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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Nonlinear electronic excitations in crystalline solids using meta-generalized gradient approximation and hybrid functional in time-dependent density functional theory

We develop methods to calculate electron dynamics in crystalline solids in real-time time-dependent density functional theory employing exchange-correlation potentials which reproduce band gap energies of dielectrics; a meta-generalized gradient approximation was proposed by Tran and Blaha [Phys. Rev. Lett. 102, 226401 (2009)] (TBm-BJ) and a hybrid functional was proposed by Heyd, Scuseria, and Ernzerhof [J. Chem. Phys. 118, 8207 (2003)] (HSE). In time evolution calculations employing the TB-mBJ potential, we have found it necessary to adopt the predictor-corrector step for a stable time evolution. We have developed a method to evaluate electronic excitation energy without referring to the energy functional which is unknown for the TB-mBJ potential. For the HSE functional, we have developed a method for the operation of the Fock-like term in Fourier space to facilitate efficient use of massive parallel computers equipped with graphic processing units. We compare electronic excitations in silicon and germanium induced by femtosecond laser pulses using the TB-mBJ, HSE, and a simple local density approximation (LDA). At low laser intensities, electronic excitations are found to be sensitive to the band gap energy: they are close to each other using TB-mBJ and HSE and are much smaller in LDA. At high laser intensities close to the damage threshold, electronic excitation energies do not differ much among the three cases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Nonlinear Matrix Approximation with Radial Basis Function Components

We introduce and investigate matrix approximation by decomposition into a sum of radial basis function (RBF) components. An RBF component is a generalization of the outer product between a pair of vectors, where an RBF function replaces the scalar multiplication between individual vector elements. Even though the RBF functions are positive definite, the summation across components is not restricted to convex combinations and allows us to compute the decomposition for any real matrix that is not necessarily symmetric or positive definite. We formulate the problem of seeking such a decomposition as an optimization problem with a nonlinear and non-convex loss function. Several modern versions of the gradient descent method, including their scalable stochastic counterparts, are used to solve this problem. We provide extensive empirical evidence of the effectiveness of the RBF decomposition and that of the gradient-based fitting algorithm. While being conceptually motivated by singular value decomposition (SVD), our proposed nonlinear counterpart outperforms SVD by drastically reducing the memory required to approximate a data matrix with the same L2 error for a wide range of matrix types. For example, it leads to 2 to 6 times memory save for Gaussian noise, graph adjacency matrices, and kernel matrices. Moreover, this proximity-based decomposition can offer additional interpretability in applications that involve, e.g., capturing the inner low-dimensional structure of the data, retaining graph connectivity structure, and preserving the acutance of images.

Rebrova, Elizaveta↗
DOE OSTI2017

A Fast Algorithm for the Convolution of Functions with Compact Support Using Fourier Extensions

In this paper, we present a new algorithm for computing the convolution of two compactly supported functions. The algorithm approximates the functions to be convolved using Fourier extensions and then uses the fast Fourier transform to efficiently compute Fourier extension approximations to the pieces of the result. Finally, the complexity of the algorithm is O(N(log N) 2 ), where N is the number of degrees of freedom used in each of the Fourier extensions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A linear surrogate for optimising functions of an orthogonal matrix with applications in wave function theory

The technique of surrogate optimisation is to use a simpler function to approximate a complex function that is time-consuming to evaluate. Here we show that the maximum of a special type of surrogate function f(U)=Tr(AU),UϵO(n) is at A T (AA T ) 1/2 , and that there is one and only one local maximum both in SO(n) and O(n)–SO(n). This function f(U) has been found to be useful in various aspects of electronic structure theory, including proving the Carlson-Keller theorem, and localising orbitals. As one other example, we apply it here to optimise the ground state of molecules using the Generalised Valence Bond wavefunction.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2026

Multiscale Neural Networks for Approximating Green’s Functions

Neural networks (NNs) have been widely used to solve partial differential equations (PDEs) in the applications of physics, biology, and engineering. One effective approach for solving PDEs with a fixed differential operator is learning Green’s functions. However, Green’s functions are notoriously difficult to learn due to their poor regularity, which typically requires larger NNs and longer training times. In this work, we address these challenges by leveraging multiscale NNs to learn Green’s functions. Through theoretical analysis using multiscale Barron space methods and experimental validation, we show that the multiscale approach significantly reduces the necessary NN size and accelerates training.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Structural, electronic, and dynamical properties of liquid water by ab initio molecular dynamics based on SCAN functional within the canonical ensemble

We perform ab initio molecular dynamics (AIMD) simulation of liquid water in the canonical ensemble at ambient conditions using the strongly constrained and appropriately normed (SCAN) meta-generalized-gradient approximation (GGA) functional approximation and carry out systematic comparisons with the results obtained from the GGA-level Perdew-Burke-Ernzerhof (PBE) functional and Tkatchenko-Scheffler van der Waals (vdW) dispersion correction inclusive PBE functional. We analyze various properties of liquid water including radial distribution functions, oxygen-oxygen-oxygen triplet angular distribution, tetrahedrality, hydrogen bonds, diffusion coefficients, ring statistics, density of states, band gaps, and dipole moments. We find that the SCAN functional is generally more accurate than the other two functionals for liquid water by not only capturing the intermediate-range vdW interactions but also mitigating the overly strong hydrogen bonds prescribed in PBE simulations. We also compare the results of SCAN-based AIMD simulations in the canonical and isothermal-isobaric ensembles. Our results suggest that SCAN provides a reliable description for most structural, electronic, and dynamical properties in liquid water.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Self-interaction-corrected Kohn–Sham effective potentials using the density-consistent effective potential method

Density functional theory (DFT) and beyond-DFT methods are often used in combination with photoelectron spectroscopy to obtain physical insights into the electronic structure of molecules and solids. The Kohn–Sham eigenvalues are not electron removal energies except for the highest occupied orbital. The eigenvalues of the highest occupied molecular orbitals often underestimate the electron removal or ionization energies due to the self-interaction (SI) errors in approximate density functionals. Here, we adapt and implement the density-consistent effective potential method of Kohut, Ryabinkin, and Staroverov (2014) to obtain SI-corrected local effective potentials from the SI-corrected Fermi–Löwdin orbitals and density in the Fermi–Löwdin orbital self-interaction correction scheme. The implementation is used to obtain the density of states (photoelectron spectra) and HOMO–LUMO gaps for a set of molecules and polyacenes. Good agreement with experimental values is obtained compared to a range of SI uncorrected density functional approximations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

First-principles wave-vector- and frequency-dependent exchange-correlation kernel for jellium at all densities

Here we propose a spatially and temporally nonlocal exchange correlation (XC) kernel for the spin-unpolarized fluid phase of ground-state jellium for use in time-dependent density functional and linear response calculations. The kernel is constructed to satisfy known properties of the exact XC kernel to accurately describe the correlation energies of bulk jellium and to satisfy frequency-moment sum rules at a wide range of bulk jellium densities, including those low densities that display strong correlation and symmetry breaking. These effects are easier to understand in the simple jellium model than in real systems. All exact constraints satisfied by the recent MCP07 kernel are maintained in the revised MCP07 (rMCP07) kernel, while others are added. The revision $f^{rMCP07}_{XC}$ (q, ω) differs from MCP07 only for nonzero frequencies ω. Only at densities much lower than those of real bulk metals is the frequency dependence of the kernel important for the correlation energy of jellium. As the wave vector q tends to zero, the kernel has a -4$πα(ω)/q^2$ divergence whose frequency-dependent ultranonlocality coefficient $α(ω)$ vanishes in jellium, and is predicted by rMCP07 to be extremely small for the real metals Al and Na.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Enhancing the efficiency of density functionals with an improved iso-orbital indicator

The accuracy and efficiency of a density functional is dependent on the basic ingredients it uses and how the ingredients are built into the functional as a whole. An iso-orbital indicator based on the electron density, its gradients, and the kinetic energy density, has proven an essential dimensionless variable that allows density functionals to recognise and correctly treat various types of chemical bonding, both strong and weak. Density functionals constructed around the iso-orbital indicator usually require dense real-space grids for numerical implementation that deteriorate computational efficiency, with poor grid convergence compromising the improved accuracy. Here, a novel iso-orbital indicator is proposed based on the same ingredients that retains the capability to identify the same chemical bonds while significantly relieving the requirement of dense grids. Furthermore, the novel iso-orbital indicator gives an improved recognition for tail regions of electron densities and is divergence-free for the exchange-correlation potential. The novel iso-orbital indicator is therefore expected to be the prime choice for further density functional development.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Tuned and screened range-separated hybrid density functional theory for describing electronic and optical properties of defective gallium nitride

We apply a hybrid density functional theory approach, based on a tuned and screened range-separated hybrid (SRSH) exchange-correlation functional, to describe the optoelectronic properties of defective gallium nitride (GaN). SRSH and time-dependent SRSH (TDSRSH) are tuned to produce accurate energetics for the pristine material and applied to the study of a series of point defects in bulk GaN, a blue light-emitting material that degrades in the presence of defects. We first establish the accuracy of the method by comparing the predicted quasiparticle gap and low-energy excitation spectra of (TD)SRSH and many-body perturbation theory for both pristine GaN and GaN containing a single nitrogen vacancy. Aided by the reduced computational cost of (TD)SRSH, we then report on three additional technologically relevant point defects and defect complexes in GaN: the gallium vacancy, the carbon interstitial, and the carbon-silicon complex. We compute the low-energy optical absorption spectra for these defects and show the presence of defect-centered transitions. Furthermore, by estimating the Stokes shift, we predict, in agreement with previous studies, that the carbon substitutional defect is a candidate for the detrimental yellow luminescence in GaN. Furthermore, this study indicates that TDSRSH is a promising and computationally feasible approach for quantitatively accurate, first-principles modeling of defective semiconductors.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Asymptotic Behavior of Memristive Circuits

The interest in memristors has risen due to their possible application both as memory units and as computational devices in combination with CMOS. This is in part due to their nonlinear dynamics, and a strong dependence on the circuit topology. We provide evidence that also purely memristive circuits can be employed for computational purposes. In the present paper we show that a polynomial Lyapunov function in the memory parameters exists for the case of DC controlled memristors. Such a Lyapunov function can be asymptotically approximated with binary variables, and mapped to quadratic combinatorial optimization problems. This also shows a direct parallel between memristive circuits and the Hopfield-Little model. In the case of Erdos-Renyi random circuits, we show numerically that the distribution of the matrix elements of the projectors can be roughly approximated with a Gaussian distribution, and that it scales with the inverse square root of the number of elements. This provides an approximated but direct connection with the physics of disordered system and, in particular, of mean field spin glasses. Using this and the fact that the interaction is controlled by a projector operator on the loop space of the circuit. We estimate the number of stationary points of the approximate Lyapunov function and provide a scaling formula as an upper bound in terms of the circuit topology only.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

The journey from forensic to predictive materials science using density functional theory

Approximate methods for electronic structure, implemented in sophisticated computer codes and married to ever-more powerful computing platforms, have become invaluable in chemistry and materials science. The maturing and consolidation of quantum chemistry codes since the 1980s, based upon explicitly correlated electronic wave functions, has made them a staple of modern molecular chemistry. Here, the impact of first principles electronic structure in physics and materials science had lagged owing to the extra formal and computational demands of bulk calculations.

36 MATERIALS SCIENCE↗