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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Understanding plasma turbulence through exact coherent structures

Plasma turbulence is a key challenge in understanding transport phenomena in magnetically confined plasmas. This work presents a generalized framework to analyze plasma turbulence that utilizes periodic orbit theory. In periodic orbit theory, doubly periodic solutions (coherent structures) of the governing equation(s) serve as building blocks of the considered turbulent dynamics. To illustrate the concept and method, the particularly simple Kuramoto–Sivashinsky (referred to here as LMRT for the original authors: LaQuey, Mahajan, Rutherford, and Tang) trapped-ion mode toy model is used. By applying numerical optimization techniques to the LMRT equation, we extract coherent spacetime patterns that represent the library of allowable fundamental structures of the equation. These structures provide a framework to systematically describe turbulence as a composition of recurrent solutions, revealing an underlying order within chaotic plasma motion. Although illustrated here using the simplified LMRT model for clarity, this framework provides a general strategy that can be extended to more complex and realistic models of plasma turbulence, including gyrokinetic systems. This offers a new method for predicting and potentially controlling transport processes in fusion plasmas by providing a bridge between nonlinear dynamical systems theory and plasma physics in the form of a generalized framework with which to analyze and understand spatially extended nonlinear partial differential equations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Simulations of Interacting Binary Systems—Pathways to Radio-bright Gamma-Ray Burst Progenitors

Although the association of gamma-ray bursts (GRBs) with massive stellar death is on firm footing, the nature of the progenitor system and the key ingredients required for a massive star to produce a GRB remain open questions. Here, we investigate the evolution of a 15–25M ⊙ massive star with a 10–15M ⊙ black hole (BH) using Modules for Experiments in Stellar Astrophysics. We quantify companion-influenced angular-momentum evolution over a stellar lifetime for orbital periods where tides are significant, varying stellar and BH masses, initial stellar spin, and accretion and dynamo prescriptions while tracking mass loss and angular momentum. The final spin is set by tidal torques versus stellar winds. For binaries that initially avoid Roche-lobe overflow, tides can spin up the star, but a late-stage expansion can drive tidal stripping; associated mass and angular-momentum loss can suppress spin-up. We find that massive-star BH binaries at comparable mass ratios may be potential GRB progenitors for short orbital periods (∼20–5 × 10 2 days) and long orbital periods (∼2 × 10 3 –4 × 10 3 days), where our suite of lifetime simulations reveals a favored parameter space with negligible mass loss and enough spin angular momentum to power a GRB jet. For initially nonrotating stars, this provides a lower limit on the final spin above a threshold estimate consistent with forming a postcollapse BH mass of 5–10M ⊙ with a spin parameter ≥ 0.5. For initially rapidly rotating stars, tidal interactions may sustain high spin when mass loss is negligible because the binary is not tidally synchronized.

Hernandez, Angel [Univ. of Colorado, Boulder, CO (↗
DOE OSTI2025

Outer Radiation Belt Dynamics During the October 2012 Storm Revisited: Rapid Inward Radial Transport From a Dynamic Outer Boundary

Earth's outer radiation belt electron flux is highly variable and can be enhanced by over an order of magnitude over timescales less than one day, as observed during the October 2012 storm. Previous studies of this storm (e.g., Reeves et al., 2013, https://doi.org/10.1126/science.1237743) have invoked local acceleration to explain this. However, here, we argue that the observations can instead be explained by fast inward radial transport. One method often invoked to distinguish between these two acceleration processes is the existence of local peaks in electron phase space density (PSD) as a function of L* at fixed first, M, and second, K, adiabatic invariants. However, this method relies on the assumption that the evolution of the PSD as a function of L* occurs over timescales slower than the satellite orbital period. Here, high spatiotemporal resolution data from the Global Positioning System (GPS) spacecraft constellation is used to show that enhancements in the PSD occur during the October 2012 storm over short timescales not resolvable by the Van Allen Probes. In addition, Geostationary Operational Environmental Satellite spacecraft data also indicate that these enhancements are consistent with relativistic electron injections. A radial diffusion model is shown to reproduce the PSD dynamics observed by the Van Allen Probes, once rapid variations at the simulation outer boundary are included, consistent with GPS data. This verifies that apparently “locally growing” peaks in PSD along high apogee satellite orbits can be produced by fast inward radial transport without requiring the action of any local acceleration processes.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2024

A convergent genus expansion for the plateau

We conjecture a formula for the spectral form factor of a double-scaled matrix integral in the limit of large time, large density of states, and fixed temperature. The formula has a genus expansion with a nonzero radius of convergence. To understand the origin of this series, we compare to the semiclassical theory of “encounters” in periodic orbits. In Jackiw-Teitelboim (JT) gravity, encounters correspond to portions of the moduli space integral that mutually cancel (in the orientable case) but individually grow at low energies. At genus one we show how the full moduli space integral resolves the low energy region and gives a finite nonzero answer.

2D Gravity↗
DOE OSTI2025

Isochronous and period-doubling diagrams for symplectic maps of the plane

Symplectic mappings of the plane serve as key models for exploring the fundamental nature of complex behavior in nonlinear systems. Central to this exploration is the effective visualization of stability regimes, which enables the interpretation of how systems evolve under varying conditions. While the area-preserving quadratic Hénon map has received significant theoretical attention, a comprehensive description of its mixed parameter-space dynamics remain lacking. This limitation arises from early attempts to reduce the full two-dimensional phase space to a one-dimensional projection, a simplification that resulted in the loss of important dynamical features. Consequently, there is a clear need for a more thorough understanding of the underlying qualitative aspects. This paper aims to address this gap by revisiting the foundational concepts of reversibility and associated symmetries, first explored in the early works of G.D. Birkhoff. We extend the original framework proposed by Hénon by adding a period-doubling diagram to his isochronous diagram, which allows to represents the system’s bifurcations and the groups of symmetric periodic orbits that emerge in typical bifurcations of the fixed point. A qualitative and quantitative explanation of the main features of the region of parameters with bounded motion is provided, along with the application of this technique to other symplectic mappings, including cases of multiple reversibility. Modern chaos indicators, such as the Reversibility Error Method (REM) and the Generalized Alignment Index (GALI), are employed to distinguish between various dynamical regimes in the mixed space of variables and parameters. These tools prove effective in differentiating regular and chaotic dynamics, as well as in identifying twistless orbits and their associated bifurcations. Additionally, we discuss the application of these methods to real-world problems, such as visualizing dynamic aperture in accelerator physics, where our findings have direct relevance.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

XRISM spectroscopy on orbital modulation of Fe Ly α lines in Cygnus X-3

To understand physical processes such as mass transfer and binary evolution in X-ray binaries, the orbital parameters of the system are fundamental and crucial information. Cygnus X-3 is a high-mass X-ray binary composed of a compact object of unknown nature and a Wolf–Rayet star, which is of great interest in the context of wind-fed mass accretion and binary evolution. Here we present XRISM/Resolve high-resolution spectroscopy, focusing on the Fe Ly$\alpha$ lines when the source was in its hypersoft state. We perform an orbital phase-resolved spectral analysis of the lines to study the orbital modulation of the emission and absorption lines. It is found that the emission lines reflect the orbital motion of the compact object whose estimated velocity amplitude is $430^{+150}_{-140}$ km s$^{-1}$, while the absorption lines show a variation that can be interpreted as originating from the stellar wind. We discuss possible mass ranges for the binary components using the mass function with the estimated value of the velocity amplitude in this work, combined with the relation between the mass-loss rate and the orbital period derivative and the empirical mass and mass-loss rate relation for Galactic Wolf–Rayet stars. They are constrained to be (1.3–5.1) and (9.3–12) M$_\odot$, respectively, for the assumed inclination angle of $i =25^\circ$, and become more relaxed, (1.3–24) and (9.3–16) M$_\odot$, for $i = 35^\circ$. Thus, it remains unclear whether the system harbors a black hole or a neutron star.

X-rays: binaries↗
DOE OSTI2025

Design of Hopfield Networks Based on Superconducting Coupled Oscillators

The global energy shortage has driven the development of many energy-efficient computational platforms beyond Moore's law, among which brain-inspired neuromorphic computing is one of the promising solutions. Associative memory and pattern recognition are important computations solved by brain-inspired Hopfield networks. Classical Hopfield networks store memories via fixed point attractors of their dynamics. In oscillatory Hopfield networks, these attractors are replaced by periodic orbits. Here, we design an oscillatory Hopfield network based on coupled superconducting oscillators. We first employ a mathematical phase reduction approach to map networks of coupled superconducting rapid single flux quantum (RSFQ) ring oscillators to coupled Kuramoto phase-oscillator networks. We use this theory to numerically optimize the hardware's mutual inductances in order to directly match the phase-reduced superconducting oscillators to a model of phase-oscillator-based Hopfield networks. The resulting network can store multiple oscillatory phase-locked memory patterns and recover the patterns based on the initial phase conditions. As different pattern recognition tasks, or learning, require tunable connectivity strengths between the oscillatory nodes, we further employ a coupler circuit that enables tuning the coupling strength between two oscillators by applying an external flux. We demonstrate the functionality of our design through numerical simulations of a small example network with oscillators operating at 86 GHz and recognizing patterns within 10 ns. Our approach enables the learning and retrieval of dynamical memory patterns with a wide range of applications where rhythmic dynamic output is beneficial.

Cheng, Ran↗
DOE OSTI2024

Occurrence of Gravitational Collapse in the Accreting Neutron Stars of Binary-driven Hypernovae

The binary-driven hypernova (BdHN) model proposes long gamma-ray bursts (GRBs) originate in binaries composed of a carbon–oxygen (CO) star and a neutron star (NS) companion. The CO core collapse generates a newborn NS and a supernova that triggers the GRB by accreting onto the NSs, rapidly transferring mass and angular momentum to them. This article aims to determine the conditions under which a black hole (BH) forms from NS collapse induced by the accretion and the impact on the GRB's observational properties and taxonomy. We perform three-dimensional, smoothed particle hydrodynamics simulations of BdHNe using up-to-date NS nuclear equations of state, with and without hyperons, and calculate the structure evolution in full general relativity. We assess the binary parameters leading either NS in the binary to the critical mass for gravitational collapse into a BH and its occurrence time, t col . We include a nonzero angular momentum of the NSs and find that t col ranges from a few tens of seconds to hours for decreasing NS initial angular momentum values. BdHNe I are the most compact (about 5 minute orbital period), promptly form a BH, and release ≳10 52 erg of energy. They form NS–BH binaries with tens of kiloyears merger timescales by gravitational-wave emission. BdHNe II and III do not form BHs, and release ~10 50 –10 52 erg and ≲10 50 erg of energy, respectively. They form NS–NS binaries with a range of merger timescales larger than for NS–BH binaries. In some compact BdHNe II, either NS can become supramassive, i.e., above the critical mass of a nonrotating NS. Magnetic braking by a 10 13 G field can delay BH formation, leading to BH–BH or NS–BH with tens of kiloyears merger timescales.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Measurement and feedback-driven adaptive dynamics in the classical and quantum kicked top

In classical dynamical systems, stochastic feedback can stabilize otherwise unstable periodic orbits, giving rise to distinct controlled and uncontrolled phases as the rate of control application is varied. In this work, we apply these control protocols in classical, semiclassical, and quantum regimes to the kicked top, a paradigmatic model of quantum chaos. The quantum kicked top, modeled as the dynamics of a spin-S object, naturally interpolates between these regimes with the spin size S acting as an effective Planck constant. We show that the dynamics of the kicked top in classical, semiclassical, and fully quantum limits can all be controlled using stochastic feedback protocols. Comparing the full quantum dynamics to a truncated Wigner approximation that captures quantum noise but neglects interference beyond the Ehrenfest time, we find that low-moment observables are largely accounted for semiclassically, while the remaining discrepancy in higher moments is consistent with contributions from interference and possibly nonlinearities in rare trajectories that explore the compact phase space. We also find rapid purification in the numerics studied for all rates of control considered, suggesting that control quenches the top's ability to encode a qubit of quantum information even in the uncontrolled phase.

Prasad, Mahaveer [Tata Inst.; Singapore U. Tech. D↗
DOE OSTI2025

Constrained nuclear–electronic orbital method for periodic density functional theory: Application to H 2 chemisorption on Si(001) surfaces

The nuclear–electronic orbital (NEO) method provides a powerful computational framework for incorporating nuclear quantum effects (NQE) in electronic structure calculations beyond the Born–Oppenheimer approximation. By incorporating additional constraints to the position operator on quantum particles like protons, the NEO method enables calculation of effective potential that accounts for NQE. Here, in this work, we present a new constrained NEO (cNEO) formulation for density functional theory (cNEO-DFT) calculations in the context of extended periodic systems. Using the nudged elastic band method, we discuss an application of the cNEO-DFT approach to studying the adsorption of a hydrogen molecule on the Si(001) surfaces. The calculation shows how NQE impacts the reaction energetics. The proton density changes are computed along the reaction pathways. This work demonstrates the capability of the new cNEO-DFT method to study a wide range of chemical processes, such as surface reactions where the quantum nature of light atoms like protons is non-negligible.

Chemical processes↗
DOE OSTI2025

Systematic uncertainties in the measurement of the neutron lifetime using the Lunar Prospector neutron spectrometer

The lifetime of free neutrons measured in the laboratory has a longstanding disparity of ≈9 s. A space-based technique has recently been proposed to independently measure the neutron lifetime using interactions between the galactic cosmic rays and a low atmosphere planetary body. This technique has not produced competitive results yet due to constraints of nonoptimized data that contain large systematic errors. We use data from the neutron spectrometer on-board NASA's Lunar Prospector, and study two large systematics in the measurement of neutron lifetime: the lunar subsurface temperature and the lunar surface composition. We use the HeCd and HeSn neutron spectrometer data when the spacecraft was in a highly elliptical orbit during the orbit insertion period. We report the neutron lifetime using four different models that each have different choices of surface temperature and composition. The 5° [Prettyman et al ., J. Geophys. Res.: Planets 111, 2005JE002656 (2006)] and 2° [Wilson et al., Phys. Rev. C 104, 045501 (2021)] rebinned maps result in 777.6±11.7 s and 739.6±10.8 s, respectively. For the 20° map (Prettyman et al., 2006), constant equatorial and a latitude-dependent temperature model result in 738.6±10.8 s and 767.3±11.2 s, respectively. Increasing the complexities of the models accounting for the systematic effects increase the measured lifetime. However, the reported measurements are not competitive with the laboratory results due to large unaccounted systematics resulting from nonoptimized measurements and modeling assumptions. This work serves as a study of systematic uncertainties for future neutron lifetime measurements using the space-based technique. We estimate the effect on the lifetime from the choice of temperature model to be to be 28.7 ±15.5 s, and choice of compositional map (for 20° and 5° maps) to be 10.3 ±12.2 s.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Lagrangian formulation of nuclear–electronic orbital Ehrenfest dynamics with real-time TDDFT for extended periodic systems

Here, we present a Lagrangian-based implementation of Ehrenfest dynamics with nuclear–electronic orbital (NEO) theory and real-time time-dependent density functional theory for extended periodic systems. In addition to a quantum dynamical treatment of electrons and selected protons, this approach allows for the classical movement of all other nuclei to be taken into account in simulations of condensed matter systems. Furthermore, we introduce a Lagrangian formulation for the traveling proton basis approach and propose new schemes to enhance its application for extended periodic systems. Validation and proof-of-principle applications are performed on electronically excited proton transfer in the o-hydroxybenzaldehyde molecule with explicit solvating water molecules. These simulations demonstrate the importance of solvation dynamics and a quantum treatment of transferring protons. This work broadens the applicability of the NEO Ehrenfest dynamics approach for studying complex heterogeneous systems in the condensed phase.

Calculus of variations↗
DOE OSTI2024

Shearless effective barriers to chaotic transport induced by even twin islands in nontwist systems

For several decades now it has been known that systems with shearless invariant tori, nontwist Hamiltonian systems, possess barriers to chaotic transport. These barriers are resilient to breakage under perturbation and therefore regions where they occur are natural places to look for barriers to transport. Here we describe a kind of effective barrier that persists after the shearless torus is broken. Because phenomena are generic, for convenience we study the standard nontwist map (SNM), an area-preserving map that violates the twist condition locally in the phase space. The barrier occurs in nontwist systems when twin even period islands are present, which happens for a broad range of parameter values in the SNM. With a phase space composed of regular and irregular orbits, the movement of chaotic trajectories is hampered by the existence of shearless curves, total barriers, and a network of partial barriers formed by the stable and unstable manifolds of the hyperbolic points. Being a degenerate system, the SNM has twin islands and, consequently, twin hyperbolic points. We show that the structures formed by the manifolds intrinsically depend on period parity of the twin islands. For this even scenario the structure that we call a torus free barrier occurs because the manifolds of different hyperbolic points form an intricate chain atop a dipole configuration and the transport of chaotic trajectories through the chain becomes a rare event. This structure impacts the emergence of transport, the escape basin for chaotic trajectories, the transport mechanism, and the chaotic saddle. The case of odd periodic orbits is different: we find for this case the emergence of transport immediately after the breakup of the last invariant curve, and this leads to a scenario of higher transport, with intricate escape basin boundary and a chaotic saddle with nonuniformly distributed points.

classical mechanics↗
DOE OSTI2024

Dynamical Correlations and Order in Magic-Angle Twisted Bilayer Graphene

The interplay of dynamical correlations and electronic ordering is pivotal in shaping phase diagrams of correlated quantum materials. In magic-angle twisted bilayer graphene, transport, thermodynamic, and spectroscopic experiments pinpoint a competition between distinct low-energy states with and without electronic order, as well as between localized and delocalized charge carriers. In this study, we utilize dynamical mean-field theory on the topological heavy fermion model of twisted bilayer graphene to investigate the emergence of electronic correlations and long-range order in the absence of strain. We contrast moment formation, Kondo screening, and ordering on a temperature basis and explain the nature of emergent correlated states based on three central phenomena: (i) the formation of local spin and valley isospin moments around 100 K, (ii) the ordering of the local isospin moments around 10 K preempting Kondo screening, and (iii) a cascadic redistribution of charge between localized and delocalized electronic states upon doping. At integer fillings, we find that low-energy spectral weight is depleted in the symmetric phase, while we find insulating states with gaps enhanced by exchange coupling in the zero-strain ordered phases. Doping away from integer filling results in distinct metallic states: a “bad metal” above the ordering temperature, where scattering off the disordered local moments suppresses electronic coherence, and a “good metal” in the ordered states with coherence of quasiparticles facilitated by isospin order. This finding reveals coherence from order as the microscopic mechanism behind the Pomeranchuk effect observed experimentally by Rozen [] and by Saito []. Upon doping, there is a periodic charge reshuffling between localized and delocalized electronic orbitals leading to cascades of doping-induced Lifshitz transitions, local spectral weight redistributions, and periodic variations of the electronic compressibility ranging from nearly incompressible to negative. Our findings highlight the essential role of charge transfer, hybridization, and ordering in shaping the electronic excitations and thermodynamic properties in twisted bilayer graphene and provide a unified understanding of the most puzzling aspects of scanning tunneling spectroscopy, transport, and compressibility experiments. Published by the American Physical Society 2024

Physics↗
DOE OSTI2024

Architecture of TOI-561 planetary system

ABSTRACT We present new observations from CHEOPS (CHaracterising ExOPlanet Satellite) and TESS (Transiting Exoplanet Survey Satellite) to clarify the architecture of the planetary system hosted by the old Galactic thick disc star TOI-561. Our global analysis, which also includes previously published photometric and radial velocity data, incontrovertibly proves that TOI-561 is hosting at least four transiting planets with periods of 0.44 d (TOI-561 b), 10.8 d (TOI-561 c), 25.7 d (TOI-561 d), and 77.1 d (TOI-561 e) and a fifth non-transiting candidate, TOI-561f with a period of 433 d. The precise characterization of TOI-561’s orbital architecture is interesting since old and metal-poor thick disc stars are less likely to host ultrashort-period super-Earths like TOI-561 b. The new period of planet -e is consistent with the value obtained using radial velocity alone and is now known to be $77.14399\pm 0.00025$ d, thanks to the new CHEOPS and TESS transits. The new data allowed us to improve its radius ($R_p = 2.517 \pm 0.045\,\mathrm{ R}_{\rm{\oplus }}$ from 5 per cent to 2 per cent precision) and mass ($M_p = 12.4 \pm 1.4\, \mathrm{ M}_{\rm{\oplus }}$) estimates, implying a density of $\rho _p = 0.778 \pm 0.097\, \rho _{\rm{\oplus }}$. Thanks to recent TESS observations and the focused CHEOPS visit of the transit of TOI-561 e, a good candidate for exomoon searches, the planet’s period is finally constrained, allowing us to predict transit times through 2030 with 20-min accuracy. We present an updated version of the internal structure of the four transiting planets. We finally performed a detailed stability analysis, which confirmed the long-term stability of the outer planet TOI-561 f.

Piotto, G. (ORCID:0000000299376387)↗
DOE OSTI2025

Frustrated electron hopping from the orbital configuration in a two-dimensional lattice

Electron hopping on spatially periodic lattices gives rise to intriguing electronic behaviour. For example, hopping on the geometrically frustrated two-dimensional kagome, dice and Lieb lattices yields electronic band structures with both massless Dirac-like and perfectly dispersion-less, flat bands. As materials featuring the dice and Lieb lattice structures are scarce, an alternative approach proposes to leverage atomic orbitals to realize the characteristic electron hopping of geometrically frustrated lattices. This strategy promises to expand the list of candidate materials with frustrated electron hopping, but is yet to be shown in experiments. Here, in this study, we demonstrate frustrated hopping in the van der Waals intermetallic Pd 5 AlI 2 , emerging from the arrangement of atomic orbitals in a primitive square lattice. Using angle-resolved photoemission spectroscopy and quantum oscillation measurements, we reveal that the band structure of Pd 5 AlI 2 includes linear Dirac-like bands intersected at their crossing point by a locally flat band—an essential characteristic of frustrated hopping in Lieb and dice lattices. Moreover, this compound shows exceptional chemical stability, with its unusual bulk band structure and metallicity persisting in ambient conditions down to the monolayer limit. Hence, our results showcase a way to realize electronic structures characteristic of geometrically frustrated lattices in non-frustrated systems.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Bounce-averaged theory in arbitrary multi-well plasmas: solution domains and the graph structure of their connections

Bounce-averaged theories provide a framework for simulating relatively slow processes, such as collisional transport and quasilinear diffusion, by averaging these processes over the fast periodic motions of a particle on a closed orbit. This procedure dramatically increases the characteristic time scale and reduces the dimensionality of the modelled system. The natural coordinates for such calculations are the constants of motion (COM) of the fast particle motion, which by definition do not change during an orbit. However, for sufficiently complicated fields – particularly in the presence of local maxima of the electric potential and magnetic field – the COM are not sufficient to specify the particle trajectory. In such cases, multiple domains in COM space must be used to solve the problem, with boundary conditions enforced between the domains to ensure continuity and particle conservation. Previously, these domains have been imposed by hand, or by recognising local maxima in the fields, limiting the flexibility of bounce-averaged simulations. Here, we present a general set of conditions for identifying consistent domains and the boundary condition connections between the domains, allowing the application of bounce-averaged theories in arbitrarily complicated and dynamically evolving electromagnetic field geometries. We also show how the connections between the domains can be represented by a directed graph, which can help to succinctly represent the trajectory bifurcation structure.

fusion plasma↗
DOE OSTI2026

One-Step Relativistic Driven Similarity Renormalization Group Multireference Perturbation Theory

We present an efficient implementation of a one-step relativistic second-order multireference perturbation theory based on the multireference driven similarity renormalization group (MR-DSRG) using the exact two-component (X2C) Hamiltonian, which we denote X2C-DSRG-MRPT2. We show that the X2C-DSRG-MRPT2 method can accurately capture spin–orbit coupling (SOC) effects in the electronic structure of strongly correlated systems containing elements across the periodic table. We further demonstrate that the X2C-DSRG-MRPT2 method, through its variational treatment of SOC effects, can yield spin–orbit splittings with mean absolute percentage errors consistently below 7% with respect to experimental values for systems containing up to sixth row elements. With its modest computational scaling (fourth power in system size for the perturbative step) and high accuracy, X2C-DSRG-MRPT2 provides a promising avenue for the routine treatment of relativistic effects in strongly correlated molecular systems.

Hamiltonians↗