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At least 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Rethinking CO adsorption on transition-metal surfaces: Effect of density-driven self-interaction errors

Adsorption of the molecule CO on metallic surfaces is an important unsolved problem in Kohn-Sham density functional theory (KS-DFT). We present a detailed study of carbon monoxide adsorption on fcc (111) surfaces of 3d, 4d, and 5d metals using nonempirical semilocal density functionals for the exchange-correlation energy: the local-density approximation (LDA), two generalized gradient approximations or GGAs [Perdew-Burke-Ernzerhof (PBE) and PBE for solids (PBEsol)], and a meta-GGA [strongly constrained and appropriately normed (SCAN) functional]. The typical error pattern (as found earlier for free molecules and for free transition-metal surfaces), in which results improve from LDA to PBE or PBEsol to SCAN, due to the satisfaction of more exact constraints, is not found here. Instead, for CO adsorption on transition-metal surfaces, we find that, while SCAN overbinds much less than LDA, it overbinds slightly more than PBE. Moreover, the tested functionals often predict the wrong adsorption site, as first pointed out for LDA and GGA in the CO/Pt (111) puzzle. This abnormal pattern leads us to suspect that the errors of PBE and SCAN for this problem are density-driven self-interaction errors associated with incorrect charge transfer between molecule and metal surface. We point out that, by the variational principle, overbinding by an approximate functional would be reduced if that functional were applied not to its self-consistent density for the adsorbed system but to an exact or more correct density for that system. Finally, we show for CO on Pt(111) that the site preference is corrected and the adsorption energy is improved for the PBE functional by using not the self-consistent PBE density but a PBE+U density. The resulting correction to the PBE total energy is much larger for the adsorbed system than for its desorbed components, showing that the error is in the density of the adsorbed system. Furthermore, this seems to solve the Feibelman 2001 CO/Pt(111) puzzle, in principle if not fully in practice.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

APPRENTICE

SF-19-096 In this software, there are multiple approaches to compute approximations to multivariate functions. This includes: (a) an approach that builds on Stieltjes process to efficiently compute the coefficients of the rational approximation, (b) an approach that is based on an optimization formulation to get pole-free coefficients of the rational approximation and (c) approaches that finds the coefficients of rational and polynomial approximations by finding the linear least-squares solution using singular value decomposition.

KRISNAMOORTHY, MOHAN↗
DOE OSTI2021

Entropy Pair Functional Theory: Direct Entropy Evaluation Spanning Phase Transitions

We prove that, within the class of pair potential Hamiltonians, the excess entropy is a universal, temperature-independent functional of the density and pair correlation function. This result extends Henderson’s theorem, which states that the free energy is a temperature dependent functional of the density and pair correlation. The stationarity and concavity of the excess entropy functional are discussed and related to the Gibbs–Bugoliubov inequality and to the free energy. We apply the Kirkwood approximation, which is commonly used for fluids, to both fluids and solids. Approximate excess entropy functionals are developed and compared to results from thermodynamic integration. The pair functional approach gives the absolute entropy and free energy based on simulation output at a single temperature without thermodynamic integration. We argue that a functional of the type, which is strictly applicable to pair potentials, is also suitable for first principles calculation of free energies from Born–Oppenheimer molecular dynamics performed at a single temperature. In conclusion, this advancement has the potential to reduce the evaluation the free energy to a simple modification to any procedure that evaluates the energy and the pair correlation function.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Weakly coupled alternating S = 1 2 chains in the distorted honeycomb lattice compound Na 2 Cu 2 TeO 6

Spin- 1 2 chains with alternating antiferromagnetic (AF) and ferromagnetic (FM) couplings exhibit quantum entanglement as the integer-spin Haldane chains and might be similarly utilized for quantum computations. Such alternating AF-FM chains have been proposed to be realized in the distorted honeycomb lattice compound Na 2 Cu 2 TeO 6 , but to confirm this picture a comprehensive understanding of the exchange interactions including terms outside of the idealized model is required. Here, we employ neutron scattering to study the spin dynamics in Na 2 Cu 2 TeO 6 and accurately determine the coupling strengths through the random phase approximation and density functional theory approaches. We find the AF and FM intrachain couplings are the dominant terms in the spin Hamiltonian, while the interchain couplings are AF but perturbative. This hierarchy in the coupling strengths and the alternating signs of the intrachain couplings can be understood through their different exchange paths. Our results establish Na 2 Cu 2 TeO 6 as a weakly coupled alternating AF-FM chain compound and reveal the robustness of the gapped ground state in alternating chains under weak interchain couplings.

1-dimensional spin chains↗
DOE OSTI2015

Semiclassical Green’s functions and an instanton formulation of electron-transfer rates in the nonadiabatic limit

We present semiclassical approximations to Green’s functions of multidimensional systems, extending Gutzwiller’s work to the classically forbidden region. Based on steepest-descent integrals over these functions, we derive an instanton method for computing the rate of nonadiabatic reactions, such as electron transfer, in the weak-coupling limit, where Fermi’s golden-rule can be employed. This generalizes Marcus theory to systems for which the environment free-energy curves are not harmonic and where nuclear tunnelling plays a role. The derivation avoids using the Im F method or short-time approximations to real-time correlation functions. A clear physical interpretation of the nuclear tunnelling processes involved in an electron-transfer reaction is thus provided. In Paper II [J. O. Richardson, J. Chem. Phys. 143, 134116 (2015)], we discuss numerical evaluation of the formulae.

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

Importance of imposing gauge invariance in time-dependent density functional theory calculations with meta-generalized gradient approximations

It has been known for more than a decade that the gauge variance of the kinetic energy density τ leads to additional terms in the magnetic orbital rotation Hessian used in linear-response time-dependent density functional theory (TDDFT), affecting excitation energies obtained with τ-dependent exchange–correlation functionals. While previous investigations found that a correction scheme based on the paramagnetic current density has a small effect on benchmark results, we report more pronounced effects here, in particular, for the popular M06-2X functional and for some other meta-generalized gradient approximations (mGGAs). In the first part of this communication, this is shown by a reassessment of a set of five Ni(II) complexes for which a previous benchmark study that did not impose gauge invariance has found surprisingly large errors for excitation energies obtained with M06-2X. These errors are more than halved by restoring gauge invariance. The variable importance of imposing gauge invariance for different mGGA-based functionals can be rationalized by the derivative of the mGGA exchange energy integrand with respect to τ. In the second part, a large set of valence excitations in small main-group molecules is analyzed. For M06-2X, several selected n → π* and π→π$^{*}_{⊥}$ excitations are heavily gauge-dependent with average changes of –0.17 and –0.28 eV, respectively, while π→π$^{*}_{∥}$ excitations are marginally affected (–0.04 eV). Similar patterns, but of the opposite signs, are found for SCAN0. Here, the results suggest that reevaluation of previous gauge variant TDDFT results based on M06-2X and other mGGA functionals is warranted.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Diffusion-Model-Assisted Supervised Learning of Generative Models for Density Estimation

Here, we present a supervised learning framework of training generative models for density estimation. Generative models, including generative adversarial networks (GANs), normalizing flows, and variational auto-encoders (VAEs), are usually considered as unsupervised learning models, because labeled data are usually unavailable for training. Despite the success of the generative models, there are several issues with the unsupervised training, e.g., requirement of reversible architectures, vanishing gradients, and training instability. To enable supervised learning in generative models, we utilize the score-based diffusion model to generate labeled data. Unlike existing diffusion models that train neural networks to learn the score function, we develop a training-free score estimation method. This approach uses mini-batch-based Monte Carlo estimators to directly approximate the score function at any spatial-temporal location in solving an ordinary differential equation (ODE), corresponding to the reverse-time stochastic differential equation (SDE). This approach can offer both high accuracy and substantial time savings in neural network training. Once the labeled data are generated, we can train a simple, fully connected neural network to learn the generative model in the supervised manner. Compared with existing normalizing flow models, our method does not require the use of reversible neural networks and avoids the computation of the Jacobian matrix. Compared with existing diffusion models, our method does not need to solve the reverse-time SDE to generate new samples. As a result, the sampling efficiency is significantly improved. We demonstrate the performance of our method by applying it to a set of 2D datasets as well as real data from the University of California Irvine (UCI) repository.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Generative Vulnerability Assessment for Cyber-Physical Systems

Cyber-physical systems (CPS) are highly susceptible to malicious attacks due to their complex dynamics and interconnectivity. A comprehensive understanding of their vulnerabilities is essential for designing effective resilience measures. This paper presents a data-driven attack generative system for evaluating the vulnerability of CPS. The proposed approach formulates the vulnerability assessment problem as determining the feasibility of a specific attack set based on two boundary functions that represent the effectiveness and stealthiness of attacks. The attack generative model is trained using a custom loss function, with two universal approximators designed to learn the effectiveness and stealthiness functions simultaneously. Theoretical results for successful generation and asymptotic convergence of the resulting training algorithm are given. As a result, the proposed approach is evaluated via numerical simulation of an IEEE 14-bus system and gas pipeline systems, demonstrating its viability in learning how to attack nonlinear CPS and identify potential vulnerabilities.

Computer systems organization↗
DOE OSTI2023

Robust scalable initialization for Bayesian variational inference with multi-modal Laplace approximations

Predictive modeling typically relies on Bayesian model calibration to provide uncertainty quantification. Variational inference utilizing fully independent (“mean-field”) Gaussian distributions are often used as approximate probability density functions. This simplification is attractive since the number of variational parameters grows only linearly with the number of unknown model parameters. However, the resulting diagonal covariance structure and unimodal behavior can be too restrictive to provide useful approximations of intractable Bayesian posteriors that exhibit highly non-Gaussian behavior, including multimodality. High-fidelity surrogate posteriors for these problems can be obtained by considering the family of Gaussian mixtures. Gaussian mixtures are capable of capturing multiple modes and approximating any distribution to an arbitrary degree of accuracy, while maintaining some analytical tractability. Unfortunately, variational inference using Gaussian mixtures with full-covariance structures suffers from a quadratic growth in variational parameters with the number of model parameters. The existence of multiple local minima due to strong nonconvex trends in the loss functions often associated with variational inference present additional complications, These challenges motivate the need for robust initialization procedures to improve the performance and computational scalability of variational inference with mixture models. In this work, we propose a method for constructing an initial Gaussian mixture model approximation that can be used to warm-start the iterative solvers for variational inference. The procedure begins with a global optimization stage in model parameter space. In this step, local gradient-based optimization, globalized through multistart, is used to determine a set of local maxima, which we take to approximate the mixture component centers. Around each mode, a local Gaussian approximation is constructed via the Laplace approximation. Finally, the mixture weights are determined through constrained least squares regression. The robustness and scalability of the proposed methodology is demonstrated through application to an ensemble of synthetic tests using high-dimensional, multimodal probability density functions. Here, the practical aspects of the approach are demonstrated with inversion problems in structural dynamics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Interpolating between small- and large-$\mathscr{g}$ expansions using Bayesian model mixing

Bayesian model mixing (BMM) is a statistical technique that can be used to combine models that are predictive in different input domains into a composite distribution that has improved predictive power over the entire input space. We explore the application of BMM to the mixing of two expansions of a function of a coupling constant $\mathscr{g}$ that are valid at small and large values of $\mathscr{g}$ respectively. This type of problem is quite common in nuclear physics, where physical properties are straightforwardly calculable in strong and weak interaction limits or at low and high densities or momentum transfers, but difficult to calculate in between. Interpolation between these limits is often accomplished by a suitable interpolating function, e.g., Padé approximants, but it is then unclear how to quantify the uncertainty of the interpolant. We address this problem in the simple context of the partition function of zero-dimensional Φ 4 theory, for which the (asymptotic) expansion at small $\mathscr{g}$ and the (convergent) expansion at large $\mathscr{g}$ are both known. We consider three mixing methods: linear mixture BMM, localized bivariate BMM, and localized multivariate BMM with Gaussian processes. Here, we find that employing a Gaussian process in the intermediate region between the two predictive models leads to the best results of the three methods. The methods and validation strategies we present here should be generalizable to other nuclear physics settings.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

Quantum Monte Carlo calculations of light nuclei with local chiral two- and three-nucleon interactions

Local chiral effective field theory interactions have recently been developed and used in the context of quantum Monte Carlo few- and many-body methods for nuclear physics. In this paper, we go over detailed features of local chiral nucleon-nucleon interactions and examine their effect on properties of the deuteron, paying special attention to the perturbativeness of the expansion. We then turn to three-nucleon interactions, focusing on operator ambiguities and their interplay with regulator effects. We then discuss the nuclear Green's function Monte Carlo method, going over both wave-function correlations and approximations for the two- and three-body propagators. Finally, following this, we present a range of results on light nuclei: Binding energies and distribution functions are contrasted and compared, starting from several different microscopic interactions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Surrogate Model Guided Optimization of Expensive Black-Box Multi-Objective Problems: A Posteriori Methods

Many engineering applications require the simultaneous optimization of multiple conflicting objective functions. Often, these objective functions are evaluated using highly accurate computer simulations that are computationally too expensive to be evaluated hundreds or thousands of times during optimization. Thus, the goal is to find good approximations of the Pareto front using as few of these expensive simulations as possible. Here, we describe an optimization approach based on surrogate models and diverse sampling strategies to accelerate the search for the Pareto solutions. We use a separate surrogate model for approximating each objective function and then we use the surrogate models to inform where additional expensive simulations should be run. The surrogate models are updated in an active learning framework whenever new information from the expensive simulations becomes available. The sampling strategies aim at balancing local improvements of the approximate Pareto front and global exploration to identify the extrema and fill in large gaps of the approximate Pareto front. We demonstrate on a large set of benchmark problems the effectiveness of the method for finding good approximations of the Pareto front.

MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Criteria for the Best Approximation by Simple Partial Fractions on Semi-Axis and Axis

We study uniform approximation of real-valued functions f, f(∞) = 0, on ℝ{sup +} and ℝ by real-valued simple partial fractions (the logarithmic derivatives of polynomials). We obtain a criterion for the best approximation on ℝ{sup +} and ℝ in terms of the Chebyshev alternance. This criterion is similar to the known criterion on finite segments. For the problem of approximating odd functions on ℝ we construct an alternance criterion with a weakened condition on the poles of fractions. We present a criterion for the best approximation by simple partial fractions on ℝ{sup +} and ℝ in terms of Kolmogorov. We prove analogs of the de la Vallee-Poussin alternation theorem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Global and local curvature in density functional theory

Piecewise linearity of the energy with respect to fractional electron removal or addition is a requirement of an electronic structure method that necessitates the presence of a derivative discontinuity at integer electron occupation. Semi-local exchange-correlation (xc) approximations within density functional theory (DFT) fail to reproduce this behavior, giving rise to deviations from linearity with a convex global curvature that is evidence of many-electron, self-interaction error and electron delocalization. Popular functional tuning strategies focus on reproducing piecewise linearity, especially to improve predictions of optical properties. In a divergent approach, Hubbard U-augmented DFT (i.e., DFT+U) treats self-interaction errors by reducing the local curvature of the energy with respect to electron removal or addition from one localized subshell to the surrounding system. Although it has been suggested that DFT+U should simultaneously alleviate global and local curvature in the atomic limit, no detailed study on real systems has been carried out to probe the validity of this statement. In this work, we show when DFT+U should minimize deviations from linearity and demonstrate that a “+U” correction will never worsen the deviation from linearity of the underlying xc approximation. However, we explain varying degrees of efficiency of the approach over 27 octahedral transition metal complexes with respect to transition metal (Sc–Cu) and ligand strength (CO, NH{sub 3}, and H{sub 2}O) and investigate select pathological cases where the delocalization error is invisible to DFT+U within an atomic projection framework. Finally, we demonstrate that the global and local curvatures represent different quantities that show opposing behavior with increasing ligand field strength, and we identify where these two may still coincide.

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

Ab-Initio Investigation of Finite Size Effects in Rutile Titania Nanoparticles with Semilocal and Nonlocal Density Functionals

In this work, we employ hybrid and generalized gradient approximation (GGA) level density functional theory (DFT) calculations to investigate the convergence of surface properties and electronic gap of rutile titania nanoparticles with particle size. The surface energies and electronic gaps are calculated for cuboidal particles with minimum dimension ranging from 3.7 Angstrom (24 atoms) to 10.3 Angstrom (384 atoms) using a highly-parallel real-space DFT code to enable hybrid level DFT calculations of larger nanoparticles than are typically practical. We deconvolute the geometric and electronic finite size effects in surface energy, and evaluate the influence of defects on electronic gap and density of states (DOS). The electronic finite size effects in surface energy vanish when the minimum length scale of the nanoparticles becomes greater than 10 Angstrom. We show that this length scale is consistent with a computationally efficient numerical analysis of the characteristic length scale of electronic interactions. The surface energy of nanoparticles having minimum dimension beyond this characteristic length can be approximated using slab calculations that account for the geometric defects. In contrast, the finite size effects on the electronic gap and DOS is highly dependent on the shape and size of these particles. Furthermore, the DOS for cuboidal particles and more realistic particles constructed using the Wulff algorithm reveal that defect states within the electronic gap play a key role in determining the eigen value distribution of nanoparticles and the electronic gap does not converge to the bulk limit for the particle sizes investigated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Technical Note: Statistical dependences between channels in radiochromic film readings. Implications in multichannel dosimetry

Purpose: This note studies the statistical relationships between color channels in radiochromic film readings with flatbed scanners. The same relationships are studied for noise. Finally, their implications for multichannel film dosimetry are discussed. Methods: Radiochromic films exposed to wedged fields of 6 MV energy were read in a flatbed scanner. The joint histograms of pairs of color channels were used to obtain the joint and conditional probability density functions between channels. Then, the conditional expectations and variances of one channel given another channel were obtained. Noise was extracted from film readings by means of a multiresolution analysis. Two different dose ranges were analyzed, the first one ranging from 112 to 473 cGy and the second one from 52 to 1290 cGy. Results: For the smallest dose range, the conditional expectations of one channel given another channel can be approximated by linear functions, while the conditional variances are fairly constant. The slopes of the linear relationships between channels can be used to simplify the expression that estimates the dose by means of the multichannel method. The slopes of the linear relationships between each channel and the red one can also be interpreted as weights in the final contribution to dose estimation. However, for the largest dose range, the conditional expectations of one channel given another channel are no longer linear functions. Finally, noises in different channels were found to correlate weakly. Conclusions: Signals present in different channels of radiochromic film readings show a strong statistical dependence. By contrast, noise correlates weakly between channels. For the smallest dose range analyzed, the linear behavior between the conditional expectation of one channel given another channel can be used to simplify calculations in multichannel film dosimetry.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Regularized machine learning on molecular graph model explains systematic error in DFT enthalpies

Abstract A major goal of materials research is the discovery of novel and efficient heterogeneous catalysts for various chemical processes. In such studies, the candidate catalyst material is modeled using tens to thousands of chemical species and elementary reactions. Density Functional Theory (DFT) is widely used to calculate the thermochemistry of these species which might be surface species or gas-phase molecules. The use of an approximate exchange correlation functional in the DFT framework introduces an important source of error in such models. This is especially true in the calculation of gas phase molecules whose thermochemistry is calculated using the same planewave basis set as the rest of the surface mechanism. Unfortunately, the nature and magnitude of these errors is unknown for most practical molecules. Here, we investigate the error in the enthalpy of formation for 1676 gaseous species using two different DFT levels of theory and the ‘ground truth values’ obtained from the NIST database. We featurize molecules using graph theory. We use a regularized algorithm to discover a sparse model of the error and identify important molecular fragments that drive this error. The model is robust to rigorous statistical tests and is used to correct DFT thermochemistry, achieving more than an order of magnitude improvement.

36 MATERIALS SCIENCE↗