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At least 865 records · Page 48
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DOE OSTI2016

Perspective: How good is DFT for water?

Kohn-Sham density functional theory (DFT) has become established as an indispensable tool for investigating aqueous systems of all kinds, including those important in chemistry, surface science, biology, and the earth sciences. Nevertheless, many widely used approximations for the exchange-correlation (XC) functional describe the properties of pure water systems with an accuracy that is not fully satisfactory. The explicit inclusion of dispersion interactions generally improves the description, but there remain large disagreements between the predictions of different dispersion-inclusive methods. We present here a review of DFT work on water clusters, ice structures, and liquid water, with the aim of elucidating how the strengths and weaknesses of different XC approximations manifest themselves across this variety of water systems. Our review highlights the crucial role of dispersion in describing the delicate balance between compact and extended structures of many different water systems, including the liquid. By referring to a wide range of published work, we argue that the correct description of exchange-overlap interactions is also extremely important, so that the choice of semi-local or hybrid functional employed in dispersion-inclusive methods is crucial. The origins and consequences of beyond-2-body errors of approximate XC functionals are noted, and we also discuss the substantial differences between different representations of dispersion. We propose a simple numerical scoring system that rates the performance of different XC functionals in describing water systems, and we suggest possible future developments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Single scale cluster expansions with applications to many Boson and unbounded spin systems

We develop a cluster expansion to show exponential decay of correlations for quite general single scale spin systems, as they arise in lattice quantum field theory and discretized functional integral representations for observables of quantum statistical mechanics. We apply our results to the small field approximation to the coherent state correlation functions of the grand canonical Bose gas at negative chemical potential, constructed by Balaban et al. [Ann. Henri Poincaré 11, 151–350 (2010c)], and to N component unbounded spin systems with repulsive two body interaction and massive, possibly complex, covariance. Our cluster expansion is derived by a single application of the Brydges-Kennedy-Abdesselam-Rivasseau interpolation formula.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Communication: Near-locality of exchange and correlation density functionals for 1- and 2-electron systems

The uniform electron gas and the hydrogen atom play fundamental roles in condensed matter physics and quantum chemistry. The former has an infinite number of electrons uniformly distributed over the neutralizing positively charged background, and the latter only one electron bound to the proton. The uniform electron gas was used to derive the local spin density approximation to the exchange-correlation functional that undergirds the development of the Kohn-Sham density functional theory. We show here that the ground-state exchange-correlation energies of the hydrogen atom and many other 1- and 2-electron systems are modeled surprisingly well by a different local spin density approximation (LSDA0). LSDA0 is constructed to satisfy exact constraints but agrees surprisingly well with the exact results for a uniform two-electron density in a finite, curved three-dimensional space. We also apply LSDA0 to excited or noded 1-electron densities, where it works less well. Furthermore, we show that the localization of the exact exchange hole for a 1- or 2-electron ground state can be measured by the ratio of the exact exchange energy to its optimal lower bound.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals

In this work, a systematic infrastructure is described that formalizes concepts implicit in previous work and greatly simplifies computer implementation of reduced-scaling electronic structure methods. The key concept is sparse representation of tensors using chains of sparse maps between two index sets. Sparse map representation can be viewed as a generalization of compressed sparse row, a common representation of a sparse matrix, to tensor data. By combining few elementary operations on sparse maps (inversion, chaining, intersection, etc.), complex algorithms can be developed, illustrated here by a linear-scaling transformation of three-center Coulomb integrals based on our compact code library that implements sparse maps and operations on them. The sparsity of the three-center integrals arises from spatial locality of the basis functions and domain density fitting approximation. A novel feature of our approach is the use of differential overlap integrals computed in linear-scaling fashion for screening products of basis functions. Finally, a robust linear scaling domain based local pair natural orbital second-order Möller-Plesset (DLPNO-MP2) method is described based on the sparse map infrastructure that only depends on a minimal number of cutoff parameters that can be systematically tightened to approach 100% of the canonical MP2 correlation energy. With default truncation thresholds, DLPNO-MP2 recovers more than 99.9% of the canonical resolution of the identity MP2 (RI-MP2) energy while still showing a very early crossover with respect to the computational effort. Based on extensive benchmark calculations, relative energies are reproduced with an error of typically <0.2 kcal/mol. The efficiency of the local MP2 (LMP2) method can be drastically improved by carrying out the LMP2 iterations in a basis of pair natural orbitals. While the present work focuses on local electron correlation, it is of much broader applicability to computation with sparse tensors in quantum chemistry and beyond.

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

Extending Parsimonious Bayesian Inference

Parsimonious Bayesian inference is a theoretical framework for efficient data assimilation that seeks to balance increased consistency between predictions and training data against corresponding increases in model complexity. Within this framework, over-training is understood as optimization that encodes excessive information within model parameters while only achieving small improvements between predictions and training data. This project aims to develop practical methods of limiting excess model information during optimization. One key observation is that practical heuristics for parsimonious learning in high-dimensions must balance expressivity, i.e. the ability of the model to capture diverse predictions with only a few non-zero parameters, against discoverability, i.e. the ability to train the model with gradient-based optimization and drive parameters to low information states. As such, we developed logical activation functions that are able to adaptively approximate arbitrary truth tables that define Boolean logic operations within a probabilistic framework. These functions have demonstrated the ability to learn exclusive disjunction (XOR) and conditioned disjunction (if [condition] then [result_if_true] else [result_if_false]) within a single layer of a neural network. To efficiently exploit these activation functions to drive parsimonious learning required several other advances within the domain of variational inference. The most efficient form of complexity suppression is structured sparsification, driving most model parameters to zero while achieving the structural coherence among nonzeros needed for bandwidth reduction. Such models are not only far more efficient at suppressing information-theoretic complexity, they also reduce the other forms of complexity (computations, communication, storage, and the number of dependencies needed to evaluate predictions). Aiming to support enhanced sparsification, this project examined new approaches to high-dimensional variational inference that allow us to calibrate and control parameter uncertainty during optimization. By identifying which parameters can sustain sparsifying perturbations with little impact on prediction quality, we can develop better pruning strategies by framing them as approximate Bayesian inference. These advances also open paths to mitigate concerns with deploying advanced learning methods in resource-constrained environments, such as running models on power-limited or communication-limited devices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Kinetic theory of turbulence for parallel propagation revisited: Low-to-intermediate frequency regime

A previous paper [P. H. Yoon, “Kinetic theory of turbulence for parallel propagation revisited: Formal results,” Phys. Plasmas 22, 082309 (2015)] revisited the second-order nonlinear kinetic theory for turbulence propagating in directions parallel/anti-parallel to the ambient magnetic field, in which the original work according to Yoon and Fang [Phys. Plasmas 15, 122312 (2008)] was refined, following the paper by Gaelzer et al. [Phys. Plasmas 22, 032310 (2015)]. The main finding involved the dimensional correction pertaining to discrete-particle effects in Yoon and Fang's theory. However, the final result was presented in terms of formal linear and nonlinear susceptibility response functions. In the present paper, the formal equations are explicitly written down for the case of low-to-intermediate frequency regime by making use of approximate forms for the response functions. The resulting equations are sufficiently concrete so that they can readily be solved by numerical means or analyzed by theoretical means. The derived set of equations describe nonlinear interactions of quasi-parallel modes whose frequency range covers the Alfvén wave range to ion-cyclotron mode, but is sufficiently lower than the electron cyclotron mode. The application of the present formalism may range from the nonlinear evolution of whistler anisotropy instability in the high-beta regime, and the nonlinear interaction of electrons with whistler-range turbulence.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Direct non-Born-Oppenheimer variational calculations of all bound vibrational states corresponding to the first rotational excitation of D{sub 2} performed with explicitly correlated all-particle Gaussian functions

Direct variational calculations where the Born-Oppenheimer approximation is not assumed are done for all rovibrational states of the D{sub 2} molecule corresponding to first excited rotational level (the N = 1 states). All-particle explicitly correlated Gaussian basis functions are used in the calculations. The exponential parameters of the Gaussians are optimized with the aid of analytically calculated energy gradient determined with respect to these parameters. The results allow to determine the ortho-para spin isomerization energies as a function of the vibrational quantum number.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2015

Quantum Effects on the Capacitance of Graphene-Based Electrodes

We recently measured quantum capacitance for electric double layers (EDL) at electrolyte/graphene interfaces. However, the importance of quantum capacitance in realistic carbon electrodes is not clear. Toward understanding that from a theoretical perspective, here we studied the quantum capacitance and total capacitance of graphene electrodes as a function of the number of graphene layers. The quantum capacitance was obtained from electronic density functional theory based on fixed band approximation with an implicit solvation model, while the EDL capacitances were from classical density functional theory. We found that quantum capacitance plays a dominant role in total capacitance of the single-layer graphene both in aqueous and ionic-liquid electrolytes but the contribution decreases as the number of graphene layers increases. Moreover, the total integral capacitance roughly levels off and is dominated by the EDL capacitance beyond about four graphene layers. Finally, because many porous carbons have nanopores with stacked graphene layers at the surface, this research provides a good estimate of the effect of quantum capacitance on their electrochemical performance.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Primordial fluctuations from complex AdS saddle points

One proposal for dS/CFT is that the Hartle-Hawking (HH) wave function in the large volume limit is equal to the partition function of a Euclidean CFT deformed by various operators. All saddle points defining the semiclassical HH wave function in cosmology have a representation in which their interior geometry is part of a Euclidean AdS domain wall with complex matter fields. We compute the wave functions of scalar and tensor perturbations around homogeneous isotropic complex saddle points, turning on single scalar field matter only. We compare their predictions for the spectra of CMB perturbations with those of a different dS/CFT proposal based on the analytic continuation of inflationary universes to real asymptotically AdS domain walls. We find the predictions of both bulk calculations agree to first order in the slow roll parameters, but there is a difference at higher order which, we argue, is a signature of the HH state of the fluctuations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Tomography of the rho meson in the QCD instanton vacuum: Transverse momentum dependent parton distribution functions

We analyze the rho meson unpolarized and polarized transverse momentum dependent parton distribution functions (TMDPDFs) in the instanton liquid model (ILM). The corresponding TMDs in ILM are approximated by a constituent quark beam function in the leading Fock state multiplied by a rapidity-dependent factor resulting from the staple-shaped Wilson lines, for fixed longitudinal momentum, transverse separation, and rapidity. At the resolution of the ILM, all of the rho meson TMDs are symmetric in parton 𝑥 for fixed transverse momentum, and Gaussian-like in the transverse momentum for fixed parton 𝑥. The latter is a direct consequence of the profiling of the quark zero modes in the ILM. The evolved TMDs at higher rapidity using the Collins-Soper kernel, and higher resolution using the renormalization group, show substantial skewness towards low parton 𝑥.

Gluons↗
DOE OSTI2024

Monte Carlo Explicitly Correlated Second-Order Many-Body Green’s Function Calculations of Semiconductor Band Gaps

A systematically converging series of ab initio, post-density-functional, size-consistent, electron-correlated approximations is desired for predictive computing of felectronic band structures of insulating, semiconducting, and metallic solids. A series that meets all of these desiderata (except the applicability to metals) is ab initio many-body Green's function theory based on Gaussian-type-orbital (GTO) basis sets. Here, its leading-order approximation, the second-order Green's function (GF2) method in the diagonal and frequency-independent approximations with the aug-cc-pVDZ basis set, is applied to the fundamental band gaps of three semiconductors (diamond, silicon, and silicon carbide in the zincblende structure) using cluster models. Corrections are made to the basis-set-incompleteness errors by the explicit-correlation (F12) ansatz (GF2-F12) for the valence band edges. The crystals are modeled as surface-passivated clusters of increasing sizes, whose wave functions are expanded by up to 2709 GTO basis functions. Immense computational costs of these calculations are overcome by the highly scalable stochastic algorithm of the Monte Carlo GF2-F12 method, whose operation cost per state increases only as a cubic power of system size, which has a tiny memory footprint and easily achieves near-perfect parallel efficiency on thousands of CPUs or on hundreds of GPUs. The correlated, F12-corrected highest-occupied and lowest-unoccupied molecular-orbital energy (HOMO-LUMO) gap is 5.78 ± 0.07 eV for C 87 H 76 as compared with the experimental value of the fundamental (indirect) band gap of bulk diamond at 5.48 eV. The correlated, F12-corrected HOMO-LUMO gaps for Si 75 H 76 and Si 32 C 43 H 76 are 2.56 ± 0.15 eV and 3.50 ± 0.12 eV, respectively, which are expected to decrease further with increasing cluster sizes. As a result, the experimental fundamental (indirect) band gaps of bulk silicon and silicon carbide are 1.17 eV and 2.42 eV, respectively.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Gaussian approximation potentials for accurate thermal properties of two-dimensional materials

Two-dimensional materials (2DMs) continue to attract a lot of attention, particularly for their extreme flexibility and superior thermal properties. Molecular dynamics simulations are among the most powerful methods for computing these properties, but their reliability depends on the accuracy of interatomic interactions. While first principles approaches provide the most accurate description of interatomic forces, they are computationally expensive. In contrast, classical force fields are computationally efficient, but have limited accuracy in interatomic force description. Machine learning interatomic potentials, such as Gaussian Approximation Potentials, trained on density functional theory (DFT) calculations offer a compromise by providing both accurate estimation and computational efficiency. Here, in this work, we present a systematic procedure to develop Gaussian approximation potentials for selected 2DMs, graphene, buckled silicene, and h-XN (X = B, Al, and Ga, as binary compounds) structures. We validate our approach through calculations that require various levels of accuracy in interatomic interactions. The calculated phonon dispersion curves and lattice thermal conductivity, obtained through harmonic and anharmonic force constants (including fourth order) are in excellent agreement with DFT results. HIPHIVE calculations, in which the generated GAP potentials were used to compute higher-order force constants instead of DFT, demonstrated the first-principles level accuracy of the potentials for interatomic force description. Molecular dynamics simulations based on phonon density of states calculations, which agree closely with DFT-based calculations, also show the success of the generated potentials in high-temperature simulations.

2D Materials↗
DOE OSTI2018

Galerkin finite element method for time-fractional stochastic diffusion equations

In this paper, Galerkin finite element method for solving the time-fractional stochastic diffusion equations with multiplicative noise is proposed and investigated. The pathwise regularity properties of solutions to the semidiscrete Galerkin approximations are demonstrated and the convergence of optimal rates are derived. And also we construct the fully discrete scheme which is based on the approximations of the Mittag–Leffler function and analyze the error estimates of convergence in L{sub 2}-norm space. Finally, numerical results are conducted to confirm our theoretical findings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Hybrid functional pseudopotentials

The consistency between the exchange-correlation functional used in pseudopotential construction and in the actual density functional theory calculation is essential for the accurate prediction of fundamental properties of materials. However, routine hybrid density functional calculations at present still rely on generalized gradient approximation pseudopotentials due to the lack of hybrid functional pseudopotentials. Here, we present a scheme for generating hybrid functional pseudopotentials, and we analyze the importance of pseudopotential density functional consistency for hybrid functionals. For the PBE0 hybrid functional, we benchmark our pseudopotentials for structural parameters and fundamental electronic gaps of the Gaussian-2 (G2) molecular dataset and some simple solids. Our results demonstrate that using our PBE0 pseudopotentials in PBE0 calculations improves agreement with respect to all-electron calculations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Simplifying activations with linear approximations in neural networks

A key step in Neural Networks is activation. Among the different types of activation functions, sigmoid, tanh, and others involve the usage of exponents for calculation. From a hardware perspective, exponential implementation implies the usage of Taylor series or repeated methods involving many addition, multiplication, and division steps, and as a result are power-hungry and consume many clock cycles. We implement a piecewise linear approximation of the sigmoid function as a replacement for standard sigmoid activation libraries. This approach provides a practical alternative by leveraging piecewise segmentation, which simplifies hardware implementation and improves computational efficiency. In this paper, we detail piecewise functions that can be implemented using linear approximations and their implications for overall model accuracy and performance gain. Our results show that for the DenseNet, ResNet, and GoogLeNet architectures, the piecewise linear approximation of the sigmoid function provides faster execution times compared to the standard TensorFlow sigmoid implementation while maintaining comparable accuracy. Specifically, for MNIST with DenseNet, accuracy reaches 99.91% (Piecewise) vs. 99.97% (Base) with up to 1.31x speedup in execution time. For CIFAR-10 with DenseNet, accuracy improves to 98.97% (Piecewise) vs. 99.40% (Base) while achieving 1.24x faster execution. Similarly, for CIFAR-100 with DenseNet, the accuracy is 97.93% (Piecewise) vs. 98.39% (Base), with a 1.18x execution time reduction. These results confirm the proposed method’s capability to efficiently process large-scale datasets and computationally demanding tasks, offering a practical means to accelerate deep learning models, including LSTMs, without compromising accuracy.

Activation function↗
DOE OSTI2019

Electronic Structure and Linhard Function of Iron-Based Superconductor La{sub 0.5−x}Na{sub 0.5 + x}Fe{sub 2}As{sub 2}

We perform theoretical studies of the iron-based superconductor La{sub 0.5−x}Na{sub 0.5 + x}Fe{sub 2}As{sub 2}. Using density functional calculation with virtual crystal approximation, band structures, density of states, and Fermi surfaces are obtained for different La/Na composition by varying x value. Furthermore, the nesting property is also investigated using the Linhard function. Our main findings are as follows: For undoped (x = 0.0) case, the magnetic and electronic structure share great similarities with extensively studied BaFe{sub 2}As{sub 2}. Upon hole doping (x = 0.3), the Q = (π,π) nesting property are preserved. However, upon electron doping (x = -0.3), the Fermi surfaces undergo a dramastic change into 3D and complex structure. We find this change is attributed to the comprehensive influence of band filling and chemical pressure of La{sup 3+}. We propose the asymmetric change of Fermi surfaces upon doping may in some sense explain the electron-hole asymmetry in phase diagram.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Low-rank canonical-tensor decomposition of potential energy surfaces: application to grid-based diagrammatic vibrational Green's function theory

Here, a new method is proposed for a fast evaluation of high-dimensional integrals of potential energy surfaces (PES) that arise in many areas of quantum dynamics. It decomposes a PES into a canonical low-rank tensor format, reducing its integral into a relatively short sum of products of low-dimensional integrals. The decomposition is achieved by the alternating least squares (ALS) algorithm, requiring only a small number of single-point energy evaluations. Therefore, it eradicates a force-constant evaluation as the hotspot of many quantum dynamics simulations and also possibly lifts the curse of dimensionality. This general method is applied to the anharmonic vibrational zero-point and transition energy calculations of molecules using the second-order diagrammatic vibrational many-body Green's function (XVH2) theory with a harmonic-approximation reference. In this application, high dimensional PES and Green's functions are both subjected to a low-rank decomposition. Evaluating the molecular integrals over a low-rank PES and Green's functions as sums of low-dimensional integrals using the Gauss–Hermite quadrature, this canonical-tensor-decomposition-based XVH2 (CT-XVH2) achieves an accuracy of 0.1 cm -1 or higher and nearly an order of magnitude speedup as compared with the original algorithm using force constants for water and formaldehyde.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2016

Multiscale Simulation Framework for Coupled Fluid Flow and Mechanical Deformation

Our work in this project is aimed at making fundamental advances in multiscale methods for flow and transport in highly heterogeneous porous media. The main thrust of this research is to develop a systematic multiscale analysis and efficient coarse-scale models that can capture global effects and extend existing multiscale approaches to problems with additional physics and uncertainties. A key emphasis is on problems without an apparent scale separation. Multiscale solution methods are currently under active investigation for the simulation of subsurface flow in heterogeneous formations. These procedures capture the effects of fine-scale permeability variations through the calculation of specialized coarse-scale basis functions. Most of the multiscale techniques presented to date employ localization approximations in the calculation of these basis functions. For some highly correlated (e.g., channelized) formations, however, global effects are important and these may need to be incorporated into the multiscale basis functions. Other challenging issues facing multiscale simulations are the extension of existing multiscale techniques to problems with additional physics, such as compressibility, capillary effects, etc. In our project, we explore the improvement of multiscale methods through the incorporation of additional (single-phase flow) information and the development of a general multiscale framework for flows in the presence of uncertainties, compressible flow and heterogeneous transport, and geomechanics. We have considered (1) adaptive local-global multiscale methods, (2) multiscale methods for the transport equation, (3) operator-based multiscale methods and solvers, (4) multiscale methods in the presence of uncertainties and applications, (5) multiscale finite element methods for high contrast porous media and their generalizations, and (6) multiscale methods for geomechanics.

97 MATHEMATICS AND COMPUTING↗