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DOE OSTI2022

Study of Self-Interaction Errors in Density Functional Calculations of Magnetic Exchange Coupling Constants Using Three Self-Interaction Correction Methods

We examine the role of self-interaction errors (SIE) removal on the evaluation of magnetic exchange coupling constants. In particular we analyze the effect of scaling down the self-interaction-correction (SIC) for three non-empirical density functional approximations (DFAs) namely, the local spin density approximation, the Perdew-Burke-Ernzerhof generalized gradient approximation, and recent SCAN family of meta-GGA functionals. To this end, we employ three one-electron SIC methods: Perdew-Zunger [Perdew, J. P.; Zunger, A. Phys. Rev. B, 1981, 23, 5048] SIC, the orbitalwise scaled SIC method [Vydrov, O. A. et al., J. Chem. Phys. 2006, 124, 094108], and the recent local scaling method [Zope, R. R. et al., J. Chem. Phys. 2019, 151, 214108]. We compute the magnetic exchange coupling constants using the spin projection and non projection approaches for sets of molecules composed of dinuclear and polynuclear H-He models, organic radical molecules, and chlorocuprate, and compare these results against accurate theories and experiment. Our results show that for the systems that mainly consist of single electron regions, PZSIC performs well but for more complex organic systems and the chlorcuprates, an overcorrecting tendency of PZSIC combined with the DFAs utilized in this work is more pronounced, and in such cases LSIC with kinetic energy density ratio performs better than PZSIC. Furthermore, analysis of the results in terms of SIC corrections to the density and to the total energy shows that both density and energy correction are required to obtain an improved prediction of magnetic exchange couplings.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Photoelectrochemically Self Improving Si/GaN Photocathode: Figure 4a Raw Data

Calculated formation energy of (0001 ̅) c-plane GaN surfaces. The density-functional theory (DFT) calculations were performed with the generalized gradient approximation, using the plane-wave pseudopotential quantum-ESPRESSO package. Ultrasoft pseudopotentials were used to describe the interaction between valence electrons and ionic cores, where Ga 3d electrons were explicitly treated as valence electrons. The wave functions and electronic density were expanded in a plane-wave basis set truncated at a cutoff energy of 30 Ry and 240 Ry, respectively. The surface was modeled using a repeated slab geometry using a (2×2) unit cell with a thickness of seven GaN bilayers, where the Ga-terminated bottom side was passivated by pseudo-hydrogen with charge of 1.25e. In addition, the (1010) surface was modeled using 8 GaN atomic layers with a lateral dimension of 9.57 Å x 10.38 Å. A vacuum width of at least 15.0 Å was introduced between consecutive slabs, and a k-point mesh of 5x5x1 and 2x2x1 was used to sample the surface Brillouin zone for the polar and non-polar surfaces, respectively. Calculated formation energy of (0001 ̅) c-plane GaN surfaces with different oxygen configuration within the anion and cation-rich limits: ideal GaN surfaces of c-plane and m-plane; configurations with 100% replacement of nitrogen by oxygen on the surface c-plane and m-plane; 100% replacement of nitrogen by oxygen in the subsurface bilayer c-plane and m-plane; and configurations with 50% replacement of nitrogen of the surface and subsurface bilayers by oxygens c-plane and m-plane. In both cases, the ideal surface is chosen as the reference.

photocathode↗

DOE OSTI2021

Photoelectrochemically Self Improving Si/GaN Photocathode: Figure 4b Raw Data

Calculated formation energy of (1010 ̅) m-plane GaN surfaces. The density-functional theory (DFT) calculations were performed with the generalized gradient approximation, using the plane-wave pseudopotential quantum-ESPRESSO package. Ultrasoft pseudopotentials were used to describe the interaction between valence electrons and ionic cores, where Ga 3d electrons were explicitly treated as valence electrons. The wave functions and electronic density were expanded in a plane-wave basis set truncated at a cutoff energy of 30 Ry and 240 Ry, respectively. The surface was modeled using a repeated slab geometry using a (2×2) unit cell with a thickness of seven GaN bilayers, where the Ga-terminated bottom side was passivated by pseudo-hydrogen with charge of 1.25e. In addition, the (1010) surface was modeled using 8 GaN atomic layers with a lateral dimension of 9.57 Å x 10.38 Å. A vacuum width of at least 15.0 Å was introduced between consecutive slabs, and a k-point mesh of 5x5x1 and 2x2x1 was used to sample the surface Brillouin zone for the polar and non-polar surfaces, respectively. Calculated formation energy of (1010 ̅) m-plane GaN surfaces with different oxygen configuration within the anion and cation-rich limits: ideal GaN surfaces of c-plane and m-plane; configurations with 100% replacement of nitrogen by oxygen on the surface c-plane and m-plane; 100% replacement of nitrogen by oxygen in the subsurface bilayer c-plane and m-plane; and configurations with 50% replacement of nitrogen of the surface and subsurface bilayers by oxygens c-plane and m-plane. In both cases, the ideal surface is chosen as the reference.

photocathode↗

DOE OSTI2022

Supervised learning of a chemistry functional with damped dispersion

Abstract Kohn–Sham density functional theory is widely used in chemistry, but no functional can accurately predict the whole range of chemical properties, although recent progress by some doubly hybrid functionals comes close. Here, we optimized a singly hybrid functional called CF22D with higher across-the-board accuracy for chemistry than most of the existing non-doubly hybrid functionals by using a flexible functional form that combines a global hybrid meta-nonseparable gradient approximation that depends on density and occupied orbitals with a damped dispersion term that depends on geometry. We optimized this energy functional by using a large database and performance-triggered iterative supervised training. We combined several databases to create a very large, combined database whose use demonstrated the good performance of CF22D on barrier heights, isomerization energies, thermochemistry, noncovalent interactions, radical and nonradical chemistry, small and large systems, simple and complex systems and transition-metal chemistry.

Liu, Yiwei (ORCID:0000000288126163)↗

DOE OSTI2024

Exploring interlayer coupling in the twisted bilayer PtTe 2

We have investigated interlayer interactions in the bilayer PtTe 2 system, which influence the electronic energy bands near the Fermi level. Our diffusion Monte Carlo (DMC) calculations for the high-symmetry bilayer stackings (AA, AB, AC) manifest distinct interlayer binding characteristics among the stacking modes by revealing significantly different interlayer separations depending on the stacking, which is critical to understanding the interlayer coupling of the twisted bilayers consisting of various local stacking arrangements. Furthermore, a comparison between the interlayer separations obtained from DMC and density functional theory (DFT) shows that meta-generalized gradient approximation (GGA)-based van der Waals–DFT results agree with DMC for different layer stackings, including twisted bilayers, but only the ground-state AA stacking matches well with GGA-based DFT predictions. This underscores the importance of accurate exchange-correlation potentials even for capturing the stacking-dependent interlayer binding properties. We further show that the variability in DFT-predicted interlayer separations is responsible for the large discrepancy of band structures in the 21 . 79 ∘ twisted bilayer PtTe 2 , affecting its classification as metallic or insulating. These results demonstrate the importance of obtaining a correct description of stacking-dependent interlayer coupling in modeling delicate bilayer systems at finite twists. Published by the American Physical Society 2024

36 MATERIALS SCIENCE↗

DOE OSTI2023

Right band gaps for the right reason at low computational cost with a meta-GGA

In density functional theory, traditional explicit density functionals such as the local density approximation and generalized gradient approximations cannot accurately predict the band gap of solids for a fundamental reason: They lack the exchange-correlation derivative discontinuity. By comparing Kohn-Sham and generalized Kohn-Sham calculations, we here show that the nonempirical meta-generalized-gradient-approximation (meta-GGA) TASK from Aschebrock and Kümmel [Phys. Rev. Res. 1, 033082 (2019)] predicts the right gaps for the right reason, i.e., as a combination of a proper Kohn-Sham gap and a substantial derivative discontinuity contribution. For many materials from small-gap semiconductors to large-gap insulators, the proper band gap is thus obtained. Here we further study a group of metal-halide perovskites for which the band gap is notoriously hard to predict. For these materials, TASK yields band gaps very similar to the nonlocal screened hybrid Heyd-Scuseria-Ernzerhof functional, yet at a fraction of the hybrid functional’s computational cost. We discuss the influence of correlation functionals, and open questions in the comparison of calculated band gaps with experimental ones.

36 MATERIALS SCIENCE↗

NASA NTRS2009

Complexity for Survival of Living Systems

A logical connection between the survivability of living systems and the complexity of their behavior (equivalently, mental complexity) has been established. This connection is an important intermediate result of continuing research on mathematical models that could constitute a unified representation of the evolution of both living and non-living systems. Earlier results of this research were reported in several prior NASA Tech Briefs articles, the two most relevant being Characteristics of Dynamics of Intelligent Systems (NPO- 21037), NASA Tech Briefs, Vol. 26, No. 12 (December 2002), page 48; and Self-Supervised Dynamical Systems (NPO- 30634) NASA Tech Briefs, Vol. 27, No. 3 (March 2003), page 72. As used here, living systems is synonymous with active systems and intelligent systems. The quoted terms can signify artificial agents (e.g., suitably programmed computers) or natural biological systems ranging from single-cell organisms at one extreme to the whole of human society at the other extreme. One of the requirements that must be satisfied in mathematical modeling of living systems is reconciliation of evolution of life with the second law of thermodynamics. In the approach followed in this research, this reconciliation is effected by means of a model, inspired partly by quantum mechanics, in which the quantum potential is replaced with an information potential. The model captures the most fundamental property of life - the ability to evolve from disorder to order without any external interference. The model incorporates the equations of classical dynamics, including Newton s equations of motion and equations for random components caused by uncertainties in initial conditions and by Langevin forces. The equations of classical dynamics are coupled with corresponding Liouville or Fokker-Planck equations that describe the evolutions of probability densities that represent the uncertainties. The coupling is effected by fictitious information-based forces that are gradients of the information potential, which, in turn, is a function of the probability densities. The probability densities are associated with mental images both self-image and nonself images (images of external objects that can include other agents). The evolution of the probability densities represents mental dynamics. Then the interaction between the physical and metal aspects of behavior is implemented by feedback from mental to motor dynamics, as represented by the aforementioned fictitious forces. The interaction of a system with its self and nonself images affords unlimited capacity for increase of complexity. There is a biological basis for this model of mental dynamics in the discovery of mirror neurons that learn by imitation. The levels of complexity attained by use of this model match those observed in living systems. To establish a mechanism for increasing the complexity of dynamics of an active system, the model enables exploitation of a chain of reflections exemplified by questions of the form, "What do you think that I think that you think...?" Mathematically, each level of reflection is represented in the form of an attractor performing the corresponding level of abstraction with more details removed from higher levels. The model can be used to describe the behaviors, not only of biological systems, but also of ecological, social, and economics ones.

Zak, Michail↗

DOE OSTI2020

Temperature dependence of nuclear quantum effects on liquid water via artificial neural network model based on SCAN meta-GGA functional

We investigate the temperature dependence of nuclear quantum effects (NQEs) on structural and dynamic properties of liquid water by training a neural network force field using first-principles molecular dynamics (FPMD) based on the strongly constrained and appropriately normed meta-generalized gradient approximation exchange-correlation approximation. The FPMD simulation based on density functional theory has become a powerful computational approach for studying a wide range of condensed phase systems. However, its large computational cost makes it difficult to incorporate NQEs in the simulation and investigate temperature dependence of various properties. To circumvent this difficulty, we use an artificial neural network model and employ the thermostatted ring polymer MD approach for studying the temperature dependence of NQEs on various properties. The NQEs generally bring the radial distribution functions closer to the experimental measurements. Translational diffusivity and rotational dynamics of water molecules are both slowed down by the NQEs. The competing inter-molecular and intra-molecular quantum effects on hydrogen bonds, as discussed by Habershon, Markland, and Manolopoulos [J. Chem. Phys. 131(2), 024501 (2019)], can explain the observed temperature dependence of the NQEs on the dynamical properties in our simulation.

Yao, Yi (ORCID:0000000299576979)↗

DOE OSTI2020

The effect of initial conditions on mixing transition of the Richtmyer–Meshkov instability

We investigate the late-time Richtmyer–Meshkov instability (RMI) growth of sinuous perturbations on an air/sulphur hexafluoride interface (Atwood number, A ~ 0.67 ) subjected to a Mach 1.2 planar shock wave at Los Alamos National Laboratory's vertical shock tube facility. Interface perturbations are established using a novel membraneless technique where cross-flowing air and SF 6 separated by an oscillating splitter plate create a perturbed density interface. The interface formed has multi-modal features and residual small perturbations, however, a dominant mode is still noticeable. The late-time perturbation growths scale with $ka_0$ initial conditions (where $k$ is the wavenumber and $a_0$ is the initial amplitude of the dominant mode) as measured at the pre-shock interface. Past nonlinear models based on potential-flow theory, heuristic/interpolation approaches, Padé approximants and numerical simulations are evaluated against present experimental results. Accounting for an explicit $ka_0$ dependence in Sadot et al.'s model, we propose an empirical rational function that captures the asymptotic behaviour of perturbation growth for a broad range of initial conditions ( 0.30 $≤ ka_0 ≤$ 0.86 ). The onset of mixing transition and its initial condition dependence are investigated with respect to the minimum state criterion ($Re =$ 1.6 $\times$ 10 5 ) for unsteady flows by Zhou. Earlier mixing transitions for higher ka0 initial conditions are noted from local and global Reynolds number estimates which are corroborated by the existence of an inertial sub-range and formation of mixing regions indicating the physical significance of the minimum state criterion in RMI flows. The transition is accompanied by the increasing teapot-like appearance of joint probability density functions of $p–q$ (invariants of the reduced velocity gradient tensor), establishing the technique as a useful tool for turbulence detection in two-dimensional diagnostics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Metal Halide Perovskites Demonstrate Radiation Hardness and Defect Healing in Vacuum

Herein, we subject formamidinium lead iodide films to oxygen-containing gases (flowing O 2 or free diffusion of lab atmosphere), inert gases (flowing He, Ar, or N 2 ), and vacuum. Our films are irradiated by Cu Ka X-rays and held at 75 °C while X-ray diffraction is recorded. Under all gas conditions, we observe a reproducible 1.1 ± 0.5 A 3 perovskite lattice contraction from an initial unit cell volume of 256.5 ± 0.8 A 3 concurrent with continuous perovskite loss and lead iodide growth. Oxygen-containing gases increase the reaction rates without materially altering perovskite structural changes. Under the same temperature and irradiation conditions in vacuo, a self-healing reaction is observed, exhibited by a reproducible (0.9 ± 0.3 A 3 ) lattice expansion and stabilization of the perovskite. Furthermore, interactions between the perovskite, defects, and minority phases are simulated by generalized gradient approximation Perdew-Burke-Ernzerhof (GGA-PBE) density functional theory. Lattice contraction indicates an increase in the concentration of Schottky defects-pairs of formamidinium and iodine vacancies. Under irradiation in every atmospheric condition, a solid solution of Schottky defects with a concentration of several percent diffuses and precipitates forming lead iodide and consuming the defects. In the presence of ionized gases, this framework is modified to include the continual loss of formamidinium and iodine ions from the perovskite forming Schottky defects.

14 SOLAR ENERGY↗

DOE OSTI2021

Analytical gradients for molecular-orbital-based machine learning

We report molecular-orbital-based machine learning (MOB-ML) enables the prediction of accurate correlation energies at the cost of obtaining molecular orbitals. Here, we present the derivation, implementation, and numerical demonstration of MOB-ML analytical nuclear gradients, which are formulated in a general Lagrangian framework to enforce orthogonality, localization, and Brillouin constraints on the molecular orbitals. The MOB-ML gradient framework is general with respect to the regression technique (e.g., Gaussian process regression or neural networks) and the MOB feature design. We show that MOB-ML gradients are highly accurate compared to other ML methods on the ISO17 dataset while only being trained on energies for hundreds of molecules compared to energies and gradients for hundreds of thousands of molecules for the other ML methods. The MOB-ML gradients are also shown to yield accurate optimized structures at a computational cost for the gradient evaluation that is comparable to a density-corrected density functional theory calculation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Interplay between electron localization, magnetic order, and Jahn-Teller distortion dictates LiMnO2 phase stability

The development of manganese (Mn)-rich cathodes for Li-ion batteries promises to alleviate potential supply chain bottlenecks in battery manufacturing. Fundamental challenges in Mn-rich cathodes arise from phenomena such as structural changes due to cooperative Jahn-Teller (JT) distortions of in octahedral environments, Mn migration, and phase transformations to spinel-like order, all of which affect the electrochemical performance. These physically complex phenomena motivate an re-examination of the Li-Mn-O rock-salt space, with a focus on the thermodynamics of the prototypical, polymorphs. It is found that the generalized gradient approximation (GGA-PBEsol) and meta-GGA ( ) density functionals with empirically fitted on-site Hubbard corrections yield spurious stable phases for , such as predicting a phase with -like order ( ) to be the ground state instead of the orthorhombic (Pmmn) phase, which is the experimentally known ground state. Accounting for antiferromagnetic order in each structure is shown to have a substantial effect on the total energies and resulting phase stability. By using hybrid-GGA (HSE06) and GGA with self-consistent Hubbard parameters (on-site and inter-site ) calculated from linear response theory, the experimentally observed phase stability trends are recovered. The calculated on-site between Mn- states in the experimentally observed orthorhombic, layered, and spinel phases are significantly smaller than in and disordered layered structures, by within GGA. The smaller values of are shown to be correlated with a collinear ordering of JT distortions, in which all orbitals are oriented in the same direction. This cooperative JT effect can lead to greater electron delocalization from Mn along the states due to increased Mn-O covalency, which contributes to the greater electronic stability compared to the phases with noncollinear JT arrangements. The structures with collinear ordering of JT distortions also generate greater vibrational entropy, which helps stabilize these phases at high temperature. These phases are shown to be strongly insulating with large calculated band gaps , which are computed using HSE06 and .

Kam, Ronald L↗

DOE OSTI2022

Evaluation of WRF simulation of deep convection in the US Southern Great Plains

The Southern Great Plains (SGP) exhibits a relatively high frequency of periods with extremely high rainfall rates (RR) and hail. Here, seven months of 2017 are simulated using the Weather Research and Forecasting (WRF) model applied at convection permitting resolution with the Mibrandt-Yau microphysics scheme. Simulation fidelity is evaluated, particularly during intense convective events, using data from ASOS stations, dual-polarization RADAR, gridded data sets and observations at the DoE Atmospheric Radiation Measurement site. The spatial gradients and temporal variability of precipitation and the cumulative density functions for both RR and wind speeds exhibit fidelity. Odds ratios >1 indicate WRF is also skillful in simulating high composite reflectivity (cREF, used as a measure of widespread convection) and RR > 5 mmhr –1 over the domain. Detailed analyses of the ten days with highest spatial coverage of cREF >30 dBZ show spatially similar reflectivity fields and high RR in both RADAR data and WRF simulations. However, during periods of high reflectivity, WRF exhibits a positive bias in terms of very high RR (> 25 mmhr –1 ) and hail occurrence, and during the summer and transition months, maximum hail size is underestimated. For some renewable energy applications fidelity is required with respect to the joint probabilities of wind speed and RR and/or hail. While partial fidelity is achieved for the marginal probabilities, performance during events of critical importance to these energy applications is currently not sufficient. Further research into optimal WRF configurations in support of potential damage quantification for these applications is warranted.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1991

The formation of molecules in protostellar winds

The production and destruction processes for molecules in very fast protostellar winds are analyzed and modeled with a one-dimensional chemical kinetics code. Radial density and temperature distributions suggested by protostellar theory are explored as are a range of mass-loss rates. The efficiency of in situ formation of heavy molecules is found to be high if the wind temperature falls sufficiently rapidly, as indicated by theory. The degree of molecular conversion is a strong function of the mass-loss rate and of density gradients associated with the acceleration and collimation of the wind. Even in cases where essentially all of the heavy atoms are processed into molecules, a significant fraction of atomic hydrogen remains so that hghly molecular, protostellar winds are able to emit the 21-cm line. Although CO has a substantial abundance in most models relevant to very young protostars, high abundances of other molecules such as SiO and H2O signify more complete association characteristic of winds containing regions of very high density. Although the models apply only to regions close to the protostar, they are in qualitative accord with recent observations at much larger distances of both atomic and molecular emission from extremely high-velocity flow.

Glassgold, A. E.↗

NASA NTRS1993

Small-scale density irregularities in the nightside Venus ionosphere - Comparison of theory and observations

The theory of the lower-hybrid-drift instability is compared with observations of plasma density irregularities. Marginal stability boundaries (gamma = 0) for the lower-hybrid-drift instability and the occurrence of small-scale density fluctuations are presented as a function of magnetic field B and density n. For plasma density gradient scale lengths in the range 2-10 km, 80-85 percent of the density fluctuations lie in the unstable B/n parameter regime (gamma greater than 0). Stability boundaries for the onset of instability at a wavelength for which the Pioneer Venus Orbiter could measure a Doppler-shifted frequency of 100 Hz are presented. The conditions on B and n for instability in this situation are more stringent than those for marginal stability, especially at low densities (n less than or equal to 5000/cu cm). In general, the instability is most likely to be active in regions of low beta: high magnetic field strength and low density, as found in ionospheric holes or troughs.

Huba, J. D.↗

NASA NTRS1995

Properties of the solar wind electrons between 1 and 3.3 AU from Ulysses thermal noise measurements

In order to describe the distribution function f(v) of the solar wind electrons, the simplest model which is commonly used consists of the sum of two Maxwellians representing two distinct populations: a core (density n(sub c), temperature T(sub c)) and a halo (density n(sub h), temperature T(sub h)). It is possible, with the latter assumptions on the electron f(v), to determine the quasi-thermal noise (QTN) induced on an antenna by the motion of the ambient electrons in the solar wind. Using this distribution and the spectroscopy of thermal noise measurements from the radio receiver on Ulysses in the ecliptic plane, we deduce the total electron density N(sub e), the core temperature T(sub c), and the core and halo kinetic pressures N(sub c)T(sub c) and N(sub h)T(sub h). From these electron parameters, we can define a 'global' electron temperature as T(sub e) = (N(sub c)T(sub c) + N(sub h)T(sub h))/N(sub e). Here we present different radial gradients of T(sub e), between 1 and 3.3 AU, as a function of three classes of N(sub e) at 1 AU: low, intermediate, and high densities. In general all these gradients are found to be positive with different polytrope power law indexes between N(sub e) and T(sub e), which are in general lower than unity. We also show different behaviors of the ratio N(sub h)T(sub h)/N(sub c)T(sub c) for each density class considered. Some possible interpretations for these observations are discussed.

Maksimovic, M.↗

DOE OSTI2022

Ab initio investigation of elastic properties of dilute Cu alloys for high-gradient accelerating structures

The elastic properties and solid solution strengthening of several Cu alloys that may be promising for high gradient applications were studied using ab initio calculations based on density functional theory. Specifically, the temperature and solute concentration dependence of elastic properties including bulk and shear moduli, thermal expansion coefficient, and heat capacity of these alloys were calculated. We found that the bulk and shear moduli are linearly dependent on the solute concentration in the dilute regime and change significantly for different Cu alloys. The thermal expansion coefficient and heat capacity are comparatively less sensitive to solute concentrations. Solid solution strengthening is observed to be linearly correlated with the change of lattice parameter of Cu. This work provides an in-depth understanding of the elastic properties of Cu alloys, which is key for predicting their performance at high gradient in normal conducting accelerating structures.

36 MATERIALS SCIENCE↗

DOE OSTI2025

A Meta-Generalized Gradient Approximation for the Cavity-Dependent Exchange-Correlation Interaction in Strongly Coupled Light–Matter Systems

Strong light–matter coupling in optical cavities enables the manipulation of chemical and physical properties without altering molecular composition. Theoretical modeling of such phenomena requires exchange-correlation (XC) functionals that account for both electron–electron and electron–photon (ep) interactions within quantum electrodynamical density functional theory (QEDFT). In this work, we develop a meta-generalized gradient approximation (meta-GGA) specifically targeting the cavity-dependent XC interaction in strongly coupled light–matter systems. This novel approximation is built upon a new semilocal polarizability approximation, which draws from the jellium-with-a-gap model, and can be extended to a “global hybrid” variant that goes beyond the isotropic model from previous approximations. The polarizability model yields significantly improved dispersion coefficients and benchmark calculations with the cavity-dependent XC functional demonstrate improved agreement with QED Hartree–Fock (QED-HF) reference energies. Application to the regioselectivity of brominated nitrobenzene intermediates reveals the functional’s capacity to capture cavity-induced energetic shifts. In conclusion, our results advance the Jacob’s ladder of functionals for QEDFT and provide a practical tool for modeling polaritonic chemistry.

Approximation↗