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DOE OSTI2018

A new modified BFGS method for unconstrained optimization problems

Using chain rule, we propose a modified secant equation to get a more accurate approximation of the second curvature of the objective function. Then, based on this modified secant equation we present a new BFGS method for solving unconstrained optimization problems. The proposed method makes use of both gradient and function values, and utilizes information from two most recent steps, while the usual secant relation uses only the latest step information. Under appropriate conditions, we show that the proposed method is globally convergent without convexity assumption on the objective function. Comparative numerical results show computational efficiency of the proposed method in the sense of the Dolan–Moré performance profiles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Spectral Analysis of 3-(Adamantan-1-yl)-4-Ethyl-1-[(4-Phenylpiperazin-1-yl) Methyl]-1H-1,2,4-Triazole-5(4H)-Thione

Vibrational IR (3200–650 cm{sup –1}) and Raman spectra (3200–150 cm{sup –1}) of adamantane-containing 3-(adamantan-1-yl)-4-ethyl-1-[(4-phenylpiperazin-1-yl)methyl]-1H-1,2,4-triazole-5(4H)-thione, which is promising for drug design, were examined. The UV/Vis spectrum (450–200 nm) of the compound in EtOH was measured. Full geometry optimization using density functional theory (DFT) in the B3LYP/cc-pVDZ approximation allowed the equilibrium configuration of the molecule to be determined and IR and Raman spectra to be calculated. Based on these, the experimental vibrational IR and Raman spectra were interpreted and the biological activity indices were predicted. The UV/Vis spectrum of the title compound was simulated at the time-dependent DFT/CAM-B3LYP/cc-pVDZ level with and without solvent effects and at the ab initio multi-reference perturbation theory XMCQDPT2 level. The UV/Vis spectrum that was simulated using the multi-reference XMCQDPT2 approximation agreed very successfully with the experimental data, in contrast to the single-reference DFT method. This was probably a consequence of intramolecular charge transfer.

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

Calculation of Young’s Modulus of MoS{sub 2}-Based Single-Wall Nanotubes Using Force-Field and Hybrid Density Functional Theory

A force field is proposed that reproduces with a high accuracy a large number of properties of the bulk crystal MoS{sub 2} phases, monolayers, and nanotubes. The reproduced values are both the experimental results and the results of quantum chemical calculations. The elaborated interaction potential can be useful primarily for investigation of multiwall MoS{sub 2} nanotubes and their thermodynamic properties, especially, since the potential is able to reproduce the frequencies of the crystal phonon spectrum. In this study the proposed potential is applied to simulate the temperature dependence of a number of properties of the armchair and zigzag nanotubes. The calculations have been performed using molecular mechanics method within the framework of quasi harmonic approximation which is carried out through the estimation of the temperature dependence of the Helmholtz free energy.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Design and analysis of machine learning exchange-correlation functionals via rotationally invariant convolutional descriptors

Here, we explore the potential of a data-driven approach to the design of exchange-correlation (xc) functionals. The approach, inspired by convolutional filters in computer vision and surrogate functions from optimization, utilizes convolutions of the electron density to form a feature space to represent local electronic environments and neural networks to map the features to the exchange-correlation energy density. These features are orbital free, and provide a systematic route to including information at various length scales. This work shows that convolutional descriptors are theoretically capable of an exact representation of the electron density, and proposes Maxwell-Cartesian spherical harmonic kernels as a class of rotationally invariant descriptors for the construction of machine learned functionals. The approach is demonstrated using data from the B3LYP functional on a number of small molecules containing C, H, O, and N along with a neural network regression model. The machine learned functionals are compared to standard physical approximations and the accuracy is assessed for the absolute energy of each molecular system as well as formation energies. The results indicate that it is possible to reproduce the exchange-correlation portion of B3LYP formation energies to within chemical accuracy using orbital-free descriptors with a spatial extent of 0.2 Å. The findings provide empirical insight into the spatial range of electron exchange, and suggest that the combination of convolutional descriptors and machine learning regression models is a promising framework for xc functional design, although challenges remain in obtaining training data and generating models consistent with pseudopotentials.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Fixed points and flow analysis on off-equilibrium dynamics in the boson Boltzmann equation

We consider fixed points of steady solutions and flow directions using the boson Boltzmann equation that is a one-dimensionally reduced kinetic equation after the angular integration. With an elastic collision integral of the two-to-two scattering process, in the dense (dilute) regime where the distribution function is large (small), the boson Boltzmann equation has approximate fixed points with a power-law spectrum in addition to the thermal distribution function. We argue that the power-law fixed point can be exact in special cases. We elaborate a graphical presentation to display evolving flow directions similarly to the renormalization group flow, which explicitly exhibits how fixed points are connected and parameter space is separated by critical lines. We discuss that such a flow diagram contains useful information on thermalization processes out of equilibrium.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Magnetic Properties of La-Doped ZnO(0001)–Zn Polar Surface with and without Vacancies: a First-Principle Study

The effects of La doping with and without vacancies on the magnetism of a ZnO(0001)–Zn polar surface were studied using the generalized gradient approximation + U (GGA + U) method of density functional theory to determine the magnetism source of La-doped ZnO. Results revealed that La doping with O vacancy did not cause ZnO ferromagnetism, but La-doped ZnO with Zn vacancy was ferromagnetic. The net magnetic moment was primarily related to the unpaired electron amount of the O 2p state and slightly modified by orbital and anomalous magnetic moments. The anomalous magnetic moment originated from the radiating magnetism moment via quantum electrodynamics and was confirmed to exist via theoretical calculations of magnetism. Formation energy showed that La doping easily generated Zn vacancies in ZnO, but magnetic quenching occurred when the ratio of La ions to Zn vacancies was 2:1. The unpaired O 2p electrons induced by Zn vacancies were the magnetism source of La-doped ZnO. Moreover, the Curie temperature of La-doped ZnO with Zn vacancy reached room temperature. Results showed that the ZnO(0001)–Zn polar surface can be utilized as the surface of ZnO-based diluted magnetic semiconductors because of its unipolarity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Evaluation of Thermal Scattering Law for U 3 Si 2 Using Temperature-Dependent Phonon Density of States

The thermal scattering law for uranium silicide, a candidate material for high-density nuclear fuel, was evaluated from the temperature-dependent phonon density of states obtained using the quasi-harmonic approximation. For uranium silicide model systems of various volumes near the equilibrium volume, Hellmann-Feynman forces were calculated by performing ab initio lattice dynamics simulations based on density functional theory. Subsequently, the quasi-harmonic approximation was applied by interpolating the results of the harmonic approximation for each volume system. As a sensitivity test, the phonon density of states was calculated for the structures with temperature-dependent volumes at 298 K and 1000 K, obtained by the quasi-harmonic approximation, and the corresponding thermal neutron scattering cross section was evaluated. The temperature-dependent volume and heat capacity of uranium silicide obtained by the quasi-harmonic approximation showed reasonable agreement with experimental data while lattice thermal expansion showed deviation from experimental observations. Thermal scattering cross sections evaluated from 0 K and temperature-dependent phonon density of states exhibited differences of up to 4.1% at 1000 K. This study examines the impact of temperature on the thermal scattering law, employing ab initio lattice dynamics simulations through the quasi-harmonic approximation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2018

Magnetic, Optoelectronic, and Thermodynamic Properties of Sr{sub 2}CrXO{sub 6} (X = La and Y): Half-Metallic and Ferromagnetic Behavior

The effects of spin polarization on the structure, magnetic, and optoelectronic properties of Cr-based series of double perovskites Sr{sub 2}CrXO{sub 6} (X = La and Y) have been studied by using the full-potential linearized augmented plane-wave method (FP-LAPW), based on the density functional theory (DFT) as implemented in the Wien2k code, within the generalized gradient approximation (GGA), GGA + U, and GGA plus Trans-Blaha-modified Becke–Johnson (TB-mBJ) as the exchange correlation. Our results show a similar half-metallic ferromagnetic ground state for both materials. From the electronic properties, it is found that Sr{sub 2}CrYO{sub 6} has a direct band gap at (Γ-Γ) direction and Sr{sub 2}CrLaO{sub 6} has an indirect band gap at (Γ-W) direction. Furthermore, we have computed the optic and thermodynamic properties which are investigated for the first time. Consequently, the magnetic, optoelectronic, and thermodynamic properties show these compounds are promising for high technological applications, namely spintronic materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Effects of Landau quantization on neutrino emission and absorption

Some neutron stars known as magnetars possess very strong magnetic fields, with surface fields as large as 10 15 G and internal fields that are possibly stronger. Recent observations of the radio pulsar GLEAM-X J1627 suggest it may have a surface field as strong as 10 16 G. In the presence of a strong magnetic field, Leinson and Perez showed and Baiko and Yakovlev confirmed that the energy levels of electrons and protons are quantized and the direct Urca process allows neutron stars to cool rapidly, even at low density. For the case of magnetic fields 𝐵 ≳ 10 16 G, we find features in the emissivity due to energy quantization that are not captured by the frequently employed quasiclassical approximation where energy levels are treated as nearly continuous. Resonances can result in amplification of the neutrino emissivity at specific densities compared to a calculation that neglects quantization, particularly at low temperature. These effects are not important for the thermal evolution of an entire neutron star, but may be relevant for phenomena that depend on behavior at specific densities. Here, we present a fully relativistic calculation of the direct Urca rate in a strong magnetic field using the standard V-A weak Lagrangian incorporating mean field nuclear effects and discuss approaches to the numerical challenge the modified wave functions present and a new semianalytic approximation. These tools are also applicable to calculating neutrino opacities in strong magnetic fields in the ejecta of binary neutron star mergers. We calculate the opacities for neutrinos capturing on free nucleons at subsaturation densities and temperatures exceeding an MeV. We find an enhancement to capture processes of the lowest energy neutrinos by an order of magnitude or more due to suppression of electron Pauli blocking in the case of capture on neutrons, and from the effect of the nucleon magnetic moments in the case of capture on protons.

astrophysical electromagnetic fields↗
DOE OSTI2023

Right band gaps for the right reason at low computational cost with a meta-GGA

In density functional theory, traditional explicit density functionals such as the local density approximation and generalized gradient approximations cannot accurately predict the band gap of solids for a fundamental reason: They lack the exchange-correlation derivative discontinuity. By comparing Kohn-Sham and generalized Kohn-Sham calculations, we here show that the nonempirical meta-generalized-gradient-approximation (meta-GGA) TASK from Aschebrock and Kümmel [Phys. Rev. Res. 1, 033082 (2019)] predicts the right gaps for the right reason, i.e., as a combination of a proper Kohn-Sham gap and a substantial derivative discontinuity contribution. For many materials from small-gap semiconductors to large-gap insulators, the proper band gap is thus obtained. Here we further study a group of metal-halide perovskites for which the band gap is notoriously hard to predict. For these materials, TASK yields band gaps very similar to the nonlocal screened hybrid Heyd-Scuseria-Ernzerhof functional, yet at a fraction of the hybrid functional’s computational cost. We discuss the influence of correlation functionals, and open questions in the comparison of calculated band gaps with experimental ones.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Pion and Kaon Valence-quark Parton Quasidistributions

Algebraic Ansatze for the Poincare-covariant Bethe-Salpeter wave functions of the pion and kaon arc used to calculate their light-front wave functions, parton distribution amplitudes, parton quasidistribution amplitudes, valence parton distribution functions, and parton quasidistribution functions (PqDFs). The light-front wave functions arc broad, concave functions, and the scale of flavor-symmetry violation in the kaon is roughly 15%, being set by the ratio of emergent masses in the s- and u-quark sectors. Parton quasidistribution amplitudes computed with longitudinal momentum P z = 1.75 GeV provide a semiquantitatively accurate representation of the objective parton distribution amplitude, but even with P z = 3 GeV, they cannot provide information about this amplitude's end point behavior. On the valence-quark domain, similar outcomes characterize PqDFs. Lastly, in this connection, however, the ratio of kaon-to-pion u-quark PqDFs is found to provide a good approximation to the true parton distribution function ratio on 0.4 ≲ x ≲ 0.8, suggesting that with existing resources computations of ratios of parton quasidistributions can yield results that support empirical comparison.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Convex Relaxations of the Network Flow Problem Under Cycle Constraints

In this paper, we consider the problem of optimizing the flows in a lossless flow network with additional nonconvex cycle constraints on nodal variables; such constraints appear in several applications, including electric power, water distribution, and natural gas networks. This problem is a nonconvex version of the minimum-cost network flow problem (NFP), and to solve it, we propose three different approaches. One approach is based on solving a convex approximation of the problem, obtained by augmenting the cost function with an entropy-like term to relax the nonconvex constraints. We show that the approximation error, for which we give an upper bound, can be made small enough for practical use. An alternative approach is to solve the classical NFP, that is, without the cycle constraints, and solve a separate optimization problem afterwards in order to recover the actual flows satisfying the cycle constraints; the solution of this separate problem maximizes the individual entropies of the cycles. The third approach is based on replacing the nonconvex constraint set with a convex inner approximation, which yields a suboptimal solution for the cyclic networks with each edge belonging to at most two cycles. We validate the practical usefulness of the theoretical results through numerical examples, in which we study the standard test systems for water and electric power distribution networks.

42 ENGINEERING↗
DOE OSTI2017

Properties of real metallic surfaces: Effects of density functional semilocality and van der Waals nonlocality

Significance It is primarily at their surfaces that solids interact with their environments. What is the physics behind the measurable properties of clean metallic surfaces? To answer this question, we calculate surface energies, work functions, and surface interlayer relaxations for aluminum and seven d -electron metals, using a sequence of exchange-correlation density functionals of increasing sophistication. While the simplest one, the local density approximation, works well through error cancellation, the usually more realistic Perdew–Burke–Ernzerhof functional underestimates both surface energies and work functions. The more advanced functionals, including the new strongly constrained and appropriately normed (SCAN) and SCAN+rVV10, demonstrate the unexpected importance of intermediate and long-range van der Waals attraction (seamlessly included in the random phase approximation).

36 MATERIALS SCIENCE↗
DOE OSTI2025

Deep Learning–Assisted Multiobjective Optimization of Geological CO 2 Storage Performance under Geomechanical Risks

In geological CO 2 storage, designing the optimal well control strategy for CO 2 injection to maximize CO 2 storage while minimizing the associated geomechanical risks is not trivial. This challenge arises due to pressure buildup, CO 2 plume migration, the highly nonlinear nature of geomechanical responses to rock-fluid interaction, and the high computational cost associated with coupled flow and geomechanics simulations. In this paper, we introduce a novel optimization framework to address these challenges. The optimization problem is formulated as follows: maximize total CO 2 storage while minimizing geomechanical risks by adjusting the injection schedules within bounded constraints. The geomechanical risks are primarily driven by injection-induced pressure build-up, which is characterized by ground displacement and the induced microseismicity. We used the Fourier neural operator (FNO)-based deep learning model to construct surrogate models, replacing the time-consuming coupled flow and geomechanics simulations for evaluating the aforementioned objective functions. The developed surrogate models have been incorporated into a multiobjective optimization framework through a genetic algorithm to reduce the computational burden. The proposed optimization framework reduces the computational cost from approximately 2,400 hours, when using objective function evaluations based on physics-based simulations, to around 20 minutes. A set of Pareto-optimal solutions of the proposed workflow yields nontrivial optimal decisions, reducing the microseismicity potential and the vertical displacement. This Pareto front highlights the optimal trade-offs between CO 2 storage amount, safety, and ground displacement, emphasizing the need for careful optimization and management of injection strategies to achieve a balanced outcome. The novelty of this work is twofold. First, we demonstrate the importance of incorporating the minimization of the geomechanical risks as objective functions into the CO 2 storage optimization workflow to mitigate the potential risk of induced microseismicity and ground displacement. Second, we leverage the FNO-based surrogate models to optimize a real-field CO 2 storage operation.

42 ENGINEERING↗
DOE OSTI2020

TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations

TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy–cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe–Salpeter methods, second-order Møller–Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE’s functionality, including excited-state methods, RPA and Green’s function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE’s current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE’s development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted.

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

Electronic Structure and Related Band Parameters of Hexagonal Wurtzite Zn{sub 1−x}Mn{sub x}O Magnetic Semiconducting Alloys

The electronic band structure and related band parameters such as, lattice parameters, energy band gaps, density of states and magnetic moment of Zn{sub 1−x}Mn{sub x}O ternary system in the hypothetical hexagonal wurtzite structure have been investigated. The calculations are performed using a full-potential linearized augmented plane wave method based on density functional theory in the generalized gradient approximation of Perdew-Burke-Ernzerhof. The evolution of the features of interest with increasing the Mn doping concentration from 0 to 1 in the ZnO structure has been examined and discussed. Our findings show that the behaviour of all studied band parameters with respect to the alloy composition x is consistent with those reported experimentally in the literature. The present study may be useful for spintronics applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Temperature dependence of nuclear quantum effects on liquid water via artificial neural network model based on SCAN meta-GGA functional

We investigate the temperature dependence of nuclear quantum effects (NQEs) on structural and dynamic properties of liquid water by training a neural network force field using first-principles molecular dynamics (FPMD) based on the strongly constrained and appropriately normed meta-generalized gradient approximation exchange-correlation approximation. The FPMD simulation based on density functional theory has become a powerful computational approach for studying a wide range of condensed phase systems. However, its large computational cost makes it difficult to incorporate NQEs in the simulation and investigate temperature dependence of various properties. To circumvent this difficulty, we use an artificial neural network model and employ the thermostatted ring polymer MD approach for studying the temperature dependence of NQEs on various properties. The NQEs generally bring the radial distribution functions closer to the experimental measurements. Translational diffusivity and rotational dynamics of water molecules are both slowed down by the NQEs. The competing inter-molecular and intra-molecular quantum effects on hydrogen bonds, as discussed by Habershon, Markland, and Manolopoulos [J. Chem. Phys. 131(2), 024501 (2019)], can explain the observed temperature dependence of the NQEs on the dynamical properties in our simulation.

Yao, Yi (ORCID:0000000299576979)↗
DOE OSTI2025

Range-separated thermal hybrid exchange-correlation density functional for accurate band-gap calculations of warm dense matter

Here, in this study, we present a range-separated thermal hybrid exchange-correlation (XC) functional, termed RS-KDT0, which provides highly accurate band-gap predictions at elevated temperature while reducing the computational cost relative to thermal global hybrid functionals. At zero temperature, RS-KDT0 recovers the widely used ground-state range-separated hybrid functional HSE06. To assess its performance across temperature regimes, we conducted static calculations of electronic pressure, band gaps, and band structures. RS-KDT0 exhibits the same level of accuracy as HSE06 in the low-temperature regime and demonstrates improved agreement with finite-temperature GW calculations at elevated temperatures when compared to other thermal XC functionals such as the generalized gradient approximation (GGA)-level KDT16 and the global hybrid KDT0.

density functional theory↗