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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Importance of self-interaction-error removal in density functional calculations on water cluster anions

Accurate description of the excess charge in water cluster anions is challenging for standard semi-local and (global) hybrid density functional approximations (DFAs). Using the recent unitary invariant implementation of the Perdew–Zunger self-interaction correction (SIC) method using Fermi-Löwdin orbitals, we assess the effect of self-interaction error on the vertical detachment energies of water cluster anions with the local spin density approximation (LSDA), Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation, and the strongly constrained and appropriately normed (SCAN) meta-GGA functionals. Our results show that for the relative energies of isomers with respect to reference CCSD(T) values, the uncorrected SCAN functional has the smallest deviation of 21 meV, better than that for the MP2 method. The performance of SIC-SCAN is comparable to that of MP2 and is better than SIC-LSDA and SIC-PBE, but it reverses the ordering of the two lowest isomers for water hexamer anions. Removing self interaction error (SIE) corrects the tendency of LSDA, PBE, and SCAN to over-bind the extra electron. The vertical detachment energies (VDEs) of water cluster anions, obtained from the total energy differences of corresponding anion and neutral clusters, are significantly improved by removing self-interaction and are better than the hybrid B3LYP functional, but fall short of MP2 accuracy. Removing SIE results in substantial improvement in the position of the eigenvalue of the extra electron. The negative of the highest occupied eigenvalue after SIC provides an excellent approximation to the VDE, especially for SIC-PBE where the mean absolute error with respect to CCSD(T) is only 17 meV, the best among all approximations compared in this work.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Free-energy orbital-free density functional theory: recent developments, perspective, and outlook

By summarizing the constraint-based development of orbital-free free-energy density functional approximations, we provide a perspective on progress over the last 15 years, the limitations of existing functionals, and the challenges awaiting resolution. We outline the chronology of the development of noninteracting and exchange-correlation free-energy orbital-free functionals and summarize the theoretical basis of existing local density approximation, second-order approximation, generalized gradient approximation (GGA), and meta-GGAs. We discuss limitations and challenges such as problems with thermodynamic derivatives, free-energy nonadditivity and the closely related issue of all-electron versus valence-only local pseudo-potential performance.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2018

Performance of the strongly constrained and appropriately normed density functional for solid-state materials

Constructed to satisfy 17 known exact constraints for a semilocal density functional, the strongly constrained and appropriately normed (SCAN) meta-generalized-gradient-approximation functional has shown early promise for accurately describing the electronic structure of molecules and solids. One open question is how well SCAN predicts the formation energy, a key quantity for describing the thermodynamic stability of solid-state compounds. To answer this question, we perform an extensive benchmark of SCAN by computing the formation energies for a diverse group of nearly 1000 crystalline compounds for which experimental values are known. Due to an enhanced exchange interaction in the covalent bonding regime, SCAN substantially decreases the formation energy errors for strongly bound compounds, by approximately 50% to 110 meV/atom, as compared to the generalized gradient approximation of Perdew, Burke, and Ernzerhof (PBE). However, for intermetallic compounds, SCAN performs moderately worse than PBE with an increase in formation energy error of approximately 20%, stemming from SCAN's distinct behavior in the weak bonding regime. The formation energy errors can be further reduced via elemental chemical potential fitting. We find that SCAN leads to significantly more accurate predicted crystal volumes, moderately enhanced magnetism, and mildly improved band gaps as compared to PBE. Altogether, SCAN represents a significant improvement in accurately describing the thermodynamics of strongly bound compounds.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Untangling Sources of Error in the Density-Functional Many-Body Expansion

The many-body expansion provides a framework for data-driven applications of electronic structure theory, including parametrization of classical force fields and machine learning. In this article, we demonstrate that its use significantly amplifies quadrature grid errors when modern density-functional approximations are employed. Standard grids that work well in conventional density-functional calculations result in runaway error accumulation when used with the many-body expansion. At the same time, delocalization error is also exacerbated, leading to exaggerated estimates of nonadditive n-body interactions. This is illustrated for anion–water clusters using the SCAN, r2SCAN, ωB97X-V and ωB97M-V functionals. By employing dense quadrature grids, the inherent self-interaction error is exposed, which can then be mitigated using a variety of other strategies.

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

Efficient Implementation of Artificial Neural Networks for Sensor Data Analysis Based on a Genetic Algorithm

The reliability of many industrial processes depends on the sensor system. However, these sensors can be affected by noise, perturbations and failures. Hence, sensor monitoring and diagnosis are fundamental to guarantee the quality of an industrial process. Nowadays, artificial neural networks (ANN) are widely used in sensor signal processing and diagnosis. However, those ANNs usually require many artificial neurons, being difficult to implement in software and hardware due to their high computational costs. This paper presents an optimized implementation of artificial neurons in ANNs for sensor data analysis using a Genetic Algorithm (GA). The objective of GA is to find an adequate segmentation to reduce the activation function approximation error. One of the advantages of the proposed approach is that the cost function used in GA considers the effect of factors such as the ANN architecture or the number of bits used in arithmetic operations. The proposed ANN implementation technique aims to get the best possible approximation for a specific ANN architecture, making easier its implementation in software and hardware. Simulation and experimental results using FPGA (Field Programmable Gate Array) prove the advantages of the proposed approach for implementing sensor data analysis systems based on ANNs.

D estefani, André↗
DOE OSTI2017

On extending Kohn-Sham density functionals to systems with fractional number of electrons

Here, we analyze four ways of formulating the Kohn-Sham (KS) density functionals with a fractional number of electrons, through extending the constrained search space from the Kohn-Sham and the generalized Kohn-Sham (GKS) non-interacting $\mathcal{v}$-representable density domain for integer systems to four different sets of densities for fractional systems. In particular, these density sets are (I) ensemble interacting N -representable densities, (II) ensemble non-interacting N -representable densities, (III) non-interacting densities by the Janak construction, and (IV) non-interacting densities whose composing orbitals satisfy the Aufbau occupation principle. By proving the equivalence of the underlying first order reduced density matrices associated with these densities, we show that sets (I), (II), and (III) are equivalent, and all reduce to the Janak construction. Moreover, for functionals with the ensemble v-representable assumption at the minimizer, (III) reduces to (IV) and thus justifies the previous use of the Aufbau protocol within the (G)KS framework in the study of the ground state of fractional electron systems, as defined in the grand canonical ensemble at zero temperature. By further analyzing the Aufbau solution for different density functional approximations (DFAs) in the (G)KS scheme, we rigorously prove that there can be one and only one fractional occupation for the Hartree Fock functional, while there can be multiple fractional occupations for general DFAs in the presence of degeneracy. This has been confirmed by numerical calculations using the local density approximation as a representative of general DFAs. This work thus clarifies important issues on density functional theory calculations for fractional electron systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Scalable Bayesian optimization with randomized prior networks

Several fundamental problems in science and engineering consist of global optimization tasks involving unknown high-dimensional (black-box) functions that map a set of controllable variables to the outcomes of an expensive experiment. Bayesian Optimization (BO) techniques are known to be effective in tackling global optimization problems using a relatively small number objective function evaluations, but their performance suffers when dealing with high-dimensional outputs. To overcome the major challenge of dimensionality, here we propose a deep learning framework for BO and sequential decision making based on bootstrapped ensembles of neural architectures with randomized priors. Using appropriate architecture choices, we show that the proposed framework can approximate functional relationships between design variables and quantities of interest, even in cases where the latter take values in high-dimensional vector spaces or even infinite-dimensional function spaces. In the context of BO, we augmented the proposed probabilistic surrogates with re-parameterized Monte Carlo approximations of multiple-point (parallel) acquisition functions, as well as methodological extensions for accommodating black-box constraints and multi-fidelity information sources. We test the proposed framework against state-of-the-art methods for BO and demonstrate superior performance across several challenging tasks with high-dimensional outputs, including a constrained multi-fidelity optimization task involving shape optimization of rotor blades in turbo-machinery.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Robust Uncertainty Quantification using Response Surface Approximations of Discontinuous Functions

This paper considers response surface approximations for discontinuous quantities of interest. Our objective is not to adaptively characterize the manifold defining the discontinuity. Instead, we utilize an epistemic description of the uncertainty in the location of a discontinuity to produce robust bounds on sample-based estimates of probabilistic quantities of interest. We demonstrate that two common machine learning strategies for classification, one based on nearest neighbors (Voronoi cells) and one based on support vector machines, provide reasonable descriptions of the region where the discontinuity may reside. In higher dimensional spaces, we demonstrate that support vector machines are more accurate for discontinuities defined by smooth manifolds. We also show how gradient information, often available via adjoint-based approaches, can be used to define indicators to effectively detect a discontinuity and to decompose the samples into clusters using an unsupervised learning technique. Numerical results demonstrate the epistemic bounds on probabilistic quantities of interest for simplistic models and for a compressible fluid model with a shock-induced discontinuity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

The exact exchange–correlation potential in time-dependent density functional theory: Choreographing electrons with steps and peaks

The time-dependent exchange–correlation potential has the unusual task of directing fictitious non-interacting electrons to move with exactly the same probability density as true interacting electrons. This has intriguing implications for its structure, especially in the non-perturbative regime, leading to step and peak features that cannot be captured by bootstrapping any ground-state functional approximation. Here, we review what has been learned about these features in the exact exchange–correlation potential of time-dependent density functional theory in the past decade or so and implications for the performance of simulations when electrons are driven far from any ground state.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Modeling of three-dimensional surfaces using high-level canonical piecewise-linear functions in cylindrical coordinates

In this paper, the potential application of the high-level canonical piecewise-linear model in the field of three-dimensional visualization is proposed. This idea emerges from the premise that a three-dimensional surface can be modeled by a continuous two-dimensional function. In this regard, the main contribution consists in providing a methodology for the construction of such function. For this purpose, the well-known algorithm used in the high-level canonical piecewise-linear model has been modified to achieve functions with greater graphing capability. One of the most notorious changes made with respect to the traditional methodology is the use of a new scheme of function domain partition. Contrary to the simplicial partitioning, in our proposal, an equally distributed angular partitioning is considered. With this, the resulting approximate function is expressed in cylindrical coordinates which overcome the typical limitation of graphs in Cartesian coordinates of only representing single-valued surfaces. Another remarkable change can be found in the range of evaluation of the function. Instead of using an open interval, in our approach, a closed interval from 0 to 2π is adopted. To support this proposal, illustrative case studies are reported. Numerical simulations demonstrate the effectiveness of this type of representation model not only in visual perception of three-dimensional surfaces, but also in more complex tasks like volume estimation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Gold-Standard Chemical Database 137 (GSCDB137): A Diverse Set of Accurate Energy Differences for Assessing and Developing Density Functionals

We present GSCDB137, a rigorously curated benchmark library of 137 data sets (8377 entries) covering main-group and transition-metal reaction energies and barrier heights, (intra- and intermolecular) noncovalent interactions, dipole moments, polarizabilities, electric-field response energies, and vibrational frequencies. Legacy data from GMTKN55 and MGCDB84 have been updated to today's best reference values; redundant or low-quality points were removed, and many new, property-focused sets were added. Testing 29 popular density functional approximations (DFAs) confirms the expected Jacob's-ladder hierarchy overall but also reveals notable exceptions: functional performance for frequencies and electric-field properties correlates poorly with that for other ground-state energetics. ωB97M-V and ωB97X-V are the most balanced hybrid meta-GGA and hybrid GGA, respectively; B97M-V and revPBE-D4 lead the meta-GGA and GGA classes. Double hybrids lower mean errors by about 30% versus their hybrid analogues but demand careful frozen-core, basis set, and spin contamination treatment. GSCDB137 offers a comprehensive, openly documented platform for rigorous validation of DFA and universal machine learning potentials, and training of the next generation of exchange-correlation functionals.

Liang, Jiashu [University of California, Berkeley,↗
DOE OSTI2019

Self-interaction-free electric dipole polarizabilities for atoms and their ions using the Fermi-Löwdin self-interaction correction

The static electric dipole polarizability of a system is a measure of the binding of its electrons. In density functional theory calculations, this binding is weakened by the presence of unphysical self-interaction in the density functional approximation (DFA), leading to overestimates of polarizabilities. In this work, to investigate this systematically we compare polarizabilities for the atoms from H to Ar and their anions and cations calculated in several DFAs and the corresponding self-interaction-corrected (SIC) DFAs with experiment and with high-level quantum chemistry reference values. The SIC results are obtained using the Fermi-Löwdin orbital self-interaction correction (FLO-SIC) method. Removing self-interaction generally leads to smaller polarizabilities that agree significantly better with reference values. In conclusion, we find that FLO-SIC improves the performance of the local spin density approximation and the generalized gradient approximation (GGA) for polarizabilities to a quality that is comparable to so-called rung 4 functionals, but slightly degrades the performance of the strongly constrained and appropriately normed meta-GGA functional.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Variational quantum simulation of the critical Ising model with symmetry averaging

Here we investigate the use of deep multiscale entanglement renormalization ansatz (DMERA) circuits as a variational ansatz. We use the exactly solvable one-dimensional critical transverse-field Ising model as a test bed. Numerically exact simulation of the quantum circuit ansatz can in this case be carried out to hundreds of qubits by exploiting efficient classical algorithms for simulating matchgate circuits. We find that, for this system, the DMERA strongly outperforms a standard quantum approximate optimization algorithm (QAOA)–style ansatz, and that a major source of systematic error in correlation functions approximated using the DMERA is the breaking of the translational and Kramers-Wannier symmetries of the transverse-field Ising model. We are able to reduce this error by up to four orders of magnitude by symmetry averaging, without incurring additional cost in qubits or circuit depth. Here, we propose that this technique for mitigating systematic error could be applied to noisy intermediate-scale quantum (NISQ) simulations of physical systems with other symmetries.

1-dimensional spin chains↗
DOE OSTI2019

Stripping off the implementation complexity of physics-based model predictive control for buildings via deep learning

Over the past decade, model predictive control (MPC) has been considered as the most promising solution for intelligent building operation. Despite extensive effort, transfer of this technology into practice is hampered by the need to obtain an accurate controller model with minimum effort, the need of expert knowledge to set it up, and the need of increased computational power and dedicated software to run it. A promising direction that tackles the last two problems was proposed by approximate explicit MPC where the optimal control policies are learned from MPC data via a suitable function approximator, e.g., a deep learning (DL) model. The main advantage of the proposed approach stems from simple evaluation at execution time leading to low computational footprints and easy deployment on embedded HW platforms. We present the energy savings potential of physics-based (also called 'white-box') MPC applied to an office building in Belgium. Moreover, we demonstrate how deep learning approximators can be used to cut the implementation and maintenance costs of MPC deployment without compromising performance. We also critically assess the presented approach by pointing out the major challenges and remaining open-research questions.

Drgona, Jan↗
DOE OSTI2026

Local Spin Density Approximation Strongly Improved by a Better-Informed Local Scaling of Its Self-Interaction Correction

The Perdew−Zunger self-interaction correction (PZSIC) makes density functional approximations (DFAs) exact for all one-electron densities. However, it overcorrects in manyelectron regions, introducing errors for the uniform-density limit, where uncorrected DFAs are exact. The locally scaled PZSIC (LSIC), based on the iso-orbital indicator zσ [which distinguishes single-orbital and slowly varying density regions and is used with the local spin density approximation (LSDA)], restores the uniform-density limit and significantly improves results for many properties, including chemical reaction barrier heights, atomization energies, and ionization potentials. Yet, LSIC performs poorly for weakly bonded systems, leaving many unbound, due to limitations of its iso-orbital indicator. To correct this, in this work we propose a new local scaling, LSIC-α, based on the iso-orbital indicator ασ (which additionally identifies regions of overlapping density tails). A two-parameter scaling function of ασ is fitted to a subset of the nonbonded appropriate norms for the SCAN and r2SCAN meta- GGAs, and tested on many properties of main-group atoms, molecules, and molecular complexes. LSIC-α greatly improves the interaction energies of weakly bonded systems in the S22 data set while retaining LSIC’s accuracy for other properties. This work shows that the errors of LSDA (and presumably of higher-level DFAs) can be largely but not entirely repaired by a proper “do no harm” self-interaction correction.

Approximation↗
DOE OSTI2024

Characterization of Deformational Isomerization Potential and Interconversion Dynamics with Ultrafast X-ray Solution Scattering

Dimeric complexes composed of d 8 square planar metal centers and rigid bridging ligands provide model systems to understand the interplay between attractive dispersion forces and steric strain in order to assist the development of reliable methods to model metal dimer complexes more broadly. [Ir 2 (dimen) 4 ] 2+ (dimen = para-diisocyanomenthane) presents a unique case study for such phenomena, as distortions of the optimal structure of a ligand with limited conformational flexibility counteract the attractive dispersive forces from the metal and ligand to yield a complex with two ground state deformational isomers. Here, in this work, we use ultrafast X-ray solution scattering (XSS) and optical transient absorption spectroscopy (OTAS) to reveal the nature of the equilibrium distribution and the exchange rate between the deformational isomers. The two ground state isomers have spectrally distinct electronic excitations that enable the selective excitation of one isomer or the other using a femtosecond duration pulse of visible light. We then track the dynamics of the nonequilibrium depletion of the electronic ground state population—often termed the ground state hole—with ultrafast XSS and OTAS, revealing a restoration of the ground state equilibrium in 2.3 ps. This combined experimental and theoretical study provides a critical test of various density functional approximations in the description of bridged d 8 –d 8 metal complexes. The results show that density functional theory calculations can reproduce the primary experimental observations if dispersion interactions are added, and a hybrid functional, which includes exact exchange, is used.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Long-range dispersion-corrected density functional for noncovalent interactions

Noncovalent interactions are important in determining structures and properties of molecular complexes and biological molecules, and for understanding adsorption processes in chemistry and biological science, and are still challenging to conventional density functional theories. In this work, the recently developed Tao-Mo (TM) meta-GGA (generalized gradient approximation) functional is combined with the D3 scheme of long-range van der Waals (vdW) interaction correction and the parameters of damping function are optimized with the S66[Formula: see text]×[Formula: see text]8 set. The resulting TM-D3 method is applied to the medium-sized molecular set S22 and large size molecular complexes set L7 to calculate intramolecular interaction energies. The TM-D3 method produces the best accuracy for the S22 set with a MAE of 0.2 kcal/mol, improving upon the PBE-D3 (MAE[Formula: see text]=[Formula: see text]0.5 kcal/mol), PBE0-D3 (MAE[Formula: see text]=[Formula: see text]0.5 kcal/mol), TPSS-D3 (MAE[Formula: see text]=[Formula: see text]0.4 kcal/mol), M06L (MAE[Formula: see text]=[Formula: see text]0.8 kcal/mol), and SCAN-D3 (MAE[Formula: see text]=[Formula: see text]0.4 kcal/mol) methods. For the large size set L7, the TM-D3 (MAE[Formula: see text]=[Formula: see text]2.1 kcal/mol) also performs better than the PBE-D3 (MAE[Formula: see text]=[Formula: see text]2.6 kcal/mol), SCAN-D3 (2.5 kcal/mol) and M06L (3.0 kcal/mol), but not accurate than the PBE0-D3 (MAE[Formula: see text]=[Formula: see text]0.8 kcal/mol) and TPSS-D3 (MAE[Formula: see text]=[Formula: see text]1.1 kcal/mol). However, overall, the TM-D3 method performs very well with an error of 2.7% of mean binding of the S22 set and an error of 12.6% of the mean binding of the L7 set for the two typical and important medium and large size molecular complex sets. The success of the dispersion-corrected TM functional benefits from the ability of the plain TM functional to capture the short-range vdW interaction or extend the short-range interaction to the middle range, and the right coupling between the TM and the long-range vdW correction D3 scheme, leading to the improved description of noncovalent interactions.

Physics↗
DOE OSTI2025

How the choice of exchange–correlation functional affects DFT-based simulations of the hydrated electron

Hydrated electrons are anionic species that are formed when an excess electron is introduced into liquid water. Building an understanding of how hydrated electrons behave in solution has been a long-standing effort of simulation methods, of which density functional theory (DFT) has come to the fore in recent years. The ability of DFT to model the reactive chemistry of hydrated electrons is an attractive advantage over semi-classical methodologies; however, relatively few density functional approximations (DFAs) have been used for the hydrated electron simulations presented in the literature. Here, we simulate hydrated electron systems using a series of exchange–correlation (XC) functionals spanning Jacob’s ladder. We calculate a variety of experimental and other observables of the hydrated electron and compare the XC functional dependence for each quantity. We find that the formation of a stable localized hydrated electron is not necessarily limited to hybrid XC functionals and that some hybrid functionals produce delocalized hydrated electrons or electrons that react with the surrounding water at an unphysically fast rate. Here, we further characterize how different DFAs impact the solvent structure and predicted spectroscopy of the hydrated electron, considering several methods for calculating the hydrated electron’s absorption spectrum for the best comparison between structures generated using different density functionals. None of the dozen or so DFAs that we investigated are able to correctly predict the hydrated electron’s spectroscopy, vertical detachment energy, or molar solvation volume.

Ab-initio molecular dynamics↗