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At least 1,621 records · Page 90
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

High-resolution neutron diffraction determination of noncollinear antiferromagnetic order in the honeycomb magnetoelectric Fe 4 ⁢Nb 2⁢ O 9

Magnetoelectric systems offer potential for device applications exploiting coupled states between electric and magnetic properties. Among magnetoelectric materials, Fe 4 ⁢Nb 2 ⁢O 9 has attracted special attention because of its pronounced dielectric signal at high magnetic transition temperatures. However, the magnetic ground state, which is essential information for understanding its unusual magnetoelectricity, remains unclarified. Here, we report a noncollinear magnetic ground state of Fe 4 ⁢Nb 2 ⁢O 9 . To examine the magnetoelectric effect associated with sequential magnetic and structural transitions upon cooling, we conducted combined x-ray diffraction, magnetic susceptibility, magnetization, dielectric constant, and magnetodielectric experiments. Powder neutron diffraction experiments revealed a series of magnetic Bragg peaks and clear splitting of peaks via structural transition. Magnetic Rietveld refinements, combined with group theory analysis, determined a noncollinear antiferromagnetic structure including a significant 𝑐-axis moment component at 1.5 K. This article provides insights into the understanding of its magnetoelectric properties.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Quasi-one-dimensional uniform spin- 1 2 Heisenberg antiferromagnet KNaCuP 2 O 7 probed by P 31 and Na 23 NMR

Here we present the structural and magnetic properties of KNaCuP 2 O 7 investigated via x-ray diffraction, magnetization, specific heat, and P 31 and Na 23 NMR measurements and complementary electronic structure calculations. The temperature-dependent magnetic susceptibility and P 31 NMR shift could be modeled very well by the uniform spin- 1 2 Heisenberg antiferromagnetic chain model with a nearest-neighbor interaction J / k B ≃ 58.7 K . The corresponding mapping using first-principles electronic structure calculations leads to J DFT / k B ≃ 59 K with negligibly small interchain couplings, further confirming that the system is indeed a one-dimensional uniform spin- 1 2 Heisenberg antiferromagnet. The diverging trend of NMR spin-lattice relaxation rates ( 1 / T 1 31 and 1 / T 1 23 ) implies the onset of a magnetic long-range ordering at around T N ≃ 1 K . From the value of T N , the average interchain coupling is estimated to be J ' / k B ≃ 0.28 K . Moreover, the NMR spin-lattice relaxation rates show the dominant contributions from uniform ( q = 0 ) and staggered ( q = ± π / a ) spin fluctuations in the high- and low-temperature regimes, respectively, mimicking one-dimensionality of the spin lattice. We have also demonstrated that 1 / T 1 31 in high temperatures varies linearly with 1 / H , reflecting the effect of spin diffusion on the dynamic susceptibility. The temperature-dependent unit cell volume could be described well using the Debye approximation with a Debye temperature of Θ D ≃ 294 K , consistent with the heat capacity data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Electronic structure of intrinsic defects in c -gallium nitride: Density functional theory study without the jellium approximation

Here, we report the first nonjellium, systematic, density functional theory (DFT) study of intrinsic and extrinsic defects and defect levels in zinc-blende (cubic) gallium nitride. We use the local moment counter charge (LMCC) method, the standard Perdew-Becke-Ernzerhoff (PBE) exchange-correlation potential, and two pseudopotentials, where the Ga 3$\textit{d}$ orbitals are either in the core ($d^0$) or explicitly in the valence set ($d^{10}$). We studied 64, 216, 512, and 1000 atom supercells, and demonstrated convergence to the infinite limit, crucial for delineating deep from shallow states near band edges, and for demonstrating the elimination of finite cell-size errors. Contrary to common claims, we find that exact exchange is not required to obtain defect levels across the experimental band gap. As was true in silicon, silicon carbide, and gallium arsenide, the extremal LMCC defect levels of the aggregate of defects yield an effective LMCC defect band gap that is within 10% of the experimental gap (3.3 eV) for both pseudopotentials. We demonstrate that the gallium vacancy is more complicated than previously reported. There is dramatic metastability–a nearest-neighbor nitrogen atom shifts into the gallium site, forming an antisite, nitrogen vacancy pair, which is more stable than the simple vacancy for positive charge states. Our assessment of the $d^0$ and $d^{10}$ pseudopotentials yields minimal differences in defect structures and defect levels. The better agreement of the $d^0$ lattice constant with experiment suggests that the more computationally economical $d^0$ pseudopotentials are sufficient to achieve the fidelity possible within the physical accuracy of DFT, and thereby enable calculations in larger supercells necessary to demonstrate convergence with respect to finite size supercell errors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

The Use of Machine Learning Models for Predicting the Dielectric Strength of Gases

Technological advancements in high voltage systems have pushed sulfur hexafluoride (SF6) to its operational limits. Furthermore, this gas has other drawbacks including a high liquefaction temperature and a high global warming potential. Therefore, there has been an urgent need to find alternative gases with high dielectric strength (DS). In this work, density functional theory (DFT) is used to calculate molecular descriptors that are fed into an artificial neural network (ANN) and a random forest (RF). These machine learning (ML) models are then used to predict the DS for hundreds of molecules. A finite element model (FEM) is also used to calculate the electric field profile of multiple simple electrode geometries as the applied voltage to the system is increased. Results indicate that the random forest model has better generalization to unseen data than the neural network. The highest DS value predicted by the RF was 2.16 relative to the experimental DS of SF6. The results also demonstrate how choosing a gas with a higher DS and a geometry with minimal edges and corners can significantly increase the operating voltage of an electrical system. Due to its superior generalization, the RF represents the most promising path toward an accurate DS predictor once sufficient experimental data are available.

Mileski, Matthew [AFIT]↗
DOE OSTI2024

GDB-9-Ex_TD-DFT-PBE0: Dataset containing Time Dependent Density Functional Theory (TDDFT) calculations for organic molecules of the GDB-9-Ex dataset.

This dataset contains data-intensive quantum chemical electronic structure calculations for 96,766 organic molecules of the GDB-9-Ex dataset. Calculations were performed using the Time Dependent Density Functional Theory (TDDFT) first principles method using the ORCA software. It provides UV-vis spectra calculations of molecules with a high level of accuracy. The optical spectra behavior was collected based on the optimized molecular geometries in the DFTB method with 3ob parameters. All calculations utilized the def2-TZVP basis sets with the auxiliary def2/J and def2-TZVP/C basis sets. The time-dependent density-functional theory (TDDFT) approach with the PBE0 exchange-correlation functional and ORCAs default integration grid was employed. For the excitation energy calculations, the lowest 50 excitation states were calculated.

AI dataset↗
DOE OSTI2023

Designing Quaternary and Quinary Refractory-Based High-Entropy Alloys: Statistical Analysis of Their Lattice Distortion, Mechanical, and Thermal Properties

The rapid evolution in materials science has resulted in a significant interest in high-entropy alloys (HEAs) for their unique properties. This study focuses on understanding both quaternary and quinary body-centered cubic (BCC) of 12 refractory-based HEAs, and on analysis of their electronic structures, lattice distortions, mechanical, and thermal properties. A comprehensive assessment is undertaken by means of density functional theory (DFT)-based first principles calculations. It is well known that multiple constituents lead to notable lattice distortions, especially in quinary HEAs. This distortion, in turn, has significant implications on the electronic structure that ultimately affect mechanical and thermal behaviors of these alloys such as ductility, lattice thermal conductivity, and toughness. Our in-depth analysis of their electronic structures revealed the role of valence electron concentration and its correlation with bond order and mechanical properties. Local lattice distortion (LD) was investigated for these 12 HEA models. M1 (WTiVZrHf), M7 (TiZrHfW), and M12 (TiZrHfVNb) have the highest LD whereas the models M3 (MoTaTiV), M5 (WTaCrV), M6 (MoNbTaW), and M9 (NbTaTiV) have the less LD. Furthermore, we investigated the thermal properties focusing on Debye temperature (ΘD), thermal conductivity (κ), Grüneisen parameter (γα), and dominant phonon wavelength (λdom). The NbTaTiV(M9) and TiVNbHf(M10) models have significantly reduced lattice thermal conductivities (κL). This reduction is due to the mass increase and strain fluctuations, which in turn signify lattice distortion. The findings not only provide an understanding of these promising materials but also offer guidance for the design of next-generation HEAs with properties tailored for potential specific applications.

Materials Science↗
DOE OSTI2022

Redox Defect Thermochemistry of FeAl 2 O 4 Hercynite in Water Splitting from First-Principles Methods

Solar thermochemical hydrogen (STCH) production is a promising route to produce fuels from sunlight via high-temperature water splitting. However, efficient and technologically viable implementations of this process only allow a narrow window of thermodynamic boundary conditions that can be used to cycle the system, thus limiting the design space for suitable metal oxide redox mediators. An oxygen defect redox mechanism can contribute a favorable reduction entropy to expand this window, and computational evaluation of materials with high oxygen defect entropies could play a pivotal role in guiding the discovery and design of suitable oxides. This study employs first-principles calculations to investigate the redox mediating defect mechanism of the STCH candidate material, hercynite (FeAl 2 O 4 ). We compare the results of total energy calculations from density functional theory (DFT) with beyond-DFT approaches, including hybrid functionals and the random phase approximation, which are among the most advanced methods currently feasible for supercell defect calculations. Using the predicted formation energies, we perform thermodynamic modeling of FeAl2O4 reduction and oxidation via free energy minimization that incorporates ideal gas, configurational, and vibrational entropy contributions evaluated within the quasi-harmonic approximation. Special attention is devoted to understanding interactions among co-existing defects, such as the association of pairs and complexes of O vacancies and cation antisite defects, and the effect of mutually compensating defect charges. Our results corroborate the notion that the details of defect interactions can be decisive for the viability of hydrogen production within the desirable STCH process window.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

The joint automated repository for various integrated simulations (JARVIS) for data-driven materials design

The Joint Automated Repository for Various Integrated Simulations (JARVIS) is an integrated infrastructure to accelerate materials discovery and design using density functional theory (DFT), classical force-fields (FF), and machine learning (ML) techniques. JARVIS is motivated by the Materials Genome Initiative (MGI) principles of developing open-access databases and tools to reduce the cost and development time of materials discovery, optimization, and deployment. The major features of JARVIS are: JARVIS-DFT, JARVIS-FF, JARVIS-ML, and JARVIS-tools. To date, JARVIS consists of ≈40,000 materials and ≈1 million calculated properties in JARVIS-DFT, ≈500 materials and ≈110 force-fields in JARVIS-FF, and ≈25 ML models for material-property predictions in JARVIS-ML, all of which are continuously expanding. JARVIS-tools provides scripts and workflows for running and analyzing various simulations. We compare our computational data to experiments or high-fidelity computational methods wherever applicable to evaluate error/uncertainty in predictions. In addition to the existing workflows, the infrastructure can support a wide variety of other technologically important applications as part of the data-driven materials design paradigm. The JARVIS datasets and tools are publicly available at the website: https://jarvis.nist.gov .

36 MATERIALS SCIENCE↗
DOE OSTI2022

Acetate formation on metals via CH 4 carboxylation by CO 2 : A DFT study

Here, density functional theory calculations have been performed to investigate CH 4 activation and coupling to CO 2 forming C 2 carboxylates such as acetate on the close-packed (111) or (0001) surfaces of ten mid-to-late transition and coinage metals (Co, Ni, Cu, Ru, Rh, Pd, Ag, Ir, Pt, and Au). Consistent with the literature, the activation energy (E a ) for the initial C-H bond scission in CH 4 is mild, being ca. 1 eV or less on all but the coinage metals, of which Ag exhibits the highest E a at 2.13 eV, followed by Au and Cu. E a for the CH 3 -CO 2 coupling step is 0.8 ~ 1.1 eV on Co, Ru, Rh, and Ag, 1.2 ~ 1.5 eV on Ni, Cu, Pd, and Ir, and 1.8 ~ 2.1 eV on Pt and Au. While the two E a are comparable for several metals in terms of DFT total energies, free energy analysis indicates CH 3 -CO 2 coupling to be much more rate-limiting than CH 4 activation. Overcoming it would require over 800 K even on the most active of the metals considered, Ru, which makes the formation of acetate not feasible on the monometallic metal surfaces. Instead, we propose that single atom alloys based on early transition metals doped into a host metal such as Ni(111) could be viable catalysts. The dopant sites serve to stabilize the transition state of C-C coupling while Ni sites continue to activate CH 4 , thereby significantly lowering the required temperature for acetate formation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Neural network potentials with effective charge separation for non-equilibrium dynamics of ionic solids: a ZnO case study

Developing neural network potentials (NNPs) accurate under non-equilibrium dynamics is challenging, as such systems require extensive sampling beyond equilibrium phases. Here we construct high-fidelity NNPs for zinc oxide (ZnO), a polymorphic ionic solid, using density functional theory (DFT) reference data. To efficiently capture transitional configurations, we combine enhanced-sampling molecular dynamics with empirical potentials, data distillation, and pretraining on short-range atomic energies (A-Train), followed by transfer learning with DFT-relabeled datasets. This hierarchical approach improves transferability across polymorphs and stress states. We further introduce effective charge separation, treating long-range Coulombic terms analytically while short-range residual interactions are learned by the NNP. The optimal effective charges fall in the range 0.5–1.0 q e , consistent with dielectric-screened values derived from formal charges but distinct from Bader estimates. Motivated by this observation, we propose a simple data-driven protocol in which effective charges are optimized by comparing DFT reference energies with explicit Coulomb calculations, without additional NNP training. This strategy improves accuracy and transferability in DFT-level predictions of energies, forces, and stress. Together, these results provide a practical charge-selection framework for robust NNP development in ionic solids, enabling reliable simulation of polymorphic phase transformations and non-equilibrium dynamics.

Chemistry↗
NASA NTRSDate not supplied

Metal Hydroxide and Oxyhydroxide Gas Database

In a high temperature combustion situation such as a gas turbine or rocket engine, combustion products include water vapor. This water vapor reacts with oxides in the hot-gas-path to form volatile hydroxides and oxyhydroxides. The oxides may be structural oxide components or protective oxides on alloys or non-oxide ceramics. In either case, this enhanced volatilization leads to degradation of components. Reliable thermochemical data for many metal hydroxides and oxyhydroxides has not been available. We review a database put together at NASA over many years based on experimental and ab initio computations for thermochemical data of Al, Si, Ti, Cr, Mn, Y, Zr, La, Ta, Gd, and Yb hydroxides and oxyhydroxides. Experimental methods for measuring thermodynamic quantities of metal hydroxides and oxyhydroxides are limited since the required high temperatures and high pressures preclude many conventional methods. Nonetheless, transpiration has proven a valuable tool in our laboratories for the Si-O-H, Cr-O-H, and Ti-O-H systems. Data are analyzed with second and third law methods. These data can be leveraged with quantum chemistry to provide reliable free energy functions for the third law calculation and comparison to the derived enthalpies of formation. Both wave function and DFT methods can be utilized for deriving the thermodynamic functions for the various metal hydroxides and oxyhydroxides. We have found that, in general, reasonable molecular geometries and spectroscopic data can be derived with a relatively low level of theory, i.e. DFT with the B3LYP functional. Accurate calculations of the enthalpy of formation require higher levels of theory, such as the Coupled Cluster, Singles, Doubles, and perturbative Triples CCSD(T) approach with complete basis sets (CBS). Also, corrections for hindered rotations and anharmonicity are necessary. For some symmetries, the anharmonic correction has proven to be a challenge and we have found that this is only treated properly by certain codes. The database lists the fHo(298), So(298), and Cp in the form Cp = A + BT + CT2 + D/T + E/T2, where A, B, C, D, and E are the fitting constants. Thus, it can be easily used in any of the common computational thermochemistry codes. To date, the database contains 51 gaseous species of the formula MOx(OH)y.

Metal Hydroxides↗
DOE OSTI2022

An evaluation for geometries, formation enthalpies, and dissociation energies of diatomic and triatomic (C, H, N, O), NO 3 , and HNO 3 molecules from the PAW DFT method with PBE and optB88-vdW functionals

The structural geometries, formation enthalpies, and dissociation energies of all diatomic and triatomic molecules consisting of the four basic elements C, H, N, and/or O are calculated using the projector augmented wave density functional theory (DFT) method with the Perdew–Burke–Ernzerhof and optB88-vdW exchange-correlation functionals. The calculations are also extended to two larger molecules NO 3 and HNO 3 , which consist of four and five atoms, respectively. In total, 82 molecules or isomers are considered in the calculations. The geometric parameters including 42 bond lengths and 15 bond angles of these molecules calculated using the planewave DFT method are highly satisfactory, relative to the available experimental data. The error analysis is also performed for 49 formation enthalpies and 138 dissociation energies (including 51 atomization energies as well as the corresponding bond dissociation energies). The results are also compared with the previous data from various atomic-orbital-based methods for molecules and from similar or different planewave DFT methods for various solids and other molecules. This provides an informative and instructive evaluation especially for calculating the large-size material systems containing these small molecules as well as for developing the DFT methods further.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Thermochemical Data for Furan-based Monomer Candidates for Frontal Ring-Opening Metathesis Polymerization (FROMP)

This dataset includes 471 furan-based monomer candidates for frontal ring-opening metathesis polymerization (FROMP) and relevant thermochemistry as calculated with density functional theory (DFT). The monomer candidates were combinatorically enumerated using Diels-Alder reactions of furan derivatives as dienes and four types of dienophiles (alkenes, alkynes, allenes, and benzynes). Common substituents were enumerated for the dienophile classes, and methyl substitution on the diene was explored. We used the SMILES arbitrary target specification (SMARTS) language to produce monomers and ring-opened structures from diene and dienophile precursor SMILES, and we studied the ring-opening reaction using a homodesmotic equation with ethene. RDKit conformers were initially generated from SMILES, then optimized with GFN2-xTB. The two conformers lowest in energy were then optimized with DFT using the wb97x-D3 functional, def2-TZVP basis set, and def2/J auxiliary basis set. Gibbs free energy corrections were obtained through frequency calculations. Structures with imaginary frequencies below -50 cm^{-1} were excluded from this work, and smaller imaginary modes were flipped to be positive for free energy calculations. Modes below 50 cm^{-1} were treated with the modified rigid rotor approximation, and all thermochemical values were calculated at T=200C. The CSV file contains the monomer SMILES, the free energy of reaction for Diels-Alder addition (G_DA_200), and the enthalpy of the ring-opening reaction (H_RO_200). All energies are given in kcal/mol. An interactive HTML is also included to visualize the monomers in this dataset.

Chua, Lauren↗
DOE OSTI2025

Importance of enforcing Hund’s rules in density functional theory calculations of rare earth magnetocrystalline anisotropy

Density functional theory (DFT) and its extensions, such as DFT+U and DFT+dynamical mean-field theory, are invaluable for studying magnetic properties in solids. However, rare-earth (R) materials remain challenging due to self-interaction errors and the lack of proper orbital polarization. We show how the orbital dependence of self-interaction error contradicts Hund’s rules and plagues magnetocrystalline anisotropy (MA) calculations, and how analyzing DFT states that respect Hund’s rules can mitigate this issue. We benchmark MA in RCo 5 , R 2 Fe 14 B, and RFe 12 , extending prior work on RMn 6 Sn 6 , achieving excellent agreement with experiments. Additionally, we illustrate a semi-analytical perturbation approach that treats crystal fields as a perturbation in the large spin-orbit coupling limit. Using Gd-4f crystal-field splitting, this method provides a microscopic understanding of MA and enables rapid screening of high-MA materials.

36 MATERIALS SCIENCE↗
DOE OSTI2022

First-Principles Calculations of the Structural, Electronic, Optical, and Mechanical Properties of 21 Pyrophosphate Crystals

Pyrophosphate crystals have a wide array of applications in industrial and biomedical fields. However, fundamental understanding of their electronic structure, optical, and mechanical properties is still scattered and incomplete. In the present research, we report a comprehensive theoretical investigation of 21 pyrophosphates A 2 M (H 2 P 2 O 7 ) 2 •2H 2 O with either triclinic or orthorhombic crystal structure. The molecule H 2 P 2 O 7 is the dominant molecular unit, whereas A = (K, Rb, NH 4 , Tl), M = (Zn, Cu, Mg, Ni, Co, Mn), and H 2 O stand for the cation elements, transition metals, and the water molecules, respectively. The electronic structure, interatomic bonding, partial charge distribution, optical properties, and mechanical properties are investigated by first-principles calculations based on density functional theory (DFT). Most of these 21 crystals are theoretically investigated for the first time. The calculated results show a complex interplay between A, M, H 2 P 2 O 7 , and H 2 O, resulting in either metallic, half-metallic, or semi-conducting characteristics. The novel concept of total bond order density (TBOD) is used as a single quantum mechanical metric to characterize the internal cohesion of these crystals to correlate with the calculated properties, especially the mechanical properties. This work provides a large database for pyrophosphate crystals and a road map for potential applications of a wider variety of phosphates.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Modeling the thermodynamics of the FeTi hydrogenation under para-equilibrium: An ab-initio and experimental study

We report FeTi-based hydrides have recently re-attracted attention as stationary hydrogen storage materials due to favorable reversibility, good sorption kinetics and relatively low costs compared to alternative intermetallic hydrides. Employing the OpenCalphad software, the thermodynamics of the (FeTi) 1-x H x (0 ≤ x ≤ 1) system were assessed as a key basis for modeling hydrogenation of FeTi-based alloys. New thermodynamic data were acquired from our experimental pressure-composition-isotherm (PCI) curves, as well as first-principles calculations utilizing density functional theory (DFT). The thermodynamic phase models were carefully selected based on critical analysis of literature information and ab-initio investigations. Key thermodynamic properties such as dissociation pressure, formation enthalpies and phase diagrams were calculated in good agreement to our performed experiments and literature-reported data. This work provides an initial perspective, which can be extended to account for higher-order thermodynamic assessments and subsequently enables the design of novel FeTi-based hydrides. In addition, the assessed thermodynamic data can serve as key inputs for kinetic models and hydride microstructure simulations.

08 HYDROGEN↗
DOE OSTI2021

Measuring the structure and equation of state of polyethylene terephthalate at megabar pressures

Abstract We present structure and equation of state (EOS) measurements of biaxially orientated polyethylene terephthalate (PET, $$({\hbox {C}}_{10} {\hbox {H}}_8 {\hbox {O}}_4)_n$$ ( C 10 H 8 O 4 ) n , also called mylar) shock-compressed to ( $$155 \pm 20$$ 155 ± 20 ) GPa and ( $$6000 \pm 1000$$ 6000 ± 1000 ) K using in situ X-ray diffraction, Doppler velocimetry, and optical pyrometry. Comparing to density functional theory molecular dynamics (DFT-MD) simulations, we find a highly correlated liquid at conditions differing from predictions by some equations of state tables, which underlines the influence of complex chemical interactions in this regime. EOS calculations from ab initio DFT-MD simulations and shock Hugoniot measurements of density, pressure and temperature confirm the discrepancy to these tables and present an experimentally benchmarked correction to the description of PET as an exemplary material to represent the mixture of light elements at planetary interior conditions.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Time-dependent orbital-free density functional theory: Background and Pauli kernel approximations

Time-dependent orbital-free density functional theory (DFT) is an efficient method for calculating the dynamic properties of large-scale quantum systems due to the low computational cost compared to standard time-dependent DFT. In this work, we formalize this method by mapping the real system of interacting fermions onto a fictitious system of noninteracting bosons. The dynamic Pauli potential and associated kernel emerge as key ingredients of time-dependent orbital-free DFT. Using the uniform electron gas as a model system, we derive an approximate frequency-dependent Pauli kernel. Pilot calculations suggest that space nonlocality is a key feature for this kernel. Nonlocal terms arise already in the second-order expansion with respect to unitless frequency and reciprocal space variable ($\frac{ω}{qk_F}$ and $\frac{q}{2k_F}$, respectively). Given the encouraging performance of the proposed kernel, we expect it will lead to more accurate orbital-free DFT simulations of nanoscale systems out of equilibrium. Additionally, the proposed path to formulate nonadiabatic Pauli kernels presents several avenues for further improvements which can be exploited in future work to improve the results.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗