arXiv subjects

Roi Baer

Publications and source records attributed to Roi Baer.

At least 55 records · Page 3Linked to original sources

arXiv2017

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.

cond-mat.quant-gas↗

arXiv2017

Minimally-corrected partial atomic charges for non-covalent electrostatic interactions

We develop a new scheme for determining molecular partial atomic charges (PACs) with external electrostatic potential (ESP) closely mimicking that of the molecule. The PACs are the "minimal corrections" to a reference-set of PACs necessary for reproducing exactly the tensor components of the Cartesian zero- first- and second- molecular electrostatic multipoles. We evaluate the quality of ESP reproduction when "minimally correcting" (MC) Mulliken, Hirshfeld or iterated-Hirshfeld reference PACs. In all these cases the MC-PACs significantly improve the ESP while preserving the reference PACs' invariance under the molecular symmetry operations. When iterative-Hirshfeld PACs are used as reference the MC-PACs yield ESPs of comparable quality to those of the ChElPG charge fitting method.

physics.chem-ph↗

arXiv2017

A Stochastic Formulation of the Resolution of Identity: Application to Second Order Møller-Plesset Perturbation Theory

A stochastic orbital approach to the resolution of identity (RI) approximation for 4-index 2-electron electron repulsion integrals (ERIs) is presented. The stochastic RI-ERIs are then applied to Møller-Plesset perturbation theory (MP2) utilizing a \textit{multiple stochastic orbital approach}. The introduction of multiple stochastic orbitals results in an $N^3$ scaling for both the stochastic RI-ERIs and stochastic RI-MP2. We demonstrate that this method exhibits a small prefactor and an observed scaling of $N^{2.4}$ for a range of water clusters, already outperforming MP2 for clusters with as few as 21 water molecules.

physics.chem-ph↗

arXiv2016

Stochastic self-consistent Green's function second-order perturbation theory (sGF2)

The second-order Green's function method (GF2) was shown recently to be an accurate self-consistent approach for electronic structure of correlated systems since the self-energy accounts for both the weak and some of the strong correlation. The numerical scaling of GF2 is quite steep however, $O({N^5})$ (where the pre-factor is often hundreds), effectively preventing its application to large systems. Here, we develop a stochastic approach to GF2 (sGF2) where the self-energy is evaluated by a random-vector decomposition of Green's functions so that the dominant part of the calculation scales quasi linearly with system size. A study of hydrogen chains shows that the resulting approach is numerically efficient and accurate, as the stochastic errors are very small, 0.05% of the correlation energy for large systems with only a moderate computational effort. The method also yields automatically efficient MP2 energies and is automatically temperature dependent.

physics.chem-ph↗

arXiv2016

Spontaneous charge carrier localization in extended one-dimensional systems

Charge carrier localization in extended atomic systems has been described previously as being driven by disorder, point defects or distortions of the ionic lattice. Here we show for the first time by means of first-principles computations that charge carriers can spontaneously localize due to a purely electronic effect in otherwise perfectly ordered structures. Optimally-tuned range-separated density functional theory and many-body perturbation calculations within the GW approximation reveal that in trans-polyacetylene and polythiophene the hole density localizes on a length scale of several nanometers. This is due to exchange-induced translational symmetry breaking of the charge density. Ionization potentials, optical absorption peaks, excitonic binding energies and the optimally-tuned range parameter itself all become independent of polymer length as it exceeds the critical localization scale. Moreover, lattice disorder and the formation of a polaron result from the charge localization in contrast to the traditional view that lattice distortions precede charge localization. Our results can explain experimental findings that polarons in conjugated polymers form instantaneously after exposure to ultrafast light pulses.

cond-mat.mes-hall↗

arXiv2015

Stochastic Optimally-Tuned Ranged-Separated Hybrid Density Functional Theory

We develop a stochastic formulation of the optimally-tuned range-separated hybrid density functional theory which enables significant reduction of the computational effort and scaling of the non-local 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 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 which is central for additional post-processing, for example in the stochastic Bethe-Salpeter approach.

physics.chem-ph↗

arXiv2015

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.

cond-mat.str-el↗

arXiv2015

Time-dependent Stochastic Bethe-Salpeter Approach

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 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.

cond-mat.mtrl-sci↗

arXiv2014

Sublinear scaling for time-dependent stochastic density functional theory

A stochastic approach to time-dependent density functional theory (TDDFT) 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 (NCs) using real-space grids and find that the overall scaling of the algorithm is sublinear with computational time and memory.

physics.chem-ph↗

arXiv2014

Deviations from piecewise linearity in the solid-state limit with approximate density functionals

In exact density functional theory (DFT) the total ground-state energy is a series of linear segments between integer electron points, a condition known as "piecewise linearity". Deviation from this condition is indicative of poor predictive capabilities for electronic structure, in particular of ionization energies, fundamental gaps, and charge transfer. In this article, we take a new look at the deviation from linearity (i.e., curvature) in the solid-state limit by considering two different ways of approaching it: a large finite system of increasing size and a crystal represented by an increasingly large reference cell with periodic boundary conditions. We show that the curvature approaches vanishing values in both limits, even for functionals which yield poor predictions of electronic structure, and therefore can not be used as a diagnostic or constructive tool in solids. We find that the approach towards zero curvature is different in each of the two limits, owing to the presence of a compensating background charge in the periodic case. Based on these findings, we present a new criterion for functional construction and evaluation, derived from the size-dependence of the curvature, along with a practical method for evaluating this criterion. For large finite systems we further show that the curvature is dominated by the self-interaction of the highest occupied eigenstate. These findings are illustrated by computational studies of various solids, semiconductor nanocrystals, and long alkane chains.

cond-mat.other↗

arXiv2014

Embedded fragment stochastic density functional theory

We develop a method in which the electronic densities of small fragments determined by Kohn-Sham density functional theory (DFT) are embedded using stochastic DFT to form the exact density of the full system. The new method preserves the scaling and the simplicity of the stochastic DFT but cures the slow convergence that occurs when weakly coupled subsystems are treated. It overcomes the spurious charge fluctuations that impair the applications of the original stochastic DFT approach. We demonstrate the new approach on a fullerene dimer and on clusters of water molecules and show that the density of states and the total energy can be accurately described with a relatively small number of stochastic orbitals.

physics.chem-ph↗

arXiv2014

Breaking the theoretical scaling limit for predicting quasi-particle energies: The stochastic GW approach

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 over 3000 electrons.

cond-mat.mes-hall↗

arXiv2013

A guided stochastic energy-domain formulation of the second order Møller-Plesset perturbation theory

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 non-separable 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.

physics.chem-ph↗

arXiv2013

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.

cond-mat.mtrl-sci↗

arXiv2012

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 Møller-Plesset correlation energies, we find that the RPA correlation energies per electron are largely independent on the nanocrystal size.

physics.chem-ph↗

arXiv2012

Expeditious stochastic approach for MP2 energies in large electronic systems

A fast stochastic method for calculating the 2nd 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 of thousands electrons using hydrogen passivated silicon spherical nanocrystals represented on a real space grids, much beyond capabilities of present day MP2 implementations.

physics.chem-ph↗

arXiv2012

Multiexciton generation in IV-VI nanocrystals: The role of carrier effective mass, band mixing, and phonon emission

We study the role of the effective mass, band mixing and phonon emission on multiexciton generation in IV-VI nanocrystals. A 4-band k dot 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.

cond-mat.mtrl-sci↗

arXiv2012

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 ratio

cond-mat.mes-hall↗