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At least 559 records · Page 31

Theoretical methods to design and test quantum simulators for the compact Abelian Higgs model

The lattice compact Abelian Higgs model is a nonperturbative regularized formulation of low-energy scalar quantum electrodynamics. In 1+1 dimensions, this model can be quantum simulated using a ladder-shaped optical lattice with Rydberg-dressed atoms. In this setup, one spatial dimension is used to carry the angular momentum of the quantum rotors. One can use truncations corresponding to spin-2 and spin-1 to build local Hilbert spaces associated with the links of the lattice. We argue that ladder-shaped configurable arrays of Rydberg atoms can be used for the same purpose. We make concrete proposals involving two and three Rydberg atoms to build one local spin-1 space (a qutrit). We show that the building blocks of the Hamiltonian calculations are models with one and two spins. We compare target and simulators using perturbative and numerical methods. The two-atom setup provides an easily controllable simulator of the one-spin model while the three-atom setup involves solving nonlinear equations. We discuss approximate methods to couple two spin-1 spaces. The article provides analytical and numerical tools necessary to design and build the proposed simulators with current technology.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Dynamic and relativistic effects on Pt–Pt indirect spin–spin coupling in aqueous solution studied by ab initio molecular dynamics and two- vs four-component density functional NMR calculations

Treating 195Pt nuclear magnetic resonance parameters in solution remains a considerable challenge from a quantum chemistry point of view, requiring a high level of theory that simultaneously takes into account the relativistic effects, the dynamic treatment of the solvent–solute system, and the dynamic electron correlation. A combination of Car-Parrinello molecular dynamics (CPMD) and relativistic calculations based on two-component zeroth order regular approximation spin–orbit Kohn–Sham (2c-ZKS) and four-component Dirac–Kohn–Sham (4c-DKS) Hamiltonians is performed to address the solvent effect (water) on the conformational changes and JPtPt1 coupling. A series of bridged PtIII dinuclear complexes [L1–Pt2(NH3)4(Am)2–L2]n+ (Am = α–pyrrolidonate and pivalamidate; L = H2O, Cl−, and Br−) are studied. The computed Pt–Pt coupling is strongly dependent on the conformational dynamics of the complexes, which, in turn, is correlated with the trans influence among axial ligands and with the angle N–C–O from the bridging ligands. The J-coupling is decomposed in terms of dynamic contributions. The decomposition reveals that the vibrational and explicit solvation contributions reduce JPtPt1 of diaquo complexes (L1 = L2 = H2O) in comparison to the static gas-phase magnitude, whereas the implicit solvation and bulk contributions correspond to an increase in JPtPt1 in dihalo (L1 = L2 = X−) and aquahalo (L1 = H2O; L2 = X−) complexes. Relativistic treatment combined with CPMD shows that the 2c-ZKS Hamiltonian performs as well as 4c-DKS for the JPtPt1 coupling.

Chemistry↗

Are All Post-starbursts Mergers? HST Reveals Hidden Disturbances in the Majority of PSBs

How do galaxies transform from blue, star-forming spirals to red, quiescent early-type galaxies? To answer this question, we analyzed a set of 26 gas-rich, shocked post-starburst galaxies with Hubble Space Telescope (HST) imaging in $B$, $I$, and $H$ bands and Sloan Digital Sky Survey (SDSS) $i$-band imaging of similar depth but lower resolution. We found that post-starbursts in our sample have intermediate morphologies between disk- and bulge dominated (Sérsic $n$ = ${1.7}_{-0.0}^{+0.3}$ ) and have red bulges, likely due to dust obscuration in the cores. A majority of galaxies in our sample are more morphologically disturbed than regular galaxies (88%, corresponding to >3$σ$ significance) when observed with HST, with asymmetry and Sérsic residual flux fraction being the most successful measures of disturbance. Most disturbances are undetected at the lower resolution of SDSS imaging. Although ~27% galaxies are clear merger remnants, we found that disturbances in another ~30% of the sample are internal, caused by small-scale perturbations or dust substructures rather than tidal features, and require high-resolution imaging to detect. We found 2.8$σ$ evidence that asymmetry features fade on timescales ~200 Myr, and may vanish entirely after ~750 Myr, so we do not rule out a possible merger origin of all post-starbursts given that asymmetric features may have already faded. This work highlights the importance of small-scale disturbances, detected only in high-resolution imaging, in understanding structural evolution of transitioning galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗

Improving Prediction of Peroxide Value of Edible Oils Using Regularized Regression Models

We present four unique prediction techniques, combined with multiple data pre-processing methods, utilizing a wide range of both oil types and oil peroxide values (PV) as well as incorporating natural aging for peroxide creation. Samples were PV assayed using a standard starch titration method, AOCS Method Cd 8-53, and used as a verified reference method for PV determination. Near-infrared (NIR) spectra were collected from each sample in two unique optical pathlengths (OPLs), 2 and 24 mm, then fused into a third distinct set. All three sets were used in partial least squares (PLS) regression, ridge regression, LASSO regression, and elastic net regression model calculation. While no individual regression model was established as the best, global models for each regression type and pre-processing method show good agreement between all regression types when performed in their optimal scenarios. Furthermore, small spectral window size boxcar averaging shows prediction accuracy improvements for edible oil PVs. Best-performing models for each regression type are: PLS regression, 25 point boxcar window fused OPL spectral information RMSEP = 2.50; ridge regression, 5 point boxcar window, 24 mm OPL, RMSEP = 2.20; LASSO raw spectral information, 24 mm OPL, RMSEP = 1.80; and elastic net, 10 point boxcar window, 24 mm OPL, RMSEP = 1.91. The results show promising advancements in the development of a full global model for PV determination of edible oils.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Reaching the equilibrium state of the frustrated triangular Ising magnet Ca 3 Co 2 O 6

Ca 3 Co 2 O 6 is a frustrated magnet consisting of a triangular arrangement of chains of Ising spins. It shows regular magnetization steps versus magnetic field every 1.2 T that are metastable with very slow dynamics. This has puzzled the community for many years and given rise to numerous potential theories. Here we approach the problem by seeking the elusive magnetic equilibrium state at T=2 K. To this end, we explore two approaches: (1) bypassing the slow dynamics produced by changing fields by instead field-cooling directly to the target temperature and (2) quantum annealing in transverse magnetic fields. While we observe no measurable effect of the quantum annealing in fields up to 7 T, which is likely due to the large Ising anisotropy of Co spins in this material, we find that for the field cooling in longitudinal fields we achieve the predicted equilibrium 1/3 magnetization. We perform Monte Carlo simulations of the ground state phase diagram and we also simulate the quantum annealing process and find good agreement between experiment and theory. Thus we present an investigation of the elusive ground state properties of the canonical frustrated triangular system Ca 3 Co 2 O 6 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Close-coupling approach to electron scattering with multielectron targets

Momentum-space close coupling calculations of electron scattering require removal of spurious and unphysical solutions. Here, we demonstrate here that removal of these solutions involve regulator operators that enforce Pauli exclusion selection rules in addition to removing spurious solutions. The form of a regular operator for e-H scattering has already been established, but a general extension to the multielectron case has been elusive. Here we present a general method for scattering on multielectron targets, atoms, or molecules, ensuring that the scattering solutions obey Pauli-exclusion selection rules. The regulator operator is obtained by finding the null space vectors of the 𝑁+1 electrons of the projectile and target atom scattering system. We demonstrate that this general procedure reduces to the e-H result and provide examples for He- and Li-like targets as well as guidance for implementation.

74 ATOMIC AND MOLECULAR PHYSICS↗

Solvent Hold Tank Sample Results for MCU-20-32-33-34 (Quarterly Report, September 2020)

In late FY13, MCU implemented the Next Generation Solvent (NGS) flow sheet. Facility personnel added a non-radioactive, NGS “cocktail” containing the new Extractant (MaxCalix) and a new Suppressor (TiDG) to the SHT heel to implement the NGS flow sheet. The resulting “blend” solvent (“NGS blend solvent”) is essentially NGS with residual amounts of calix[4]arene-bis(tert-octylbenzo-crown-6) (BOBCalixC6) and trioctylamine (TOA). For process monitoring, SHT samples are sent to Savannah River National Laboratory (SRNL) to examine solvent composition changes over time. With the exception of Isopar™ L which is regularly added to the SHT due to its high vapor pressure, this report shows the cumulative chemical composition data, including impurities like mercury, of the September 2020 (MCU-20-32-33-34) solvent SHT sample. A summary report of the September SHT solvent sample was issued earlier. This report examines the cumulative results from these and several past monthly reports. These samples are intended to verify that the solvent is within the specified composition range. A baseline “scratch” solvent - a scratch solvent is a preparation of all 6 solvent components (this includes the old extractant BoBCalix and the old suppressor TrioctylAmine that remained when solvent was converted to Next Generation Solvent [NGS]) of the composition that approximates the blend of cocktail and heel solvent - was prepared in the lab (September 2018) and used for comparison and evaluation. The results from the analyses are presented in this document. This report is the last characterization analysis of the SHT solvent. MCU entered a lay-up state and about 128 gallons of the SHT solvent were pumped into 55 gallons drums for future disposal.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

A comparative study of Bi, Sb, and BiSb for electrochemical nitrogen reduction leading to a new catalyst design strategy

Recent studies identified Bi as one of the most promising non-noble metal elements that can promote the electrochemical N 2 reduction reaction (ENRR) to produce NH 3 . The electronic features that make Bi a promising ENRR catalyst may also be owned by Sb that belongs to the same group as Bi. Thus, the ENRR properties of Bi, Sb, and a BiSb alloy were investigated comparatively to identify common characteristics that facilitate the ENRR. These catalysts were prepared as uniform coating layers on high surface area carbon felt electrodes, which could serve as both regular electrodes and pseudo-gas diffusion electrodes. The experimental results demonstrated that while Bi and Sb show comparable ENRR performances, the formation of a BiSb alloy distinctively increases the faradic efficiency for NH 3 production. Additionally, the X-ray photoelectron spectroscopy results revealed that Bi in BiSb possesses a partial positive charge while Sb in BiSb possesses a partial negative charge, which can impact the way the catalyst surface interacts with the reactants and reaction intermediates of the ENRR and hydrogen evolution reaction (HER), the major competing reaction with the ENRR. Computational investigations including the Bader charge analysis and Gibbs free energy calculations for the elemental steps of the ENRR and HER provided an explanation of how the formation of a BiSb alloy can change the selectivity for the ENRR. The combined experimental and theoretical results and discussion contained in this study lead to a new strategy for designing efficient metal catalysts for the ENRR. Additionally, this study investigated how the use of gas phase and dissolved N 2 affected the ENRR performances of the Bi, Sb, and BiSb catalysts.

36 MATERIALS SCIENCE↗

In-pixel automatic threshold calibration for the CMS Endcap Timing Layer readout chip

We present the implementation and verification of an in-pixel automatic threshold calibration circuit for the CMS Endcap Timing Layer (ETL) in the High-Luminosity LHC upgrade. The discriminator threshold of the ETL readout chip (ETROC) needs to be calibrated regularly to mitigate the circuit baseline change. Traditional methods need a lot of communication through a slow control system hence are time-consuming. This paper describes an in-pixel automatic scheme with improvements in operating time and usability. In this scheme, a sample-accumulation circuit is used to measure the average discriminator output. A binary successive approximation and linear combination scan are applied to find the equivalent baseline. The actual calibration procedure has been first implemented in FPGA firmware and tested with the ETROC front-end prototype chip (ETROC0). The calibration circuit has been implemented with Triple Modular Redundancy (TMR) and verified with Single Event Effects (SEEs) simulation. A complete calibration process lasts 35 ms with a 40 MHz clock. In the worst case, the dynamic and static power consumption are estimated to be 300 uW and 10.4 uW, respectively. The circuit design, implemented in a 65 CMOS technology, will be integrated into ETROC2, the next iteration of the ETROC with a 16 x16 pixel matrix.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Third-Order Møller–Plesset Theory Made More Useful? The Role of Density Functional Theory Orbitals

The practical utility of Møller–Plesset (MP) perturbation theory is severely constrained by the use of Hartree–Fock (HF) orbitals. It has recently been shown that the use of regularized orbital-optimized MP2 orbitals and scaling of MP3 energy could lead to a significant reduction in MP3 error. In this work, we examine whether density functional theory (DFT)-optimized orbitals can be similarly employed to improve the performance of MP theory at both the MP2 and MP3 levels. We find that the use of DFT orbitals leads to significantly improved performance for prediction of thermochemistry, barrier heights, noncovalent interactions, and dipole moments relative to the standard HF-based MP theory. Indeed, MP3 (with or without scaling) with DFT orbitals is found to surpass the accuracy of coupled-cluster singles and doubles (CCSD) for several data sets. We also found that the results are not particularly functional sensitive in most cases (although range-separated hybrid functionals with low delocalization error perform the best). As such, MP3 based on DFT orbitals thus appears to be an efficient, noniterative O(N 6 ) scaling wave-function approach for single-reference electronic structure computations. Scaled MP2 with DFT orbitals is also found to be quite accurate in many cases, although modern double hybrid functionals are likely to be considerably more accurate.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Data-Driven Kinetic Reaction Networks for Separation Chemistry

Understanding complex, multistep chemical reactions at the molecular level is a major challenge whose solution would greatly benefit the design and optimization of numerous chemical processes. The separation of rare-earth (4f) and actinide (5f) elements is an example where improving our chemical understanding is important for designing and optimizing new chemistries, even with a limited number of observations. Here, in this work, we leverage data-driven artificial intelligence and machine-learning approaches to develop kinetic reaction networks that describe the liquid–liquid extraction mechanism of uranium using N,N-di-2-ethylhexyl-isobutyramide (DEHiBA). Specifically, we compare and contrast the properties of two classes of models: (1) purely data-driven models that are regularized using chemistry-agnostic, L1 regression and (2) chemistry-informed models that are regularized using relative reaction energies provided by quantum mechanical calculations. We observe that purely data-driven models are unbiased, simple, and accurate in their predictions of experimental measurements when provided with sufficient data but are difficult to fully constrain and interpret. In contrast, chemistry-informed models exhibit significantly improved chemical interpretability and consistency, providing a detailed description of the separation process while achieving high accuracy through ensemble averaging. Overall, the dominant species predicted to be extracted into the organic phase is UO 2 (NO 3 ) 2 (DEHiBA) 2 , agreeing with experimental slope analysis, thermodynamic modeling, EXAFS, and crystal structures. This work demonstrates that leveraging the fundamental structure of the problem can lead to efficient learning schemes that provide both accurate predictions and chemical insights at a low computational cost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Topology-Bounded Superfluid Weight in Twisted Bilayer Graphene

While regular flat bands are good for enhancing the density of states and hence the gap, they are detrimental to the superfluid weight. We show that the predicted nontrivial topology of the two lowest flat bands of twisted bilayer graphene (TBLG) plays an important role in the enhancement of the superfluid weight and hence of superconductivity. We derive the superfluid weight (phase stiffness) of the TBLG superconducting flat bands with a uniform pairing, and show that it can be expressed as an integral of the Fubini-Study metric of the flat bands. This mirrors results already obtained for nonzero Chern number bands even though the TBLG flat bands have zero Chern number. We further show that the metric integral is lower bounded by the topological $C_{2z}T$ Wilson loop winding number of TBLG flat bands, which renders that the superfluid weight is also bounded by this topological index. In contrast, trivial flat bands have a zero superfluid weight. The superfluid weight is crucial in determining the Berezinskii-Kosterlitz-Thouless transition temperature of the superconductor. Based on the transition temperature measured in TBLG experiments, we estimate the topological contribution of the superfluid weight in TBLG.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Anharmonic phonon behavior via irreducible derivatives: Self-consistent perturbation theory and molecular dynamics

Cubic phonon interactions are now regularly computed from first principles, and the quartic interactions have begun to receive more attention. Given this realistic anharmonic vibrational Hamiltonian, the classical phonon Green's function can be precisely measured using molecular dynamics, which can then be used to rigorously assess the range of validity for self-consistent diagrammatic approaches in the classical limit. Here we use the bundled irreducible derivative approach to efficiently and precisely compute the cubic and quartic phonon interactions of CaF 2 , systematically obtaining the vibrational Hamiltonian purely in terms of irreducible derivatives. We demonstrate that the 4-phonon sunset diagram has an important contribution to the optical phonon linewidths beyond T = 500 K. Reasonable results are obtained even at T = 900 K when performing self-consistency using the 4-phonon loop diagram and evaluating the 3-phonon bubble and 4-phonon sunset diagrams post-self-consistency. Further improvements are obtained by performing quasiparticle perturbation theory, where both the 4-phonon loop and the real part of the 3-phonon bubble are employed during self-consistency. Finally, our irreducible derivative approach to self-consistent perturbation theory is a robust tool for studying anharmonic phonons in both the quantum and classical regimes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Self-Supported Branched Poly(ethylenimine) Monoliths from Inverse Template 3D Printing for Direct Air Capture

3D-printed inverse templates are combined with ice templating to develop self-supported branched poly(ethylenimine) monoliths with regular channels of varying channel density and ordered macropores. A maximum uptake of 0.96 mmol of CO 2 /g of monolith from ambient air containing 45.5% RH is achieved from dynamic breakthrough experiments, which is a 31% increase compared to the CO 2 uptake from adsorption under dry conditions for the same duration. The breakthrough experiments show characteristics of internal mass-transfer limitations. The cyclic dynamic breakthrough experiments indicate stable operation without significant loss in CO 2 uptake across eight cycles. Moreover, the self-supported monolith shows minimal loss in adsorption capacity (7.7%) upon exposure to air containing 21% oxygen at 110 °C, in comparison to a conventional sorbent consisting of poly(ethylenimine) impregnated on Al 2 O 3 (18.9%). The monoliths exhibit good mechanical stability, contributed by elastic deformation, corresponding to up to 74% strain and lower pressure drop compared to many existing monoliths in the literature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Soft factorisation and exponentiation from Schwinger-space geometry

Infrared divergences in Quantum Field Theory govern the low-energy dynamics of many physical theories, and their understanding is a crucial ingredient in predicting the outcomes of collider experiments. We present a novel approach to deriving the structure of these divergences by employing the Schwinger parametrization of Feynman integrals. After using tropical geometry to identify divergent limits, we study the all-orders asymptotic properties of Feynman diagrams via matrix manipulations of graph Laplacians, which allows us to analyse their IR behaviour systematically. We explicitly demonstrate the soft-hard factorization of the integrand for a broad class of diagrams, and reveal that when written in terms of worldline distances, topologically distinct diagrams asymptote to the same integrand at leading order in the soft limit. In particular, for the case of Quantum Electrodynamics (with massive fermions), we use this fact to show how ladder-type diagrams combine in Schwinger-parameter space to yield the correct exponentiated soft anomalous dimension. This framework provides a foundation for extending these methods to more complex theories like Quantum Chromodynamics and offers a pathway towards a systematic understanding of infrared divergences in perturbative amplitudes.

Factorization↗

Design and performance of an in-vacuum, magnetic field mapping system for the Muon g-2 experiment

The E989 Muon g-2 experiment at Fermilab aims to measure the anomalous magnetic moment, a$_\mu$, of the muon with a precision of 140 parts-per-billion. This requires a precise measurement of both the anomalous spin precession frequency, $\omega_a$, and the average magnetic field in terms of the equivalent, free proton Larmor frequency, $\omega_p$. The measurement of $\omega_p$ with a total systematic uncertainty of 70 parts-per-billion involves a combination of various NMR probes. There are 378 probes in fixed locations constantly monitoring field drifts. A water-based probe provides the calibration in terms of $\omega_p$. A crucial element for the multi-step measurement of $\omega_p$ is the regular mapping of the magnetic field over the muon storage region. The former E821 experiment at Brookhaven employed an in-vacuum field mapping system equipped with 17 NMR probes, which was developed by the University of Heidelberg. We have refurbished and upgraded this system with new probes and electronics. The upgrades include a new communication scheme incorporating time-division multiplexing to separate the important NMR reference clock from the data communication. The addition digitization of the NMR signals replaced the hardware-implemented zero-crossing counting of the E821 system. The digitized signals offer new capabilities in the NMR frequency analysis and its related systematic uncertainties. While the mechanical systems that move the field mapper around the ring have been mostly refurbished, the motion control system was completely replaced with a custom-built electronics centered around a commercial Galil motion controller. Both the field mapping NMR system and its motion control were successfully commissioned at Fermilab and have been in reliable operation during the first data taking periods. This article provides details of the upgrades of the field mapper and its performance.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Double-Shell Tank Primary Bottom Visual Inspection Results - 20025

A pressing need for the Double-Shell Tank Integrity Program at Hanford is of the ability to inspect the bottom of the tanks. Though the DSTs' annulus spaces (the space between the internal and external tank walls) have been inspected visually since 1992 and with Ultrasonic Testing (UT) since 1996, inspections of the tank bottoms have been able to be conducted due to limitations of available technology, omitting about 40 percent of the tank surface below the maximum fill level from routine inspection. Visual inspections of the tank annulus have been conducted up to five times in some DSTs and portions of the annulus space for all of the DSTs has been inspected twice with UT. This region includes the walls of the primary tank and secondary liner along with accessible portions of the secondary liner bottom. Due to this lack of technology, the degradation of the primary tank bottom in Tank AY-102 was undetected until the tank leaked into its annulus space, confirmed in 2012. Since that time, WRPS has been working with the nondestructive examination community and the Pacific Northwest National Laboratory, to evaluate potential technologies to conduct these challenging remote inspections. Recent work has included the development, testing, and deployment of several remote visual inspection technologies to observe the condition of the primary tank bottom of the DSTs by leveraging air distribution slots in the refractory pad on which it rests. Robotic solutions to conduct this inspection were developed with a detailed understanding of the physical configuration and operational logistics. Understanding and subsequent communication of these details to vendors within the robotics and nondestructive examination community was a critical component to the successful production of these new tools. Throughout the FY16-FY18 years, vendors from nondestructive examination community were solicited for ideas to meet the tank bottom inspection challenge. Two tank bottom visual inspection solutions were then pursued to meet that challenge. Both tools were successfully deployed at Tank AP-107, and provided valuable visuals, never before obtained from the under tank environment of a double-shell tank. While there are minor opportunities for improvement identified with each system, general outcomes were overwhelmingly positive. Both systems were successfully able to navigate the refractory air slot pattern from the outer edge to the tank center and record video footage. The micro-crawler provided high quality and very stable footage through the air slot pattern, but took longer to deploy into the slots and traverse through them than the alternative system. The push-pull tethered camera was able to navigate all seven of its target air slots in a matter of a few hours, which included deployment, movement between slot entrances, and complete removal of the system from the annulus environment. Through these air slots, new information was gained about the tank bottom and refractory pad condition of tank AP-107, AP-106, AP-108, and AN-102. While some debris was noted in the air slots, including sand, chipped refractory, and construction materials, the refractory was found to be structurally stable and adequately supporting the primary tank bottom through the full diameter of the tank. Primary tank bottom steel exterior was found to be in good condition, free of ongoing or aggressive corrosion conditions. Looking toward the future, robotic access to and visual inspection of refractory air slots and the primary tank bottom steel has now proven viable. Incorporating periodic air slot inspections as a regular practice within the Double-Shell Tank Integrity Program is the next step, allowing trending of any changes in condition. As ultrasonic testing infrastructure was leveraged to complete the initial system deployments described in this report, it makes sense to adopt that same strategy for ongoing periodic examinations and deploy these primary tank bottom inspection tools alongside ultrasonic testing operations. Development of visual inspection tools to evaluate the primary tank bottom region of the double-shell tanks was planned as the first stage of inspection. Continued development of volumetric sensors and incorporation of these inspection tools into Hanford's ongoing Double-Shell Tank Integrity Program are the next steps, seeking to continuously expand understanding of asset integrity and remaining useful life. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Shadow energy functionals and potentials in Born–Oppenheimer molecular dynamics

In Born–Oppenheimer molecular dynamics (BOMD) simulations based on the density functional theory (DFT), the potential energy and the interatomic forces are calculated from an electronic ground state density that is determined by an iterative self-consistent field optimization procedure, which, in practice, never is fully converged. The calculated energies and forces are, therefore, only approximate, which may lead to an unphysical energy drift and instabilities. Here, we discuss an alternative shadow BOMD approach that is based on backward error analysis. Instead of calculating approximate solutions for an underlying exact regular Born–Oppenheimer potential, we do the opposite. Instead, we calculate the exact electron density, energies, and forces, but for an underlying approximate shadow Born–Oppenheimer potential energy surface. In this way, the calculated forces are conservative with respect to the approximate shadow potential and generate accurate molecular trajectories with long-term energy stabilities. We show how such shadow Born–Oppenheimer potentials can be constructed at different levels of accuracy as a function of the integration time step, δt, from the constrained minimization of a sequence of systematically improvable, but approximate, shadow energy density functionals. For each energy functional, there is a corresponding ground state Born–Oppenheimer potential. These pairs of shadow energy functionals and potentials are higher-level generalizations of the original “zeroth-level” shadow energy functionals and potentials used in extended Lagrangian BOMD. The proposed shadow energy functionals and potentials are useful only within this extended dynamical framework, where also the electronic degrees of freedom are propagated as dynamical field variables together with the atomic positions and velocities. The theory is quite general and can be applied to MD simulations using approximate DFT, Hartree–Fock, or semi-empirical methods, as well as to coarse-grained flexible charge models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗