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DOE OSTI2024

Approaching periodic systems in ensemble density functional theory via finite one-dimensional models

Ensemble density functional theory (EDFT) is a generalization of ground-state DFT, which is based on an exact formal theory of finite collections of a system's ground and excited states. EDFT in various forms has been shown to improve the accuracy of calculated energy level differences in isolated model systems, atoms, and molecules, but it is not yet clear how EDFT could be used to calculate band gaps for periodic systems. We extend the application of EDFT toward periodic systems by estimating the thermodynamic limit with increasingly large finite one-dimensional 'particle in a box' systems, which approach the uniform electron gas (UEG). Using ensemble-generalized Hartree and local spin density approximation exchange-correlation functionals, we find that corrections go to zero in the infinite limit, as expected for a metallic system. However, there is a correction to the effective mass, with results comparable to other calculations on 1D, 2D, and 3D UEGs, which indicates promise for non-trivial results from EDFT on periodic systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Lineshape theory of pigment-protein complexes: How the finite relaxation time of nuclei influences the exciton relaxation-induced lifetime broadening

In pigment-protein complexes, often the excited states are partially delocalized and the exciton-vibrational coupling in the basis of delocalized states contains large diagonal and small off-diagonal elements. This inequality may be used to introduce potential energy surfaces (PESs) of exciton states and to treat the inter-PES coupling in Markov and secular approximations. The resulting lineshape function consists of a Lorentzian peak that is broadened by the finite lifetime of the exciton states caused by the inter-PES coupling and a vibrational sideband that results from the mutual displacement of the excitonic PESs with respect to that of the ground state. So far analytical expressions have been derived that relate the exciton relaxation-induced lifetime broadening to the Redfield [T. Renger and R. A. Marcus, J. Chem. Phys. 116, 9997 (2002)] or modified Redfield [M. Schröder, U. Kleinekathöfer, and M. Schreiber, J. Chem. Phys. 124, 084903 (2006)] rate constants of exciton relaxation, assuming that intra-PES nuclear relaxation is fast compared to inter-PES transfer. Here, we go beyond this approximation and provide an analytical expression, termed Non-equilibrium Modified Redfield (NeMoR) theory, for the lifetime broadening that takes into account the finite nuclear relaxation time. In an application of the theory to molecular dimers, we find that, for a widely used experimental spectral density of the exciton-vibrational coupling of pigment-protein complexes, the NeMoR spectrum at low-temperatures (T < 150 K) is better approximated by Redfield than by modified Redfield theory. At room temperature, the lifetime broadening obtained with Redfield theory underestimates the NeMoR broadening, whereas modified Redfield theory overestimates it by a similar amount. A fortuitous error compensation in Redfield theory is found to explain the good performance of this theory at low temperatures. Since steady state spectra of PPCs are often measured at low temperatures, Redfield theory still provides a numerically efficient alternative to NeMoR theory. At higher temperatures, we suggest to use NeMoR theory, because it has the same numerical costs as modified Redfield theory, but is more accurate.

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

Machine-learning Kohn–Sham potential from dynamics in time-dependent Kohn–Sham systems

Abstract The construction of a better exchange-correlation potential in time-dependent density functional theory (TDDFT) can improve the accuracy of TDDFT calculations and provide more accurate predictions of the properties of many-electron systems. Here, we propose a machine learning method to develop the energy functional and the Kohn–Sham potential of a time-dependent Kohn–Sham (TDKS) system is proposed. The method is based on the dynamics of the Kohn–Sham system and does not require any data on the exact Kohn–Sham potential for training the model. We demonstrate the results of our method with a 1D harmonic oscillator example and a 1D two-electron example. We show that the machine-learned Kohn–Sham potential matches the exact Kohn–Sham potential in the absence of memory effect. Our method can still capture the dynamics of the Kohn–Sham system in the presence of memory effects. The machine learning method developed in this article provides insight into making better approximations of the energy functional and the Kohn–Sham potential in the TDKS system.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Galaxy and Mass Assembly (GAMA): Exploring the WISE Web in G12

We present an analysis of the mid-infrared Wide-field Infrared Survey Explorer (WISE) sources seen within the equatorial GAMA G12 field, located in the North Galactic Cap. Our motivation is to study and characterize the behavior of WISE source populations in anticipation of the deep multiwavelength surveys that will define the next decade, with the principal science goal of mapping the 3D large-scale structures and determining the global physical attributes of the host galaxies. In combination with cosmological redshifts, we identify galaxies from their WISE W1 (3.4 μm) resolved emission, and we also perform a star-galaxy separation using apparent magnitude, colors, and statistical modeling of star counts. The resulting galaxy catalog has ≃590,000 sources in 60 deg{sup 2}, reaching a W1 5σ depth of 31 μJy. At the faint end, where redshifts are not available, we employ a luminosity function analysis to show that approximately 27% of all WISE extragalactic sources to a limit of 17.5 mag (31 μJy) are at high redshift, z>1. The spatial distribution is investigated using two-point correlation functions and a 3D source density characterization at 5 Mpc and 20 Mpc scales. For angular distributions, we find that brighter and more massive sources are strongly clustered relative to fainter sources with lower mass; likewise, based on WISE colors, spheroidal galaxies have the strongest clustering, while late-type disk galaxies have the lowest clustering amplitudes. In three dimensions, we find a number of distinct groupings, often bridged by filaments and superstructures. Using special visualization tools, we map these structures, exploring how clustering may play a role with stellar mass and galaxy type.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Quantum Monte Carlo analysis of a charge ordered insulating antiferromagnet: The Ti 4 O 7 Magneli phase

The Magneli phase Ti 4 O 7 is an important transition metal oxide with a wide range of applications because of its interplay between charge, spin, and lattice degrees of freedom. At low temperatures, it has non-trivial magnetic states very close in energy, driven by electronic exchange and correlation interactions. We have examined three low- lying states, one ferromagnetic and two antiferromagnetic, and calculated their energies as well as Ti spin moment distributions using highly accurate Quantum Monte Carlo methods. We compare our results to those obtained from density functional theory- based methods that include approximate corrections for exchange and correlation. Our results confirm the nature of the states and their ordering in energy, as compared with density-functional theory methods. However, the energy differences and spin distributions differ. Here, a detailed analysis suggests that non-local exchange-correlation functionals, in addition to other approximations such as LDA+U to account for correlations, are needed to simultaneously obtain better estimates for spin moments, distributions, energy differences and energy gaps.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Non-local thermodynamic equilibrium 1.5D modeling of red giant stars

Spectra for two-dimensional (2D) stars in the 1.5D approximation are created from synthetic spectra of one-dimensional (1D) non-local thermodynamic equilibrium (NLTE) spherical model atmospheres produced by the PHOENIX code. The 1.5D stars have the spatially averaged Rayleigh-Jeans flux of a K3-4 III star while varying the temperature difference between the two 1D component models (ΔT {sub 1.5D}) and the relative surface area covered. Synthetic observable quantities from the 1.5D stars are fitted with quantities from NLTE and local thermodynamic equilibrium (LTE) 1D models to assess the errors in inferred T {sub eff} values from assuming horizontal homogeneity and LTE. Five different quantities are fit to determine the T {sub eff} of the 1.5D stars: UBVRI photometric colors, absolute surface flux spectral energy distributions (SEDs), relative SEDs, continuum normalized spectra, and TiO band profiles. In all cases except the TiO band profiles, the inferred T {sub eff} value increases with increasing ΔT {sub 1.5D}. In all cases, the inferred T {sub eff} value from fitting 1D LTE quantities is higher than from fitting 1D NLTE quantities and is approximately constant as a function of ΔT {sub 1.5D} within each case. The difference between LTE and NLTE for the TiO bands is caused indirectly by the NLTE temperature structure of the upper atmosphere, as the bands are computed in LTE. We conclude that the difference between T {sub eff} values derived from NLTE and LTE modeling is relatively insensitive to the degree of the horizontal inhomogeneity of the star being modeled and largely depends on the observable quantity being fit.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Pressure induced magnetic phase transition in RhFe{sub 3}N and IrFe{sub 3}N: An ab-initio study

The structural, electronic, elastic and magnetic properties of RhFe{sub 3}N and IrFe{sub 3}N are investigated using ab-initio calculations based on density functional theory as implemented in VASP code within the gradient generalized approximation. The non-spin polarized and spin polarized calculations are performed for these nitrides at normal and high pressures. It is found that these ternary nitrides are stable in ferromagnetic state at normal pressure. The lattice constant and bulk modulus values are calculated. The electronic structure reveals that these nitrides are metallic at normal pressure. The calculated elastic constants indicate that they are mechanically stable at ambient pressure. Ferromagnetic to nonmagnetic phase transition is observed in RhFe{sub 3}N and IrFe{sub 3}N at high pressure. Ferromagnetism is quenched in these nitrides at high pressure.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Fractional charge and spin errors in self-consistent Green’s function theory

We examine fractional charge and spin errors in self-consistent Green’s function theory within a second-order approximation (GF2). For GF2, it is known that the summation of diagrams resulting from the self-consistent solution of the Dyson equation removes the divergences pathological to second-order Møller-Plesset (MP2) theory for strong correlations. In the language often used in density functional theory contexts, this means GF2 has a greatly reduced fractional spin error relative to MP2. The natural question then is what effect, if any, does the Dyson summation have on the fractional charge error in GF2? To this end, we generalize our previous implementation of GF2 to open-shell systems and analyze its fractional spin and charge errors. We find that like MP2, GF2 possesses only a very small fractional charge error, and consequently minimal many electron self-interaction error. This shows that GF2 improves on the critical failings of MP2, but without altering the positive features that make it desirable. Furthermore, we find that GF2 has both less fractional charge and fractional spin errors than typical hybrid density functionals as well as random phase approximation with exchange.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2012

Hydrogen adsorption at the graphene surface: A vdW-DF perspective

We use the recently developed van der Waals density functional (vdW-DF) along with the C09x exchange functional to explore the interactions of molecular hydrogen with a single sheet of graphene. Our calculations demonstrate the importance of the inclusion of dispersion interactions for evaluating the adsorption capacity of graphitic, sparsely packed materials. In particular we show that, although the commonly used local density approximation (LDA) exchange-correlation functional gives reasonable H$_2$-graphene separation distances, these interactions are in fact too strong and decrease too rapidly as the H$_2$-graphene distance increases. On the other hand, calculations employing the generalized gradient approximation (GGA) for exchange and correlation exhibit very little binding. The vdW-DF$^{\rm C09x}$ functional, however, gives binding very similar to benchmark second-order M$\o$ller-Plesset (MP2) theory results for the H$_2$-coronene interaction and has an appropriate long range interaction with the graphene sheet. This shortcoming of the LDA and GGA functionals is shown to have significant consequences on the overall adsorption densities of H$_2$ near the graphene, thus emphasizing the fundamental importance of properly characterizing the interactions of adsorbed molecules in porous media.

08 HYDROGEN↗
DOE OSTI2017

Goal-Oriented Optimal Approximations of Bayesian Linear Inverse Problems

We propose optimal dimensionality reduction techniques for the solution of goal-oriented linear-Gaussian inverse problems, where the quantity of interest (QoI) is a function of the inversion parameters. These approximations are suitable for large-scale applications. In particular, we study the approximation of the posterior covariance of the QoI as a low-rank negative update of its prior covariance and prove optimality of this update with respect to the natural geodesic distance on the manifold of symmetric positive definite matrices. Assuming exact knowledge of the posterior mean of the QoI, the optimality results extend to optimality in distribution with respect to the Kullback--Leibler divergence and the Hellinger distance between the associated distributions. We also propose the approximation of the posterior mean of the QoI as a low-rank linear function of the data and prove optimality of this approximation with respect to a weighted Bayes risk. Both of these optimal approximations avoid the explicit computation of the full posterior distribution of the parameters and instead focus on directions that are well informed by the data and relevant to the QoI. These directions stem from a balance among all the components of the goal-oriented inverse problem: prior information, forward model, measurement noise, and ultimate goals. We illustrate the theory using a high-dimensional inverse problem in heat transfer.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Deep Learning without Global Optimization by Random Fourier Neural Networks

Here we introduce a new training algorithm for deep neural networks that utilize random complex exponential activation functions. Our approach employs a Markov chain Monte Carlo sampling procedure to iteratively train network layers, avoiding global and gradient-based optimization while maintaining error control. It consistently attains the theoretical approximation rate for residual networks with complex exponential activation functions, determined by network complexity. Additionally, it enables efficient learning of multiscale and high-frequency features, producing interpretable parameter distributions. Despite using sinusoidal basis functions, we do not observe Gibbs phenomena in approximating discontinuous target functions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

A comparative density functional study on electrical properties of layered penta-graphene

We present a comparative study of the influence of the number of layers, the biaxial strain in the range of −3% to 3%, and the stacking misalignments on the electronic properties of a new 2D carbon allotrope, penta-graphene (PG), based on hybrid-functional method within the density functional theory (DFT). In comparison with local exchange-correlation approximation in the DFT, the hybrid-functional provides an accurate description on the degree of p{sub z} orbitals localization and bandgap. Importantly, the predicted bandgap of few-layer PG has a weak layer dependence. The bandgap of monolayer PG is 3.27 eV, approximately equal to those of GaN and ZnO; and the bandgap of few-layer PG decreases slowly with the number of layers (N) and converge to 2.57 eV when N ≥ 4. Our calculations using HSE06 functional on few-layer PG reveal that bandgap engineering by stacking misalignment can further tune the bandgap down to 1.37 eV. Importantly, there is no direct-to-indirect bandgap transition in PG by varying strain, layer number, and stacking misalignment. Owing to its tunable, robustly direct, and wide bandgap characteristics, few-layer PG is promising for optoelectronic and photovoltaic applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Water dissociation on Ni(100) and Ni(111): Effect of surface temperature on reactivity

Water adsorption and dissociation on Ni(100) and Ni(111) surfaces are studied using density functional theory calculations. Water adsorbs on top site on both the surfaces, while H and OH adsorb on four fold hollow and three fold hollow (fcc) sites on Ni(100) and Ni(111), respectively. Transition states (TS) on both surfaces are identified using climbing image-nudged elastic band method. It is found that the barrier to dissociation on Ni(100) surface is slightly lower than that on Ni(111) surface. Dissociation on both the surfaces is exothermic, while the exothermicity on Ni(100) is large. To study the effect of lattice motion on the energy barrier, TS calculations are performed for various values of Q (lattice atom coordinate along the surface normal) and the change in the barrier height and position is determined. Calculations show that the energy barrier to reaction decreases with increasing Q and increases with decreasing Q on both the surfaces. Dissociation probability values at different surface temperatures are computed using semi-classical approximation. Results show that the influence of surface temperature on dissociation probability on the Ni(100) is significantly larger compared to that of Ni(111). Moreover, on Ni(100), a dramatic shift in energy barrier to lower incident energy values is observed with increasing surface temperature, while the shift is smaller in the case of Ni(111)

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Trapped energetic electron driven modes with second stable regime in tokamak plasmas

Features of fishbone-like trapped energetic electrons driven modes (TEEMs), which are a particular manifestation of the fishbone gap modes, are investigated taking into account model radial profile and the pitch angle distribution of the energetic electrons (EEs). The TEEMs are found unstable only when the beta values of EEs β{sub h} (=pressure of the energetic electrons/pressure of magnetic field) are higher than certain critical values which are proportional to perturbed energy δW{sup ^}{sub c} of background plasma and much lower than that for traditional fishbone modes. In addition, TEEMs become stable again and enter a second stable regime when β{sub h} values are higher than second critical values. Furthermore, the modes can only be excited in plasmas which are stable for MHD instabilities. The real frequency and growth rate of the modes are approximately linear and parabolic functions of β{sub h}, respectively. The real frequency is very low but not zero in the vicinity of lower beta region, whereas it is comparable to the toroidal precession frequency of the EEs in higher critical beta region. The numerical results show that the second stable regime is easy to form when q = 1 flux surface is close to the magnetic axis. Suitable density gradient of EEs and magnetic shear are other two necessary conditions for excitation of the TEEMs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Design of Distributed Controllers Seeking Optimal Power Flow Solutions Under Communication Constraints

This paper focuses on power distribution networks featuring inverter-interfaced distributed energy resources (DERs), and develops feedback controllers that drive the DER output powers to solutions of time-varying AC optimal power flow (OPF) problems. Control synthesis is grounded on primal-dual-type methods for regularized Lagrangian functions, as well as linear approximations of the AC power-flow equations. Convergence and OPF-solution-tracking capabilities are established while acknowledging: i) communication-packet losses, and ii) partial updates of control signals. The latter case is particularly relevant since it enables asynchronous operation of the controllers where DER setpoints are updated at a fast time scale based on local voltage measurements, and information on the network state is utilized if and when available, based on communication constraints. As an application, the paper considers distribution systems with high photovoltaic integration, and demonstrates that the proposed framework provides fast voltage-regulation capabilities, while enabling the near real-time pursuit of solutions of AC OPF problems.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2018

Intensity Distribution of the Three-Wave Diffraction from Dislocation Epitaxial Layers in the Reciprocal Space

The three-wave X-ray diffraction in strongly disordered epitaxial layers of GaN and ZnO is experimentally investigated. The charts of the intensity distribution in the reciprocal space are plotted in coordinates q{sub θ} and q{sub ϕ} for the most intensive three-wave combination (1010)/(1011) by means of subsequent θ- and ϕ-scanning. A nontrivial shape of the θ-sections of these contours at a distance from the ϕ center of reflection is revealed; it is different for different samples. For the θ-curves at the center of reflection, we observed a common peak that may be approximated by the Voigt function with a power-low decrease in the intensity at the wings; the decrease law (from–4.5 to–5.0) is found to be considerably greater than that for the similar curves of two-wave diffraction and not depending on the dislocation density and distribution in layers. In some films we observed a coarse-block structure; in addition, it follows from the distribution in the reciprocal space that these blocks are turned with respect to each other around a normal to the surface, which allows us to suggest the existence of low-angle boundaries between them, consisting exclusively of edge dislocations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Quinone 1 e – and 2 e – /2 H + Reduction Potentials: Identification and Analysis of Deviations from Systematic Scaling Relationships

Quinones participate in diverse electron transfer and proton-coupled electron transfer processes in chemistry and biology. To understand the relationship between these redox processes, an experimental study was carried out to probe the 1 e – and 2 e – /2 H + reduction potentials of a number of common quinones. The results reveal a non-linear correlation between the 1 e – and 2 e – /2 H + reduction potentials. This unexpected observation prompted a computational study of 134 different quinones, probing their 1 e – reduction potentials, p K a values, and 2 e – /2 H + reduction potentials. We report the density functional theory calculations reveal an approximately linear correlation between these three properties and an effective Hammett constant associated with the quinone substituent(s). However, deviations from this linear scaling relationship are evident for quinones that feature intramolecular hydrogen bonding, halogen substituents, charged substituents, and/or sterically bulky substituents. These results, particularly the different substituent effects on the 1 e – versus 2 e – /2 H + reduction potentials, have important implications for designing quinones with tailored redox properties.

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

Exploring the Random Phase Approximately for materials chemistry and physics

This proposal focuses on improved accuracy for the delicate energy differences of interest in materials chemistry with the fully nonlocal random phase approximation (RPA) in a density functional context. Could RPA or RPA-like approaches become standard methods of first-principles electronic-structure calculation for atoms, molecules, solids, surfaces, and nano-structures? Direct RPA includes the full exact exchange energy and a nonlocal correlation energy from the occupied and unoccupied Kohn-Sham orbitals and orbital energies, with an approximate but universal description of long-range van der Waals attraction. RPA also improves upon simple pair-wise interaction potentials or vdW density functional theory. This improvement is essential to capture accurate energy differences in metals and different phases of semiconductors. The applications in this proposal are challenges for the simpler approximations of Kohn-Sham density functional theory, which are part of the current “standard model” for quantum chemistry and condensed matter physics. Within this project we already applied RPA on different structural phase transitions on semiconductors, metals and molecules. Although RPA predicts accurate structural parameters, RPA has proven not equally accurate in all kinds of structural phase transitions. Therefore a correction to RPA can be necessary in many cases. We are currently implementing and testing a nonempirical, spatially nonlocal, frequency-dependent model for the exchange-correlation kernel in the adiabatic-connection fluctuation-dissipation context. This kernel predicts a nearly-exact correlation energy for the electron gas of uniform density. If RPA or RPA-like approaches prove to be reliably accurate, then expected increases in computer power may make them standard in the electronic-structure calculations of the future.

74 ATOMIC AND MOLECULAR PHYSICS↗