Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “local density approximations”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Energy Level Gradients from Surface to Bulk in Hybrid Metal-Halide Perovskite Thin Films

Variations in local strain, defect densities, and composition of hybrid metal-halide perovskites have been reported to create heterogeneous energy landscapes in thin films, which impact charge-carrier diffusion and recombination dynamics. Here, we employ one- and two-photon transient absorption spectroscopy to selectively probe the dynamics of charge carriers from surface and bulk regions of methylammonium lead bromide thin films. Differences in the transient absorption spectra indicate that an energy gradient of approximately 100 meV is formed between the higher band-gap surface and lower band-gap bulk regions. Thus, during their lifetime, photoexcited carriers move away from the surface to recombine in the bulk, where our experiments detect long-lived charge populations despite the significant band splitting that has conventionally been assumed to inhibit efficient radiative recombination. Supported by first-principles calculations, we demonstrate that bright emission can still arise from the bulk with states that occupy a wide range of momenta in the vicinity of the band extrema, which show strong dipole transitions. Our results report that photoexcitations in the hybrid perovskites avoid defect-rich surface regions, and that particularly strong emission is generated from accumulated excitation populations in the bulk. Published by the American Physical Society 2024

Bourelle, Sean A.↗
DOE OSTI2024

Damage evolution and ductile fracture of commercially-pure titanium sheets subjected to simple tension and cyclic bending under tension

This paper describes a study into the evolution of damage in commercial-purity titanium (CP–Ti) sheets subjected to cyclic bending under tension (CBT) and uniaxial tension (simple tension, ST). Sections were taken from sheets that were strained to various levels under both methods and were imaged using X-ray computed tomography (XCT) to reveal insights into the size, density, and distribution of microvoids in the sheets. Digital image correlation (DIC) was also used to observe the surface strain of CBT and ST sheets during testing. These results showed that elongation to failure (ETF) for CBT deformation is about 2.5× higher than for ST, local longitudinal strains in the bulk of the CBT sample are around 1.3× higher than the peak strain in the ST necked region, and 1.7× higher in the localized region of CBT failure. It was found that the volume-density of voids in both sheets followed a similar exponential increase with strain, reaching nearly 45× higher in the CBT than the ST sheets before the onset of failure, mainly due to the higher strain levels achieved. A higher volume density of voids developed in the center of sheets at high levels of strain, for both processes, with the density in the sheet center becoming approximately double that found near the edges. Scanning electron microscopy (SEM) was used to examine the fracture surface of CBT and ST sheets after failure. The observations are presented and discussed highlighting the CBT process as effective to delay ductile fracture of the CP-Ti sheets.

Commercially pure titanium↗
DOE OSTI2024

Bond length alternation of π -conjugated polymers predicted by the Fermi–Löwdin orbital self-interaction correction method

π-conjugated polymers have been used in a wide range of practical applications, partly due to their unique properties that originate in the delocalization of electrons through the polymer backbone. The level of delocalization can be characterized by the induced bond length alternation (BLA), with shorter BLA connected with strong delocalization and vice versa. The accurate description of this structural parameter can be considered a benchmark for testing the capability of different electronic structure methods for self-interaction error (SIE) removal and electron correlation inclusion. Density functional theory (DFT), in its local or semi-local flavors, suffers from SIE and, thus, underestimates the BLA compared to self-interaction-free methods. In this work, we utilize the Fermi–Löwdin orbital self-interaction correction (FLOSIC) method for one-electron self-interaction removal to characterize the BLA of five oligomers with increasing length extrapolated to the polymeric limit. We compare the self-interaction-free BLA to several DFT approximations, Møller–Plesset second-order perturbation theory (MP2), and the BLA obtained with the domain based local pair natural orbital CCSD(T) [DLPNO-CCSD(T)] approximation. Our findings show that FLOSIC corrects for the small BLA given by (semi-)local DFT approximations, but it tends to overcorrect with respect to CAM-B3LYP, MP2, and DLPNO-CCSD(T).

Chemistry↗
DOE OSTI2022

FSISPH: An SPH formulation for impacts between dissimilar materials

Here, we present an SPH formulation with several new features designed to better model the fully-compressible interaction of dissimilar materials. We developed the new method to simulate the atmospheric entry and break-up of small celestial bodies in planetary atmospheres. The formulation uses a unity-based, density-energy discretization of the hydrodynamic conservation laws with linear-corrected kernel gradients. To account for variations in compressibility, we use an HLLC approximate Riemann solver to adjust the velocity gradient at material interfaces. To handle large transverse velocity discontinuities, we introduce a simple slip interface model that limits the artificial viscosity at material interfaces. Diffusion is optionally applied through the velocity gradient and this allows the density and specific thermal energy to evolve in a manner more consistent with the first law of thermodynamics in comparison to other more direct diffusion schemes. We also introduce a material-local second-order artificial conduction scheme used to smooth the specific thermal energy field. Material damage fits neatly under this framework by treating the damage front as a material interface. The method has been implemented as a solver, FSISPH, within the code, Spheral++, and is publicly available on github. We test our new solver on a number of classic shock, mixing, and multi-material problem. The components we outline can significantly improve accuracy of SPH for problems with sharp contact discontinuities.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Mott vs Kondo: Influence of various density functional based methods on the Ce isostructural phase transition mechanism

The cerium iso-structural phase transition (γ–α) is dominated by f-electron localization changes that results in a magnetic ordering change and a volume collapse. Generally, these physics are difficult to capture with ab initio and first principles methods. However, previous works have shown various methods to be successful in predicting at least some of the physics of the γ to α phase transition. Therefore, here, we perform a broad survey of density functional based methods across three levels of theory and types of functions [GGA (generalized gradient approximation), MetaGGA, and hybrid functionals] and compare the results, focusing on hydrostatic compression across the phase boundary at zero kelvin. For the methods that best reproduce experimental results, we directly probe the predicted mechanisms and frame the results in the Mott/Kondo debate, assessing how the underlying methods and assumptions of different functionals can assess the physical drivers in the phase transition, providing insight into the governing processes of this unique phase transition.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Autoregressive Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation

The theory of open quantum systems lays the foundation for a substantial part of modern research in quantum science and engineering. Rooted in the dimensionality of their extended Hilbert spaces, the high computational complexity of simulating open quantum systems calls for the development of strategies to approximate their dynamics. In this Letter, we present an approach for tackling open quantum system dynamics. Using an exact probabilistic formulation of quantum physics based on positive operator-valued measure, we compactly represent quantum states with autoregressive neural networks; such networks bring significant algorithmic flexibility due to efficient exact sampling and tractable density. We further introduce the concept of string states to partially restore the symmetry of the autoregressive neural network and improve the description of local correlations. Efficient algorithms have been developed to simulate the dynamics of the Liouvillian superoperator using a forward-backward trapezoid method and find the steady state via a variational formulation. Our approach is benchmarked on prototypical one-dimensional and two-dimensional systems, finding results which closely track the exact solution and achieve higher accuracy than alternative approaches based on using Markov chain Monte Carlo method to sample restricted Boltzmann machines. Our Letter provides general methods for understanding quantum dynamics in various contexts, as well as techniques for solving high-dimensional probabilistic differential equations in classical setups.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Electronic Structure of Excitons in Hematite Fe 2 O 3

We present a computational study of the electronic structure of excitons in hematite Fe 2 O 3 using density functional theory (DFT) and time-dependent DFT theory. Excitons resulting from solar light absorption are precursors to photogenerated charge carriers, which are the active species in solar-to-fuel redox conversions. Upon vertical excitation, the lowest energy exciton is found to have a multideterminantal wave function, describing an electron excited from O 2p states to Fe 3d states of the nearest basal plane, possibly supporting a recent XUV-derived exciton structure with a radius of a single Fe–O bond. Subsequently, the exciton self-traps into stable electron–hole pair structures whose wave functions are well-approximated by single excitations conveniently labeled “HOMO–LUMO”. Self-trapping yields electron–hole pair structures whereby the electron state (electron polaron-like) is separated from the hole state (hole polaron-like) by 3, 5, 7, 9, ... basal planes in structures referred to as Exc-3, Exc-5, Exc-7, Exc-9, ... The natural transition orbitals (electron–hole states) exhibit a strong “localized” character. The hole state is best described as a (FeO 6 ) + octahedral moiety carrying ~0.65 h + charge, and overall ~70% of the hole is assigned to O 2p atomic states, mostly on the four (4) equatorial O atoms of the moiety. The electron state is best described as a (FeFe) – moiety carrying ~0.80 e – charge in Fe 3d atomic states. The lattice distortions around the hole site exhibit Fe–O bond shortening due to the removal of electron density from an orbital state with O–Fe–O antibonding character. The electron site shows Fe–Fe distance shortening due to excess electron density added to an orbital state with in-phase Fe–Fe interactions. Furthermore, these excitonic structures with increasing electron–hole separation can be viewed as the onset of exciton separation into isolated electrons and hole polarons.

36 MATERIALS SCIENCE↗
DOE OSTI2023

pyGWBSE: a high throughput workflow package for GW-BSE calculations

Abstract We develop an open-source python workflow package, py GWBSE to perform automated first-principles calculations within the GW-BSE (Bethe-Salpeter) framework. GW-BSE is a many body perturbation theory based approach to explore the quasiparticle (QP) and excitonic properties of materials. GW approximation accurately predicts bandgaps of materials by overcoming the bandgap underestimation issue of the more widely used density functional theory (DFT). BSE formalism produces absorption spectra directly comparable with experimental observations. py GWBSE package achieves complete automation of the entire multi-step GW-BSE computation, including the convergence tests of several parameters that are crucial for the accuracy of these calculations. py GWBSE is integrated with Wannier90 , to generate QP bandstructures, interpolated using the maximally-localized wannier functions. py GWBSE also enables the automated creation of databases of metadata and data, including QP and excitonic properties, which can be extremely useful for future material discovery studies in the field of ultra-wide bandgap semiconductors, electronics, photovoltaics, and photocatalysis.

36 MATERIALS SCIENCE↗
DOE OSTI2023

A complete spectroscopic catalogue of local galaxies in the northern spring sky: Gas properties and nuclear activity in different environments

With the aim of providing the complete demography of galaxies in the local Universe, including their nuclear properties, we present SPRING, a complete census of local galaxies limited to the spring quarter of the northern sky (10h < RA < 16h; 0° < Dec < 65°). The SPRING catalogue is a flux- and volume-limited sample (r < 17.7 mag, cz < 10 000 km s -1 ) of 30 597 galaxies, including the Virgo, Coma, and A1367 clusters. Images and spectra were individually examined to clear the sample from unwanted entries. To inspect possible secular and environmental dependencies of the various nuclear excitation properties (star-forming versus active nuclei), we performed a multi-dimensional analysis by dividing the total sample according to: (i) their position in the (NUV - i) versus M star diagram, (ii) the local galaxy density, (iii) the stellar mass, (iv) the halo mass of the group to which galaxies belong, and (v) the neutral hydrogen content. We present a new calibration of the optical diameter-based H I-deficiency parameter H I def , employing a reference sample of isolated galaxies extracted from SPRING. At intermediate distances between Virgo and Coma, we identify a ring-like structure of galaxies constituted by three large filaments, each with a length of approximately 20h -1 Mpc, mostly composed of blue-cloud galaxies with stellar masses M star ≲ 10 10 M ⊙ . The fraction of H I-deficient galaxies within the filament (~30%) suggests that filaments are a transitioning environment between lower- and higher-overdensity environments in terms of H I content, as we find a clear progression from field galaxies to the filament and cluster galaxies for an increasing H I def parameter. We classify the nuclear spectra according to the four-line Baldwin-Phillips-Terlevich (BPT) and the two-line EWHα versus [NII]/Hα (WHAN) diagnostic diagrams, and investigate the variation in the fraction of active nuclei hosts with stellar mass, as well as their colours and environments. We observe that the fraction of low-ionisation nuclear emitting regions (LINERs) is a steep function of stellar mass, for example, it is consistent with zero up to M star ≲ 10 9.5 M ⊙ and becomes ~40% for M star ≳ 101 0.5 M ⊙ , whereas, for M star ≲ 10 9 - 9.5 M ⊙ , almost the entire spectroscopic sample is constituted of galaxies with star-forming nuclei. We investigate whether the nuclear-excitation fractions depend predominantly on the stellar mass or, conversely, on the galaxy environment. In general, we observe that the mass dependence of the fraction of Seyfert nuclei is not very sensitive to the galaxy environment, whereas the fraction of star-forming nuclei is a steeper function of stellar mass in lower-density environments and in blue-cloud galaxies. We find that the fraction of LINERs depends on galaxy colour and, for M star ≳ 10 9.5 - 10 M ⊙ , increases in galaxies belonging to the green valley.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Synchronizing the consistency relation

We study the N-point function of the density contrast to quadratic order in the squeezed limit during the matter-dominated (MD) and radiation-dominated (RD) eras in synchronous gauge. Since synchronous gauge follows the free-fall frame of observers, the equivalence principle dictates that in the gradient approximation for the long-wavelength mode there is only a single, manifestly time-independent consistency relation for the N-point function. This simple form is dictated by the initial mapping between synchronous and local coordinates, unlike Newtonian gauge and its correspondingly separate dilation and Newtonian consistency relations. Dynamical effects only appear at quadratic order in the squeezed limit and are again characterized by a change in the local background, also known as the separate universe approach. We show that for the 3-point function the compatibility between these squeezed-limit relations and second-order perturbation theory requires both the initial and dynamical contributions to match, as they do in single-field inflation. This clarifies the role of evolution or late-time projection effects in establishing the consistency relation for observable bispectra, which is especially important for radiation acoustic oscillations and for establishing consistency below the matter-radiation equality scale in the MD era. Defining an appropriate angle and time average of these oscillations is also important for making separate universe predictions of spatially varying local observables during the RD era, which can be useful for a wider range of cosmological predictions beyond N-point functions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Effect of Si Content in Electrode and SiO2 Additions to the Slag during Electroslag Remelting

Evolution of Si concentration in 316 stainless steel electrodes was observed during a melting campaign consisting of recycling electroslag remelted (ESR) ingots to make new electrodes using vacuum induction melting (VIM). This campaign consisted of iterations of VIM + ESR operations to optimize melting parameters. The effect of Si content on the melt parameters and ingot quality was further evaluated and additions of SiO2 to the slag chemistry were studied using research-scale experiments, x-ray diffraction (XRF), combustion analysis, visual inspections, and computational tools. The Si concentration was found to decrease by approximately 600 ppm following ESR of 150 lb. research-scale electrodes. Eventually, this led to failure of the slag skin and direct ingot/crucible contact. Additions of SiO2 to the slag at levels matching the original calculated Si concentration in the electrode did not eliminate the slag skin failure and the current during steady state increased to maintain a constant melt rate. In this investigation, we propose a mechanism of slag skin failure consisting of local concentration of current density due to absence, or breakage, of the SiO2 layer around the molten metal drop during ESR. This theory was reinforced by additional experiments in which Nb was added to the electrode to change the structure of the oxide layer around the drops.

Jablonski, Paul↗
DOE OSTI2022

The role of supernova convection for the lower mass gap in the isolated binary formation of gravitational wave sources

ABSTRACT Understanding the astrophysical phenomena involving compact objects requires an insight about the engine behind the core-collapse supernovae (SNe) and the fate of the stellar collapse of massive stars. In particular, this insight is crucial in developing an understanding of the origin and formation channels of the growing populations of the detected black hole–black hole, black hole–neutron star, and neutron star–neutron star mergers. The time-scale of convection growth may have a large effect on the strength of SN explosion and therefore also on the mass distribution of stellar remnants. We adopt new formulas for the relation between the pre-SN star properties and their remnants and check how they impact the population of double compact object (DCO) mergers formed via the isolated binary evolution. The new formulas give one the ability to test a wide spectrum of assumptions on the convection growth time. In particular, the different variants allow for a smooth transition between having a deep mass gap and a remnant mass distribution filled by massive neutron stars and low-mass black holes. We present the distribution of masses, mass ratios, and the local merger rate densities of DCO for the different variants of new formulas and test them together with different approaches to other highly uncertain processes. We find that the mass distribution of DCO mergers is sensitive to the adopted assumption on the SN convection growth time-scale up to $m_1+m_2 \lesssim 35 \, \mathrm{M}_{\odot }$. Between the two extreme tested variants the probability of compact object formation within the mass gap may differ by up to approximately two orders of magnitude.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Microscopic theory of onset of decaging and bond-breaking activated dynamics in ultradense fluids with strong short-range attractions

We theoretically study thermally activated “in cage” elementary dynamical processes that precede full structural relaxation in ultra-dense particle liquids interacting via strong short range attractive forces. The analysis is based on a microscopic theory formulated at the particle trajectory level built on the dynamic free energy concept and an explicit treatment of how attractive forces control the formation and lifetime of physical bonds. Mean time scales for bond breaking, the early stage of cage escape, and non-Fickian displacement by a fixed amount are analyzed in the repulsive glass, bonded repulsive (attractive) glass, fluid, and dense gel regimes. The theory predicts a strong length-scale-dependent growth of these time scales with attractive force strength at fixed packing fraction, a much weaker slowing down with density at fixed attraction strength, and a strong decoupling of the shorter bond breaking time with the other two time scales that are controlled mainly by perturbed steric caging. All results are in good accord with simulations, and additional testable predictions are made. In conclusion, the classic statistical mechanical projection approximation of replacing all bare attractive and repulsive forces with a single effective force determined by pair structure incurs major errors for describing processes associated with thermally activated escape from transiently localized states.

36 MATERIALS SCIENCE↗
DOE OSTI2021

First-principles modeling of plasmons in aluminum under ambient and extreme conditions

The theoretical understanding of plasmon behavior is crucial for an accurate interpretation of inelastic scattering diagnostics in many experiments. In this work, we highlight the utility of linear response time-dependent density functional theory (LR-TDDFT) as a first-principles framework for consistently modeling plasmon properties. We provide a comprehensive analysis of plasmons in aluminum from ambient to warm dense matter conditions and assess typical properties such as the dynamical structure factor, the plasmon dispersion, and the plasmon lifetime. We compare our results with scattering measurements and with other TDDFT results as well as models such as the random phase approximation, the Mermin approach, and the dielectric function obtained using static local field corrections of the uniform electron gas parametrized from path-integral Monte Carlo simulations. We conclude that results for the plasmon dispersion and lifetime are inconsistent between experiment and theories and that the common practice of extracting and studying plasmon dispersion relations is an insufficient procedure to capture the complicated physics contained in the dynamic structure factor in its full breadth.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Heat transport in liquid water from first-principles and deep neural network simulations

In this work, we compute the thermal conductivity of water within linear response theory from equilibrium molecular dynamics simulations, by adopting two different approaches. In one, the potential energy surface (PES) is derived on the fly from the electronic ground state of density functional theory (DFT) and the corresponding analytical expression is used for the energy flux. In the other, the PES is represented by a deep neural network (DNN) trained on DFT data, whereby the PES has an explicit local decomposition and the energy flux takes a particularly simple expression. By virtue of a gauge invariance principle, established by Marcolongo, Umari, and Baroni, the two approaches should be equivalent if the PES were reproduced accurately by the DNN model. We test this hypothesis by calculating the thermal conductivity, at the GGA (PBE) level of theory, using the direct formulation and its DNN proxy, finding that both approaches yield the same conductivity, in excess of the experimental value by approximately 60%. Besides being numerically much more efficient than its direct DFT counterpart, the DNN scheme has the advantage of being easily applicable to more sophisticated DFT approximations, such as meta-GGA and hybrid functionals, for which it would be hard to derive analytically the expression of the energy flux. We find in this way that a DNN model, trained on meta-GGA (SCAN) data, reduces the deviation from experiment of the predicted thermal conductivity by about 50%, leaving the question open as to whether the residual error is due to deficiencies of the functional, to a neglect of nuclear quantum effects in the atomic dynamics, or, likely, to a combination of the two.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Integrated Quantum-Classical Protocol for the Realistic Description of Solvated Multinuclear Mixed-Valence Transition-Metal Complexes and Their Solvatochromic Properties

Linear cyanide-bridged polymetallic complexes, which undergo photoinduced metal-to-metal charge transfer, represent prototypical systems for studying long-range electron-transfer reactions and understanding the role played by specific solute–solvent interactions in modulating the excited-state dynamics. Here, to tackle this problem, while achieving a statistically meaningful description of the solvent and of its relaxation, one needs a computational approach capable of handling large polynuclear transition-metal complexes, both in their ground and excited states, as well as the ability to follow their dynamics in several environments up to nanosecond time scales. Here, we present a mixed quantum classical approach, which combines large-scale molecular dynamics (MD) simulations based on an accurate quantum mechanically derived force field (QMD-FF) and self-consistent QMD polarized point charges, with IR and UV–vis spectral calculations to model the solvation dynamics and optical properties of a cyano-bridged trinuclear mixed-valence compound (trans-[(NC) 5 Fe III (μ-CN)Ru II (pyridine) 4 (μ-NC)Fe III (CN) 5 ] 4– ). We demonstrate the reliability of the QMD-FF/MD approach in sampling the solute conformational space and capturing the local solute–solvent interactions by comparing the results with higher-level quantum mechanics/molecular mechanics (QM/MM) MD reference data. The IR spectra calculated along the classical MD trajectories in different solvents correctly predict the red shift of the CN stretching band in the aprotic medium (acetonitrile) and the subtle differences measured in water and methanol, respectively. By explicitly including the solvent molecules around the cyanide ligands and calculating the thermal averaged absorption spectra using time-dependent density functional theory calculations within the Tamm–Dancoff approximation, the experimental solvatochromic shift is quantitatively reproduced going from water to methanol, while it is overestimated for acetonitrile. This discrepancy can likely be traced back to the lack of important dispersion interactions between the solvent cyano groups and the pyridine substituents in our micro solvation model. The proposed protocol is applied to the ground state in water, methanol, and acetonitrile and can be flexibly generalized to study excited-state nonequilibrium solvation dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Anomalous resistivity and electron heating by lower hybrid drift waves inside reconnecting current sheets

Inside an electron diffusion region of laboratory reconnection experiments, the quasi-electrostatic lower hybrid drift wave (ES-LHDW) is observed when a significant guide field component is present. Through direct measurement of the anomalous drag term and quasilinear analysis, it is shown that ES-LHDW can account for approximately 20% of the mean reconnection electric field in a case with moderate guide field. This value exceeds the contribution from classical resistivity, which is around 10%. The effects of the Lorentz force term, often neglected for electrostatic waves, are crucial for the observed correlation between electric field and density fluctuations. Anomalous electron heating by the perturbed current and resistivity (2.6 MW/m 3 ) also surpasses the classical Ohmic heating, which is about 2.0 MW/m 3 . For the case with a high guide field, significantly higher local electron temperatures were observed during periods of strong ES-LHDW activity. A statistical analysis further supports electron heating by LHDW, showing a larger increase in electron temperature with a high guide field. Finally, data from the Magnetospheric Multiscale mission provide evidence of Landau damping of ES-LHDW, suggesting that ES-LHDW may contribute to the generation of nonthermal electrons along the direction parallel to the magnetic field.

Magnetic reconnection↗
DOE OSTI2025

Evaluating the gradients of localized diabatic state energies and couplings at minimum cost

We calculate the gradients of Boys diabatic state energies and couplings when the electronic vector space is generated by configuration interaction singles. Our approach follows the Lagrangian approach of Paz and Glover (rather than direct differentiation of the adiabatic-to-diabatic approaches that have been published previously). The result is that we achieve a dramatic increase in savings over previous approaches, and the present approach should be immediately useful to scientists focused on electronic relaxation, especially chemists studying electron transfer who wish to go beyond the Condon approximation. Here, a future extension to time-dependent density functional theory in the Tamm–Dancoff approximation is clear.

Chemical physics↗