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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Trends in Spitzer Secondary Eclipses

It is well established that the magnitude of the incident stellar flux is the single most important factor in determining the day–night temperature gradients and atmospheric chemistries of short-period gas giant planets. However, it is likely that other factors, such as planet-to-planet variations in atmospheric metallicity, C/O ratio, and cloud properties, also contribute to the observed diversity of infrared spectra for this population of planets. In this study, we present new 3.6 and 4.5 μm secondary eclipse measurements for five transiting gas giant planets: HAT-P-5b, HAT-P-38b, WASP-7b, WASP-72b, and WASP-127b. We detect eclipses in at least one bandpass for all five planets and confirm circular orbits for all planets except WASP-7b, which shows evidence for a nonzero eccentricity. Building on the work of Garhart et al., we place these new planets into a broader context by comparing them with the sample of all planets with measured Spitzer secondary eclipses. We find that incident flux is the single most important factor for determining the atmospheric chemistry and circulation patterns of short-period gas giant planets. Although we might also expect surface gravity and host star metallicity to play a secondary role, we find no evidence for correlations with either of these two variables.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

6D Simulations of PIP-II Booster Injection

The PIP-II superconducting linac will deliver 2 mA average H⁻ beam current at 800 MeV to the existing Booster synchrotron over a period of 0.55 ms (285 turns). As a result, the injected beam power will quadruple to 17 kW. Safe operation at the increased beam power implies careful attention to the origin, magnitude, and distribution of both controlled and uncontrolled losses. Uncontrolled losses are due to neutral ions in excited states stripped in downstream magnets and large angle scattered protons from parasitic foil hits. The relative magnitudes of these loss mechanisms is used to determine the optimal foil thickness. A transverse painting scheme involving closed orbit motion will be used to mitigate space charge effects and minimize parasitic foil hits. Using a detailed full 6D simulation of the injection process, we compute large angle scattering losses and compare results to back of the envelope estimates. We investigate possible impact of space charge on the emittance and beam distribution both during and at the conclusion of the injection period.

43 PARTICLE ACCELERATORS↗
DOE OSTI2020

Forward Modeling the Orbits of Companions to Pulsating Stars from Their Light Travel Time Variations

Mutual gravitation between a pulsating star and an orbital companion leads to a time-dependent variation in path length for starlight traveling to Earth. These variations can be used for coherently pulsating stars, such as the δ Scuti variables, to constrain the masses and orbits of their companions. Observing these variations for δ Scuti stars has previously relied on subdividing the light curve and measuring the average pulsation phase in equally sized subdivisions, which leads to undersampling near periapsis. We introduce a new approach that simultaneously forward models each sample in the light curve and show that this method improves upon current sensitivity limits—especially in the case of highly eccentric and short-period binaries. We find that this approach is sensitive enough to observe Jupiter mass planets around δ Scuti stars under ideal conditions, and use gravity-mode pulsations in the subdwarf B star KIC 7668647 to detect its companion without radial velocity data. We further provide robust detection limits as a function of the signal-to-noise ratio of the pulsation mode and determine that the minimum detectable light travel time amplitude for a typical Kepler δ Scuti is around 2 s. This new method significantly enhances the application of light travel time variations to detecting short-period binaries with pulsating components, and pulsating A-type exoplanet host stars, especially as a tool for eliminating false positives.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

True Masses of the Long-period Companions to HD 92987 and HD 221420 from Hipparcos–Gaia Astrometry

The extensive time span of modern radial velocity surveys has made the discovery of long-period substellar companions more common in recent years; however, measuring the true masses of these objects remains challenging. Astrometry from the Gaia mission is expected to provide mass measurements for many of these long-period companions, but these data are not yet available. However, combining proper-motion data from Gaia DR2 and the earlier Hipparcos mission makes it possible to measure true masses of substellar companions in favorable cases. In this work, we combine radial velocities with Hipparcos–Gaia astrometry to measure the true masses of two recently discovered long-period substellar companion candidates, HD 92987 B and HD 221420 b. In both cases, we find that the true masses are significantly higher than implied by radial velocities alone. A 2087 ± 19 m s{sup −1} astrometric signal reveals that HD 92987 B is not close to its 17 M {sub J} minimum mass but is instead a 0.2562 ± 0.0045 M {sub ⊙} star viewed at a near-polar orbital inclination, whereas the 22.9 ± 2.2 M {sub J} HD 221420 b can be plausibly interpreted as a high-mass “superplanet” or a low-mass brown dwarf. With semimajor axes of ∼10 au, both companions are interesting targets for direct imaging, and HD 221420 b in particular would be a benchmark metal-rich substellar object if it proves possible to directly detect. Our results demonstrate the power of Hipparcos–Gaia astrometry for studying long-period planet and brown dwarf candidates discovered from radial velocity surveys.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Computational analysis of interface-driven spin-orbit coupling in molecular adsorbates on transition metal dichalcogenides

Spin-orbit coupling (SOC) lifts molecular orbital degeneracy, enabling bilevel electronic platforms suitable for next-generation digital devices. However, common light-atom molecular feedstocks exhibit weak SOC due to the absence of heavy elements. To enhance SOC without synthesizing new materials, we leverage interfacial interactions between molecules and transition-element-based solid-state materials. This computational study investigates SOC splitting in metal-phthalocyanine adsorbed on transition metal dichalcogenides (TMDs) using density functional theory (DFT). The enhanced SOC splitting is attributed to strong orbital hybridization at the molecule-substrate interface. Specifically, Zn-phthalocyanine (ZnPC) on monolayer Mo⁢S 2 achieves a notable SOC splitting of ∼8 meV. Furthermore, when ZnPC forms self-assembled chains on Mo⁢S 2 , the splitting increases to ∼20 meV, driven by the formation of hybrid bands modulated by molecular periodicity. Furthermore, these findings highlight the role of interfacial and intermolecular interactions in inducing and enhancing SOC in surface-adsorbed molecules, providing a new strategy for molecular spintronic materials without complex synthetic efforts.

2-dimensional systems↗
DOE OSTI2020

Unveiling the Finite Temperature Physics of Hydrogen Chains via Auxiliary Field Quantum Monte Carlo

The ability to accurately predict the finite temperature properties and phase diagrams of realistic quantum solids is central to uncovering new phases and engineering materials with novel properties ripe for device applications. Nonetheless, there remain comparatively few many-body techniques capable of elucidating the finite temperature physics of solids from first principles. Here, we take a significant step toward developing such a technique by generalizing our previous, exact fully ab initio finite temperature Auxiliary Field Quantum Monte Carlo (FT-AFQMC) method to model periodic solids and employing it to uncover the finite temperature physics of periodic hydrogen chains. Our chains’ unit cells consist of 10 hydrogen atoms modeled in a minimal basis, and we sample 5 k-points from the first Brillouin zone to arrive at a supercell consisting of 50 orbitals and 50 electrons. Based upon our calculations of these chains’ many-body energies, free energies, entropies, heat capacities, double and natural occupancies, and charge and spin correlation functions, we outline their metal–insulator and magnetic ordering as a function of both H–H bond distance and temperature. At low temperatures approaching the ground state, we observe both metal–insulator and ferromagnetic–antiferromagnetic crossovers at bond lengths between 0.5 and 0.75 Å. We then demonstrate how this low-temperature ordering evolves into a metallic phase with decreasing magnetic order at higher temperatures. In order to contextualize our results, we compare the features we observe to those previously seen in one-dimensional, half-filled Hubbard models at finite temperature and in ground state hydrogen chains. Interestingly, we identify signatures of the Pomeranchuk effect in hydrogen chains for the first time and show that spin and charge excitations that typically arise at distinct temperatures in the Hubbard model are indistinguishably coupled in these systems. Beyond qualitatively revealing the many-body phase behavior of hydrogen chains in a numerically exact manner without invoking the phaseless approximation, our efforts shed light on the further theoretical developments that will be required to construct the phase diagrams of the more complex transition metal, lanthanide, and actinide solids of longstanding interest to physicists.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Modeling dark- and light-induced crystal structures and single-crystal optical absorption spectra of ruthenium-based complexes that undergo SO 2 -linkage photoisomerization

A family of coordination complexes of the type [Ru(SO 2 )(NH 3 ) 4 X] m+ Y n – (m, n = 1 or 2) exhibit optical switching capabilities in their single-crystal states. This striking effect is caused by the light-induced formation of SO 2 -linkage photoisomers, which are metastable if kept at suitably cool temperatures. We modeled the dark- and light-induced states of these large crystalline complexes via plane-wave (PW)- and molecular-orbital (MO)-based density functional theory (DFT) and time-dependent DFT in order to calculate their structural and optical properties; the calculated results are compared with experimental data. We show that the PW-DFT-based periodic models replicate the structural properties of these complexes more effectively than the MO-DFT-based molecular-fragment models, observing only small deviations in key bond lengths relative to the experimentally derived crystal structures. The periodic models were also found to more effectively simulate trends seen in experimental optical absorption spectra, with optical absorbance and coverage of the visible region increasing with the formation of the photoinduced geometries. The contribution of the metastable photoisomeric species more heavily focuses on the lower-energy end of the spectra. Spectra generated from the molecular-fragment models are limited by the geometry of the fragment used and the number of excited-state roots considered in those calculations. In general, periodic models outperform the molecular-fragment models owing to their ability to better appreciate the periodic phenomena that are present in these crystalline materials as opposed to MO approaches, which are finite methods. We thus demonstrate that PW-DFT-based periodic models should be considered as a more than viable method for simulating the optical and electronic properties of these single-crystal optical switches.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Detection Limits of Low-mass, Long-period Exoplanets Using Gaussian Processes Applied to HARPS-N Solar Radial Velocities

Radial velocity (RV) searches for Earth-mass exoplanets in the habitable zone around Sun-like stars are limited by the effects of stellar variability on the host star. In particular, suppression of convective blueshift and brightness inhomogeneities due to photospheric faculae/plage and starspots are the dominant contribution to the variability of such stellar RVs. Gaussian process (GP) regression is a powerful tool for statistically modeling these quasi-periodic variations. We investigate the limits of this technique using 800 days of RVs from the solar telescope on the High Accuracy Radial velocity Planet Searcher for the Northern hemisphere (HARPS-N) spectrograph. These data provide a well-sampled time series of stellar RV variations. Into this data set, we inject Keplerian signals with periods between 100 and 500 days and amplitudes between 0.6 and 2.4 m s{sup −1}. We use GP regression to fit the resulting RVs and determine the statistical significance of recovered periods and amplitudes. We then generate synthetic RVs with the same covariance properties as the solar data to determine a lower bound on the observational baseline necessary to detect low-mass planets in Venus-like orbits around a Sun-like star. Our simulations show that discovering planets with a larger mass (∼0.5 m s{sup −1}) using current-generation spectrographs and GP regression will require more than 12 yr of densely sampled RV observations. Furthermore, even with a perfect model of stellar variability, discovering a true exo-Venus (∼0.1 m s{sup −1}) with current instruments would take over 15 yr. Therefore, next-generation spectrographs and better models of stellar variability are required for detection of such planets.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

TOI-2076 and TOI-1807: Two Young, Comoving Planetary Systems within 50 pc Identified by TESS that are Ideal Candidates for Further Follow Up

We report the discovery of two planetary systems around comoving stars: TOI-2076 (TIC 27491137) and TOI-1807 (TIC 180695581). TOI-2076 is a nearby (41.9 pc) multiplanetary system orbiting a young (204 ± 50 Myr), bright (K = 7.115 in TIC v8.1) start. TOI-1807 hosts a single transiting planet and is similarly nearby (42.58 pc), similarly young (180 ± 40 Myr ), and bright. Both targets exhibit significant, periodic variability due to starspots, characteristic of their young ages. Using photometric data collected by TESS we identify three transiting planets around TOI-2076 with radii of R {sub b} = 3.3 ± 0.04 R {sub ⊕}, R {sub c} = 4.4 ± 0.05 R {sub ⊕}, and R {sub d} = 4.1 ± 0.07 R {sub ⊕}. Planet TOI-2076b has a period of P {sub b} = 10.356 days. For both TOI-2076c and d, TESS observed only two transits, separated by a 2 yr interval in which no data were collected, preventing a unique period determination. A range of long periods (<17 days) are consistent with the data. We identify a short-period planet around TOI-1807 with a radius of R {sub b} = 1.8 ± 0.04 R {sub ⊕} and a period of P {sub b} = 0.549 days. Their close proximity, and bright, cool host stars, and young ages make these planets excellent candidates for follow up. TOI-1807b is one of the best-known small (R < 2 R{sub ⊕}) planets for characterization via eclipse spectroscopy and phase curves with JWST. TOI-1807b is the youngest ultra-short-period planet discovered to date, providing valuable constraints on formation timescales of short-period planets. Given the rarity of young planets, particularly in multiple-planet systems, these planets present an unprecedented opportunity to study and compare exoplanet formation, and young planet atmospheres, at a crucial transition age for formation theory.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Nearly Periodic Maps and Geometric Integration of Noncanonical Hamiltonian Systems

Abstract M. Kruskal showed that each continuous-time nearly periodic dynamical system admits a formal U (1)-symmetry, generated by the so-called roto-rate. When the nearly periodic system is also Hamiltonian, Noether’s theorem implies the existence of a corresponding adiabatic invariant. We develop a discrete-time analog of Kruskal’s theory. Nearly periodic maps are defined as parameter-dependent diffeomorphisms that limit to rotations along a U (1)-action. When the limiting rotation is non-resonant, these maps admit formal U (1)-symmetries to all orders in perturbation theory. For Hamiltonian nearly periodic maps on exact presymplectic manifolds, we prove that the formal U (1)-symmetry gives rise to a discrete-time adiabatic invariant using a discrete-time extension of Noether’s theorem. When the unperturbed U (1)-orbits are contractible, we also find a discrete-time adiabatic invariant for mappings that are merely presymplectic, rather than Hamiltonian. As an application of the theory, we use it to develop a novel technique for geometric integration of non-canonical Hamiltonian systems on exact symplectic manifolds.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Renormalization of the 3D exciton spectrum by the disorder

Effect of short-range disorder on the excited states of the exciton is studied. Disorder causes an obvious effect of broadening. Microscopically, an exciton, as an entity, is scattered by the large-scale disorder fluctuations. Much less trivial is that short-scale fluctuations, with a period of the order of the Bohr radius, cause a well-defined down-shift of the exciton levels. We demonstrate that this shift exceeds the broadening parametrically and study the dependence of this shift on the orbital number. Difference of the shifts for neighboring levels leads to effective renormalization of the Bohr energy. Most remarkable effect is the disorder-induced splitting of S and P exciton levels. The splitting originates from the fact that disorder lifts the accidental degeneracy of the hydrogen-like levels. We draw an analogy between this splitting and the Lamb shift in quantum electrodynamics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Drift kinetic theory of alpha transport by tokamak perturbations

We report that upcoming tokamak experiments fuelled with deuterium and tritium are expected to have large alpha particle populations. Such experiments motivate new attention to the theory of alpha particle confinement and transport. A key topic is the interaction of alpha particles with perturbations to the tokamak fields, including those from ripple and magnetohydrodynamic modes like Alfvén eigenmodes. These perturbations can transport alphas, leading to changed localization of alpha heating, loss of alpha power and damage to device walls. Alpha interaction with these perturbations is often studied with single-particle theory. In contrast, we derive a drift kinetic theory to calculate the alpha heat flux resulting from arbitrary perturbation frequency and periodicity (provided these can be studied drift kinetically). Novel features of the theory include the retention of a large effective collision frequency resulting from the resonant alpha collisional boundary layer, correlated interactions over many poloidal transits and finite orbit effects. Heat fluxes are considered for the example cases of ripple and the toroidal Alfvén eigenmode (TAE). The ripple heat flux is small. The TAE heat flux is significant and scales with the square of the perturbation amplitude, allowing the derivation of constraints on mode amplitude for avoidance of significant alpha depletion. A simple saturation condition suggests that TAEs in one upcoming experiment will not cause significant alpha transport via the mechanisms in this theory. However, saturation above the level suggested by the simple condition, but within numerical and experimental experience, which could be accompanied by the onset of stochasticity, could cause significant transport.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

On the theory of nonhomogeneous nonequilibrium superconductivity in 2D systems with massless fermions

Here we analyze static and nonequilibrium superconducting properties of a 2D relativistic-like model system with local electron-electron interaction, Rashba spin-orbit interaction αR in presence of time-dependent in-plane magnetic field H(t). It is shown that similar to the 2D case with ordinary massive quasiparticle dispersion ε(k)~|k| 2 at large fields, such a system demonstrates a nonhomogeneous superconducting stripe phase with the order parameter Δ(r)=Δ(0)cos(2[μ B B×r]n/$\hbarυ_F$) (B is the magnetic induction, υF is the Fermi velocity, n is the normal to the plane, μ B is the Bohr magneton, and αR$\ll$υF) where the stripes are oriented along the B direction. In the considered system, the inter-stripe period L and the magnitude of the magnetic field B are related by a universal relation BL=$\hbarυ_F$/μ B ≃0.714∙10 -4 Tm. Contrary to the case of massive quasiparticles, where the condition α R ~υ F can be, in principle, satisfied by increasing α R or by charge doping (Fermi velocity decreasing), in a relativistic-like system, where υF is doping-independent and one-two orders of magnitude larger than typical Fermi velocity in the “standard” 2D systems, the stripe phase can be the ground state at a rather low doping level. We also analyzed the nonequilibrium properties of the system with a focus on the melting of the stripe order (when the magnetic field is quenched to a lower value) and stripe dynamics (when the field is rotated by 90° degrees) and found several notable results. In particular, it was shown that the stripe domains melt according to law R~1$\sqrt{t}$ at initial times, while at longer times they shrink exponentially. In the case of the flipped magnetic field, the stripe orientation gradually turns from x- to y-direction, and the intermediate “crossed-stripe” phase takes place during times of order of picoseconds. Such a crossed phase is built of periodic superconducting bubbles that potentially may have applications in modern ultrafast superconducting technologies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

In-orbit operation of Resolve Filter Wheel and modulated X-ray source

The Resolve soft X-ray spectrometer is a high spectral resolution microcalorimeter spectrometer for the X-ray Imaging and Spectroscopy Mission. In the beam of Resolve, there is a filter wheel containing X-ray filters. In the beam, there is also an active calibration source, the modulated X-ray source (MXS), which can provide pulsed X-rays to facilitate gain calibration. The filter wheel consists of six filter positions. Two open positions, one 55 Fe source to aid in spectrometer characterization during the commissioning phase, and three transmission filters: a neutral density filter, an optical blocking filter, and a beryllium filter. The X-ray intensity, pulse period, and pulse separation of an MXS are highly configurable. Furthermore, the switch-on time is synchronized with the spacecraft’s internal clock to give accurate start and end times of the pulses. One of the issues raised during ground testing was the susceptibility of an MXS at high voltage to ambient light. Although measures were taken to mitigate the light leak, the efficacy of those measures must be verified in orbit. Along with an overview of issues raised during ground testing, we will discuss the calibration source and the filter performance in-flight and compare with the transmission curves present in the Resolve calibration database.

X-ray Imaging and Spectroscopy Mission/Resolve↗
DOE OSTI2025

Orbital selective band re-normalization induced Lifshitz transition in TiSe 2

A Lifshitz transition is a sudden change in Fermi surface topology, often linked to quantum phenomena, with major impact on transport and sometimes superconductivity. Here we demonstrate a Lifshitz transition in TiSe 2 using micro–angle-resolved photoemission spectroscopy. At low temperatures an electron pocket appears at the Brillouin-zone center, whereas at higher temperatures spectral weight from a hole-like valence band dominates the Fermi level. Unlike previously reported cases typically driven by rigid band shifts, in TiSe 2 an orbital-selective strong band renormalization induces the crossover near 160 K. This mechanism naturally explains the longstanding resistivity anomaly of TiSe 2 , which peaks around 160 K. Our results clarify its puzzling transport behavior and open avenues to investigate how periodic lattice distortions interact with strong electronic correlations.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Quantum algorithm for electronic band structures with local tight-binding orbitals

While the main thrust of quantum computing research in materials science is to accurately measure the classically intractable electron correlation effects due to Coulomb repulsion, designing optimal quantum algorithms for simpler problems with well-understood solutions is a useful tactic to advance our quantum “toolbox”. With this in mind, we consider the quantum calculation of a periodic system’s single-electron band structure over a path through reciprocal space. Previous efforts have used the Variational Quantum Eigensolver algorithm to solve the energy of each band, which involves numerically optimizing the parameters of a variational quantum circuit to minimize a cost function, constructed as the expectation value of a Hamiltonian operator. Traditionally, a unique Hamiltonian operator is constructed for each k-point, so that many cost functions, each with their own parameter space, must be optimized to generate a single band. Similarly, calculating higher bands than the first has traditionally involved modifying the cost function with additional overlap terms to ensure higher-energy eigenstates are orthogonal to those of lower bands. In this paper, we adopt a direct space approach, using a novel hybrid first/second-quantized qubit mapping which allows us to construct a single Hamiltonian, and a single cost-function, suitable for solving the entire electronic band structure. In contrast to previous approaches, the k-point and the band index are selected by additional parameters in our quantum circuit, rather than through modifications to the cost function. The result is a technically and conceptually simpler approach to band structure calculations on a quantum computer. Moreover, we expect that the tools developed herein will motivate new strategies for tackling highly-correlated materials beyond the grasp of classical computing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Shapiro steps and stability of skyrmions interacting with alternating anisotropy under the influence of ac and dc drives

Here we use atomistic simulations to examine the sliding dynamics of a skyrmion in a two-dimensional system containing a periodic one-dimensional stripe pattern of variations between low and high values of the perpendicular magnetic anisotropy. The skyrmion changes in size as it crosses the interface between two anisotropy regions. On applying combined dc and ac driving in either parallel or perpendicular directions, we observe a wide variety of Shapiro steps, Shapiro spikes, and phase-locking phenomena. The phase-locked orbits have two-dimensional dynamics due to the gyrotropic or Magnus dynamics of the skyrmions and are distinct from the phase-locked orbits found for strictly overdamped systems. Along a given Shapiro step when the ac drive is perpendicular to the dc drive, the velocity parallel to the ac drive is locked while the velocity in the perpendicular direction increases with increasing drive to form Shapiro spikes. At the transition between adjacent Shapiro steps, the parallel velocity jumps up to the next step value, and the perpendicular velocity drops. The skyrmion Hall angle shows a series of spikes as a function of increasing dc drive, where the jumps correspond to the transition between different phase-locked steps. At high drives, the Shapiro steps and Shapiro spikes are lost. When both the ac and dc drives are parallel to the stripe periodicity direction, Shapiro steps appear, while if the dc drive is parallel to the stripe periodicity direction and the ac drive is perpendicular to the stripe periodicity, then there are only two locked phases, and the skyrmion motion consists of a combination of sliding along the interfaces between the two anisotropy values and jumping across the interfaces.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Linearized Pair-Density Functional Theory with Spin–Orbit Coupling

Here, we include spin–orbit coupling (SOC) effects in linearized pair-density functional theory (L-PDFT), which is a multistate extension of multiconfiguration pair-density functional theory (MC-PDFT). Both 1-electron and 2-electron SOC integrals are computed using Breit-Pauli and Douglas–Kroll–Hess Hamiltonians in the atomic mean-field approximation. SO-L-PDFT removes the unphysical J-symmetry breaking observed in MC-PDFT. The accuracy of SO-L-PDFT is validated by calculations of zero-field splittings, fine-structure excitation energies, and low-energy excited-state spectra for a diverse group of atoms and molecules spanning the whole range of the periodic table, including atoms of groups 3, 11, and 13–17, the Ce 3+ and U 5+ ions, group 16 monohydrides, group 17 monoxides, lanthanide hexachlorides ([CeCl 6 ] 3− , [PrCl 6 ] 3− , and [NdCl 6 ] 3− ), actinyl ions ([UO 2 ] + , [NpO 2 ] 2+ ), and tricarbonatoactinyl complexes ([UO 2 (CO 3 ) 3 ] 5− , [NpO 2 (CO 3 ) 3 ] 4− ). We also compare the results to new spin–orbit-inclusive calculations by single-state and multistate multireference perturbation theory.

Hamiltonians↗