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At least 433 records · Page 24

Photoinduced Dirac semimetal in ZrTe5

Abstract Novel phases of matter with unique properties that emerge from quantum and topological protection present an important thrust of modern research. Of particular interest is to engineer these phases on demand using ultrafast external stimuli, such as photoexcitation, which offers prospects of their integration into future devices compatible with optical communication and information technology. Here, we use MeV Ultrafast Electron Diffraction (UED) to show how a transient three-dimensional (3D) Dirac semimetal state can be induced by a femtosecond laser pulse in a topological insulator ZrTe 5 . We observe marked changes in Bragg diffraction, which are characteristic of bond distortions in the photoinduced state. Using the atomic positions refined from the UED, we perform density functional theory (DFT) analysis of the electronic band structure. Our results reveal that the equilibrium state of ZrTe 5 is a topological insulator with a small band gap of ~ 25 meV, consistent with angle-resolved photoemission (ARPES) experiments. However, the gap is closed in the presence of strong spin-orbit coupling (SOC) in the photoinduced transient state, where massless Dirac fermions emerge in the chiral band structure. The time scale of the relaxation dynamics to the transient Dirac semimetal state is remarkably long, τ ~ 160 ps, which is two orders of magnitude longer than the conventional phonon-driven structural relaxation. The long relaxation is consistent with the vanishing density of states in Dirac spectrum and slow spin-repolarization of the SOC-controlled band structure accompanying the emergence of Dirac fermions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Ion Manipulation from Liquid Xe to Vacuum: Ba-Tagging for a nEXO Upgrade and Future 0 νββ Experiments

Neutrinoless double beta decay (0𝜈𝛽𝛽) provides a way to probe physics beyond the Standard Model of particle physics. The upcoming nEXO experiment will search for 0𝜈𝛽𝛽 decay in 136 Xe with a projected half-life sensitivity exceeding 10 28 years at the 90% confidence level using a liquid xenon (LXe) Time Projection Chamber (TPC) filled with 5 tonnes of Xe enriched to ∼90% in the 𝛽𝛽-decaying isotope 136 Xe. In parallel, a potential future upgrade to nEXO is being investigated with the aim to further suppress radioactive backgrounds and to confirm 𝛽𝛽-decay events. This technique, known as Ba-tagging, comprises extracting and identifying the 𝛽𝛽-decay daughter 136 Ba ion. One tagging approach being pursued involves extracting a small volume of LXe in the vicinity of a potential 𝛽𝛽-decay using a capillary tube and facilitating a liquid-to-gas phase transition by heating the capillary exit. The Ba ion is then separated from the accompanying Xe gas using a radio-frequency (RF) carpet and RF funnel, conclusively identifying the ion as 136 Ba via laser-fluorescence spectroscopy and mass spectrometry. Simultaneously, an accelerator-driven Ba ion source is being developed to validate and optimize this technique. The motivation for the project, the development of the different aspects, along with the current status and results, are discussed here.

a-tagging↗

Traveling wakefield tube: THz source powered by nonrelativistic electron beam

High peak power, tunable, narrowband terahertz emitters are becoming sought after given their portability, efficiency, and ability to be deployed in the field for industrial, medical, and military applications. The use of accelerator systems producing THz frequencies via Cherenkov radiation, generated by passing an electron beam through a slow-wave wakefield structure, is a promising method to meet future THz requirements. To date, efforts have been dedicated to analysis and design of sources utilizing laser seeded bunched electron beam drivers with relativistic energies beyond 5 MeV. Presented here is a wakefield THz generation scheme based on passing a long quasi-dc nonrelativistic beam (200 keV) through a dielectric loaded travelling wave structure. Reduced energy allows for compactness and portability of the accelerator as the size and weight of the dielectric slow wave structure is vanishingly small compared to the accelerator unit. The presented scheme can serve as a tunable high peak power THz source operated between 0.4-1.6 THz and produces power gain by a factor of five with an average efficiency of 6.8%

43 PARTICLE ACCELERATORS↗

Lagrangian statistics of a shock-driven turbulent dynamo in decaying turbulence

Small-scale fluctuating magnetic fields of order nG are observed in supernova shocks and galaxy clusters, where its amplification is likely caused by the Biermann battery mechanism. However, these fields cannot be amplified further without the turbulent dynamo, which generates magnetic energy through the stretch-twist-fold (STF) mechanism. Thus, we present here novel 3D magnetohydrodynamic (MHD) simulations of a laser-driven shock propagating into a stratified, multiphase medium, to investigate the post-shock turbulent magnetic field amplification via the turbulent dynamo. The configuration used here is currently being tested in the shock tunnel at the National Ignition Facility (NIF). In order to probe the statistical properties of the post-shock turbulent region, we use 384 × 512 × 384 tracers to track its evolution through the Lagrangian framework, thus providing a high-fidelity analysis of the shocked medium. Our simulations indicate that the growth of the magnetic field, which accompanies the near-Saffman kinetic energy decay (E kin ∝ t -1.15 ) without turbulence driving, exhibits slightly different characteristics as compared to periodic box simulations. Seemingly no distinct phases exist in its evolution because the shock passage and time to observe the magnetic field amplification during the turbulence decay are very short (~0.3 of a turbulent turnover time). Yet, the growth rate is still consistent with those expected for compressive (curl-free) turbulence driving in subsonic, compressible turbulence. Phenomenological understanding of the dynamics of the magnetic and velocity fields are also elucidated via Lagrangian frequency spectra, which are consistent with the expected inertial range scalings in the Eulerian–Lagrangian bridge.

79 ASTRONOMY AND ASTROPHYSICS↗

Experimental and theoretical investigation into the high pressure deflagration products of 2,6-diamino-3,5-dinitropyrazine-1-oxide (LLM-105)

Diamond anvil cell (DAC) laser ignition experiments and reactive ab initio molecular dynamics (AIMD) simulations were performed on the high explosive (HE) LLM-105 to investigate its high pressure (HP) deflagration chemistry. Raman and optical spectroscopy measurements reveal LLM-105 reacts into an opaque carbonaceous product at 4–25 GPa. At pressures >~ 27 GPa, the reaction product consists of an amorphous optically transparent solid and nitrogen (N 2 ) in the solid phase. While not a one-to-one comparison due to the small time and length scales, the HP AIMD simulations show that some of the product is molecular N 2 , in qualitative agreement with experiment, while above 20 GPa most of the product consists of large amorphous C x H y N z O k clusters. Clustering is enhanced with pressure and reduces with temperature. In the experiments with initial sample pressure >~ 25 GPa, the pressure within the DAC decreases with minimal change in DAC cavity area. At initial sample pressures of 43.9 GPa, when quenched to 0 K, simulations predict a product experiencing a lower pressure consistent with the experimental measurement at lower load pressures. In conclusion, the results are important for understanding the HP deflagration chemistry of LLM-105.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Fe-carbide/Fe-oxide-based nanocomposites synthesized as magnetic nanomaterials via laser ablation synthesis in solution (LASiS)

Magnetic nanostructured materials (MNMs) have gained prominence in materials technology developments owing to their potential biomedical applications for hyperthermia cancer treatment, and transplant organ cryopreservation. Herein, we report the facile and cost-effective synthesis of Fe-based composite MNMs, comprising both Fe@Fe 2 O 3 and Fe 3 C@C core-shell nanoparticles (NPs), via Laser Ablation Synthesis in Solution (LASiS) using Fe targets ablated under acetone and toluene. Detailed materials characterizations using electron microscopy-based imaging, diffraction studies, and spectroscopic analyses - including Raman and Mössbauer spectroscopy - relate the structure-composition properties for different Fe-oxide/carbide phases in the aforesaid MNMs to their respective magnetic responses. Specifically, we confirm the presence of ultra-small (2–10 nm) amorphous Fe-oxide NPs, as well as Fe@Fe 2 O 3 core-shell NPs (20–40 nm) in the samples synthesized by ablating Fe under acetone. In contrast, samples synthesized under toluene indicate a higher concentration of Fe 3 C@C core-shell NPs (20–40 nm) with a relatively low concentration of Fe 2 O 3 NPs (2–10 nm). Furthermore, the crystallinity of the metallic phases and carbonaceous shell coatings are systematically increased by carrying out LASiS under heated toluene (up to ~95 °C). Importantly, mössbauer spectroscopy results indicate that the elevation in toluene temperature leads to an increase in the concentrations of Fe 3 C@C NPs from ~40 % to ~53 % (at.).

36 MATERIALS SCIENCE↗

X-ray atomic mapping of quantum dots

We report a model-independent atomic-mapping technique for quantum dots (QDs) by combining Bragg reflection x-ray standing wave (XSW) and grazing incidence diffraction (GID) measurements. In this study, we choose GaAs capped InGaAs QDs/GaAs(001) as a model system to show the locations and arrangements of indium atoms within the QDs along various [hkl] directions. This technique directly reveals the actual amount of positional anisotropy and ordering fraction of indium atoms within the QDs by probing the (1¯11), (111), (311), (1¯31), (113), and (1¯13) crystallographic planes. We find that indium atoms are outwardly shifted along the [001] direction by small fractions of the lattice constant, 0.04a GaAs and 0.06a GaAs from Ga sites for 50- and 150-Å GaAs capped InGaAs QDs, respectively. We observe that an improved coherency factor of the indium atoms within the QDs by 45–60% along the [001] and [011] directions reduces the photoluminescence linewidth by 22%, thus making the QDs efficient for QD-laser and optoelectronic device applications. Here, we also find that the position and ordering of In atoms along the (113) and (1¯13) planes are most sensitive to the thickness of the GaAs cap layer. Our XSW-based results are supported by numerical calculations using a QD-macroscopic structural model based on our GID study. We thus show that this atomic-mapping technique will be useful for studying various quantum structures and tuning their properties.

36 MATERIALS SCIENCE↗

Magnetized laser–plasma interactions in high-energy-density systems: Parallel propagation

In this study, we investigate parametric processes in magnetized plasmas, driven by a large-amplitude pump light wave. Our focus is on laser–plasma interactions relevant to high-energy-density (HED) systems, such as the National Ignition Facility and the Sandia MagLIF concept. We present a self-contained derivation of a “parametric” dispersion relation for magnetized three-wave interactions, meaning the pump wave is included in the equilibrium, similar to the unmagnetized work of Drake et al., Phys. Fluids 17, 778 (1974). For this, we use a multi-species plasma fluid model and Maxwell's equations. The application of an external B field causes right- and left-polarized light waves to propagate with differing phase velocities. This leads to Faraday rotation of the polarization, which can be significant in HED conditions. Phase-matching and linear wave dispersion relations show that Raman and Brillouin scattering have modified spectra due to the background B field, though this effect is usually small in systems of current practical interest. We study a scattering process we call stimulated whistler scattering, where a light wave decays to an electromagnetic whistler wave (ω≲ω ce ) and a Langmuir wave. This only occurs in the presence of an external B field, which is required for the whistler wave to exist.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Application and performance of the novel Elcomat 5000 autocollimator in slope-measuring profilometry of beamline optics

Autocollimators are used in profilometers for the precise form measurement of beam-shaping optics for synchrotron light sources and x-ray free-electron lasers. This application requires using an aperture stop, typically 2.5 mm in diameter, which limits the footprint of the autocollimator’s measuring beam on the optics to achieve a sufficiently high lateral resolution. Central to the development of profilometry has been the availability of commercial autocollimators, such as the Elcomat 3000 from Möller–Wedel Optical. Although autocollimators are generally not designed for use with small apertures, this device has proven capable and has become the de facto standard. Now that it has been replaced by the Elcomat 5000, we evaluate the performance of several autocollimators of this type at small apertures, including the characterization of instrument transfer functions with a chirped height profile. We demonstrate that the Elcomat 5000 is capable of repeatable angle measurements with a standard deviation of 0.014 arcsec at an aperture diameter of 1.6 mm, whereas the Elcomat 3000 achieves 0.03 arcsec at 2.5 mm, comparing models with modified reticle designs. Here, we also investigate the influence of optical aberrations of the autocollimator’s objective and their changes with the path length to the surface under test. We characterize the sensitivity of the angle measurement to changes in environmental parameters, in particular, barometric pressure. These efforts are aimed at approaching fundamental limits in the characterization of the shape of optical surfaces with autocollimator-based profilometers so that these are ready for characterizing the next generation of synchrotron and XFEL beamline optics.

angle metrology↗

Temporal evolution of scalar modes in Richtmyer–Meshkov instability of inclined interface using high-speed PIV and PLIF measurements at 60 kHz

Abstract The current work presents simultaneous, high-speed measurements at 60,000 fields per second of velocity and mole fraction using particle image velocimetry (PIV) and planar laser induced acetone-fluorescence in a Richtmyer–Meshkov instability of an inclined interface (Atwood number, At = 0.22). Specifically, around 2 ms of temporal evolution of the vortex structures and their associated scalar modes immediately following the interface-reshock interaction is presented. Two initial interface conditions are discussed—(a) a sharp, inclined ‘single mode’ interface and (b) a ‘multi-mode’ interface where small perturbations are imposed on the single mode case. A 2D wavelet decomposition of the scalar flow field shows a highly intermittent distribution of small-scale variance throughout the interface even at late times. These are correlated strongly with the vortex structures and local turbulence intensity, where each small-scale scalar mode is sandwiched between two co-rotating vortex structures. This indicates that the interstitial regions between the vortices are significant hotspots of entrainment, which is then dispersed by the induced, counter-flow velocity fields. The multimode case demonstrates similar organization at large scales, while the scalar field is much more homogeneous at smaller scales. These observations highlight the importance of capturing the early time vortex evolution to accurately estimate any late time intermittency, especially where deposition of intense vorticity on sharp interfaces is present.

Engineering↗

Exploration of LIBS as a novel and rapid elemental mapping technique of nuclear fuels in the form of surrogate TRISO particles

Laser-induced breakdown spectroscopy (LIBS) was employed to characterize coatings on surrogate fuel particles. Tri-structural isotropic (TRISO) particles are a proposed nuclear fuel alternative for high temperature reactors. These particles are constructed of a ZrO 2 kernel (as a surrogate to uranium), surrounded by an inner pyrolytic carbon layer and are surrounded by an outer carbide layer (ZrC, presented here) to act as a barrier to fission products generated during nuclear reactions. These particles are embedded within a graphite compact and housed within the reactor core. Simply put, due to their robust nature, performing elemental analysis of these particles poses a challenge. Presented here, LIBS is explored as a method for characterizing elemental constituents of these particles, with the focus being on rapid elemental mapping and depth profiling. Different from traditional elemental analysis techniques (e.g., inductively coupled plasma – based methods), LIBS is advantageous because it can directly analyze the sample surface and can detect light elements such as C and O, making it a viable technique for the analysis of small, multilayered particles as spatial elemental information is warranted in the production of these particles. In the work presented here, LIBS was successfully used for discerning small layers (30–50 μm), detecting the location of carbon and oxygen layers, providing fast 2-D mapping (<5 min per particle) and rapid depth profiling (10 s per particle).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Impact of Oxygen Non-Stoichiometry on Near-Ambient Temperature Ionic Mobility in Polaronic Mixed-Ionic-Electronic Conducting Thin Films

Enhanced ionic mobility in mixed ionic and electronic conducting solids contributes to improved performance of memristive memory, energy storage and conversion, and catalytic devices. Ionic mobility can be significantly depressed at reduced temperatures, for example, due to defect association and therefore needs to be monitored. Measurements of ionic transport in mixed conductors, however, proves to be difficult due to dominant electronic conductivity. This study examines the impact of different levels of quenched-in oxygen deficiency on the oxygen vacancy mobility near room temperature as measured by a novel dynamic current-voltage analysis. A Pr 0.1 Ce 0.9 O 2-δ film was grown by pulsed laser deposition and subsequently annealed, from 400-600° C, in various oxygen partial pressures to modify its oxygen vacancy concentration while minimizing microstructural growth and cation segregation. To monitor changes in film non-stoichiometry, we leverage the existence of an optical absorption center, related to the oxidation state of Pr ions in Pr0.1Ce0.9O2-δ. The oxygen vacancy migration enthalpy was found to exhibit a small increase from 0.73± 0.04 to 0.79 ± 0.02 eV with increasing oxygen deficiency, while the pre-factor was found to increase by a factor of 135. Here, a nearly 13-fold increase in ionic mobility at 60 °C for increases in oxygen non-stoichiometry from 0.032 ± 0.001 to 0.042± 0.001 was thereby detected. Raman spectroscopy was employed to rule out changes in strain as the primary cause for the significant change in mobility. Several factors potentially contributing to the large pre-factor changes are examined and discussed. Insights into how ionic defect concentration can markedly impact ionic mobility should help in elucidating the origins of variations seen in nanoionic devices.

36 MATERIALS SCIENCE↗

Automatic Differentiation in MetaPhysicL and Its Applications in MOOSE

Efficient solution via Newton’s method of nonlinear systems of equations requires an accurate representation of the Jacobian, corresponding to the derivatives of the component residual equations with respect to the degrees of freedom. In practice these systems of equations often arise from spatial discretization of partial differential equations used to model physical phenomena. These equations may involve domain motion or material equations that are complex functions of the systems’ degrees of freedom. Computing the Jacobian by hand in these situations is arduous and prone to error. Finite difference approximations of the Jacobian or its action are prone to truncation error, especially in multiphysics settings. Symbolic differentiation packages may be used, but often result in an excessive number of terms in realistic model scenarios. An alternative to symbolic and numerical differentiation is automatic differentiation (AD), which propagates derivatives with every elementary operation of a computer program, corresponding to continual application of the chain rule. Automatic differentiation offers the guarantee of an exact Jacobian at a relatively small overhead cost. In this work, we outline the adoption of AD in the Multiphysics Object Oriented Simulation Environment (MOOSE) via the MetaPhysicL package. We describe the application of MOOSE’s AD capability to several sets of physics that were previously infeasible to model via hand-coded or Jacobian-free simulation techniques, including arbitrary Lagrangian-Eulerian and level-set simulations of laser melt pools, phase-field simulations with free energies provided through neural networks, and metallic nuclear fuel simulations that require inner Newton loop calculation of nonlinear material properties.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Ultrafast infrared plasmon switching in aligned carbon-nanotube optical resonators

Reconfigurable plasmonic materials are crucial components in active photonic devices for optical communication, signal processing, and sensing applications. Certain candidates including transparent conducting oxides, small-bandgap semiconductors (i.e. Ge, InSb), and conducting polymers can exhibit switchable free carrier concentrations triggered by optical, electrical or thermal excitations. Here, we show that aligned films of single-walled carbon nanotubes (SWCNTs) can serve as all-optically tunable plasmonic material in the mid-infrared range, thereby adding them to the library of switchable plasmonic materials. Interband optical pumping with femtosecond laser pulses results in the photoexcitation of free charge carriers, which transiently blueshifts the plasmon resonances of patterned, periodic SWCNT nano-resonators spanning the mid-infrared spectral range from 1700 to 2700 cm -1 . Furthermore. the ultrafast plasmon modulation exhibits a nearly single-picosecond decay time, attributed to interband carrier relaxation and inter-tube charge transfer. Given that aligned films of SWCNTs have high thermal stability, excellent photostability, epsilon-near-zero property, and extremely large optical anisotropy, their dynamic tunability represents a promising pathway towards active optical devices in the technologically important mid-infrared range.

single-walled carbon nanotubes↗

Optical cycling on thorium monoxide for an improved test of fundamental symmetries

Optical cycling refers to repeated excitation and spontaneous emission on an electronic transition in an atom or molecule. Optical cycling in molecules can enable a wide range of quantum control and readout techniques, but unfortunately it has only been demonstrated on a small class of alkalilike or alkaline-earth-like molecules. Thorium monoxide (ThO), a molecule used in one of the most precise permanent electron electric dipole moment (eEDM) searches (ACME†) [Andreev et al., Nature (London) 562, 355 (2018)], does not fall into this category. In this work, we demonstrate the first optical cycling on this nonconventional class over a range of experimental parameter space, including laser intensity, polarization switching rate, and interaction time. We show that both the 𝐽 = 1 and 𝐽 = 2 rotational levels of ThO molecule are capable of cycling an average of 11(2) photons with a single laser, at scattering rates of 1.9⁢(6) × 10 6 and 2.3⁢(7) × 10 6 s −1 , respectively, before population is lost to other vibronic levels. We outline a scheme to apply this demonstrated optical cycling in an ACME-style eEDM measurement, improving the detection efficiency by over fourfold compared to noncycling fluorescence detection. This would lead to over a twofold enhancement in the statistical sensitivity of the eEDM search. This optical-cycling scheme can be further extended to scatter ∼100 photons, which would enable a wider range of quantum control and sensing using ThO molecules.

Atomic & molecular processes in external fields↗

Thermal Conductivity of AM Fabricated Stainless Steel 316L Part

Thermal properties are an integral part of many diverse engineering applications, and additive manufacturing (AM), particularly laser powder bed fusion (LPBF) is shown to affect thermal properties due to the laser processing parameters. For 316L stainless steel, there is little prior research to determine the effects of the process on thermal properties. In this work, the temperature gradient is shown to create uniform, chess board-like distributions of grains in the build direction. These zones create dislocations which were visualized with EBSD techniques. Processing parameters cause hierarchal grain size distribution, with localized concentrations of small grains and large grains. Thermomechanical stresses in the rapid solidification increases dislocation density during grain formation. Previous research shows a higher density of dislocations decreases local thermal conductivity. Local and bulk thermal conductivity are shown in this work to have statistically lowered values to an average of 10-12 W/m-K compared to 14 W/m-K for conventional 316L.

36 MATERIALS SCIENCE↗

Design of experiments to spectroscopically characterize radiation flow in stochastic media

Precise characterization of experimental radiation flow is required to validate the high energy density physics models, numerical methods, and codes that are used to simulate radiation-hydrodynamics phenomena such as thermal radiation transport in stochastic media. The Cassio code is used to simulate thermal radiation flow through inhomogeneous, stochastic-media-foam configurations containing optically thick clumps dispersed within an optically thin background aerogel. Cassio can model small inhomogeneous problems directly, but most problems require approximations to meet computer limitations on run-times and memory usage. Various examples of these approximations are methods that produce, in one calculation, an ensemble-averaged solution and associated standard deviation; reduced spatial dimensionality with approximate geometries; and full material homogenization with no geometric detail. Cassio simulations are used to design experiments at the OMEGA-60 Laser Facility that can measure the radiation flow using the spatially resolved COAX absorption spectroscopy diagnostic. The experimental platforms flow radiation through foam targets ranging from a background-only aerogel, to a single configuration of a specified stochastic medium, to a fully homogenized foam of the background and clump materials. Under constant total clump mass, larger clumps (here, larger than 10 μm diameter) will mix more slowly with the background such that the bulk radiation flow is faster than it would be in a fully homogenized material. The COAX platform can be used to infer temperature and density profiles in both the background material and clumps, simultaneously, and therefore to differentiate radiation flow in a range of stochastic and homogeneous media.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Infrared spectroscopy of the syn -methyl-substituted Criegee intermediate: A combined experimental and theoretical study

An IR–vacuum ultraviolet (VUV) ion-dip spectroscopy method is utilized to examine the IR spectrum of acetaldehyde oxide (CH3CHOO) in the overtone CH stretch (2νCH) spectral region. IR activation creates a depletion of the ground state population that reduces the VUV photoionization signal on the parent mass channel. IR activation of the more stable and populated syn-CH3CHOO conformer results in rapid unimolecular decay to OH + vinoxy products and makes the most significant contribution to the observed spectrum. The resultant IR–VUV ion-dip spectrum of CH3CHOO is similar to that obtained previously for syn-CH3CHOO using IR action spectroscopy with UV laser-induced fluorescence detection of OH products. The prominent IR features at 5984 and 6081 cm−1 are also observed using UV + VUV photoionization of OH products. Complementary theoretical calculations utilizing a general implementation of second-order vibrational perturbation theory provide new insights on the vibrational transitions that give rise to the experimental spectrum in the overtone CH stretch region. The introduction of physically motivated small shifts of the harmonic frequencies yields remarkably improved agreement between experiment and theory in the overtone CH stretch region. The prominent features are assigned as highly mixed states with contributions from two quanta of CH stretch and/or a combination of CH stretch with an overtone in mode 4. The generality of this approach is demonstrated by applying it to three different levels of electronic structure theory/basis sets, all of which provide spectra that are virtually indistinguishable despite showing large deviations prior to introducing the shifts to the harmonic frequencies.

Chemistry↗