146 research outputs found
Biexciton generation rates in CdSe nanorods are length independent
We study how shape affects multiexciton generation (MEG) rates in a
semiconducting nanocrystal by considering CdSe nanorods with varying diameters
and aspect ratios. The calculations employ an atomistic semiempirical
pseudopotential model combined with an efficacious stochastic approach applied
to systems containing up to 20,000 atoms. The effect of nanorod diameter and
aspect ratio on multiexciton generation rates is analyzed in terms of the
scaling of the density of trion states and the scaling of the Coulomb
couplings. Both show distinct scaling from spherical nanocrystals leading to a
surprising result where the multiexciton generation rates are roughly
independent of the nanorod aspect ratioComment: 4 pages, 3 figure
Stochastic method for calculating the ground state reduced density matrix of trapped Bose particles in one dimension
The reduced density matrix (RDM) is a fundamental contraction of the
Bose-Einstein condensate wave function, encapsulating its one-body properties.
It serves as a major analysis tool with which the condensed component of the
density can be identified. Despite its cardinal importance, calculating the
ground-state RDM of trapped interacting bosons is challenging and has been
fully achieved only for specific models or when the pairwise interaction is
weak. In this paper we discuss a new approach to compute the RDM based on a
double-walker diffusion Monte Carlo random walk coupled with a stochastic
permanent calculation. We here describe the new method and study some of its
statistical convergence and properties applying it to some model systems
Quantum memory effects on the dynamics of electrons in gold clusters
Electron dynamics in metallic clusters are examined using a time-dependent
density functional theory that in-cludes a "memory term", i.e. attempts to
describe temporal non-local 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. Two-dimensional
pump-probe spectroscopy is used to study the temporal decay profile of the
plasmon, finding a fast decay followed by slower tail. Finally, we examine
memory effects on high harmonic generation, finding memory narrows emission
lines
Smoothing and extrapolating shifted-contour auxiliary-field Monte Carlo signals using discrete Laguerre functions
We develop a new smoothing or extrapolating method, based on discrete
Laguerre functions, for systematically analyzing the stochastic signal of
shifted-contour auxiliary-field Monte Carlo. We study the statistical errors
and extrapolation errors using full configuration-interaction energies for the
doubly stretched water molecule. The only free parameter is the order N of the
fit. We show that low N emphasizes stability while higher N enable improved
extrapolation, at the cost of increased statistical errors. Typically, one
should use low order for signals based on a small number of iterations while
higher order is efficacious for signals based on large number of iterations. We
provide a heuristic algorithm for determining the order to be used and show its
utility
Prevalence of the adiabatic exchange-correlation potential approximation in time-dependent density functional theory
Time-dependent (TD) density functional theory (TDDFT) promises a numerically
tractable account of many-body electron dynamics provided good simple
approximations are developed for the exchange-correlation (XC) potential
functional (XCPF). The theory is usually applied within the adiabatic XCPF
approximation, appropriate for slowly varying TD driving fields. As the
frequency and strength of these fields grows, it is widely held that memory
effects kick in and the eligibility of the adiabatic XCPF approximation
deteriorates irreversibly. We point out however that when a finite system of
electrons in its ground-state is gradually exposed to a very a high-frequency
and eventually ultra-strong homogeneous electric field, the adiabatic XCPF
approximation is in fact rigorously applicable. This result not only helps to
explain recent numerical results for a 1D-helium atom subject to a strong
linearly-polarized laser pulse (Thiel et al, Phys. Rev. Lett. 100, 153004,
(2008)) but also shows that it is applicable to any number of electrons and in
full 3D
Self-averaging stochastic Kohn-Sham density functional theory
We formulate the Kohn-Sham density functional theory (KS-DFT) as a
statistical theory in which the electron density is deter-mined from an average
of correlated stochastic densities in a trace formula. The key idea is that it
is sufficient to converge the total energy per electron to within a predefined
statistical error in order to obtain reliable estimates of the electronic band
structure, the forces on nuclei, the density and its moments, etc. The
fluctuations in the total energy per electron are guaranteed to decay to zero
as the system size increases. This facilitates "self-averaging" which leads to
the first ever report of sublinear scaling KS-DFT electronic structure. The
approach sidesteps calculation of the density matrix and thus is insensitive to
its evasive sparseness, as demonstrated here for silicon nanocrystals. The
formalism is not only appealing in terms of its promise to far push the limits
of application of KS-DFT, but also represents a cognitive change in the way we
think of electronic structure calculations as this stochastic theory seamlessly
converges to the thermodynamic limit.Comment: 4 pages, 4 figure
Stochastic Time-Dependent DFT with Optimally Tuned Range-Separated Hybrids: Application to Excitonic Effects in Large Phosphorene Sheets
We develop a stochastic approach to time-dependent DFT with optimally-tuned
range-separated hybrids containing non-local exchange, for calculating optical
spectra. The attractive electron-hole interaction, which leads to the formation
of excitons, is included through a time-dependent linear-response technique
with a non-local exchange interaction which is computed very efficiently
through a stochastic scheme. The method is inexpensive and scales quadratically
with the number of electrons, at almost the same (low) cost of time dependent
Kohn-Sham (TDKS) with local functionals. Our results are in excellent agreement
with experimental data and the efficiency of the approach is demonstrated on
large finite phosphorene sheets containing up to 1958 valence electrons
Conical intersections induced by the Renner effect in polyatomic molecules
Characterizing and localizing electronic energy degeneracies is important for
describ-ing and controlling electronic energy flow in molecules. We show, using
topological phase considerations that the Renner effect in polyatomic molecules
with more than 3 nuclei is necessarily accompanied by 'satellite' conical
intersections. In these intersections the non-adiabatic coupling term is on the
average half an integer. We present ab-inito results on the tetra-atomic
radical cation C2H2+ to demonstrate the theor
Expeditious Stochastic Calculation of Random-Phase Approximation Energies for Thousands of Electrons in 3 Dimensions
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. The method scales,
at most, quadratically with the system size but in practice, due to
self-averaging, 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. In contrast to 2nd order
M{\o}ller-Plesset correlation energies, we find that the RPA correlation
energies per electron are largely independent on the nanocrystal size.Comment: 4 page, 3 figure
Expeditious stochastic approach for MP2 energies in large electronic systems
A fast stochastic method for calculating the 2nd order M{\o}ller-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 of
thousands electrons using hydrogen passivated silicon spherical nanocrystals
represented on a real space grids, much beyond capabilities of present day MP2
implementations.Comment: 4 pages, 2 figure
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