space Calculations), we present an accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory (DFT) for extended systems. Specifically, employing a local formulation of the electrostatics, the Chebyshev polynomial filtered self-consistent field iteration, and a reformulation of the non-local force component, we develop a finite-difference framework wherein both the energy and atomic forces can be efficiently calculated to within desired accuracies in DFT. We demonstrate using a wide variety of materials systems that SPARC achieves high convergence rates in energy and forces with respect to spatial discretization to reference plane-wave result; exponential convergence in energies and forces with respect to vacuum size for slabs and wires; energies and forces that are consistent and display negligible ‘egg-box’ effect; accurate properties of crystals, slabs, and wires; and negligible drift in molecular dynamics simulations. We also demonstrate that the weak and strong scaling behavior of SPARC is similar to well-established and optimized plane-wave implementations for systems consisting up to thousands of electrons, but with a significantly reduced prefactor. Overall, SPARC represents an attractive alternative to plane-wave codes for performing DFT simulations of extended systems. Program summaryProgram title: SPARCCatalogue identifier: AFBR_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFBR_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU GPL v3No. of lines in distributed program, including test data, etc.: 93822No. of bytes in distributed program, including test data, etc.: 1386659Distribution format: tar.gzProgramming language: C/C++.Computer: Any system with C/C++ compiler.Operating system: Linux.RAM: Problem dependent. Ranges from 80 GB to 800 GB for a system with 2500 electrons.Classification: 7.3.External routines: PETSc 3.5.3 (http://www.mcs.anl.gov/petsc), MKL 11.2 (https://software.intel.com/en-us/intel-mkl), and MVAPICH2 2.1 (http://mvapich.cse.ohio-state.edu/).Does the new version supersede the previous version?: YesNature of problem: Calculation of the static and dynamic properties of isolated and extended systems in the framework of Kohn–Sham Density Functional Theory (DFT).Solution method:High-order finite-difference discretization. Local reformulation of the electrostatics in terms of the electrostatic potential and pseudocharge densities. Application of Bloch-periodic and zero-Dirichlet boundary conditions on the orbitals in the direction of periodicity and vacuum, respectively. Application of periodic and Dirichlet boundary conditions on the electrostatic potential in the direction of periodicity and vacuum, respectively. Integration over the Brillouin zone for extended systems using the Monkhorst–Pack grid. Calculation of the electronic ground-state using the Chebyshev polynomial filtered self-consistent field iteration in conjunction with Anderson based extrapolation/mixing schemes. Reformulation of the non-local component of the force. Geometry optimization using the Polak–Ribiere variant of non-linear conjugate gradients with secant line search. NVE molecular dynamics using the leapfrog method. Parallelization via domain decomposition and over Brillouin zone integration.Reasons for new version:To enable the study of extended systems like crystals, slabs, and wires using SPARC.Summary of revisions:Incorporated the ability to study the static and dynamic properties of crystals, slabs, and wires.Restrictions:System size less than ∼4000 electrons. Local Density Approximation (LDA). Troullier–Martins pseudopotentials without relativistic or non-linear core corrections. Domain has to be cuboidal.Running time:Problem dependent. Timing results for selected examples provided in the paper.

SPARC: Accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory: Isolated clusters

As the first component of SPARC (Simulation Package for Ab-initio Real-space Calculations), we present an accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory (DFT) for isolated clusters. Specifically, utilizing a local reformulation of the electrostatics, the Chebyshev polynomial filtered self-consistent field iteration, and a reformulation of the non-local component of the force, we develop a framework using the finite-difference representation that enables the efficient evaluation of energies and atomic forces to within the desired accuracies in DFT. Through selected examples consisting of a variety of elements, we demonstrate that SPARC obtains exponential convergence in energy and forces with domain size; systematic convergence in the energy and forces with mesh-size to reference plane-wave result at comparably high rates; forces that are consistent with the energy, both free from any noticeable ‘egg-box’ effect; and accurate ground-state properties including equilibrium geometries and vibrational spectra. In addition, for systems consisting up to thousands of electrons, SPARC displays weak and strong parallel scaling behavior that is similar to well-established and optimized plane-wave implementations, but with a significantly reduced prefactor. Overall, SPARC represents an attractive alternative to plane-wave codes for practical DFT simulations of isolated clusters.Program summaryProgram title: SPARCCatalogue identifier: AFBL_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFBL_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU GPL v3No. of lines in distributed program, including test data, etc.: 47525No. of bytes in distributed program, including test data, etc.: 826436Distribution format: tar.gzProgramming language: C/C++.Computer: Any system with C/C++ compiler.Operating system: Linux.RAM: Problem dependent. Ranges from 80 GB to 800 GB for a system with 2500 electrons.Classification: 7.3.External routines: PETSc 3.5.3 (http://www.mcs.anl.gov/petsc), MKL 11.2 (https://software.intel.com/en-us/intel-mkl), and MVAPICH2 2.1 (http://mvapich.cse.ohio-state.edu/).Nature of problem:Calculation of the electronic and structural ground-states for isolated clusters in the framework of Kohn–Sham Density Functional Theory (DFT).Solution method:High-order finite-difference discretization. Local reformulation of the electrostatics in terms of the electrostatic potential and pseudocharge densities. Calculation of the electronic ground-state using the Chebyshev polynomial filtered Self-Consistent Field (SCF) iteration in conjunction with Anderson extrapolation/mixing. Evaluation of boundary conditions for the electrostatic potential through a truncated multipole expansion. Reformulation of the non-local component of the force. Geometry optimization using the Polak–Ribiere variant of non-linear conjugate gradients with secant line search.Restrictions:System size less than ∼4000 electrons. Local Density Approximation (LDA). Troullier–Martins pseudopotentials without relativistic or non-linear core corrections.Running time:Problem dependent. Timing results for selected examples provided in the paper.

Implementation and Validation of Fully Relativistic GW Calculations: Spin-Orbit Coupling in Molecules, Nanocrystals, and Solids.

We present an implementation of G0W0 calculations including spin-orbit coupling (SOC) enabling investigations of large systems, with thousands of electrons, and we discuss results for molecules, solids, and nanocrystals. Using a newly developed set of molecules with heavy elements (called GW-SOC81), we find that, when based upon hybrid density functional calculations, fully relativistic (FR) and scalar-relativistic (SR) G0W0 calculations of vertical ionization potentials both yield excellent performance compared to experiment, with errors below 1.9%. We demonstrate that while SR calculations have higher random errors, FR calculations systematically underestimate the VIP by 0.1 to 0.2 eV. We further verify that SOC effects may be well approximated at the FR density functional level and then added to SR G0W0 results for a broad class of systems. We also address the use of different root-finding algorithms for the G0W0 quasiparticle equation and the significant influence of including d electrons in the valence partition of the pseudopotential for G0W0 calculations. Finally, we present statistical analyses of our data, highlighting the importance of separating definitive improvements from those that may occur by chance due to a limited number of samples. We suggest the statistical analyses used here will be useful in the assessment of the accuracy of a large variety of electronic structure methods.

Large scale GW calculations.

We present GW calculations of molecules, ordered and disordered solids and interfaces, which employ an efficient contour deformation technique for frequency integration and do not require the explicit evaluation of virtual electronic states nor the inversion of dielectric matrices. We also present a parallel implementation of the algorithm, which takes advantage of separable expressions of both the single particle Green's function and the screened Coulomb interaction. The method can be used starting from density functional theory calculations performed with semilocal or hybrid functionals. We applied the newly developed technique to GW calculations of systems of unprecedented size, including water/semiconductor interfaces with thousands of electrons.

A spectral scheme for Kohn–Sham density functional theory of clusters

Starting from the observation that one of the most successful methods for solving the Kohn–Sham equations for periodic systems – the plane-wave method – is a spectral method based on eigenfunction expansion, we formulate a spectral method designed towards solving the Kohn–Sham equations for clusters. This allows for efficient calculation of the electronic structure of clusters (and molecules) with high accuracy and systematic convergence properties without the need for any artificial periodicity. The basis functions in this method form a complete orthonormal set and are expressible in terms of spherical harmonics and spherical Bessel functions. Computation of the occupied eigenstates of the discretized Kohn–Sham Hamiltonian is carried out using a combination of preconditioned block eigensolvers and Chebyshev polynomial filter accelerated subspace iterations. Several algorithmic and computational aspects of the method, including computation of the electrostatics terms and parallelization are discussed. We have implemented these methods and algorithms into an efficient and reliable package called ClusterES (Cluster Electronic Structure). A variety of benchmark calculations employing local and non-local pseudopotentials are carried out using our package and the results are compared to the literature. Convergence properties of the basis set are discussed through numerical examples. Computations involving large systems that contain thousands of electrons are demonstrated to highlight the efficacy of our methodology. The use of our method to study clusters with arbitrary point group symmetries is briefly discussed.

Compact femtosecond electron diffractometer with 100 keV electron bunches approaching the single-electron pulse duration limit

We present the design and implementation of a highly compact femtosecond electron diffractometer working at electron energies up to 100 keV. We use a multi-body particle tracing code to simulate electron bunch propagation through the setup and to calculate pulse durations at the sample position. Our simulations show that electron bunches containing few thousands of electrons per bunch are only weakly broadened by space-charge effects and their pulse duration is thus close to the one of a single-electron wavepacket. With our compact setup, we can create electron bunches containing up to 5000 electrons with a pulse duration below 100 fs on the sample. We use the diffractometer to track the energy transfer from photoexcited electrons to the lattice in a thin film of titanium. This process takes place on the timescale of few-hundred femtoseconds and a fully equilibrated state is reached within 1 ps.

Diagnostics of an artificial relativistic electron beam interacting with the atmosphere

AbstractWe use a Monte Carlo model to simulate the interaction of a beam of relativistic (0.5–10 MeV) electrons with the upper atmosphere as they are injected downward from a notional high‐altitude (thermospheric/ionospheric) injection platform. The beam parameters, defined by realistic parameters of a compact linear accelerator, are used to create a distribution of thousands of electrons. Each electron is injected downward from 300 km altitude toward the dense atmosphere, where it undergoes elastic and inelastic collisions, leading to secondary ionization, optical emissions, and X‐rays via bremsstrahlung. In this report we describe the model initialization (i.e., development of the electron distribution), essential features of the Monte Carlo model, and secondary outputs, including optical emissions, X‐ray fluxes, secondary ionization, and backscattered energetic electron fluxes. Optical emissions are propagated to the ground through the lower atmosphere, including the effects of atmospheric absorption and scattering, to estimate the brightness of the emission column for a given beam current and energy. Similarly, X‐ray fluxes are propagated to hypothetical detectors on balloons and satellites. Secondary ionization is used to estimate the radar signal returns from various ground‐based radar facilities. Finally, simulated backscattered electron fluxes are measured at the injection location. The simulation results show that each of these diagnostics should be readily detectable by appropriate instruments.

Quantum Dots and Their Clinical Applications

Quantum dots (QDs) are a landmark development in the field of nanotechnology. These zero-dimensional semiconductors, unlike their physical attributes, have enormous capacity to store energy within themselves. This energy is contained in several thousands of electrons that constitute the nanoparticles. QDs are synthesized by both organic and inorganic methods, the choice being dependent upon the desired efficacy of the resultant product. The process of synthesis is auto regulated by the phenomenon of nucleation threshold, whilst quality control occurs through ostwald ripening, given by Gibbs Thompson equation. The optical and electronic properties of these particles are dependent upon the transitions of constituent electrons between the valence and conductance bands and this phenomenon is exploited in synthesizing QDs to be employed as biomarkers. Fluorescence is obtained when electrons return to the ground state from the lowest vibrational level of an excited state, emitting quanta of radiation in the process. As wavelength varies with each energy state, a rainbow of fluorescence is seen with quantum dots of different sizes and shapes. The properties of these nanoparticles are largely attributed to their high surface area to volume ratio, with the former parameter being subjected to modifications like capping and functionalization. This not only enhances their quantum yield but also multiplies their fluorescing abilities. As biomarkers, these particles find many clinical applications, in an array of in vivo and in vitro techniques, ranging from drug delivery systems to interstitial target tracking. However, one special clinical application of QDs that demands reverence for their utility, is their specific and selective cancer cell imaging activity. Photosensitizers may be linked to QDs, bound to monoclonal antibodies, and targeted to cancer cells, where they may generate reactive oxygen species (ROS) upon exposure to light. This could help in the treatment of metastatic malignancies and form a part of photodynamic therapy. On the other side lies the toxic effect of these particles that can be traced to their heavy metal crystalline cores. However, pursuit is on, to overcome this drawback, so that QDs can be used more effectively in vivo for a longer period of time. Keywords: Biomarkers, clinical applications, photodynamic therapy, tumor targeting, quantum dots.